Witold Beluch

The identification of cracks using boundary elements and evolutionary algorithms

This paper is devoted to the identification problems for structures which contain cracks. The problem of crack identification is formulated as the minimization of the difference between the measured and computed values of displacements or stresses at selected boundary nodes. The coupling of the dual boundary element method and evolutionary algorithms is proposed to solve the problem. The identification of single cracks of different shapes is presented. The multiple crack identification is also considered. The problem of the identification of unknown number of cracks is formulated by introducing a special kind of chromosome. The influence of random errors in experimentally measured displacements on a convergence of the evolutionary identification is examined. A hybrid evolutionary approach based on sensitivity information of the fitness function is tested. Several numerical examples are presented.

Evolutionary Identification and Optimization of Composite Structures

Composite materials, especially composite laminates, play a significant role in the modern industry. Laminate is a material built by joining two materials and it usually consists of two phases: the matrix and the reinforcement. The laminate is typically build of many plies (laminas) having different ply angles. Laminates are popular due to two main reasons: i) the high weight-strength ratio (in comparison with the conventional materials); ii) the possibility to tailor the material properties to the designer requirements by manipulating several parameters like: components material, stacking sequence, fibres orientation or layer thickness [1]. If laminas are composed of the different materials the laminate is called a hybrid one.

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.

Optimization of Composite Structures Using Bio-inspired Methods

The paper deals with an application of the artificial immune system (AIS) and the particle swarm optimizer (PSO) to the optimization problems. The AIS and PSO are applied to optimize of stacking sequence of plies in composites. The optimization task is formulated as maximization of minimal difference between the first five eigenfrequencies and the external excitation frequency. Recently, immune and swarm methods have found various applications in mechanics, and also in structural optimization. The AIS is a computational adaptive system inspired by the principles, processes and mechanisms of biological immune systems. The algorithms typically use the characteristics of the immune systems like learning and memory to simulate and solve a problem in a computational manner. The swarm algorithms are based on the models of the animals social behaviours: moving and living in the groups. The main advantage of the AIS and PSO, contrary to gradient methods of optimization, is the fact that they do not need any information about the gradient of fitness function. The numerical examples demonstrate that the new method based on immune and particle computation is an effective technique for solving computer aided optimal design.

Parallel artificial immune system in optimization and identification of composite structures

The paper deals with the application of the Artificial Immune System to the optimization and identification of composites. To reduce the computational time parallel computations are performed. Composite structures in form of multilayered laminates are taken into account. Simple and hybrid (with laminas made of different materials) laminates are examined. Different optimization criteria connected with stiffness and modal properties of laminate structures are considered. Continuous and discrete variants of design variables are regarded. The aim of the identification is to find laminate elastic constants on the basis of measurements of state variable values. The Finite Element Method is employed to solve the boundary-value problem for laminates. Numerical examples presenting effectiveness of proposed method are attached.

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.

Numerical homogenization of inhomogeneous media with imprecise parameters

This paper is devoted to the numerical homogenization of porous materials with parameters uncertainty, represented by information granularity. The aim of the analysis is to obtain range of homogenized material properties reducing number of necessary homogenization calculation comparing with classic attitude. The uncertainties are represented by means of interval numbers. The directed interval arithmetic is employed to narrow the results range. Interval finite element method is employed to solve a boundary-value problem in micro scale. Numerical examples presenting the efficiency of proposed attitude are attached.

Multiscale Evolutionary Optimization of Functionally Graded Porous Materials

This paper deals with the optimization of the microstructure of selected porous functionally graded materials (FGMs). Porous materials are inhomogeneous structural materials whose properties at macroscale strongly depend on their microstructure. The designing of porous materials as FGMs allows obtaining structures well-tailored to their operation conditions, which require the use of optimization methods. As it is assumed that multiple contradictory optimization criteria are defined, the multiobjective optimization is performed. Multiobjective Genetic Algorithm (MOGA) included in ANSYS Workbench software is employed in the work as the optimization tool. The application of the global optimization algorithms allows avoiding problems with multimodal objective functions and the calculation of the objective function gradient algorithm. Microstructural material parameters are optimization design variables. Numerical homogenization with the use of representative volume element (RVE) is applied to obtain equivalent homogeneous properties of inhomogeneous structures. The finite element method software ANSYS Workbench is used to solve the boundary-value problem in both scales. The use of FEM software and optimization algorithm included in a single software package significantly reduces the time needed to exchange data between independent systems. The numerical example presenting the optimization results in the form of Pareto frontiers of non-dominated solutions shows an efficiency of the proposed attitude.

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.