Reliability analysis of discrete-state performance functions via adaptive sequential sampling with detection of failure surfaces

The paper presents a new efficient and robust method for rare event probability estimation for computational models of an engineering product or a process returning categorical information only, for example, either success or failure. For such models, most of the methods designed for the estimation of failure probability, which use the numerical value of the outcome to compute gradients or to estimate the proximity to the failure surface, cannot be applied. Even if the performance function provides more than just binary output, the state of the system may be a non-smooth or even a discontinuous function defined in the domain of continuous input variables. In these cases, the classical gradient-based methods usually fail. We propose a simple yet efficient algorithm, which performs a sequential adaptive selection of points from the input domain of random variables to extend and refine a simple distance-based surrogate model. Two different tasks can be accomplished at any stage of sequential sampling: (i) estimation of the failure probability, and (ii) selection of the best possible candidate for the subsequent model evaluation if further improvement is necessary. The proposed criterion for selecting the next point for model evaluation maximizes the expected probability classified by using the candidate. Therefore, the perfect balance between global exploration and local exploitation is maintained automatically. The method can estimate the probabilities of multiple failure types. Moreover, when the numerical value of model evaluation can be used to build a smooth surrogate, the algorithm can accommodate this information to increase the accuracy of the estimated probabilities. Lastly, we define a new simple yet general geometrical measure of the global sensitivity of the rare-event probability to individual variables, which is obtained as a by-product of the proposed algorithm.Comment: Manuscript CMAME-D-22-00532R1 (Computer Methods in Applied Mechanics and Engineering

Adaptive sequential sampling for reliability estimation of binary functions

A novel method for estimation of rare event probability is proposed, which works also for computational models returning categorical information only: success or failure. It combines the robustness of simulation methods (counting failure events) with the strength of approximation methods which refine the boundary between the failure and safe sets. Two basic tasks are identified: (i) extension of the experimental design (ED) and (ii) estimation of probabilities. The new extension algorithm adds points for limit state evaluation to the ED by balancing the global exploration and local exploitation, and the estimation uses the pointwise information to build a simple surrogate and perform a novel optimized importance sampling. No connection is presumed between the limit function value at point and its proximity to the failure surface. A new global sensitivity measure of the failure probability to individual variables is proposed and obtained as a by-product of the proposed methods

Development of norms of correlation resulting from random swapping of order of elements

Příspěvek se zabývá vlastnostmi procesu vývoje statistické korelace dvou náhodných vektorů při náhodných záměnách pořadí jednotlivých elementů. V praxi se tato metoda používá pro zavedení požadované korelace nebo pro odstranění nechtěné statistické závislosti mezi vektory vzorků (souřadnice) náhodných veličin.The contribution deals with properties of a process of statistical correlation between two vectors – samples of random variables. The process results from random swaps of the mutual order of elements. This method is being applied when controlling correlations or removing undesired statistical dependence

Analytické a numerické přístupy pro modelování koroze v železobetonových konstrukcích

Corrosion of reinforcement in concrete is one of the most influencing factors causing the degradation of RC structures. This paper attempts at the application of an analytical and numerical approaches to simulation of concrete cracking due to reinforcement corrosion. At first, a combination with detailed analysis of two analytical models proposed by Liu and Weyers (1998) and Li et al. (2006) is suggested and presented. Four distinct phases of the corrosion process are identified and a detailed guide through the mathematical development is described. Next, numerical computations obtained with nonlinear finite element code are presented. The model features the state-of-the-art in nonlinear fracture mechanics modelling and the heterogeneous structure of concrete is modelled via spatially varying parameters of the constitutive law. Finally, the results of the analytical studies are compared to numerical computations and the paper concludes with the sketch of a real-life numerical exampleKoroze ocelové výztuže v betonu je jedním z hlavních příčin degradace železobetonových konstrukcí. Tento příspěvek předkládá možnosti analytických a numerických přístupů modelování rozvoje trhlin v betonu vzniklých působením koroze výztuže. Nejprve je prezentována kombinace a detailní analýza dvou analytických modelů od Liu a Weyerse (1998) a Li a kol. (2006). Jsou identifikovány čtyři fáze vývoje koroze s detailním popisem matematického modelu. Dále jsou prezentovány numerické výpočty získané nelineární konečně prvkostní analýzou. Použitý model využívá nejnovější nástroje nelineárního modelování s uplatněním přístupů lomové mechaniky. Heterogenní struktura betonu je modelována pomocí náhodného pole vstupních parametrů. Na závěr jsou porovnány výsledky analytických a numerických výpočtů a je uveden příklad aplikace na reálné části konstrukc

