TEKREVOLUTION is a high-tech service and consulting company from Italy with huge experience in R&D activities. One of their main activities is to explore intelligent additive manufacturing to provide higher stress-to-weight ratio solutions for the market.

## Challenge
For the space sector, it is important to reduce the weight to the minimum possible, while maintaining excellent performance. That is why it is very important to choose the right selection of materials for each component of the structure, depending on the stress supported and its density.

In this case, we are analyzing the selection of the optimum material for a retainer belonging to the Spring Separation System of Interstage 2/3 of the Vega C launcher (Fig. 1). The actual design of the retainer is made of Aluminium AL7050 and the component is manufactured by machining it from an Aluminium billet. Nevertheless, due that the load supported by the retainer is not very big (around 600 N), it is possible to use polymeric materials such as PPS CF, PEEK or Carbon PEEK using Additive Manufacturing techniques making the component lighter.

For this study, two main properties of the material are considered. The density, and the Young Modulus. The objective is to see in which ranges those variables can be while matching the structural behavior in terms of maximum displacement, stress supported and natural modes to understand which kind of polymeric material is more efficient for this task. It is important to remark that some constraints on the inputs and outputs were set during the optimization process to avoid unrealistic materials, and that a Safety Factor = 2 was requested in terms of allowable Von Misses stress. 

![retainer_image4.jpg](https://uptimai-website.s3.eu-central-1.amazonaws.com/retainer_image4_016d92b219.jpg)
*Fig 1. Retainer geometry*

## Tools
For this problem, we used two Uptimai new optimization features. The first one is the Direct Optimizer which aims at minimizing (or maximizing) a function of interest with one single output with so-called Evolutionary Algorithms which mimic the behavior of a population of living beings in an environment subject to natural selection. Inside the Direct Optimizer we are proposing two different algorithms, depending on the problem: Differential Evolution (DE). This algorithm creates a population of potential samples and makes it evolve at each generation. The evolution process involves independent and random mutation of each coordinate of each member of the population. This evolution process is repeated multiple times in a looping fashion and at each iteration, the population members are replaced by the new members (children) only if they provide a better result (lower function value).

The algorithm stops when the population has converged closely enough to a minimum point or the maximum allowed number of function evaluations is attained. Because each coordinate is mutated independently this algorithm is subject to the curse of dimensionality. This is why the decoupling option is recommended for high dimensional problems (dimension >= 10). Hybrid method of DE and Covariance Matrix Adaptation. The Covariance Matrix Adaptation (CMA) is an algorithm that evolves the population by generating children according to a multivariate Gaussian distribution. The best child elements are selected for the next population and the parameters of the Gaussian distribution are adjusted in a heuristic manner. Again the algorithm stops in case of convergence of the population or if the maximum number of function evaluations has been reached. The Hybrid Method performs a decoupling process to separate 1D-subproblems and ND-subproblems. Then, the DE algorithm is applied to 1D-subproblems and the CMA algorithm is applied to ND-subproblems.

To tackle the curse of dimensionality, for both algorithms, the UptimAI software use a decoupling process (also known as variable separation in the literature) that transforms the main domain into smaller subdomains. Then the optimization process is separated into lower-dimensional subproblems, providing better performance and converging faster.

On the other hand, the Multi-Objective Optimizer is designed to minimize multiple concurrent outputs. It works in a similar way that the Direct Optimizer does. However, it is not usable with decoupling and uses an evolutionary algorithm called NSGA-II. Unlike the Direct Optimizer, the Multi-Objective Optimizer provides multiple solutions approximating a Pareto Front of the problem.

## Solution
We coupled the UptimAI tool with the simulation software MSC Nastran, without the need of interfering with its code or interface. Then the MSC Nastran started running simulations for the sample points (different material properties) indicated by the UptimAI algorithm for converging into the optimum solution.

![retainer_image1.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/retainer_image1_7d8e8dd2f4.png)
*Fig 2. Results obtained from Nastran MSC for a specific sample*

For this case, approximately 500 simulations were performed to get a converged solution. Uptimai Multidisciplinary Optimization software gave as result the Pareto front of the duo density - young modulus that was improving both displacement, Natural mode and stress (the last one isn’t represented in Fig. 3). From the results obtained, we could extract the properties of the wanted material and by consequence the type of polymeric material that should be used to reduce the weight of the retainer while maintaining an excellent performance.

![retainer_image3.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/retainer_image3_e78fdb3425.png)
*Fig 3. Pareto Front showing zone of optimum properties, and the outputs achieved*

## Benefits
- **Interpretation of variables effect.** Understanding the effect of each variable on the output
- **Optimization of the results.** Obtention of the Pareto Front that is improving all the outputs at the same time
- **Reduction of computational cost.** Our increased convergence rate makes that fewer samples are needed to achieve the solution.

Design, analysis and optimization of retainer materials

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Retainer Optimization

IGW POWER drives solutions for gears, gearbox assemblies and prismatic parts. Although most known for its efficient and reliable products for the rail industry, the company also supplies a diverse amount of applications and markets from construction machinery to medical devices.

## Challenge
Besides the overall reliability and durability, the noise characteristics are one of the key topics for the gear and gearbox design. This parameter is expected to be as low as possible since it strongly affects the operability of the final product and its environment.

The current state of the art in gear noise analysis is the finite element method approach. For the initial stages of the design, it is important to quickly identify parameters of the design crucial for its noise characteristics. However, the cost of such an activity cannot be excessive from the perspective of time and resources. This is why the fast Uptimai Preliminary analysis tool was used for the first sensitivity analysis of the gearwheel.

The goal of this preliminary study was to evaluate the sensitivity of noise-related phenomena to 6 geometrical parameters of the gearwheel. Using the method of Uptimai, only 19 computations were required to reach this goal, which can be later used as a baseline for follow-up design steps.

![gearwheel.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/gearwheel_eba402edf0.png)
*Fig. 1. Example of the analysed gearwheel type*

## Solution
This type of very fast analysis was also used because there was no fully automatic connection between the wheel geometry model of the wheel, the meshing software and the MSC Nastran that provided the amplitude-frequency characteristics of the gearwheel noise. This increased the cost of each simulation and therefore only very few were available to be made. The main focus of the study was on the maximum noise level (equivalent radiated power, ERP), frequency of this ERP peak, and the probability of resonating frequencies to occur.

![gearwheel_image2.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/gearwheel_image2_b3836f4e78.png)
*Fig. 2. Example of the extracted amplitude-frequency characteristics*

During this process, it is the Uptimai algorithm that decides which input parameter combinations have to be computed in the next step. These input data are provided in small batches, where every new iteration is proposed based on the results of the previous ones. This adaptivity gives the analysis the key advantage in accuracy and cost over traditional methods of statistical analysis.

![gearwheel_image3.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/gearwheel_image3_7d179739fd.png)
*Fig. 3. Sensitivity analysis of the equivalent radiated power and its frequency*

As a result, the Uptimai sensitivity analysis was presented in the post-processing environment, showing the effect of wheel geometry parameters on the overall variance of results. For three of four observed output variables, parameters defining the gearwheel rib thickness (especially A1) are among those most influential. E.g. for the frequency with the highest ERP level (output 2), the effect of other parameters was found to be negligible.

![gearwheel_image1.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/gearwheel_image1_43453fb14a.png)
*Fig. 4. Sensitivity analysis of output related to resonating frequencies*

However, the distance of holes in the rib from the axis and their number affects the maximum of ERP as well. The number of holes in the rib, R9, becomes partially important when finding if the last observed ERP peak frequency is in the resonance with the previous one, the number of holes is the key input parameter. (see Fig.1 for reference).

The only parameter neglected for all outputs is the hole diameter D_6. Other input parameters related to holes in the rib are probably relatively much more significant than this one and D_6 is just “hidden in their shadow”.

This, and other findings as well, can be gathered within the following analysis steps. A simple model will be created from additionally computed samples, allowing to find the effect of interactions between input parameters. Then, the creation of the full statistical model reveals the complete set of insights into the design.

## Benefits
- **Definition of the problem.** Clear identification of relevant variables.
- **Efficient process.** A fast algorithm requires a minimum number of samples.
- **Insights for future improvement and optimization of the gearbox.**

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Gearwheel sensitivity analysis

ŠKODA AUTO is the largest car manufacturer in the Czech Republic and part of the Volkswagen Group since 1991. The company uses highly advanced simulation tools in its R&D departments to meet all design goals, where passenger safety is one of the top priorities.

