Novel and faster ways for solving semi-markov processes: mathematical and numerical issues

Processos semi-Markovianos (SMP) contínuos no tempo são importantes ferramentas estocásticas para modelagem de métricas de confiabilidade ao longo do tempo para sistemas para os quais o comportamento futuro depende dos estados presente e seguinte assim como do tempo de residência. O método clássico para resolver as probabilidades intervalares de transição de SMP consiste em aplicar diretamente um método geral de quadratura às equações integrais. Entretanto, esta técnica possui um esforço computacional considerável, isto é, N2 equações integrais conjugadas devem ser resolvidas, onde N é o número de estados. Portanto, esta tese propõe tratamentos matemáticos e numéricos mais eficientes para SMP. O primeiro método, o qual é denominado 2N-, é baseado em densidades de frequência de transição e métodos gerais de quadratura. Basicamente, o método 2N consiste em resolver N equações integrais conjugadas e N integrais diretas. Outro método proposto, chamado Lap-, é baseado na aplicação de transformadas de Laplace as quais são invertidas por um método de quadratura Gaussiana, chamado Gauss Legendre, para obter as probabilidades de estado no domínio do tempo. Formulação matemática destes métodos assim como descrições de seus tratamentos numéricos, incluindo questões de exatidão e tempo para convergência, são desenvolvidas e fornecidas com detalhes. A efetividade dos novos desenvolvimentos 2N- e Lap- serão comparados contra os resultados fornecidos pelo método clássico por meio de exemplos no contexto de engenharia de confiabilidade. A partir destes exemplos, é mostrado que os métodos 2N- e Lap- são significantemente menos custosos e têm acurácia comparável ao método clássic

Failure and reliability prediction by support vector machines regression of time series data

International audienceSupport Vector Machines (SVMs) are kernel-based learning methods, which have been successfully adopted for regression problems. However, their use in reliability applications has not been widely explored. In this paper, a comparative analysis is presented in order to evaluate the SVM effectiveness in forecasting time-to-failure and reliability of engineered components based on time series data. The performance on literature case studies of SVM regression is measured against other advanced learning methods such as the Radial Basis Function, the traditional MultiLayer Perceptron model, Box-Jenkins autoregressive-integrated-moving average and the Infinite Impulse Response Locally Recurrent Neural Networks. The comparison shows that in the analyzed cases, SVM outperforms or is comparable to other techniques

Zastosowanie maszyn wektorów nośnych zoptymalizowanych metodą roju cząstek oraz technik przetwarzania wstępnego do oceny pozostałego okresu użytkowania łożysk

The useful life time of equipment is an important variable related to system prognosis, and its accurate estimation leads to several competitive advantage in industry. In this paper, Remaining Useful Lifetime (RUL) prediction is estimated by Particle Swarm optimized Support Vector Machines (PSO+SVM) considering two possible pre-processing techniques to improve input quality: Empirical Mode Decomposition (EMD) and Wavelet Transforms (WT). Here, EMD and WT coupled with SVM are used to predict RUL of bearing from the IEEE PHM Challenge 2012 big dataset. Specifically, two cases were analyzed: considering the complete vibration dataset and considering truncated vibration dataset. Finally, predictions provided from models applying both pre-processing techniques are compared against results obtained from PSO+SVM without any pre-processing approach. As conclusion, EMD+SVM presented more accurate predictions and outperformed the other models.Okres użytkowania sprzętu jest ważną zmienną związaną z prognozowaniem pracy systemu, a możliwość jego dokładnej oceny daje zakładom przemysłowym znaczną przewagę konkurencyjną. W tym artykule pozostały czas pracy (Remaining Useful Life, RUL) szacowano za pomocą maszyn wektorów nośnych zoptymalizowanych rojem cząstek (SVM+PSO) z uwzględnieniem dwóch technik przetwarzania wstępnego pozwalających na poprawę jakości danych wejściowych: empirycznej dekompozycji sygnału (Empirical Mode Decomposition, EMD) oraz transformat falkowych (Wavelet Transforms, WT). W niniejszej pracy, EMD i falki w połączeniu z SVM wykorzystano do prognozowania RUL łożyska ze zbioru danych IEEE PHM Challenge 2012 Big Dataset. W szczególności, przeanalizowano dwa przypadki: uwzględniający kompletny zestaw danych o drganiach oraz drugi, biorący pod uwagę okrojoną wersję tego zbioru. Prognozy otrzymane na podstawie modeli, w których zastosowano obie techniki przetwarzania wstępnego porównano z wynikami uzyskanymi za pomocą PSO + SVM bez wstępnego przetwarzania danych. Wyniki pokazały, że model EMD + SVM generował dokładniejsze prognozy i tym samym przewyższał pozostałe badane modele

