Aplicação de bootstrap para teste de durbin-watson - uma contribuição para cenários na economia.

Em economia, trabalhar com modelos de regressão linear clássicos com o intuito de investigar comportamentos sejam macroeconômicos ou microeconômicos é algo bastante comum de se encontrar. Entretanto, dada as várias as suposições que devem ser atendidas ao se utilizar este método, e dada à natureza de algumas variáveis econômicas, é comum se violar uma ou mais hipóteses. Para diagnosticar a presença de erros autocorrelacionados, o teste de Durbin-Watson é o mais usado, porém apresenta a limitação de não fornecer valores críticos exatos para a distribuição de probabilidade de sua estatística de teste, tornando-se inconclusivo em determinados casos. Com o intuito de fornecer uma solução para esta limitação, propõem-se dois algoritmos bootstrap. Um deles pode ser aplicado em situações onde se pode afirmar que os erros “bem comportados” seguem uma distribuição normal com média zero e variância (bootstrap paramétrico). O outro, por sua vez,não requer qualquer suposição sobre a sua distribuição (bootstrap não-paramétrico). Os algoritmos propostos são aplicados a dois exemplos práticos e são obtidos, para cada um deles, os valores críticos exatos da distribuição da estatística de Durbin-Watson para os níveis de significância de 1%, 5% e 10%, bem como o formato resultante da densidade de probabilidade empírica

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

Combining generalized renewal processes with non-extensive entropy-based q-distributions for reliability applications

The Generalized Renewal Process (GRP) is a probabilistic model for repairable systems that can represent the usual states of a system after a repair: as new, as old, or in a condition between new and old. It is often coupled with the Weibull distribution, widely used in the reliability context. In this paper, we develop novel GRP models based on probability distributions that stem from the Tsallis' non-extensive entropy, namely the q-Exponential and the q-Weibull distributions. The q-Exponential and Weibull distributions can model decreasing, constant or increasing failure intensity functions. However, the power law behavior of the q-Exponential probability density function for specific parameter values is an advantage over the Weibull distribution when adjusting data containing extreme values. The q-Weibull probability distribution, in turn, can also fit data with bathtub-shaped or unimodal failure intensities in addition to the behaviors already mentioned. Therefore, the q-Exponential-GRP is an alternative for the Weibull-GRP model and the q-Weibull-GRP generalizes both. The method of maximum likelihood is used for their parameters' estimation by means of a particle swarm optimization algorithm, and Monte Carlo simulations are performed for the sake of validation. The proposed models and algorithms are applied to examples involving reliability-related data of complex systems and the obtained results suggest GRP plus q-distributions are promising techniques for the analyses of repairable systems.CNP