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Machine learning assisted modelling of uncertainty for lightweight structures

Name: Athira Anil Kumar

Department: Aerospace Engineering

Program: M. Tech. (Structures)

Name of supervisor: Prof. Susmita Naskar


Introduction and applications of the research:

The development in human civilization is identified by the prominent materials of that age. We have witnessed the stone, bronze and iron age and are currently in the age of advanced, lightweight materials like composites. Composite structures have seen an exponential growth in research and applications due to their high strength to weight ratio, high stiffness and damping, toughness, corrosion resistance, improved thermal conductivity and electrical permittivity. 

Composite materials are functions of a lot more parameters than their metallic counterparts which gives rise to two major problems. Consideration of multiple parameters during design process can make the analysis computationally expensive and increase in number of parameters also results in an increase in the uncertainties associated with it. In structural modelling, uncertainties arising from material properties, system loading, model parameters and manufacturing processes due to laminate stacking sequence can affect the performance of composite structures. Therefore, it is important to consider the inevitable uncertainties at various levels while studying the behaviour of composite materials. Deterministic models do not give realistic predictions due to inherent system uncertainties and can sometimes lead to over-constrained systems. Using statistical approaches, computational analysis can be done with more accuracy by incorporating the variability bounds of the random variables. The main objective of uncertainty quantification is to pin-point the input parameters whose variations or probability distributions are analysed to give a specific output. This process will help identify the key parameters whose uncertainties influence the output responses, thus helping build more reliable structures. 

Figure 1: Flowchart highlighting the important steps in uncertainty modelling using machine learning techniques

Novelty and methodologies:

The analysis is performed in broadly three steps: modelling of uncertainty at input level, propagation of uncertainty to global level and quantification of global responses, which includes dynamic and stability characteristics. When it comes to modelling of uncertainties, accounting for spatial randomness of material properties makes the analysis more practical. After modelling the uncertainties, the effect of uncertainty needs to be propagated to the global responses. This is done by using a stochastic computational model of the structure based on Monte Carlo simulation (MCS). However, this requires thousands of expensive model evaluations to be carried out corresponding to the random realizations. To overcome this, a meta-modelling/ machine learning (ML) modelling approach can be adopted, where the uncertainty propagation is realized following an efficient mathematical medium. The final step is uncertainty quantification of output responses, which is effectively carried out by deriving the probabilistic distributions and statistical moments.

Figure 2: Histogram plot of first natural frequency obtained by original MCS simulation model and Kriging model for randomness in micro-mechanical (left) and macro-mechanical (right) properties

Based on the examination of the available literature, several studies have been done in this domain. However, the use of Kriging model has not been explored extensively for the study of effect of randomness. For the chosen laminate which represents the stiffened panel of a conventional aircraft wing, studies related to their free vibration analysis could not be found. The use of ML models to predict the performance of the structure took 95% lesser time as compared to the corresponding finite element model evaluation, which showcases its computational effectiveness.

Results and discussions:

For computing the required evaluations, a composite laminate made of AS4 carbon/3501-6 epoxy is considered. Validation and convergence study are done to determine the optimum sampling technique and sample size for obtaining data to generate the machine-learning model. Another validation and convergence study are performed to verify the finite element model and choose the optimum mesh size for free vibration analysis.

Figure 3: Probability density function plots for the first two natural frequencies considering different degrees of stochasticity in micro-mechanical and macro-mechanical properties

The input-output data obtained from the original finite element model is used to train a Kriging model and the accuracy is studied for randomness in both micro-scale and macro-scale material properties. The ML model is then used to highlight the sensitivity of natural frequencies to certain input parameters. Varying the degree of randomness in the input parameters also showed a significant variation in the output responses, where the response bounds increased with increasing stochasticity. The model can be developed by include a greater number of uncertainties at different length scales. Further study can done to study the effect of events such as damages and cracks in the composite structure. 



  • Kumar, A. (2021). Machine learning assisted modelling of uncertainty for lightweight structures, M. Tech. Thesis, Indian Institute of Technology Bombay
  • Naskar, S., Mukhopadhyay, T., & Sriramula, S. (2018). Probabilistic micromechanical spatial variability quantification in laminated composites. Composites Part B: Engineering, 151, 291–325. https://doi.org/10.1016/j.compositesb.2018.06.002