## Challenge
Although side collisions occur less likely than front or rear crashes, it is still a very common type of car accident, especially in cities. Moreover, at the same speed, these can cause more severe injuries to passengers inside the vehicle. Thus, it is crucial for design engineers to know the most important aspects of side crash behavior. Finite element method computations are used to analyze the impact of a car collision on passengers. Computations are performed repeatedly with variations in design parameters to see their effect on forces acting on passengers. However, the total number of FEM computations is limited since these can be a lengthy process even with powerful computers. Side crash is a complex problem depending on a large number of parameters and it was not possible to investigate all of them in this study. In the first step, the ŠKODA AUTO experts simplified the problem and selected 11 parameters which should be important or interesting to analyse. In the second step, a preliminary analysis applied on these 11 preselected parameters to assess their importance. Then within just 65 computations, the preliminary analysis of Uptimai software was able to propose a reduction of this list further to 6 most influential parameters.

![side_impact_image4.jpg](https://uptimai-website.s3.eu-central-1.amazonaws.com/side_impact_image4_1261be2614.jpg)
*Fig. 1. Side collision testing, photo by Euro NCAP*

## Solution
In the beginning, we coupled the Uptimai tool with the simulation software PAM-Crash using the sampling based approach. Then, the UptimAI tool began to set combinations of inputs for the PAM-Crash, automatically varying design parameters of the car. The **Uptimai algorithm** starts to analyze the task using a very effective logical scheme. From the results of only 40 FEM simulations, the program is able to identify the sensitivities of input variables. This is about 50% of simulations required by the second-order polynomial chaos, an advanced statistical method used today.

The **Uptimai sensitivity analysis** allows to see not only the effect of inputs on the overall variance of the results but also how they affect the mean value of the probabilistic result from the so-called preliminary surrogate model. As mentioned earlier, the main goal of the analysis so far was to perform the sensitivity analysis with the lowest possible use of resources. To complement data with FEM results required to build the preliminary surrogate model, additional PAM-Crash calls were made. In the end, 65 samples were used in total for both observed outputs - rib force and rib deformation. This is a significantly lower number than for design-of-experiment methods commonly used in engineering. E.g. Box-Behnken experimental design would require almost three times more FEM computations for this task with 11 input variables.

![side_impact_image2.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/side_impact_image2_d484be6a61.png)
*Fig. 2. Sensitivity analysis of rib force and rib deformation*

The information learned from the sensitivity analysis was further visualized in the **Uptimai histograms**, showing clearly the effect of each input variable on the probability distribution of results. The so-called influencer plot is the graphic representation of changes in results caused by the selected parameter. Thus, engineers had a straightforward illustration of changes in the mean value and the variance of results.

![side_impact_image1.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/side_impact_image1_a16e6ed302.png)
*Fig. 3. Example of an input parameter influencing only one output*

Another piece of information gained from the model was the probability of inputs to interact with the others. It was only possible due to the novel methodology used in the Uptimai software, its smart scheme and principles of model residuals handling. Based on all these data, the number of input parameters was reduced from 11 to 6. In the following stage of the project, this allowed to obtain the detailed surrogate models of both outputs for only 255 FEM simulations. The model of acting forces was the more demanding, the model of deformations used 99 simulations and these were already solved for the first output.

## Benefits
- **The low number of required FEM simulations.** Reducing the total number of simulations to 50%.
- **Identification of influential parameters.** Fast recognition of variables with high impact on results.
- **Visualisation of effects of variables.** Better handling of analysis results with illustrative plots.

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Side Impact Analysis

Turbo-fans are one type of airbreathing jet engine that is widely used in aircraft propulsion. Despite being more complex, it can obtain higher efficiencies than its brother the turbojet for subsonic flights.

## Challenge
Designers of turbofans have to increase the Force that is able to produce together with the Specific Impulse, which is a measure of the efficiency of the engine. The result of this is normally an engineering trade-off as both outputs are independent.

![turbo_optimization_image4.jpg](https://uptimai-website.s3.eu-central-1.amazonaws.com/turbo_optimization_image4_b5ce3689a1.jpg)

The objective is to study the performance of multiple staged compressors, and to preliminary design the pressure ratio desired for every stage, taking into account the physical uncertainties of flight conditions.

For this problem, we were studying how seven parameters were affecting both the Thrust Force and the Specific Impulse to get insights into how each variable is affecting the solution and how it is possible to optimize both outputs at the same time. It was a complex problem, as the inputs were interconnected, and multiple combinations of them were left for unfeasible options.

## Solution
We started the project by coupling the Uptimai tool with the calculation software. In this case, the external software was a Python script, that was reading the inputs given by Uptimai software, computing all the outputs and feeding its result back. With these results, the AI would choose where would be more efficient to locate the following sample adaptively, and automatically repeat the process until the desired accuracy is achieved.

![turbo_optimization_image6.jpg](https://uptimai-website.s3.eu-central-1.amazonaws.com/turbo_optimization_image6_609697a2c7.jpg)

Our **Uptimai Sensitivity Analysis** showed us which were the most relevant parameters and which ones could be neglected as its effect was almost negligible. For both outputs, we saw that the inputs in which we should focus to improve the design were in the compressor side, in particular the pressure ratio that both the low and high compressors are able to produce. In the case of the Adimensional Force, the bypass ratio was also a very important factor.

![turbo_optimization_image3.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/turbo_optimization_image3_649c25c43e.png)

To understand how those relevant variables are actually affecting the outputs we used the **Uptimai Increment Functions**. That allows us for both, for learning about how each variable was affecting each output, but also as a preliminary optimization tool, where we could distinguish in which ranges each variable should be to maximize the output. In the case of the bypass ratio, we found that the best option for improving the Thrust Force would be to have it between 10 and 13.

![turbo_optimization_image5.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/turbo_optimization_image5_4d21fd2a85.png)

Thanks to the **Uptimai Histograms** we could get a statistical view of how the turbofan was behaving, and the uncertainty around it. As can be seen, there are some combinations of inputs that make the engine behave in a non-desirable way (below Fad = 3), but thanks to the influences we could tune the parameters to be always above 4.5.

![turbo_optimization_image2.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/turbo_optimization_image2_7267903a50.png)

As with the studies with the meta-model, we saw that it was impossible to get a particular design point that was maximizing both outputs (some variables had conflictive effects), we used our **MultiObjective Optimization** feature. With the MOO, we were able to get the Pareto Front that was maximizing both outputs, with the selected constraints for the outputs. That allowed to choose effectively the design point for different engine needs.

## Benefits
- **Definition of the problem.** A clear description of relevant variables
- **A deeper understanding** of the physics behind the problem, and how each variable affects the outputs
- **Multiobjective optimization.** Having all the possible values that are maximizing at the same time both outputs


Optimizing Force and Specific Impulse of a turbofan

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Turbo Engine Preliminary Optimization

VARROC LIGHTING SYSTEMS is a leading global passenger car exterior lighting supplier. It provides complete solutions from design to manufacturing, which are supported by engineers and other experts in a worldwide network of modern R&D centers and factories.

## Challenge
Modern automobile headlamps are complex optical components consisting of a large number of parts. The optics inside do not only work with the light shining out from the headlamp but also reflect sun rays coming from the outer world. In some cases, these might cause local overheating of certain areas inside the headlamp and lead to damage of used plastic materials. The presented study is a typical task of the optical department. Its purpose is to identify the sun direction leading to the highest concentration of sun rays on each part of the headlamp. The sun direction is defined by its azimuth and inclination, the sunlight intensity was set to a constant equal to the possible maximum. Thus, the results are always on the safe side regardless of the daytime or the orientation of the vehicle towards the Sun. The resulting maps of the sunload, created for each headlamp part, are an important input for further examinations using FEM computations studying the ability of a given sunload to create critical temperatures in headlamp parts.

