Parameter identification problems are formulated in a probabilistic language, where the randomness reflects the uncertainty about the knowledge of the true values. This setting allows conceptually easily to incorporate new information, e.g. through a measurement, by connecting it to Bayes's theorem. The unknown quantity is modelled as a (may be high-dimensional) random variable. Such a description has two constituents, the measurable function and the measure. One group of methods is identified as updating the measure, the other group changes the measurable function. We connect both groups with the relatively recent methods of functional approximation of stochastic problems, and introduce especially in combination with the second group of methods a new procedure which does not need any sampling, hence works completely deterministically. It also seems to be the fastest and more reliable when compared with other methods. We show by example that it also works for highly nonlinear non-smooth problems with non-Gaussian measures.

This paper presents several types of evolutionary algorithms (EAs) used for global optimization on real domains. The interest has been focused on multimodal problems, where the difficulties of a premature convergence usually occurs. First the standard genetic algorithm (SGA) 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 firstly published by R. Storn and K. Price [17], and the simplified real-coded differential genetic algorithm SADE proposed by the authors [11]. 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 [1] 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.

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.

In this work we deal with the optimal design and optimal control of structures undergoing large rotations. In other words, we show how to find the corresponding initial configuration and the corresponding set of multiple load parameters in order to recover a desired deformed configuration or some desirable features of the deformed configuration as specified more precisely by the objective or cost function. The model problem chosen to illustrate the proposed optimal design and optimal control methodologies is the one of geometrically exact beam. First, we present a non-standard formulation of the optimal design and optimal control problems, relying on the method of Lagrange multipliers in order to make the mechanics state variables independent from either design or control variables and thus provide the most general basis for developing the best possible solution procedure. Two different solution procedures are then explored, one based on the diffuse approximation of response function and gradient method and the other one based on genetic algorithm. A number of numerical examples are given in order to illustrate both the advantages and potential drawbacks of each of the presented procedures.

with spatially varying coefficients defined by random fields.

Abstract. This paper presents an approach to constructing microstructural enrichment functions to local fields in non-periodic heterogeneous materials with applications in 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. Feasibility of the proposed methodology is demonstrated on constructions of stress enrichment functions for two-dimensional mono-disperse particulate media.

Nowadays, the numerical models of real-world structures are more precise, more complex and, of course, more time-consuming. Despite the growth of a computational performance, the exploration of model behaviour remains a complex task. The sensitivity analysis is a basic tool for investigating the sensitivity of the model to its inputs. One widely used strategy to assess the sensitivity is based on a finite set of simulations for a given sets of input parameters, i.e. points in the design space. An estimate of the sensitivity can be then obtained by computing correlations between the input parameters and the chosen response of the model. The accuracy of the sensitivity prediction depends on the choice of design points called the design of experiments. The aim of the presented paper is to review and compare available criteria for the assessment of design of experiments suitable for sampling-based sensitivity analysis.

Microstructure reconstruction and compression techniques are designed to find a microstructure with desired properties. While the microstructure reconstruction searches for a microstructure with prescribed statistical properties, the microstructure compression focuses on efficient representation of material morphology for a purpose of multiscale modelling. Successful application of those techniques, nevertheless, requires proper understanding of underlying statistical descriptors quantifying material morphology. In this paper we focus on the lineal path function designed to capture namely shortrange effects and phase connectedness, which can be hardly handled by the commonly used two-point probability function. The usage of the lineal path function is, however, significantly limited by huge computational requirements. So as to examine the properties of the lineal path function within the computationally exhaustive compression and reconstruction processes, we start with the acceleration of the lineal path evaluation, namely by porting part of its code to the graphics processing unit using the CUDA (Compute Unified Device Architecture) programming environment. This allows us to present a unique comparison of the entire lineal path function with the commonly used rough approximation based on the Monte Carlo and/or sampling template. Moreover, the accelerated version of the lineal path function is then compared with the two-point probability function within the compression and reconstruction of two-phase morphologies. Their significant features are thoroughly discussed and illustrated on a set of artificial periodic as well