Anna Kučerová

Improvements of real coded genetic algorithms based on differential operators preventing premature convergence

This paper presents several types of evolutionary algorithms used for global optimization on real domains. The interest has been focused on multimodal problems, where the difficulties of a premature convergence usually occur. First the standard genetic algorithm using binary encoding of real values and its unsatisfactory behavior with multimodal problems is briefly reviewed together with some improvements of fighting premature convergence. Two types of real encoded methods based on differential operators are examined in detail: the differential evolution (DE), a very modern and effective method first published by Storn and Price [NAPHIS, 1996], and the simplified real-coded differential genetic algorithm SADE proposed by the authors [Contributions to mechanics of materials and structures, 2000]. In addition, an improvement of the SADE method, called CERAF technology, enabling the population of solutions to escape from local extremes, is examined. All methods are tested on an identical set of objective functions and a systematic comparison based on a reliable methodology [Adv. Engng Software 32 (2000) 49] is presented. It is confirmed that real coded methods generally exhibit better behavior on real domains than the binary algorithms, even when extended by several improvements. Furthermore, the positive influence of the differential operators due to their possibility of self-adaptation is demonstrated. From the reliability point of view, it seems that the real encoded differential algorithm, improved by the technology described in this paper, is a universal and reliable method capable of solving all proposed test problems.

A competitive comparison of different types of evolutionary algorithms

Abstract This paper presents comparison of several stochastic optimization algorithms developed by authors in their previous works for the solution of some problems arising in civil engineering. The introduced optimization methods are: the integer augmented simulated annealing (IASA), the real-coded augmented simulated annealing (RASA) [Comp. Meth. Appl. Mech. Eng. 190 (13–14) (2000) 1629], the differential evolution (DE) in its original fashion developed by Storn and Price [R. Storn, On the usage of differential evolution for function optimization, NAPHIS, 1996] and simplified real-coded differential genetic algorithm (simplified atavistic differential evolution, SADE) [O. Hrstka, A. Kucerova, Search for optimization methods on multi-dimensional real domains, Contributions to Mechanics of Materials and Structures, CTU Reports 4, 2000, pp. 87–104]. Each of these methods was developed for some specific optimization problem; namely the Chebychev trial polynomial problem, the so called type 0 function and two engineering problems––the reinforced concrete beam layout and the periodic unit cell problem, respectively. Detailed and extensive numerical tests were performed to examine the stability and efficiency of proposed algorithms. The results of our experiments suggest that the performance and robustness of RASA, IASA and SADE methods are comparable, while the DE algorithm performs slightly worse. This fact together with a small number of internal parameters promotes the SADE method as the most robust for practical use.

Novel anisotropic continuum‐discrete damage model capable of representing localized failure of massive structures: Part II: identification from tests under heterogeneous stress field

Purpose – The purpose of this paper is to discuss the identification of the model parameters for constitutive model capable of representing the failure of massive structures, from two kinds of experiments: a uniaxial tensile test and a three‐point bending test. Design/methodology/approach – A detailed development of the ingredients for constitutive model for failure of massive structures are presented in Part I of this paper. The salient feature of the model is in its ability to correctly represent two different failure mechanisms for massive structures, the diffuse damage in so‐called fracture process zone with microcracks and localized damage in a macrocrack. The identification of such model parameters is best performed from the tests under heterogeneous stress field. Two kinds of tests are used: the simple tension test and the three‐point bending test. The former allows us illustrate the non‐homogeneity of the strain field at failure even under homogeneous stress, whereas the latter provides a very good illustration for the proposed inverse optimization problem for which the specimen is subjected to a heterogeneous stress field. Findings – Several numerical examples are presented in order to illustrate a very satisfying performance of the proposed methodology for identifying the corresponding material parameters of the constitutive model for failure of massive structures. Originality/value – The paper confirms that one can make a very good use of the proposed identification procedure for estimating the corresponding parameters of damage model for localized failure of massive structure, and the advantages to using the experimental results obtained by testing under heterogeneous stress field.

Parameter identification in a probabilistic setting

Abstract The parameters to be identified are described as random variables, the randomness reflecting the uncertainty about the true values, allowing the incorporation of new information through Bayes’s theorem. Such a description has two constituents, the measurable function or random variable, and the probability measure. One group of methods updates the measure, the other group changes the function. We connect both with methods of spectral representation of stochastic problems, and introduce a computational procedure without any sampling which works completely deterministically, and is fast and reliable. Some examples we show have highly nonlinear and non-smooth behaviour and use non-Gaussian measures.

Competitive comparison of optimal designs of experiments for sampling-based sensitivity analysis

A widely used strategy to explore the sensitivity of the model to its inputs is based on a finite set of simulations. These are usually performed for a chosen set of points in a parameter space. An estimate of the sensitivity can be then obtained by computing correlations between the model inputs and outputs. The accuracy of the sensitivity prediction depends on a quality of the points distribution in the parameter space, so-called the design of experiments. The aim of the presented paper is to review and compare available criteria determining an optimal design of experiments for sampling-based sensitivity analysis.

