The use of direct inverse maps to solve material identification problems: pitfalls and solutions

Abstract

Material parameter identification is a technique that is used to calibrate material models, often a precursor to perform an industrial analysis. Conventional material parameter identification methods estimate the material parameters for a material model by solving an optimisation problem. An alternative but lesser-known approach, called a direct inverse map, directly maps the measured response to the parameters of a material model. In this study we investigate the potential pitfalls of the well-known stochastic noise and lesser-known model errors when constructing direct inverse maps. We show how to address these problems, explaining in particular the importance of projecting the measured response onto the domain of the simulated responses before mapping it to the material parameters. This paper concludes by proposing partial least squares regression as an elegant and computationally efficient approach to address stochastic and systematic (model) errors. This paper also gives insight into the nature of the inverse problem under consideration.

A promising azeotrope-like mosquito repellent blend

“…The liquid compositions were determined by an inverse mapping approach. A surrogate model of the inverse system was constructed to map the measured system response to the system parameters directly 23 . Partial least squares regression (PLSR) was used to construct the inverse map 15 , 24 .…”

External Tyre Loading Predictions from Inner Tyre Deformation Measurements

“…Experiment can be tightly controlled and therefore there is no uncertainty in whether or not the inverse method finds the true answer (Wilke et al, 2010;Asaadi et al, 2017;Ben Turkia et al, 2019). One first generates a virtual experiment for a given loading condition which returns stresses, strains, deformations, and forces.…”

Constituent Parameter Identification of Braided Composite Based on Sensitivity Analysis

“…Rahmani et al identified the constituent mechanical properties with an improved regularized model updating (RMU), which reduces the influence of measured noise simultaneously [22]. Other methods such as the Kalman filter, regularized virtual fields Levenberg-Marquardt, and direct inverse maps [42] were proposed to identify parameters of composite material. Images were also used to predict the mechanical properties of materials [43].…”