Miroslav Vořechovský

FReET: Software for the statistical and reliability analysis of engineering problems and FReET-D: Degradation module

Abstract The objective of the paper is to present methods and software for the efficient statistical, sensitivity and reliability assessment of engineering problems. Attention is given to small-sample techniques which have been developed for the analysis of computationally intensive problems. The paper shows the possibility of “randomizing” computationally intensive problems in the manner of the Monte Carlo type of simulation. In order to keep the number of required simulations at an acceptable level, Latin Hypercube Sampling is utilized. The technique is used for both random variables and random fields. Sensitivity analysis is based on non-parametric rank-order correlation coefficients. Statistical correlation is imposed by the stochastic optimization technique – simulated annealing. A hierarchical sampling approach has been developed for the extension of the sample size in Latin Hypercube Sampling, enabling the addition of simulations to a current sample set while maintaining the desired correlation structure. The paper continues with a brief description of the user-friendly implementation of the theory within FReET commercial multipurpose reliability software. FReET-D software is capable of performing degradation modeling, in which a large number of reinforced concrete degradation models can be utilized under the main FReET software engine. Some of the interesting applications of the software are referenced in the paper.

Hierarchical Refinement of Latin Hypercube Samples

In this article, a novel method for the extension of sample size in Latin Hypercube Sampling LHS is suggested. The method can be applied when an initial LH design is employed for the analysis of functions g of a random vector. The article explains how the statistical, sensitivity and reliability analyses of g can be divided into a hierarchical sequence of simulations with subsets of samples of a random vector in such a way that i the favorable properties of LHS are retained the low number of simulations needed for statistically significant estimations of statistical parameters of function g with low estimation variability; ii the simulation process can be halted, for example, when the estimations reach a certain prescribed statistical significance. An important aspect of the method is that it efficiently simulates subsets of samples of random vectors while focusing on their correlation structure or any other objective function such as some measure of dependence, spatial distribution uniformity, discrepancy, etc. This is achieved by employing a robust algorithm based on combinatorial optimization of the mutual ordering of samples. The method is primarily intended to serve as a tool for computationally intensive evaluations of g where there is a need for pilot numerical studies, preliminary and subsequently refined estimations of statistical parameters, optimization of the progressive learning of neural networks, or during experimental design.

Effect of Twist, Fineness, Loading Rate and Length on Tensile Behavior of Multifilament Yarns (A Multivariate Study)

The purpose of the present study was a multivariate experimental analysis of continuous multifilament glass yarns. The experimental design involved four main factors affecting the yarn tensile behavior, namely twist, fineness, loading rate and specimen length. In the evaluation, both the main effects and their interactions were considered. In the initial test design, each factor had been covered by at least two levels. The performed analysis of variance on the constructed response surface allowed us to exclude some factors and interactions and to narrow the test design space in the second step. The interaction effect of twist and fineness could be well documented. In particular, the nonlinear effect of twist with a pronounced maximum allowed us to discuss the role of local interactions due to pressure sensitive frictional bond that gets amplified at a particular level of twist.

Modification of the Audze-Eglājs criterion to achieve a uniform distribution of sampling points

Audze-Eglźjs criterion for DoE provides nonuniformly distributed experimental points.Simple improvement of AE criterion that ensures uniform distribution is presented.The improvement lies in considering periodicity of the design space.Extensive calculations verifying biased and improved uniform sampling are included. Display Omitted The Audze-Eglźjs (AE) criterion was developed to achieve aźuniform distribution of experimental points in aźhypercube. However, the paper shows that the AE criterion provides strongly nonuniform designs due to the effect of the boundaries of the hypercube. We propose aźsimple remedy that lies in the assumption of periodic boundary conditions. The biased behavior of the original AE criterion and excellent performance of the modified criterion are demonstrated using simple numerical examples focused on (i) the uniformity of sampling density over the design space and, (ii) statistical sampling efficiency measured through the ability to correctly estimate the statistical parameters of functions of random variables. An engineering example of reliability calculation is presented, too.