## Solution
The first step of the project was the coupling of the Uptimai tool with Varroc’s internal software for ray-tracing simulations. These two software use open-format files for communication, thus, there was no need to interfere with their codes. Within the created automatic loop, the **Uptimai algorithm** was preparing inputs for the ray-tracing software which supplied the algorithm with sunload results. Every other set of sunload computations was set to address sun directions leading to a significant response in the sunload of the examined headlamp part. There is no fixed grid of azimuth and inclination angles as in the standard process of sunload analysis. Contrary, the algorithm adaptively reacts to variations of results received from the ray-tracing software, actively predicting sun direction angles with the high possibility of an excessive value of the sunload. The step between sun direction angles is set automatically by the algorithm according to the actual needs of the solved problem without other interventions of the user. Thus, there is an optimal precision-to-cost ratio of the computation process. The resulting maps of the sunload can be depicted in the **Uptimai function plot** postprocessing tool. From the interpolation of the prepared surrogate model of the sunload, it can obtain results for any combination of azimuth and inclination angles within the examined domain. It also supports results generation based on a list of prescribed input combinations, so the user is able to prepare the usual analysis outputs presented on an even grid with the specified resolution.

![sunload_image2.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/sunload_image2_351ab80894.png)
*Fig. 1. Resulting sunload maps generated for selected headlamp parts*

## Benefits
- **Quick identification of peaks in sunload.** The algorithm is capable of finding all important local extremities of sunload.
- **Decreasing the computational time.** Adaptive seeking for variances in the sunload is much more efficient than the analysis on a fixed grid.
- **Comprehensive result review.** From the surrogate model, it is possible to generate sunload maps on various grid resolutions.

Speeding up the ray-tracing inside the headlamp

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Sunload Simulation Process

## Optimization of fan characteristics under various flow-rate
CFD SUPPORT is an engineering company dealing primarily with the CFD and FEA simulations, and also other activities related to numerical simulations of physical phenomena. Its own-developed TCAE software is a comprehensive environment of standalone modules for engineering simulations.

## Challenge
Large centrifugal fans may be used for various industrial applications, such as in ventilation units for manufacturing facilities. Although the fan presented in this study is not a part of a used solution, it was derived from an existing fan, for which the comparison of the CFD results with measurement has been made. The study shows a comprehensive analysis of main fan characteristics. These were observed for the varying volumetric flow rate, which is a typical flow parameter for analysing the fan performance. Additionally, the impeller geometry has changed during the analysis to find the most promising fan configuration for a given range of volumetric flow rate and a fixed volute geometry.

![centrifugal_fan_image2.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/centrifugal_fan_image2_6de673d6b9.png)
*Fig. 1. Centrifugal Fan in the volute*

Six parameters (volumetric flow rate, blade radius, blade thickness, number of blades, blade angle, b1,2 – blade depth), and six outputs (efficiency, total pressure difference, power, flow number, compression number and axial force) had to be evaluated in the study. During the analysis, the Uptimai tool successfully dealt with discontinuities in results, localizing them properly while suppressing oscillations in results. The created surrogate model can be used for the prediction of centrifugal fan characteristics without additional CFD computations.

## Solution
At the beginning of the project, the Uptimai tool was very easily connected to the automated CFD analysis process used by the CFD Support company in their TCAE simulation environment. This loop received values of input parameters from the Uptimai software and was able to automatically generate the geometry of the fan, create the computational mesh, and run and post-process the CFD simulation. Values of input parameters were ordered by Uptimai’s smart algorithm and then it used CFD results to build surrogate models of the fan’s characteristics.

![centrifugal_fan_image5.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/centrifugal_fan_image5_0657fcb6a4.png)
*Fig. 2. Simulated flow through the fan*

The **Uptimai Sensitivity Analysis** (Fig. 3.) confirmed the importance of the volumetric flow rate through the fan as the main flow parameter, which has to be considered in the fan design. From the impeller parameters point of view, the width of the impeller (b12) and the number of its blades have a main effect on the overall performance. Partially, it is due to the fact these inputs are interacting with the volumetric flow rate – the best setting of geometric variables depends on the flow rate. Thus, these interactions need to be considered when designing the fan to be working well in a wider range of the flow rate.

![centrifugal_fan_image1.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/centrifugal_fan_image1_91a01e8d3f.png)
*Fig. 3. Sensitivity Analysis of the Total Pressure Difference*

Then, in the **Uptimai Increment plot** (Fig. 4.) is shown exactly how the efficiency of the fan is dependent on the flow rate and the impeller width. As indicated by the zero efficiency, it can be noted that the impeller of very low width is incapable of handling high flow rates. It suggests the width b12 should be higher than 0.2m to ensure there will be a reasonable efficiency of the fan for the whole range of possible flow rates. Also, it is the way to avoid excessive axial forces which might lead to an eventual fan malfunction.

![centrifugal_fan_image4.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/centrifugal_fan_image4_8ebcc6300d.png)
*Fig. 4. Fan efficiency (left) and axial force (right) based on impeller width and volumetric flow rate*

The **Uptimai Histogram** Plot (Fig. 5.) shows the actual potential of the design under various operational conditions. There is a high probability to reach an efficiency of about 80% with a maximum of 86%. On the other hand, the histogram confirms the possibility of designs not matching specific flow rate conditions. As demonstrated above, these can be avoided by restricting ranges of geometry parameters.

![centrifugal_fan_image6.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/centrifugal_fan_image6_f87d668781.png)
*Fig. 5. Probability distribution of efficiency of all theoretically possible designs*

New ranges of inputs were identified using the **Uptimai Preliminary Optimization** tool which proposes input distributions leading to the statistical improvement in results. Once the volumetric flow rate was one of the input parameters, the optimization tool could be also used to visualize the flow rates best fitting for the current design concept. As seen in Fig. 6., it was generated for all outputs and these were compared against each other. It showed the best efficiency for flow rates about 25m/s and was checked if there is a conflict with e.g. axial forces.

![centrifugal_fan_image7.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/centrifugal_fan_image7_a94dd0a583.png)
*Fig. 6. A trade-off can be easily done by comparing of Regions of Preference/Avoidance generated for different outputs*

## Benefits
- **Definition of influential parameters.** There is only a minor effect of selected impeller parameters other than its width and also the number of blades.
- **Comprehensive design review.** Taking multi-objective considerations into account for optimization of different outputs with specific constraints.
- **Identification of fan usability.** Investigation of the design limits of all the variables to assure a correct fan operability.

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Centrifugal Fan

The VIRTUAL VEHICLE Research GmbH is Europe’s largest R&D center for virtual vehicle technology, the innovation catalyst for future vehicle technologies. Their focus is on the linking of numerical simulations and hardware testing, creating automated testing and validation procedures.

## Challenge
The fastly growing e-cars market excites the need for advanced methods for design and analysis specifically for this sector. VIRTUAL VEHICLE works on modelling the vehicle battery electric behavior, allowing improvements in the battery design. For the “Single-Particle” model (SPM), an optimal setting for the model’s 31 parameters was found in the previous research to obtain the best-known match with the measured data.

In this study, the goal was to enrich existing data with comprehensive statistical insights. In the initial stage, the problem was split into a series of iteratively created surrogates. First iterations were dedicated to searching for domain limits and identification of parameter ranges for a stable battery model. Then, the domain was restricted to the effect on statistical aspects of results from iteration to iteration.

Another part of the project investigated the close surroundings of the optimum used as the reference. The statistical analysis examined the robustness of the solution and gave the answers to whether or not some parameters may be omitted from the model. Also, it revealed there is still room for fine tuning of parameters to achieve the match between modelled and measured battery cycle.

![battery_cycle_image3.jpg](https://uptimai-website.s3.eu-central-1.amazonaws.com/battery_cycle_image3_bedc5ee3d8.jpg)
*Fig. 1. Electric vehicle battery (photo by Gereon Meyer CC BY-SA 4.0)*

## Solution
Coupling of the Uptimai tool with VIRTUAL VEHICLE’s FEMToolbox software for battery cycle simulation was easily done without the need of interfering with neither simulation nor UQ code. The already existing interface of the VIRTUAL VEHICLE’s software was modified to pass data to the Uptimai tool after post-processing of the simulation results. Uptimai algorithm used these outputs created for altering input parameters to build a surrogate model of the behaviour of the simulated battery cycle. Results presented here are for the model created for the close surroundings (20% of the complete input range) of the reference point.

The **Uptimai algorithm** was used to process simulation results into the metamodel of agreement between measured and computed battery-cell cycles. The level of agreement was defined as normalized Root Mean Square Error (RMSE), observed for each simulation. The metamodel consists of dependencies between input parameter changes and the simulation results, allowing a detailed description of the battery cycle.