Failure Probability Estimation and Detection of Failure Surfaces via Adaptive Sequential Decomposition of the Design Domain

We propose an algorithm for an optimal adaptive selection of points from the design domain of input random variables that are needed for an accurate estimation of failure probability and the determination of the boundary between safe and failure domains. The method is particularly useful when each evaluation of the performance function g(x) is very expensive and the function can be characterized as either highly nonlinear, noisy, or even discrete-state (e.g., binary). In such cases, only a limited number of calls is feasible, and gradients of g(x) cannot be used. The input design domain is progressively segmented by expanding and adaptively refining mesh-like lock-free geometrical structure. The proposed triangulation-based approach effectively combines the features of simulation and approximation methods. The algorithm performs two independent tasks: (i) the estimation of probabilities through an ingenious combination of deterministic cubature rules and the application of the divergence theorem and (ii) the sequential extension of the experimental design with new points. The sequential selection of points from the design domain for future evaluation of g(x) is carried out through a new learning function, which maximizes instantaneous information gain in terms of the probability classification that corresponds to the local region. The extension may be halted at any time, e.g., when sufficiently accurate estimations are obtained. Due to the use of the exact geometric representation in the input domain, the algorithm is most effective for problems of a low dimension, not exceeding eight. The method can handle random vectors with correlated non-Gaussian marginals. The estimation accuracy can be improved by employing a smooth surrogate model. Finally, we define new factors of global sensitivity to failure based on the entire failure surface weighted by the density of the input random vector.Comment: 42 pages, 24 figure

Fracture in random quasibrittle media: I. Discrete mesoscale simulations of load capacity and fracture process zone

Numerical simulations of concrete fracture performed with a probabilistic mesoscale discrete model are presented. The model represents a substantial part of material randomness by assigning random locations to the largest aggregates. The remaining part of randomness is introduced by causing material parameters to fluctuate randomly via a homogeneous random field. An extensive numerical study performed with the model considers prisms loaded in uniaxial tension with both fixed and rotating platens, and also beams with and without a notch loaded in three point bending. The results show the nontrivial effect of (i) autocorrelation length and (ii) variance of the random field on the fracture behavior of the model. Statistics of the peak load are presented as well as the size and shape of the fracture process zone at the moment when the maximum load is attained. Local averaging within the fracture process zone and weakest-link are identified as underlying mechanisms explaining the reported results. The companion paper, Part II [64], introduces an analytical model capable of predicting the distribution of the peak load obtained with the probabilistic discrete model via the simple estimation of extremes of a random field obtained as moving average of local strength.Comment: 26 pages, 16 figures, 4 table

Design of experiment using simulation of a discrete dynamical system

The topic of the presented paper is a promising approach to achieve optimal Design of Experi- ment (DoE), i.e. spreading of points within a design domain, using a simulation of a discrete dynamical system of interacting particles within an n-dimensional design space. The system of mutually repelling particles represents a physical analogy of the Audze-Eglājs (AE) optimization criterion and its period- ical modification (PAE), respectively. The paper compares the performance of two approaches to im- plementation: a single-thread process using the JAVA language environment and a massively parallel solution employing the nVidia CUDA platform

Car speed measurement

Měření rychlosti vozidla pomocí Dopplerova efektuCar speed measurement using the Doppler effect

Failure probability estimation of functions with binary outcomes via adaptive sequential sampling

the Czech Science Foundation under project no. 22-06684

Branch site haplotypes that control alternative splicing

We show that the allele-dependent expression of transcripts encoding soluble HLA-DQβ chains is determined by branchpoint sequence (BPS) haplotypes in DQB1 intron 3. BPS RNAs associated with low inclusion of the transmembrane exon in mature transcripts showed impaired binding to splicing factor 1 (SF1), indicating that alternative splicing of DQB1 is controlled by differential BPS recognition early during spliceosome assembly. We also demonstrate that naturally occurring human BPS point mutations that alter splicing and lead to recognizable phenotypes cluster in BP and in position −2 relative to BP, implicating impaired SF1-BPS interactions in disease-associated BPS substitutions. Coding DNA variants produced smaller fluctuations of exon inclusion levels than random exonic substitutions, consistent with a selection against coding mutations that alter their own exonization. Finally, proximal splicing in this multi-allelic reporter system was promoted by at least seven SR proteins and repressed by hnRNPs F, H and I, supporting an extensive antagonism of factors balancing the splice site selection. These results provide the molecular basis for the haplotype-specific expression of soluble DQβ, improve prediction of intronic point mutations and indicate how extraordinary, selection-driven DNA variability in HLA affects pre-mRNA splicin