Using Python for scientific computing: Efficient and flexible evaluation of the statistical characteristics of functions with multivariate random inputs ✩

Abstract This paper examines the feasibility of high-level Python based utilities for numerically intensive applications via an example of a multidimensional integration for the evaluation of the statistical characteristics of a random variable. We discuss the approaches to the implementation of mathematically formulated incremental expressions using high-level scripting code and low-level compiled code. Due to the dynamic typing of the Python language, components of the algorithm can be easily coded in a generic way as algorithmic templates. Using the Enthought Development Suite they can be effectively assembled into a flexible computational framework that can be configured to execute the code for arbitrary combinations of integration schemes and versions of instantiated code. The paper describes the development cycle using a simple running example involving averaging of a random two-parametric function that includes discontinuity. This example is also used to compare the performance of the available algorithmic and executional features. The implemented package including further examples and the results of performance studies have been made available via the free repository [1] and CPCP library. Program summary Program title: spirrid Catalogue identifier: AENL_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AENL_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Special licence provided by the author No. of lines in distributed program, including test data, etc.: 10722 No. of bytes in distributed program, including test data, etc.: 157099 Distribution format: tar.gz Programming language: Python and C. Computer: PC. Operating system: LINUX, UNIX, Windows. Classification: 4.13, 6.2. External routines: NumPy ( http://numpy.scipy.org/ ), SciPy ( http://www.scipy.com ) Nature of problem: Evaluation of the statistical moments of a function of random variables. Solution method: Direct multidimensional integration. Running time: Depending on the number of random variables the time needed for the numerical estimation of the mean value of a function with a sufficiently low level of numerical error varies. For orientation, the time needed for two included examples: examples/fiber_tt_2p/fiber_tt_2p.py with 2 random variables: few milliseconds examples/fiber_po_8p/fiber_po_8p.py with 8 random variables: few seconds

Efficient random fields simulation for stochastic FEM analyses

Publisher Summary This chapter presents a paper that discusses efficient random fields simulation for stochastic finite element method analyzes. Simulation of random fields is the fundamental task in stochastic finite element method (SFEM). There are many techniques available nowadays, but for computationally intensive problems, one is constrained by small number of Monte Carlo type simulations. This paper proposes a method that combines spectral decomposition of covariance matrix and improved Latin hypercube sampling (LHS). It uses a method for diminishing spurious correlation based on stochastic optimization method. This leads to decrease of the scatter of autocorrelation function of simulated random fields. An advantage is that there is no strict restriction concerning small number of random field simulations. This paper assesses the quality of simulated random fields. The best performance, the convergence to target values of statistics with low variability is achieved in case of LHS.

Adaptive probabilistic modeling of localization, failure and size effect of quasi-brittle materials

Objective simulation of response of nonlinear structures must reflect the spatial variability of local material properties. The main target of the paper is to present ideas behind a computational tool oriented toward adaptive nonlinear simulation driven by spatially (and randomly) varying model properties which is currently under development by authors. In particular, we focus on detailed tracing of the evolution of damage or other nonlinear phenomena during loading of structure with varying properties by nonlinear finite element method with mesh refinement/coarsening in highly/low stressed or damaged regions. We have developed the major ingredients of the algorithm and we present the current stage of progress on the computational platform in this paper. The computations is illustrated on a simple one-dimensional example involving a bar made of plastic material with hardening under uniaxial tension.

Improved formulation of Audze-Eglājs criterion for space-filling designs

The Audze–Eglājs (AE) criterion was developed to achieve uniform distribution of experimental points in a hypercube. However, the paper shows that the AE criterion provides strongly nonuniform designs due to the effect of boundaries of the hypercube. We propose a simple remedy that lies in the assumption of periodic boundary conditions. The biased behavior of the original AE criterion and excellent performance of the modified criterion is demonstrated using simple numerical examples focused on (i) uniformity of the samples density over the design space and, (ii) statistical sampling efficiency measured through the ability to correctly estimate statistics of functions of random variables.

Identification of the effective bundle length in a multifilament yarn from the size effect response

The article proposes a method for characterizing the in situ interaction between filaments in a multifilament yarn. The stress transfer between neighboring filaments causes the reactivation of a broken filament at some distance from the break. The utilized statistical bundle models predict a change in the slope of the mean size effect curve once the specimen length becomes longer than the stress transfer length. This fact can be exploited in order to determine the stress transfer length indirectly using the yarn tensile test with appropriately chosen test lengths. The identification procedure is demonstrated using two test series of tensile tests with AR-glass and carbon yarns.

On the influence of the interaction laws of a dynamical particle system for sample optimization

Abstract The presented paper investigates the effect of the formulation of the energy potential of a dynamical particle system used for the optimization of statistical point sampling. The dynamical particle system, originally developed as a physical analogy to the Audze-Eglajs (AE) optimization criterion and its periodical modification (PAE), effectively demonstrated that the originally proposed energy potential performs well only in poorly applicable scenarios featuring low-dimensional design domains filled with a rather high number of design points. A remedy is presented which involves a refined formulation of the energy potential, as well as its derivation. The reasoning behind this approach is also dealt with in detail.