Specific response to changes in particular input variables was observed using the **Uptimai Increment plot**. This feature allows treating each dependency separately but is also able to perform a cross-comparison of variables against each other. Fig. 2 depicts the total response to the three most influential variables. Note the peak in results caused by the cumulative effect of these variables close to their upper boundary. This combination of input parameter values should be avoided when seeking a better battery cycle model.

![battery_cycle_image4.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/battery_cycle_image4_52076fb2fd.png)
*Fig. 2. Extremity localized on the increment function plot*

The **Uptimai Sensitivity Analysis** confirmed the tight connection of variables through high-order interactions, which in sum create a considerable portion of the uncertainty of results. For the most influential variable ocv_Li(ci)_1, interactions are responsible for 2/3 of variance in results caused by this input variable. Although the surrogate model was much simpler than in the above-mentioned case of the iterative approach, mutual interactions of up to four variables had to be investigated.

![battery_cycle_image5.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/battery_cycle_image5_c7bc6c1a0d.png)
*Fig. 3. Sensitivity Analysis of the reduced domain*

Also, another surrogate model was created for seven input variables indicated as statistically negligible in all previously done UQ analyses. It confirmed that even in this highly focused domain some variables, especially D_1, are not able to affect the results (see Fig. 3). As proven by the **Uptimai Histogram Plots** (Fig. 5), the cumulative response of all variables in the reduced domain is much lower than the effect of the most influential input. However, since the nominal point of the reduced domain was set to the so far known optimum, findings of this very precise surrogate were used to obtain an even better result. The new optimum increases the quality of the battery cycle model by more than 20%.

![battery_cycle_image2.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/battery_cycle_image2_70a71e5e2f.png)
*Fig. 4. Comparison of effects of the most influential variable of the full domain against all variables of the reduced domain*

## Benefits
- **Definition of valid design space.** The Uncertainty Quantification was able to explore and identify correct ranges for the input domain where the Single-Particle model always converges.
- **Suggestions for stable optimum** – addressing ranges of input parameters responsible for better-than-average results allowed to **improve the current optimum by 20%.**
- **Deep statistical insights** into the Single-Particle model behaviour with **identification of the most influential input variables.**

Electro-chemical battery model validation

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Discharge battery cycle

## Design, analysis and optimization of a CubeSat structure
TEKREVOLUTION is a high-tech service and consulting company from Italy with huge experience in R&D activities. One of their main activities is to explore intelligent additive manufacturing to provide higher stress-to-weight ratio solutions for the market.

## Challenge
For the space sector, it is important to reduce the weight to the minimum possible, while maintaining excellent performance. That is why it is important to comprehend that it is more optimum to have different thicknesses and material properties through different zones with particular characteristics. Moreover, it is interesting to understand which parts of the component are affecting more to the behavior when loaded. For this reason, in this case, the component was divided into 10 different parts whose properties would be studied individually. Three different aspects were examined, the displacement of the center of mass of the payload, the first natural mode and the maximum stress supported with the objective of minimizing the CubeSat weight. Overall, we considered the thickness of each of the 10 parts that composed the model and the Young Modulus of the material. A high resolution study was made with only 143 Nastran simulations.

![cubesat_image5.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/cubesat_image5_e3f9af6106.png)
*Fig. 1. Scheme of the CubeSat Structure*

## Solution
We coupled the UptimAI tool with the simulation software Nastran, without the need of interfering with its code or interface. Then the Nastran started running simulations for the sample points indicated by the UptimAI algorithm for creating a metamodel of the behavior of the component under load.

The **UptimAI Sensitivity Analysis** (Fig. 2.) helped to identify which parts of the component were the most crucial, and supported most of the load, measuring which input had more influence in the three outputs (displacement, first natural mode and stress). Also, it was very useful to determine which parts of the component weren’t supporting the load at all, so its thickness could be reduced without affecting the overall performance at all. In this case, only the thickness of the load area had an important effect on the maximum stress supported by the structure, being able from now on to focus on that two parts and knowing that it is possible to reduce the thickness on the other parts to reduce the weight without affecting the stress performance.

![cubesat_image4.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/cubesat_image4_daed8090cc.png)
*Fig. 2. Sensitivity Analysis of the Maximum Stress on the CubeSat*

Details of specific zones of the domain can be easily seen in the **UptimAI Increment plot** (Fig. 3.). It shows the shape of increment functions illustrating the interactions and dependencies between the values of the input parameters and the displacement. That allows to easily identify high response zones, for avoiding in the design phase and reduce both the variability of the displacement and to reduce its average response. In this case it was necessary to have at least one of the loading areas with a thickness higher than 2.5 mm, to operate in a stable condition.

![cubesat_image3.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/cubesat_image3_bc67d9500b.png)
*Fig. 3. Interaction between thicknesses of loading parts in the displacement of the payload*

The histogram (Fig. 4.) is showing the position of the 1st Natural Mode. The Nastran computations were cut to 120 Hz as maximum because there is no interest in knowing the exact value of the first frequency if it is higher than this value, as it already surpasses the safety restraints (NOTE: the metamodel accurately caught this aspect). The histogram allows to check which is the average response (around 110 Hz), and to study in detail the input conditions of the left tail of the distribution that make appear undesired behavior of the structure.

![cubesat_image6.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/cubesat_image6_6f8607e641.png)
*Fig. 4. Statistical Modal Response of the CubeSat*

Finally, the engineers used the **UptimAI Preliminary Optimization** tool to establish new input distributions. These proposed distributions show which zones of the domain carry an statistical improvement, and which zones should be avoided. That way it helps the engineering team on the decision making of which combination of input parameters are more interesting to explore. Using the thickness distributions for the loading parts suggested by the UptimAI algorithm, the average displacement was halved and the variance was largely decreased, leading to a better and more reliable performance.

![cubesat_image1.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/cubesat_image1_343b1974f0.png)
*Fig. 5. Statistical response of the displacement of the payload before and after improvements*

## Benefits
- **Definition of influential parameters.** The parameters of the component that were relevant to the results were reduced by more than 60%
- **Optimization of the results.** Decreasing the average displacement of the payload to the half and its variance to input parameters while complying with modal restrictions.
- **Deeper insights** into the structural behavior of the component under high loadings.


Reduction of weight while increasing performance

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CubeSat structural design

IDIADA CZ is part of an international engineering company Applus IDIADA. In the Czech Republic, more than 200 experts deliver a portfolio of services from technical simulations and design proposals over conception designs up to design and series manufacture for automotive, aerospace, and other industries.

## Challenge
In order to ensure good agreement between simulation and real part test, a robust material model must be available. Typically a tensile and creep sample tests are provided for calibration of the material model. Calibration of a material model is an iterative process of tuning several (typically around 10) parameters. After running the tensile and creep simulation using these parameters, a comparison to the original test data is made. Based on the correlation between simulation and the test data a new set of parameters is suggested.

Using standard simulation tools is time-costly proportionally to the number of parameters. Therefore it is desirable to decrease the number of iterations. This can be achieved by a smart analytical tool that can quickly recognize the optimal value of parameters.

This is what UptimAI’s solution excels at. Suggested algorithm decreased the number of iterations from thousands to several hundred. Furthermore, UptimAI has provided deep insight into parameter interaction.

For this study, the FEM structural solver Abaqus was used, allowing only a limited number of simulations within the timeframe of the project. Thus, the problem was described in a series of iteratively created surrogate models. In each iteration, a smaller section of the design space was selected in order to focus on ranges of parameters with a higher probability of a better match of material characteristics. Despite the surrogate model being built four times in total, the number of required computations dropped from thousands to hundreds.

![material_model_tuning_image6.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/material_model_tuning_image6_173b5eadfb.png)
*Sample of the material under the virtual “testing” in Abaqus (picture: IDIADA CZ)*

## Solution
Coupling of Abaqus and UptimAI software was easy and straightforward. A standard approach was used, where input files required by Abaqus solver (these are text files in essence) were altered by UptimAI tool. After the simulation has finished, a unified post-processing python script produces resulting tensile and creep curves (in a form of a CSV table).

The **UptimAI algorithm** is used to process simulation results into the metamodel of agreement between measured and computed material characteristics. The level of agreement was defined as Normalised Mean Square Error (NMSE), observed separately for each material test (tensile test and three tests of creep – at stress 4MPa, 5MPa, and 6MPa). Results presented here are for the creep test at 4MPa.

