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.

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.

*Fig. 1. Electric vehicle battery (photo by Gereon Meyer CC BY-SA 4.0)*

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.

*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.

*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%.

*Fig. 4. Comparison of effects of the most influential variable of the full domain against all variables of the reduced domain*

**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**.

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.

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.

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.

*Fig. 1. Scheme of the CubeSat Structure*

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.

*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.

*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.

*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.

*Fig. 5. Statistical response of the displacement of the payload before and after improvements*

**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.

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.

Read more ]]>Material characteristics

Tuning parameters of the material model

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.

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.

Sample of the material under the virtual “testing” in Abaqus (picture: IDIADA CZ)

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.

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.

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.

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.

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.

**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.

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.

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.

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.

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%.

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.

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.

**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**.

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.

]]>The article was written by CzechInvest with the help of our Head of Application, Tomáš Koutník.

Read the full article here.

]]>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/

]]>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 SMB clients** **(up to 500 employees) **for the first year without any commitments. Request a demo and we will be happy to provide you more information.