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

• Published in: International journal for numerical and analytical methods in geomechanics Vol. 33; no. 12; pp. 1485 - 1511
• Main Authors: Levasseur, S., Malecot, Y., Boulon, M., Flavigny, E.
• Format: Journal Article Web Resource
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 25.08.2009; Wiley; John Wiley & Sons
• Subjects: Applied sciences; Approximation; Buildings. Public works; Civil engineering; Computation methods. Tables. Charts; Ellipsoids; Engineering Sciences; Engineering, computing & technology; Exact sciences and technology; finite element method; genetic algorithm; Genetic algorithms; Geotechnics; Ingénierie civile; Ingénierie, informatique & technologie; Inverse; inverse analysis; Mathematical analysis; Mathematical models; Mechanics; Optimization; Principal component analysis; Soil investigations. Testing; soil parameters identification; soil parameters identification; Structural analysis. Stresses; synthetic data; finite element method; Parameter estimation; Statistical analysis; Property of soil; Identification; Optimization; Inverse problem; Finite element method; Excavating; Genetic algorithm; synthetic data; inverse analysis; Application; Principal component analysis; Geotechnics; soil parameters identification; Nonuniqueness; Pressuremeter tests; constitutive equation; Geotechnical measurement; Genetic-algorithm optimizations; experimental study; Identification (control systems); Soil constitutive model; Optimal values; Genetic algorithms; genetic algorithm; identification method; finite element method; optimization; Geologic models; Solution set; Population sizes; Soil parameters; uncertainty analysis; Experimental application; parameterization; Population statistics; Soils; Inverse problems; reliability analysis; soil analysis; pressuremeter; First-order approximations; principal component analysis; Synthetic data
• ISSN: 0363-9061; 1096-9853; 1096-9853
• DOI: 10.1002/nag.776

This 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. Copyright © 2009 John Wiley & Sons, Ltd.