Piotr Orantek

Optimization and defect identification using distributed evolutionary algorithms

Abstract The aim of the paper is to present the application of the distributed evolutionary algorithms to selected optimization and defect identification problems. The coupling of evolutionary algorithms with the finite element method and the boundary element method creates a computational intelligence technique that is very suitable in computer aided optimal design. Several numerical examples for shape, topology optimization and identification are presented for elastic, thermoelastic and elastoplastic structures.

Evolutionary methods in inverse problems of engineering mechanics

Publisher Summary This paper deals with applications of evolutionary algorithms to inverse problems of engineering mechanics. Evolutionary algorithms are considered as modified and generalized classical genetic algorithms in which populations of chromosomes are coded by floating point representation, and the new modified crossover and mutation operations are introduced. The evolutionary algorithm starts with a population of randomly generated chromosomes from a feasible solution domain. These chromosomes, which have the vector structure, evolve toward better solutions by applying genetic operators such as selection, mutation, and crossover. After applying genetic operators, the new population has a better fitness. The probability of crossover and mutation does not have to be constant as in classical genetic algorithms and it can change during the evolutionary process. An objective function (fitness function) with constraints plays the role of the environment to distinguish between good and bad chromosomes and to select the better solution.

Hybrid Evolutionary Algorithms in Optimization of Structures under Dynamical Loads

This paper is devoted to the application of hybrid evolutionary algorithm (HEA) in optimization of structures under dynamical loads. The HEA algorithms is a coupling of evolutionary and gradient algorithms, additionally the artificial neural network is used to control the selected parameters of this algorithm. The NURBS curves were used to model the shape of the structure. Three special types of chromosomes were tested to control the number of internal voids in the case topology optimization. The boundary element method [2] was need to compute the fitness function. The fitness function was expressed as the function depending on the displacements, stresses, mass, eigenfrequencies and compliance. Several tests were made [7], more interesting ones are presented in this paper.

The Optimization and Identification Problems of Structures with Fuzzy Parameters

This paper is devoted to optimization and identification problems of structures with fuzzy parameters. The elasticity problem is considered in the paper. The fuzzy shape of the body, boundary conditions and material parameters are assumed.

Evolutionary Computation in Inverse Problems

Evolutionary computations in identification of multiple material defects (voids and cracks) in mechanical systems and identification of shape and position of a tumor region in the biological tissue domain are presented. The identification belongs to inverse problems and is treated here as an output (measurement) error minimization, which is solved using numerical optimization methods. The output error is defined in the form of a functional of boundary displacements or temperature fields. An evolutionary algorithm is employed to minimize of the functional. Numerical tests of internal defects identification and some anomalies in the tissue are presented.

Uncertain Identification Problems in the Context of Granular Computing

The chapter is devoted to applications of selected methods of computational intelligence: evolutionary algorithms and artificial neural networks, in identification of physical systems being under the uncertain conditions. Uncertainties can occur in boundary conditions, in material coefficients or some geometrical parameters of systems and are modeled by three kinds of granularity: interval mathematics, fuzzy sets and theory of probability. In order to evaluate fitness functions the interval, fuzzy and stochastic finite element methods are applied to solve granular boundary-value problems for considered physical systems. Several numerical tests and examples of identification of uncertain parameters are presented.

The Topology Optimization Using Evolutionary Algorithms

The coupling of modern, alternative optimization methods such as evolutionary algorithms with the effective tool for analysis of mechanical structures - BEM, gives a new optimization method, which allows to perform the generalized shape optimization (a simultaneous shape and topology optimization) for elastic mechanical structures. This new evolutionary method is free from typical limitations connected with classical optimization methods. In the paper results of researches on the application of evolutionary methods in the domain of mechanics are presented. Numerical examples for some topology optimization problems are presented, too.

Granular Computing in Evolutionary Identification

The paper deals with the application of the Two–Stage Granular Strategy (TSGS) to the identification problems. Identification of selected parameters of the structures is performed. The identification problem is formulated as the minimization of some objective functionals which depend on measured and computed fields. It is assumed that identified constants and measurements have non–deterministic character. Three forms of the information granularity are considered: interval numbers, fuzzy numbers and random variables. The strategy combines the following techniques: Evolutionary Algorithms (EAs), Artificial Neural Networks (ANNs), local optimization methods (LOMs) and Finite Element Method (FEM). All techniques are appropriately modified to deal with non–deterministic data. The EA is used in the first stage to perform the global optimization. The LOM supported by ANN is used in the second stage. The FEM computations are performed to solve the boundary–value problem. Numerical examples presenting the efficiency of the TSGS in different applications are attached.

Evolutionary BEM Computation in Shape Optimization Problems

The aim of the paper is to develop of the coupling of the boundary element method (BEM) and evolutionary algorithms (EA) to shape optimization problems in applied sciences and engineering. New approaches of the evolutionary BEM computation in optimization are proposed to: (i) shape optimization of structures under statical and dynamical loading, (ii) shape optimization of structures under thermomechanical loading, (iii) shape optimization of cracked structures for criteria expressed by stress intensity factors, and (iv) shape optimization of elasto-plastic structures. Several numerical examples for optimization of 2-D structures are presented.

Identification of Dynamical Systems in the Fuzzy Conditions

The paper deals with the identification of the fuzzy parameters of material and shape of structures. In many identification and optimization problems for the structures being under dynamical loads one should find some unknown parameters, e.g. materials properties, boundary conditions or geometrical parameters. An identification problem can be formulated as the minimization of some objective functions depending on measured and computed state fields, as displacements, strains, eigenfrequencies or temperature. In order to obtain the unique solution of the identification problem the global minimum of the objective function should be found. In many engineering dynamical cases it is not possible to determine the parameters of the system precisely, so it is necessary to introduce some uncertain parameters which describe the granular character of data. There exist different models of information granularity: interval numbers, fuzzy numbers, rough sets, random variables, etc. In the present paper the granularity of information is represented in the form of the fuzzy numbers. In order to solve an identification problem, some optimization methods have to be used. In the proposed approach the fuzzy version of the evolutionary algorithm (FEA) is used as the first step of the identification procedure. The fuzzy steepest descent method with multilevel artificial neural network (ANN) is used in the second step. The special type of fuzzy ANN for the approximation of the fuzzy fitness function value and the special type of fuzzy fitness function gradient are used. The usage of the ANN enables the reduction of the computation time. The fuzzy finite element method (FFEM) is employed to solve the boundary-value problem.