The analysis of the metamodels began with the **UptimAI sensitivity analysis**. It revealed that in the first metamodel (the first iteration of the study) one parameter of the material model is dominant. Thus, the range of this parameter, C10, was reduced for the next iteration. There, other parameters showed their importance too, since local extremities they caused were more focused on now. Nevertheless, the effect of some parameters, like δς or δε, is still too negligible even for the last iteration created for the smallest input domain.

![material_model_tuning_image3.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/material_model_tuning_image3_7929642653.png)
*Sensitivity analysis – on a smaller domain, the mathematical model is able to describe the problem in more detail*

The overall statistical properties of each metamodel were apparent from **UptimAI histograms**. It was found that the material model has a large overall variance, where any slight modification of the input parameters leads to significant changes in the accuracy of material characteristics. From the second iteration, it suggested the appearance of a distinct local extreme value. It also showed that interactions with parameters Sratio and n are responsible for this behaviour.

![material_model_tuning_image2.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/material_model_tuning_image2_6b55f49798.png)
*Contribution of the parameter Sratio to the statistical result*

Position and origin of the extremity were later found on **UptimAI total incremental plots**. These depicted the sum of direct responses in the match of material curves to changes in particular input parameters and their combination. The figure allowed localizing the extremity with respect to ranges of material parameters, setting the base for the next iteration and reduction of the input domain.

![material_model_tuning_image4.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/material_model_tuning_image4_51bf5da792.png)
*Total incremental plot – sum of increments to the output based on changes in three interacting input parameters*

New ranges of input parameters were set according to results of the **UptimAI preliminary optimization** tool. It used the statistical nature of the model to give recommendations leading to a new reduced input domain with a higher probability of a good match of material characteristics. This method also allows easy graphical comparison of proposed regions for multiple outputs. Here it has shown that model parameters affect all examined cases of creep behaviour (at 4MPa to 6MPa) in the same way. On the other hand, they are often contrary to the tensile behaviour, and thus, the iterative process was repeated again with the main focus on the tensile behaviour of the material.

![material_model_tuning_image1.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/material_model_tuning_image1_fd23b7a519.png)
*Left: Example of proposed ranges of parameter Sratio inducing shift of output towards higher/lower values. Right: Adjusted probability distributions of NMSE values after all proposed input regions are applied.*

## Benefits
- **Definition of influential parameters.** The number of parameters could be reduced, since some of the inputs are negligible for the agreement of material characteristics.
- **Lower computational time.** Even though the process was iterative, the number of simulations required in total was cut significantly.
- **Deeper insights into the task.** Evaluation of the iterative process revealed the complex behaviour of the material model on a wide range of its input parameters.


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Tuning parameters of the material model

ALTRAN CZ is a leading provider of development services, especially for the automotive industry. With more than 25 years of experience with virtual design, part prototyping, and own accredited testing facility, it contributes to safe and effective individual transportation in Europe.

## Challenge
For the kinematics of the tripod manipulator, it is crucial to know how the constellation of actuators, based on their actual displacement, can affect the resulting position of the carried optical point in all six degrees of freedom ‐ all displacements and all rotations.

Moreover, the manipulator itself has to withstand all forces and stress resulting from the displacement of actuators. The tripod is also stabilized with three springs, each of them loaded with the prestress. Positions of these springs also may be changed during the design of the manipulator.

In total, there were 12 input parameters of the task, which is a massive extension to a previous study with only actuator displacements considered. For these three input parameters, a full-factorial scheme was used, leading to 27 computations in MSC.Nastran. However, this approach covered only the corners of the design space with a fixed interpolant level. Now, only 155 evaluations were needed for the expanded set of inputs and the creation of mathematical models for all ten outputs.

![tripod_manipulator_image4.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/tripod_manipulator_image4_807e3bc814.png)

## Solution
In the beginning, we coupled the UptimAI tool with the simulation software MSC.Nastran, with no need to interfere with its code or features. Then, the UptimAI tool began to set combinations of inputs for the Nastran. It used the **UptimAI algorithm** to process simulation results into the metamodel of forces and displacements of the tripod manipulator.

Features of the mathematical model could be easily shown on the example of one of the outputs, the von Mises stress. **UptimAI sensitivity analysis** identified input parameters with the significant ability to change the output. Unlike most of the other outputs, the stress is dependent almost entirely on displacements of actuators. The effect of springs and their positions is too low to be measurable.

![tripod_manipulator_image1.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/tripod_manipulator_image1_0f5936228f.png)

From the **UptimAI histogram**, the overall information about the range of this output was shown as well as the shape of the probability density function. Besides, it was possible to visualize the effect of each variable to the statistical properties of the model. Here the stress is ranging from 110 to 380MPa. From the influence analysis, it is apparent that setting the displacement of actuator 402 cannot lower the minimum value of stress below 110MPa. However, the probable maximum can be reduced by almost 30%.

![tripod_manipulator_image6.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/tripod_manipulator_image6_50b5f0da70.png)

Details responses of the von Mises stress level to changes in input parameters were apparent from **UptimAI increment plots**. Depicted dependencies of the output on particular inputs are separate from their mutual interactions. The UptimAI algorithm was able to catch the discontinuity in behavior based on the actuator displacements. That increased significantly the precision of the mathematical model over the commonly used interpolation with the quadratic polynomials. The model itself then consists of the summation of its all available increments.

![tripod_manipulator_image3.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/tripod_manipulator_image3_3524f1ab3e.png)

The statistical nature of the model and the performed analysis was also used for the definition of design recommendation. The **UptimAI preliminary optimization** tool was used to identify ranges of input parameters resulting in decreased stress values in the tripod. The result suggesting the lowest actuator displacement possible was not a big surprise. Nevertheless, it was the explicit mathematical confirmation of conclusions based on general engineering intuition.

![tripod_manipulator_image5.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/tripod_manipulator_image5_fb87366ed9.png)

## Benefits
- **Deeper insight into the statistical effects** on tripod’s behavior.
- **Fast design exploration.** Set of only 155 FEM computations was sufficient to describe the problem with 12 input parameters and 10 outputs.
- **Simplified design task.** The number of input parameters can be reduced **while keeping the precision of the model**.

Influence analysis of the actuator displacements on stresses

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Tripod manipulator

Commuter airplanes are typically used on short regional routes. They often operate in broken terrain of lands with underdeveloped infrastructure where they have to serve small regional airports with short landing strips.

## Challenge
Designers of STOL (Short Take-Off and Landing) airplanes had to reduce the landing ground distance to a minimum. To achieve the required aircraft performance, it was necessary to increase the maximum wing lift coefficient. Therefore, they had to design a new kinematic concept of a trailing-edge flap.

Due to the novelty of the concept, the performance of the new flap could not be assumed from measurements of well-known flap designs. Hence, it was necessary to understand how geometry and kinematics of the flap affect the maximum of the lift coefficient of the flapped airfoil. However, the standard methods of design exploration did not work, the development was delayed, and there was a failure to comply with deadlines.

There were 10 input parameters of the task. The standard approach of the Design Of Experiment required at least 1045 CFD computations in the Ansys FLUENT solver. In addition, achieving the quality of data interpolation and its sufficiency to mimic the real behavior of the flap aerodynamics was uncertain.

![stol_image6.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/stol_image6_05e4a90fe8.png)

## Solution
In the beginning, we coupled the UptimAI tool with the simulation software Ansys FLUENT, with no need to interfere with its code or features. Then, the UptimAI tool begun to set combinations of inputs for the FLUENT. It used the **UptimAI algorithm** to process simulation results into the metamodel of the flapped airfoil aerodynamics.

Important general information about the performance of the chosen flap concept was given by UptimAI histograms. The probability distribution of the resulting increment in the maximal lift coefficient had the mean value 1.7, which refers to the very well-tuned slotted flap (closer to the typical Fowler flap performance). It also showed a fair probability of an increase in the lift coefficient of the flapped airfoil by more than 2.5! Therefore, it was confirmed that the proposed flap concept has the potential to improve the airplane’s flight characteristics.

![stol_image3.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/stol_image3_375e2ef1bd.png)

**UptimAI histograms** also depicted particular probability distributions of results describing the influence of each input parameter and each interaction of input parameters. This helped to detect extreme values of the lift coefficient increments and their causes. A good example is the interaction of parameters describing the position of the pivot point, the flap deflection angle, and the deflection angle of the flap cove trailing edge. All three parameters together determine the size of the slot between the flap and the wing, which turned out to be crucial for the value of the lift coefficient.

