Statistical inverse analysis based on genetic algorithm and principal component analysis: Method and developments using synthetic data

Abstract

SUMMARYThis study concerns the identification of parameters of soil constitutive models from geotechnical measurements by inverse analysis. To deal with the non-uniqueness of the solution, the inverse analysis is based on a genetic algorithm (GA) optimization process. For a given uncertainty on the measurements, the GA identifies a set of solutions. A statistical method based on a principal component analysis (PCA) is, then, proposed to evaluate the representativeness of this set. It is shown that this representativeness is controlled by the GA population size for which an optimal value can be defined. The PCA also gives a first-order approximation of the solution set of the inverse problem as an ellipsoid. These developments are first made on a synthetic excavation problem and on a pressuremeter test. Some experimental applications are, then, studied in a companion paper, to show the reliability of the method.

Statistical inverse analysis based on genetic algorithm and principal component analysis: Applications to excavation problems and pressuremeter tests

“…However, due to both the uncertainty on the measurements, U e , and the simplification of the associated model, a discrepancy, U n , between the measurements and the model is inevitable. Then, rather than an exact unique solution, it was showed in this companion paper [1] that an inverse problem has a lot of approximated solutions.…”

“…In the companion paper [1], it was shown that the identification ratio is controlled by the GA population size for which an optimal value can be defined. For this optimal population size, the GA identifies, at a minimum calculation cost, a set of parameter vectors that is, statistically, representative of all the solutions of the inverse problem.…”

“…In a companion paper [1], an identification method was presented and tested to identify soil parameters from a synthetic pressuremeter test and from a synthetic excavation problem. To deal with different kinds of measurements, the inverse problem was solved, using a minimization procedure.…”

“…Moreover, it overcomes the non-uniqueness of the inverse problem solution and provides several parameter vectors as a solution. To characterize the set of solutions provided by the GA, the process was extended, in the companion paper [1], with a statistical method based on a principal component analysis (PCA). The PCA is a factorial analysis method that permits to define the main directions and the scattering of a set of points [6].…”

A survey of geotechnical system identification techniques

“…16) of 2-D quay wall-soil systems [110]. The concept of employing experimental data sets and local in-situ measurements to calibrate complex constitutive laws with large number of parameters have been systematically investigated by Yang and Elgamal [100], Levasseur et al [56,57], Hashash et al [46,35], and Calvello and Finno: [15].…”