B. Pichler:
"Parameter Identification for Material Models by Means of Structural Back-Analyses";
Talk: 12th Inter-Institute Seminar on Nonlinear Computational Mechanics, Budapest, Hungary; 2000-10-27 - 2000-10-29.
Material models for the FEM contain material parameters. Unfortunately, some of these parameters cannot be determined a priori with sufficient accuracy. Therefore, they need to be determined by means of curve fitting, i.e., numerically obtained curves are compared with respective curves obtained from measurements. This type of parameter-determination is commonly referred to as back analysis. Solutions of the respective inverse problems can be based on both, gradient-based and gradient-free optimization methods. In order to establish a parameter identification procedure which does not depend on the material model and the integration scheme, a gradient-free optimization method has been developed. The applicability of the method is demonstrated by optimizing parameters of a material model for soil by Spira for sheartests described by Sterpi (see Spira's contribution to the seminar).A backpropagation artificial neural-network (BPANN) with one hidden layer is used to map inputparameters of the FE-simulations onto values of shear stress, resulting from the obtained stress-displacement diagrams. In order to keep the number of FE-simulations for the parameter identification as small as possible, the data sets consisting of both, parameters and numerically obtained values of shear stress, are not split into training patterns and testing patterns. Since the BPANN is used to perform a nonlinear regression, all available data sets are used to train the network. The number of neurons in the hidden layer is chosen such that the output values of the BPANN agree with the values of the shear stress after distinctive training with an accuracy equal to or higher than a specified tolerance. As the number of neurons in the hidden layer is comparatively small, the trained network provides reliable interpolations between the data sets.
After training of the BPANN, a genetic algorithm (GA) is used for determination of a near-optimal set of parameters. The GA generates combinations of parameters. These values are passing through the BPANN according to the feedforward procedure. The percental differences between the output values of the BPANN, i.e., the interpolated values of the shear stress, and the measurements are squared and summed up, yielding a value of the error. Its reciprocal value represents the fitness of the respective set of parameters. The GA searches for a parameter-combination such that the respective output values of the BPANN agree with the measurements as well as possible. The best combination of parameters in the sense of the aforementioned definition of the error is determined by a gradient-descent method starting from the near-optimal set of parameters, which follows out of the GA. Hereby, an extended version of the backpropagation algorithm is used.
It is shown that the rate of convergence of the proposed parameter identification is satisfactory. It is intended to apply the method for identification of soil parameters in the context of tunnelling according to the New Austrian Tunnelling Method.
Keywords: parameter identification, inverse problem, neural network, genetic algorithm, soft computing