![stol_image1.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/stol_image1_00544fc558.png)

The importance of each input parameter in terms of aerodynamics was clearly shown in the **UptimAI sensitivity analysis**. It identified parameters emulating the additional camber of the flap (“4” – camber position, “9” – camber magnitude) as having just little influence on the lift coefficient. Concurrently they do not interact with other input parameters, thus, other criteria can be considered in their design, such as manufacturing. The same can be applied to the geometry of the flap cove entrance radius.

![stol_image2.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/stol_image2_d8f77c965f.png)

Details of the dependence of the flap aerodynamics regard to changes in input parameters can be examined in **UptimAI increment plots**. Using these, designers were able to find ranges of inputs responsible for the steep drop in values of the lift coefficient which had to be avoided in the design to prevent deterioration of the result. This approach led to the design insensitive to manufacturing tolerances and deformations under loading. Increment plots were used as well for simulation points where the CFD solver failed to converge.

![stol_image4.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/stol_image4_367221964d.png)

## Benefits
- **Increasing the maximum lift coefficient by up to 2.5** due to optimized flap geometry and position. The achieved properties significantly exceeded the defined expectations.
- **Landing ground distance shortened by up to 18%** compared to the original design with a slot flap.
- **Saving 450 hours of computational time.** The required number of CFD simulations (146) was only **14% of the original assumption.**


Landing ground distance shortened by up to 18%

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Landing configuration of a STOL commuter airplane

The glide ratio, or the ratio between the lift and the drag coefficient, is one of the most important aerodynamic characteristics of an airfoil. It represents the aerodynamic efficiency of the airfoil and affects aircraft’s flight performance values such as the maximum range or angle of a climb after take-off.

## Challenge
The main goals for new airfoil design were to increase the glide ratio (efficiency) and decrease the sensitivity of airfoil’s aerodynamics to manufacturing tolerances and imperfections of its surface. Therefore, it was necessary to create a mathematical model describing dependencies between the glide ratio of the airfoil on its geometry.

The geometry was parameterized with a slightly modified PARSEC method. There were ten geometrical parameters in the task together with the Reynolds number describing flight conditions. Airfoil aerodynamics was analyzed in the panel method software Xfoil.

One computation in the Xfoil takes about 20 seconds; thus, this task was also suitable for validation of the mathematical model against the results of the Monte Carlo simulation. Result values interpolated from the metamodel were compared with the results of computations performed with the Xfoil.

![airfoil_design_image4.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/airfoil_design_image4_68a60f11d4.png)

## Solution
In the beginning, we coupled the UptimAI tool with the panel method code Xfoil, with no need to interfere with its code or features. Then, the UptimAI tool began to set combinations of inputs for the Xfoil. It used the **UptimAI algorithm** to process computation results into the metamodel of the airfoil aerodynamics.

As shown in the **UptimAI histogram** and its probability density function, ranges of input parameters were set broad enough to conclude in the large variance of resulting values of the maximum glide ratio. It demonstrates possibilities of the chosen parameterization method and the capability of the Xfoil software to converge when solving aerodynamics of airfoils with multiple curvatures. A comparison of probability distribution of results, based on the glide ratio computed in Xfoil coincided well with the distribution of the modeled values of the maximum glide ratio, proving the accuracy of the metamodel. For the comparison, around 40,000 Xfoil computations were made in total with randomized values of input parameters (the Monte Carlo method). In contrast, the metamodel was created from only 161 Xfoil computations.

![airfoil_design_image3.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/airfoil_design_image3_df7f58ff60.png)

**UptimAI sensitivity analysis** showed the influence of each input parameter on the maximum glide ratio. It confirmed the major effect of inputs describing the upper surface of the airfoil, especially its maximum thickness. On the other hand, the influence of the trailing edge taper was lower than expected, but this could be a result of the defined range of this input parameter. The leading edge radius of the upper surface did not affect the glide ratio either.

![airfoil_design_image2.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/airfoil_design_image2_0177ea072b.png)

Then, direct response of the maximum value of the glide ratio to changes in each of the influential inputs was examined using the **UptimAI increment plot**. The shape of these functions was key to the airfoil design. This can be demonstrated on the position of the maximum thickness on the airfoil’s upper surface. For this input parameter, the range of values could be identified with a low response in result values as well as the region with a steep gradient of the output. For the first range, the glide ratio becomes insensitive to surface imperfections. The second one leads to significant aerodynamic improvements, only when the manufacturing of the airfoil is flawless.

![airfoil_design_image1.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/airfoil_design_image1_0289314682.png)

## Benefits
- **Deeper insight into the statistical effect** on the airfoil aerodynamics.
- **Increase in the average value of the glide ratio from 113 to 166**. All of the newly designed airfoils have a maximum glide ratio higher than 125.
- **Validation of the metamodel** – probability distribution of interpolates results coincide with results computed in Xfoil.


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Airfoil Design

ŠKODA AUTO is the largest car manufacturer in the Czech Republic and part of the Volkswagen Group since 1991. The company uses highly advanced simulation tools in its R&D departments to meet all design goals, where passenger safety is one of the top priorities.

## Challenge
During the development of a new car model, it was necessary to increase the amount of energy absorbed during a crash incident. Thus, engineers had to learn and understand how can the geometry of certain body parts affect the amount of energy needed for deformation of these parts. To validate the new know-how before its use for car design, results of performed simulations had to be compared against the real testing. However, test results were prone to correct settings and adjustment of the testbed. The task had 27 input parameters in total. Standard approaches of design exploration would require at least 4000 runs of the PAM-Crash simulation software, making the study unfeasible. On the other hand, when reduced, the study would fail to give complete information about the behavior of the car part and relations between inputs and the absorbed energy.

![boxbeam-car.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/boxbeam_car_b7eceeb94e.png)

## Solution
In the beginning, we coupled the UptimAI tool with the simulation software PAM-Crash, with no need to interfere with its code or features. Then, the UptimAI tool begun to set combinations of inputs for the PAM-Crash. It used the UptimAI algorithm to process simulation results into the metamodel of the tested part under deformation.

There were geometrical input parameters in the task meant to be adjusted to increase the performance of the part. Once the metamodel was ready, UptimAI identified ranges of selected parameters raising the probability of an increase in the energy absorbed by the deformed part. At the same time, these new ranges were designed to decrease the variance of results as much as possible. This approach diminishes the influence of uncertainties in the rest of the inputs.

![boxbeam_1_EN.PNG](https://uptimai-website.s3.eu-central-1.amazonaws.com/boxbeam_1_EN_4cebbd013b.PNG)

**UptimAI sensitivity analysis** and **UptimAI histograms** helped to identify input parameters with a major influence on both, the variance and the mean value of the amount of energy absorbed during part deformation. It was revealed that the variance of results is strongly affected by barrier rotation – the inclination angle between the testbed impactor and the tested part. Thus, one of the optimization goals was the minimization of the influence of this particular parameter.

![boxbeam_2_EN.PNG](https://uptimai-website.s3.eu-central-1.amazonaws.com/boxbeam_2_EN_a2b90ba17f.PNG)

Another guidance to understanding the problem of the deformed box beam was given by the **UptimAI increment plot**. It showed shapes of increment functions depicting dependencies and relations of input parameters and the value of absorbed energy. To reduce the influence of uncertainties on the testbed, UptimAI recommended setting ranges of inputs with the lowest gradient of corresponding increment functions. One example – material quality check of used sheet metals is one of the ways how to diminish the influence of the impactor rotation.

![boxbeam_3_EN.PNG](https://uptimai-website.s3.eu-central-1.amazonaws.com/boxbeam_3_EN_f4acf54d6e.PNG)

The UptimAI software also found input parameters connected with others through higher-order interactions. Then, engineers used the **UptimAI preliminary optimization** tool to identify ranges of inputs resulting in increased absorbed energy and also ranges to be avoided. A good example of such output is the recommendation to choose distinct thicknesses of two sheet metals welded together to form the tested part. There was a larger amount of absorbed energy in comparison to the case with both sheet metals being thicker. Additionally, the results of an older study recommending non-equidistant positions of spot welds were confirmed.

![boxbeam_4_EN.PNG](https://uptimai-website.s3.eu-central-1.amazonaws.com/boxbeam_4_EN_cb670c85b8.PNG)

## Benefits
- **The absorbed impact energy of optimized geometries increased by 10% on average**, the lowest value (absorbed energy due to the most adverse combination of inputs) increased by 18%.
- Decrease of result sensitivity to testing conditions – **the variance of the results decreased by 63%**.
- **Significant reduction of the computational time** – necessary number of simulation runs (280) was reduced to **7% of the original estimate**.


