Nanotubes material

This project was developed with a US company in the defense sector and was about creating a material based on nanotubes for armoring. Because of confidentiality in this document, the inputs and outputs won't be named, as well as the data and models have been normalized, simplified, and slightly modified.

Challenge

Material creation in laboratories is a multifaceted process, where a variety of inputs must be carefully controlled and optimized to achieve desired outcomes. One of the primary factors that influence the final material properties is the selection of raw materials. The purity, composition, and even the source of the materials can play a pivotal role in determining the final product’s characteristics. Enriching base materials by adding specific additives or dopants—such as rare earth metals in semiconductors or carbon nanotubes in polymers—can enhance particular properties like strength, electrical conductivity, or thermal stability. The process of introducing these enriching agents must be precisely controlled, as even slight variations in concentration can result in significant differences in performance, particularly in advanced materials like high-performance alloys, biomaterials, or nanomaterials.

Equally important are the physical conditions under which materials are synthesized. Temperature, pressure, and reaction time can all influence the formation and microstructure of the material, potentially enriching its properties. For example, by varying the temperature during a synthesis reaction, researchers can influence the crystallization rate, which in turn can enhance the material’s mechanical or electrical properties. High-pressure environments are often used to simulate extreme conditions that materials may encounter in real-world applications, leading to the creation of enriched, high-density materials with superior strength or resilience. Furthermore, innovative techniques like high-energy ball milling or laser-assisted deposition can alter the morphology of materials on the nanoscale, enriching their performance in ways that conventional methods cannot achieve.

The fabrication method also plays a crucial role in enriching material properties. Techniques like additive manufacturing (3D printing), chemical vapor deposition (CVD), or sol-gel processing enable precise control over material structure at the atomic or molecular level. These methods can incorporate enriched components, such as nanoparticles or fibers, into matrices to improve properties like strength, conductivity, or corrosion resistance. By tailoring the microstructure during fabrication, researchers can create advanced composites or functional materials that offer superior performance for specific applications, from aerospace to biomedical devices.

For this study, multiple variables (>60) have been taken into account to study 9 different relevant material characteristics in order to understand how they are affecting the material and how its performance could be optimized from a multi-objective perspective.

Target:

• Find a model that can track the properties of the material
• Find the right combination of additives to fulfill the required properties
• Find the multidisciplinary optimal point
• Suggest new measurements to improve the quality of the final model
• Reduce the cost of production if possible

Solution

In this case, a very small set of experiments in the laboratory were already performed and the objective was to find which new combinations of variables would be of high interest for a new testing campaign in order to maximize the probability of a better material finding. That way it was a problem for the AI modeller and only data was provided.

Uptimai tool is used to read the data (in the form of .csv table) and create a digital twin of the material itself, giving insights into the problem. The first thing to do after creating the model is validate it, to understand the expected error order of magnitude that we are taking into account.

In this case, we can see that even having a very small dataset Uptimai is able to find a proper Digital twin model that is actually explaining the behaviour of the problem. The error is randomly distributed against all relevant variables and against the output, showing that the model is properly fitted in the whole domain, i.e. we have an accurate model using a very limited number of samples.

The second thing that was done, once the models were ensured to be accurate, was to do a sensitivity analysis (compare the importance). This shall allow us to target additive parts, which can be replaced with cheaper solutions as they will not impact the studied property of the problem.

Three variables were the most relevant, two being the quantity of presence of an additive and one a manufacturing process. It turns out that high-level interaction played an important role in the process and thus, it was suggested to study this interaction closer, if the production cost would play an important role.

To create a statistical analysis, one needs a large portion of samples. Our algorithm created distributions using only a limited number of samples allowing for inter-outcome statistical analysis.

Checking the posterior distribution based on the few data (distributions generated using our algorithm) showed that there is the possibility to obtain good results. In other words, the thick distribution on the right side (Figure above) suggests that the found optimum shall be stable and not be sensitive to production tolerances and additive impurities.

Using our statistical tooling for maximal and minimal regions (Figure below), we quickly established the bounds for each variable. It can be easily seen that being in the lower domain we get a high probability of high outcome. Easily, we can establish bounds on the additives, i.e. how the range for additive material shall be from 0 to 0.2.

Interesting statistical analysis between various outputs shows a strong correlation between outputs 7 and 6. With an interesting point of stability around higher values of output 7 and output 6. Studying this desired spot allows us to tune the material according to the needs of the customer and simultaneously make the material cheaper to produce. In order to make the final solution cheaper, we do not aim for the maximum values of outcome 6 but slightly less. This allowed us to find a stable solution that is insensitive to outside influences, e.g. production tolerances.

From Figure above, we can see a strong correlation between outcomes 7 and 6. It allowed us to establish design flexibility for each outcome. In other words, outcomes 7 and 6 have a sweet spot around 0.23 for variable 2, but to prevent a low outcome for output 7, one has to make sure that values of variable 2 are not below 0.02, i.e. close to zero and also above 0.5 as it would steadily decrease performance for both outcomes.

Lastly in this case it was important to find how the relevant variables were affecting the different outputs. For the first step, there are important directions and potential gradients of the domain.

For output 3 (Figure below), it is found that the interaction between variables 1 and 2 forms a plateau where the output remains constant, except for a specific zone where both variables are set to zero, where there is a huge decrease in the performance of the material. It is necessary to avoid that zone at all costs, as it creates an unstable performance and potential customer complaints on quality.

Also for output 3, but for variables 2 and 3, it can be seen that for a better performance of the material, variables 2 and 3 (which are related to the addition of two different additives), have a direct correlation, needing that both additives are added at the same proportion to have a positive impact on the result. This simplified the production process as measuring the same portions is easier to track.

Finally, for Output 4, there was an important interaction between 3 variables that indicated the position of an optimum in a very specific part of the domain, where variable 4 was in the range of 3 to 4.

With the crossed information of all outputs, we have a desired zone where to find the optimum. New tests following Uptimai indications ended up with the desired material found with a very low number of lab tests.

Benefits

• Understanding of the physics behind the problem
• Reduction of cost and time during the R&D processes Fewer laboratory tests)
• Increase the performance of the material, as a better optimum is found
• Multidisciplinary optimum analysis
• Stable region obtained with stable outcomes, i.e. insensitive to production tolerances
• Ways to decrease production costs