Compressing random microstructures via stochastic Wang tilings.

This Rapid Communication presents a stochastic Wang tiling-based technique to compress or reconstruct disordered microstructures on the basis of given spatial statistics. Unlike the existing approaches based on a single unit cell, it utilizes a finite set of tiles assembled by a stochastic tiling algorithm, thereby allowing to accurately reproduce long-range orientation orders in a computationally efficient manner. Although the basic features of the method are demonstrated for a two-dimensional particulate suspension, the present framework is fully extensible to generic multidimensional media.

Soft computing-based calibration of microplane M4 model parameters: Methodology and validation

Abstract Constitutive models for concrete based on the microplane concept have repeatedly proven their ability to well-reproduce non-linear response of concrete on material as well as structural scales. The major obstacle to a routine application of this class of models is, however, the calibration of microplane-related constants from macroscopic data. The goal of this paper is twofold: (i) to introduce the basic ingredients of a robust inverse procedure for the determination of dominant parameters of the M4 model proposed by Bažant et al. (2000) based on cascade artificial neural networks trained by evolutionary algorithm and (ii) to validate the proposed methodology against a representative set of experimental data. The obtained results demonstrate that the soft computing-based method is capable of delivering the searched response with an accuracy comparable to the values obtained by expert users.

Microstructural enrichment functions based on stochastic Wang tilings

This paper presents an approach to constructing microstructural enrichment functions to local fields in non-periodic heterogeneous materials with applications in the partition of unity and hybrid finite element schemes. It is based on a concept of aperiodic tilings by the Wang tiles, designed to produce microstructures morphologically similar to original media and enrichment functions that satisfy the underlying governing equations. An appealing feature of this approach is that the enrichment functions are defined only on a small set of square tiles and extended to larger domains by an inexpensive stochastic tiling algorithm in a non-periodic manner. The feasibility of the proposed methodology is demonstrated on constructions of stress enrichment functions for two-dimensional mono-disperse particulate media.

Artificial neural networks in the calibration of nonlinear mechanical models

Last decades witness rapid development in numerical modelling of structures as well as materials and the complexity of models increases quickly together with their computational demands. Despite the growing performance of modern computers and clusters, calibration of such models from noisy experimental data remains a nontrivial and often computational exhaustive task. The layered neural networks thus represent a robust and effi cient technique to overcome the timeconsuming simulations of a calibrated model. The potential of neural networks consists in simple implementation and high versatility in approximating nonlinear relationships. Therefore, there were several approaches proposed to accelerate the calibration of nonlinear models by neural networks. This contribution reviews and compares three possible strategies based on approximating (i) model response, (ii) inverse relationship between the model response and its parameters and (iii) error function quantifying how well the model fits the d ata. The advantages and drawbacks of particular strategies are demonstrated on calibration o f four parameters of affi nity hydration model from simulated data as well as from experimental measurements. This model is highly nonlinear, but computationally cheap thus allowing its calibration without any approximation and better quantification of results obtained by the examine d calibration strategies.Paper reviews applications of artificial neural networks in model calibration.Neural network-based calibration strategies are classified into three groups.Identification strategies are compared on calibration of affinity hydration model.The most precise strategy uses an ANN-based surrogate of each response component.Principal component-based inverse mapping is the best for a repeated use on new data. Rapid development in numerical modelling of materials and the complexity of new models increase quickly together with their computational demands. Despite the growing performance of modern computers and clusters, calibration of such models from noisy experimental data remains a nontrivial and often computationally intensive task. Layered neural networks provide a robust and efficient technique for overcoming the time-consuming simulations of calibrated models. The potential advantages of neural networks include simple implementation and high versatility in approximating nonlinear relationships. Therefore, there were several approaches proposed in literature for accelerating the calibration of nonlinear models by neural networks. This contribution reviews and compares three possible strategies based on approximating (i) the model response, (ii) the inverse relationship between the model response and its parameters and (iii) an error function quantifying how well the model fits the data. The advantages and drawbacks of particular strategies are demonstrated with the calibration of four parameters of an affinity hydration model from simulated data as well as from experimental measurements. The affinity hydration model is highly nonlinear but computationally cheap, thus allowing its calibration without any approximation and better quantification of results obtained by the examined calibration strategies. This paper can be viewed as a guide for engineers to help them develop an appropriate strategy for their particular calibration problems.

Uncertainty updating in the description of coupled heat and moisture transport in heterogeneous materials

To assess the durability of structures, heat and moisture transport need to be analyzed. To provide a reliable estimation of heat and moisture distribution in a certain structure, one needs to include all available information about the loading conditions and material parameters. Moreover, the information should be accompanied by a corresponding evaluation of its credibility. Here, the Bayesian inference is applied to combine different sources of information, so as to provide a more accurate estimation of heat and moisture fields [1]. The procedure is demonstrated on the probabilistic description of heterogeneous material where the uncertainties consist of a particular value of individual material characteristic and spatial fluctuations. As for the heat and moisture transfer, it is modelled in coupled setting [2].