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Car Box Beam Deformation

Case Studies

We are happy to share that we have been nominated as one of the top Machine Learning companies in the Czech Republic by Best Startup EU!

In the published article, Best Startup EU picks the companies that are taking approaches to innovate the Machine Learning industry in all kinds of industries, and selects the companies that excel in one of these categories:
- Innovation
- Growth
- Management
- Societal impact

You can read the full article [here](https://beststartup.eu/41-top-machine-learning-startups-and-companies-in-czech-republic/).

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Top ML company in Czech Republic

Uptimai has been selected as one of the 28 most innovative Czech Republic companies that use Machine Learning Technology by Futurology Life.

Futurology Life is a media company based in London that aims to boost inbound investment into innovative companies and startups by addressing the information asymmetry between small innovative startups and institutional investors.

The companies were selected by their performance in the following categories: Innovation, Growth, Management and Social Impact.

You can check the complete article for more information [here](https://futurology.life/28-most-innovative-czech-republic-based-machine-learning-companies/).

![news15_image2.png](https://uptimai-website.s3.eu-central-1.amazonaws.com/news15_image2_6966c9ce19.png)



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Innovative Machine Learning Company

Our CEO Martin Kubicek and Head Developer Jiri Otoupal visited the University of Defense in Brno. During the visit our team made a presentation to show the capabilities of our software and engineering team. Our cutting-edge Uncertainty Quantification approach leads to deeper insights and better designs for all the different performance conditions for both civil and military purposes.

Events like this one allows to create links between the civilian and the military industry, and to reinforce our commitment with the academia.

![news14_image2.jpg](https://uptimai-website.s3.eu-central-1.amazonaws.com/news14_image2_7435b1c7b4.jpg)



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Visit to the University of Defense

## A Problem of Probability Density Function Estimation for Large Dimensional Spaces With Many Low-Influential Dimensions
*Jergus Suja, Martin Kubicek and Tomas Koutnik*

### Abstract
All engineering problems consider uncertainties. These range from small production uncertainties to large-scale uncertainties coming from outside, such as variable wind speed or sunlight. Currently, modern methods for uncertainty propagation have large difficulties with estimation of statistics for large-scale problems which considers hundreds of these uncertain parameters. Due to the complexity of the problem and limitations of the modern methods, a common approach for modelling large scale problems is to select a few important parameters and model statistics for these parameters. However, this can lead to an important problem. In this paper, an application of the UptimAI’s UQ propagation algorithm is used to discuss a new problem arising from very high dimensional spaces where a large number of parameters have negligible impact on the final solution. In other words, when a problem consists of a great number of uncertain design parameters, common practice is to focus on the most important ones and neglect the non-influential ones. However, a combination of a great number of noninfluential parameters can lead to completely different results. This is especially a problem for modelling large dimensional statistical models where a common approach is to perform sensitivity analysis and neglect the non-influential variables, i.e. set the non-influential variables to nominal value. Therefore, using a common approach of neglecting the non-influential variables could lead to a dramatic error and hence, we call this problem ”many times nothing killed a horse”. This problem cannot be observed for cases with a small number of design parameters, which are commonly solved in statistical modelling. The reason for this issue is that the combined influence of neglected variables is extremely small and such that has no influence on the final output. Application of the UptimAl’s UQ propagation algorithm to modern engineering problems and the possibilities of mitigation of the cumulative influence of non-influential parameters is discussed in detail. The problem is shown on a case of economic load dispatch (ELD) problem which consist of 140 dimensions [1]. To this problem was applied UptimAI’s UQ propagation algorithm to obtain accurate statistics for the problem and to get deeper insight into the statistics. Using the accurate model obtained by UptimAI’s algorithm, we compare statistics of using only important variables and using all variables. This lead to a significant difference between results and such that put a large question mark on standard approach. The obtained results are validated with the Monte Carlo simulation applied directly to ELD problem. Application of UptimAl’s UQ propagation algorithm to modern engineering problems and the possibilities of mitigation of the cumulative influence of non-influential parameters is discussed in detail.

Link to a full article [here](https://www.scipedia.com/public/Suja_et_al_2021a).

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Problem of Large Dimensional Spaces

Our CEO Martin Kubicek and Head Developer Jiří Otoupal attended the third **Czech-American Defense and Cybersecurity Forum in Prague.**

In the beginning, Deputy Minister Kopečný and many other government & security officials emphasized how useful and important these regular meetings are. **If companies want to keep pace in technological progress they have to find a way to collaborate with a variety of organizations** and such events are a great way to do so.

The event was designed to strengthen bilateral cooperation between the US and the Czech Republic. It brought together the U.S and Czech defense suppliers with senior defense and industry leaders **to share important information, and to forge and develop new connections.** The collaboration between the two countries is obviously paying off because the export of military materials is **increasing in the last decade.**

It was a high-profile opportunity for us so we are glad that we were given the opportunity to take part.

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*Our staff and ambassador Stephen B. King*

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Czech-American Defense and Cybersecurity Forum

Take advantage of the current situation, invest in internal process improvement and be ready for upcoming market changes. **Market leaders see this rather difficult time as an opportunity to develop and become stronger.** Once the challenges are settled down, those who already implemented advanced technological and automated solutions will be the ones with a competitive advantage.

When almost the entire world is working from home and business may seem to slow down, making everything as effective as possible is crucial. From everyday tasks to top-level decisions, each activity is being re-evaluated for its actual value to the whole company and future steps. **Wrong decisions and double work are now more costly than ever. **The design process in manufacturing needs to be optimized to prevent failures that eventually lead to wasted resources.

**Our one-of-a-kind solution has proven to reduce design costs, scrap rates and to save many hours of work.** Being able to redistribute these resources smartly elsewhere is vital, especially in the present circumstances.

**We have shifted to fully remote mode and we are able to implement UptimAI virtually everywhere.** We are ready to help you fasten and optimize the design process. Take the first step today for an efficient process tomorrow.

[Get in touch with us and learn more](https://uptim.ai/). 

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Why invest in AI technology now?

The evolution of the UptimAI software has begun at the University of Strathclyde in Glasgow, where its prototype was used by researchers to identify impact trajectories of the space debris. **For the first time, it became possible to create complex mathematical models with an even lower amount of simulations than is the number of problem parameters.** To prove technology’s abilities on practical engineering problems, it was used for the analysis of the novel design of the flapped airfoil for commuter aircraft. The model of the problem created by UptimAI confirmed that the proposed flap concept has large potential to **improve** the airplane’s flight performance and shorten the landing distance. Compared to commonly used Design of Experiments methods, the UptimAI approach **saved more than 450 hours of computational time.** Moreover, it allows designers to easily find the direct way to stable aerodynamic characteristics which can be relied upon even if the flap is being deformed under loading. The article was written by CzechInvest with the help of our Head of Application, Tomáš Koutník.

Read the full article [here](https://www.czechinvest.org/en/Homepage/News/September-2020/What-does-space-do-for-the-aero?fbclid=IwAR2l9jMvcs-aW81prkCUC6tLFfqYZHgJWSrHOOMIUK1AETcaFF3uHawAIA4).

*Source: European Space Agency*

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What does space do for the aero?

The world is dealing with the global pandemic longer than we expected and the impact of COVID-19 is inevitable. Although the times are unpleasant and connected to a lot of potential obstacles **it is necessary to be even more creative and effective.** We are at that point, where the production is in a state of stagnation but the new products need to be in the continual process of development. **Constant innovation is crucial when it comes to the long-term survival of a business.**

All of us have to be in some way prepared for future events and think further when the situation will get better. That’s the reason why we decided to step up to help in these difficult times by **making our product more affordable, and accessible to support your development and be part of your success.**

Today´s post is dedicated to an **exclusive discount**. How does it work? **We offer a 60 % off subscription fee for all new SME clients (up to 500 employees)** for the first year without any commitments. [Request a demo](https://uptim.ai/) and we will be happy to provide you more information.