On the q-Weibull distribution for reliability applications: An adaptive hybrid artificial bee colony algorithm for parameter estimation

The q-Weibull model is based on the Tsallis non-extensive entropy [22] and is able to model various behaviors of the hazard rate function, including bathtub curves, by using a single set of parameters. Despite its flexibility, the q-Weibull has not been widely used in reliability applications partly because of the complicated parameters estimation. In this work, the parameters of the q-Weibull are estimated by the maximum likelihood (ML) method. Due to the intricate system of nonlinear equations, derivative-based optimization methods may fail to converge. Thus, the heuristic optimization method of artificial bee colony (ABC) is used instead. To deal with the slow convergence of ABC, it is proposed an adaptive hybrid ABC (AHABC) algorithm that dynamically combines Nelder-Mead simplex search method with ABC for the ML estimation of the q-Weibull parameters. Interval estimates for the q-Weibull parameters, including confidence intervals based on the ML asymptotic theory and on bootstrap methods, are also developed. The AHABC is validated via numerical experiments involving the qWeibull ML for reliability applications and results show that it produces faster and more accurate convergence when compared to ABC and similar approaches. The estimation procedure is applied to real reliability failure data characterized by a bathtub-shaped hazard rate

A Particle Swarm-optimized Support Vector Machine for Reliability Prediction

Article first published online: 22 JUN 2011International audienceSystem reliability depends on inherent mechanical and structural aging factors as well as on operational and environmental conditions, which could enhance (or smoothen) such factors. In practice, the involved dependences may burden the modeling of the reliability behavior over time, in which traditional stochastic modeling approaches may likely fail. Empirical prediction methods, such as support vector machines (SVMs), become a valid alternative whenever reliable time series data are available. However, the prediction performance of SVMs depends on the setting of a number of parameters that influence the effectiveness of the training stage during which the SVMs are constructed based on the available data set. The problem of choosing the most suitable values for the SVM parameters can be framed in terms of an optimization problem aimed at minimizing a prediction error. In this work, this problem is solved by particle swarm optimization (PSO), a probabilistic approach based on an analogy with the collective motion of biological organisms. SVM in liaison with PSO is then applied to tackle reliability prediction problems based on time series data of engineered components. Comparisons of the obtained results with those given by other time series techniques indicate that the PSO+SVM model is able to provide reliability predictions with comparable or great accuracy

A multi-objective approach for solving a replacement policy problem for equipment subject to imperfect repairs

This paper proposes a multi-objective approach to model a replacement policy problem applicable to equipment with a predetermined period of use (a planning horizon), which may undergo critical and non-critical failures. Corrective replacements and imperfect repairs are taken to restore the system to operation respectively when critical and non-critical failures occur. Generalized Renewal Process (GRP) is used to model imperfect repairs. The proposed model supports decisions on preventive replacement intervals and the number of spare parts purchased at the beginning of the planning horizon. A Multi-Objective Genetic Algorithm (MOGA) coupled with discrete event simulation (DES) is proposed to provide a set of solutions (Pareto-optimum set) committed to the different objectives of a maintenance manager in the face of a replacement policy problem, that is, maintenance cost, rate of occurrence of failures, unavailability, and investment on spare parts. The proposed MOGA is validated by an application example against the results obtained via the exhaustive approach. Moreover, examples are presented to evaluate the behavior of objective functions on Pareto set (trade-off analysis) and the impact of the repair effectiveness on the decision making.CAPES 001 - National Council for Scientific and Technological Development (CNPq