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COVID-19 SMB Discount

We are happy to announce that UptimAI has become a part of **Composites United cluster!**

Composites United is a Berlin-based association for **sustainable fiber-based multi-material lightweight construction** with a farseeing vision and a progressive mission. The cluster brings together about 400 members from various industries, regions and countries, united by the same goal of developing new approaches and solutions for fiber-based constructions. A membership in the Composites United clusters gives members the opportunity of participation in research and development projects, access to new international markets, help with funding and promotion and many more.

The main goals of UptimAI as fresh members are cooperating with the wide network of Composites United, meeting **new potential partners and clients**, and presenting to them our **cutting-edge solution**.

Check the [Composites-United website](https://composites-united.com/).

Learn more about [how our solution works](https://uptim.ai/) and request a demo to give it a try!

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We are a member of Composites United!

UptimAI company was incubated in the **European Space Agency Business Incubator** in Prague to enable the use of our cutting-edge algorithm for a wide range of industrial applications. **At the moment, we are able to connect UptimAI with any CAE simulation platform without any limitations.** In cooperation with ESA BIC Prague, we created a video to show you our Uncertainty Quantification solution in more detail.

[Get in touch](https://uptim.ai/) with us to discuss possible use-cases for your CAE challenges. **You will be amazed by the efficiency of our product!**

![esa-bic-video](https://uptimai-website.s3.eu-central-1.amazonaws.com/ESA_UPtimAI.mp4)
Video: [https://www.youtube.com/watch?v=dEKTxXobQDg](https://www.youtube.com/watch?v=dEKTxXobQDg)






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ESA BIC Prague introduces UptimAI

UptimAI was shortlisted for the TOP30 in a startup competition organized by Vodafone. It is a really great opportunity for us to show our solution to the jury and get feedback from experienced entrepreneurs. **Additionally, there is a chance to win valuable prizes or up to €3.75M investment!**

More information about the competition can be found [here](https://napadroku.cz/en/). **Wish us luck! **

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Vodafone Idea of the Year TOP30

We got into PowerUp! Country Final Czechia, where 8 startups are going to pitch and compete to advance to Grand Final, multi-million Euro investments, and wide support from InnoEnergy.

PowerUp! is the challenge for start-ups, scale-ups, and SMEs from Central and Eastern Europe whose products in the fields of energy, smart technologies, mobility are solving today’s problems with tomorrow’s technology.

Who to expect? Ibatt.energy, BatteryCheck, ENMON Technologies, Pocket Virtuality, UptimAI, Topíte, Skymaps, and Mileus.

**[REGISTER for the event](https://www.eventbrite.com/e/virtual-powerup-country-final-czechia-tickets-102906020678) to save your spot.** Even the online seats are limited!

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PowerUp! Country Final

We are honored to announce that we will take part in **Industry Space Days 2020 (ISD).** This virtual event will take place on 16-17th September 2020.

The ISD is an event organized by ESA which brings together **important European players in the space sector through B2B meetings and conferences.**

The main purpose is to connect and increase involvement in space activities. Companies are encouraged to share their visions and ideas to produce better results. So it provides us a **great chance** to introduce our product, meet potential clients, or create new business collaboration.

Stay tuned and catch us there!

Check the official websites [https://isd.esa.int/](https://isd.esa.int/)

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ISD SPACE DAYS 2020

We’ve been named one of **@hellotmrc**’s Deep Tech Pioneers, from over 5,000 applications from 128 countries!

HELLO TOMORROW is an organization that identifies, and analyses innovation trends & dynamics leveraging experts. It connects the best minds and builds a worldwide community of science entrepreneurs, investors, corporates and academics to work together to untap the enormous potential of deep technologies. The most anticipated technology event in the world will happen this fall and we will be a part of the Deep Tech week.

Upcoming Summit will cover four major topics: Space, Planet, Human and Machine.

**Come and meet us at the Hello Tomorrow Global Summit in Paris on the 12th – 13th of March 2020!**

**EDIT: POSTPONED TO 22nd – 23rd of October 2020.** We will keep you posted. **<u>[Find more information here](link)</u>**

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We are Deep Tech Pioneers!

At the end of 2019, we participated in an acceleration program that supported our company’s growth significantly. With the investment from Lighthouse Ventures, we have been able to advance the tool development, rebrand and expand the business.

“**Martin Kubíček has developed a unique product that is ten times faster and significantly more accurate than similar solutions on the market.** Thanks to our acceleration the program, we want to help him turn technology into business success on the international market,” explained Michal Zálešák, the Managing Partner at Lighthouse Ventures.

UptimAI offers full automation and simple connection to standard simulation tools. This leads to high efficiency while offering deeper insights and a different perspective on product optimization. **This is a revolution for the simulation area.** One tool that combines an otherwise lengthy process of simulation set-up, code synchronization, and the creation of a simplified model. Thanks to the unique algorithm, for example, engines are more efficient, cars safer or bridge structures more stable. The solution can be applied in a wide range of industries. Use for the solution can be limitless, for instance, aircraft and spaceships manufacturing, engineering and medicine.

“Since we are engineers by profession, **we understand that existing optimization methods are not applicable to conventional engineering designs.** Instead of a clear optimum, our algorithm will offer the engineer a wider field of choice, which is much more practical than the standard approach,” says Martin.

One of the successful pilot projects that was our jump start for the investment was executed for Škoda Auto in Mladá Boleslav, where our startup worked on the so-called box beam. This is the part of the car that absorbs impact energy and significantly increases the chances of survival in an accident.

“We helped to improve the element to be resistant to many directions of impact and not just to the front impact. We also helped set the element so that its absorbed energy is not affected by external circumstances,” says Martin. Since the pilot, we have continued our cooperation with Škoda.

The article was written by Czech Crunch, which interviewed Martin Kubíček, the founder of UptimAI.

**Read the full article [here](https://cc.cz/vyvinul-algoritmus-ktery-pomaha-skodovce-a-zachranuje-zivoty-ted-na-nej-martin-kubicek-ziskava-miliony-korun/)** (Czech version only).

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The investment accelerates our development

The whole project started as an off-spin of Martin’s projects during his PhD studies at Starthclyde University. This new algorithm for the propagation of uncertainties was based on a fundamentally new approach to meta-modeling (https://en.wikipedia.org/wiki/Metamodeling), which was later targeted to engineering problems. It turned out that the developed code was very efficient and very robust. Moreover, the technique provided some new insight into the problem and helped to inform a deeper understanding of the problem. It’s first application was the uncertainty propagation for re-entry of orbital debris, where it has shown the importance of statistical propagation. Results clearly showed that a common assumption of ‘Plus-minus’ around the result is completely wrong as you can see in the picture below.

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The statistics have a profound influence on the expected result and sometimes it can create some famous quotes such as ‘Houston, we have a problem’. Well, engineers were probably not very happy about this infamous space catastrophe.Moreover, the result was something unexpected even for the team who was working on the re-entry case. We tested the result with an experiment by throwing small balls into the air and observing their impact locations. It turns out that the results of the experiment were very similar to our algorithm, which proved that our algorithm worked very well.

The second case was the re-entry of GOCE and its flight parameters . Here again the algorithm showed its strengths and some interesting ‘wow’ moments about the re-entry. However, it showed a very important aspect of the algorithm, that it can work very efficiently for virtually any problem. Hence, it was decided to transform the algorithm into something industry can use to improve their products.

In the first year, the algorithm started to change to suit industrial needs. It was a very turbulent time, but after many hours of programming, testing and developing, an improved version of the algorithm was created. This new algorithm was used for the collapse of the car box-beam, which was done in cooperation with MECAS ESI in Pilsen. Again, the algorithm proved its robustness and showed that it is working very well even for such complex cases. More importantly, we came up with some interesting ideas on how to provide engineers with even deeper insight. This case impressed Skoda Auto and we started to cooperate on passive safety of cars.

After the first year and with a successful application of our code in industry, we were accepted into ESA Incubator in Prague (http://www.esa-bic.cz). Empowered with new ideas, experienced with industrial problems and full of enthusiasm, we started to develop a new industry target platform. After two years of successful incubation, we can proudly say that we developed a tool, which can tackle even the most difficult cases with an efficiency never seen before. Moreover, apart from standard analysis, our tool provides unique insight, which is only available due to our unique approach. Our tool already helps engineers to develop a product, which is more reliable, efficient and ahead of it’s competition.

Today, industry and academia are using our tool, but we will not stop there. We have plenty of new ideas on how to improve our code in its efficiency and even more ideas on how to provide engineers additional insight to produce a better product – so stay tuned.


Case studies