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A conditional probability density function model for fatigue damage estimation in broadband non-Gaussian stochastic processes

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INTERNATIONAL JOURNAL OF FATIGUE 2025年 197卷

作者： Zhu, Yuhao Yao, Weixing Nanjing Univ Aeronaut & Astronaut Coll Aerosp Engn Nanjing 210016 Peoples R China

To address the issue of the inability of the probability density function of stress amplitude under Gaussian processes to be applied to fatigue damage estimation in non-Gaussian processes, a conditional probability density function model of the mean given amplitude is developed in this paper. The relation between the unknown parameter of the conditional probability density function and the bandwidth parameters of stochastic processes is established utilizing a four-parameter nonlinear regression model. The conditional probability density function can be multiplied with an approximate probability density function model of rainflow amplitude under broadband Gaussian stochastic processes to form a joint probability density function of amplitude and mean. By introducing the Hermite transformation function, the joint probability density function can be extended to fatigue damage estimation in broadband non-Gaussian stochastic processes. Through case studies of constructed standard spectra and the vibration response of 2A12 aluminum alloy edge-notch specimens, the accuracy of the proposed method is verified by comparisons with the non-Gaussian Tovo-Benasciutti method and the timedomain method.

关键词： Fatigue damage conditional probability density function Gaussian Non-Gaussian

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Bivariate exponentiated half logistic distribution: Properties and application

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2021年第24期50卷 6099-6121页

作者： Alotaibi, Refah Mohammed Rezk, Hoda Ragab Ghosh, Indranil Dey, Sanku Princess Nourah Bint Abdulrahman Univ Coll Sci Math Sci Dept Riyadh Saudi Arabia Al Azhar Univ Dept Stat Cairo Egypt Univ N Carolina Dept Math & Stat Wilmington NC USA St Anthonys Coll Dept Stat Shillong Meghalaya India

The exponentiated half logistic (EHL) distribution can be mostly and effectively used in modeling lifetime data. It is very similar to the gamma and exponentiated exponential distributions with two parameters. The major advantage of EHL distribution over the gamma distribution is that its cumulative distribution has a closed form. In this research, we develop a new bivariate exponentiated half logistic (BEHL) distribution with univariate EHL distribution as the marginals. The joint probability density function and the joint cumulative distribution function were expressed in explicit forms. This article also presents the various properties of the proposed distribution such as marginal, conditional distributions and product moments. The maximum likelihood estimates for the unknown parameters of BEHL distribution and their approximate variance- covariance matrix have been obtained. Monte Carlo simulations have been conducted to check the performances of the maximum likelihood estimators with applications to a real data set. Analysis showed that the BEHL distribution gives a better fit than other rival bivariate probability models.

关键词： Bivariate exponentiated half logistic distribution joint probability density function conditional probability density function product moments maximum likelihood estimators

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An alternative approach to modelling relapse in cancer with an application to adenocarcinoma of the prostate

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MATHEMATICAL BIOSCIENCES 2006年第1期199卷 38-54页

作者： Veestraeten, D Univ Amsterdam Dept Econ NL-1018 WB Amsterdam Netherlands

This paper proposes an alternative approach to modelling relapse in cancer. In particular, the dynamic model for the tumor or biomarker will be subjected to a lower elastic boundary at which the process either will be absorbed or reflected. The likelihood of reflection then can be interpreted as the probability of relapse. This framework will be exemplified for prostatic cancer by extending the recently proposed stochastic model of Dayananda et al. [P.W.A. Dayananda, J.T. Kemper, M.M. Shvartsman, A stochastic model for prostate-specific antigen levels, Math. Biosci. 190 (2004) 113] that focussed on the dynamics of the prostate-specific antigen (PSA) biomarker. Analytical results for the conditional density function, given a non-negative lower boundary, are obtained for the extreme cases of certain cure and of certain relapse. Simulations illustrate the relevance of the relapse probability and of the normal value of the biomarker for the design of treatment strategies. The paper thus points to two additional (patient-specific) characteristics that might enter treatment design and monitoring of progress in therapy. (c) 2005 Elsevier Inc. All rights reserved.

关键词： absorbing boundary cancer conditional probability density function elastic boundary prostate cancer prostate-specific antigen (PSA) reflecting boundary relapse stochastic differential equations

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A neural network approach to the simulation of load histories by considering the influence of a sequence of rainflow load cycles

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INTERNATIONAL JOURNAL OF FATIGUE 2002年第11期24卷 1109-1125页

作者： Klemenc, J Fajdiga, M Univ Ljubljana Fac Mech Engn SI-1000 Ljubljana Slovenia

A modeller was developed that simulates random load histories by considering a statistical distribution and a sequence of load cycles that correspond to a rainflow algorithm. The random load histories are generated stepwise by putting together series of load cycles, successively predicted by the modeller. The core of the modeller is a conditional probability density function of load cycles, which is modelled by a multilayer perceptron. The theoretical foundations of the modeller and three examples of its application for the simulation of random load histories are presented in the paper. We concluded from the examples that it is possible to simulate new random load histories on the basis of the load cycles, extracted from the original load history with the rainflow method, so that the statistical distribution and the sequence of load cycles from the original load history are preserved in simulated load histories. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： modelling of load histories rainflow counting method sequence of load cycles conditional probability density function mixture of multivariate Gaussian functions multilayer perceptron

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A novel estimation method for failure-probability-based-sensitivity by conditional probability theorem

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2020年第4期61卷 1589-1602页

作者： He, Liangli Lu, Zhenzhou Feng, Kaixuan Northwestern Polytech Univ Sch Aeronaut Xian 710072 Shaanxi Peoples R China

By the average absolute difference between the unconditional failure probability and the conditional one on fixing an input at its realization, the failure-probability-based-sensitivity (FP-S) is defined to quantify the effect of the fixed input on the failure probability, which provides important information for reliability-based design optimization of the structure. Among the estimation methods for FP-S, the Bayes theorem-based methods are competitive, but the conditional probability density function (PDF) should be estimated in this type method. To alleviate the computational complexity of estimating conditional PDF, a novel FP-S estimation method is proposed by use of the conditional probability theorem. In the proposed method, the conditional failure probability on fixing the input at its realization is approximated by the conditional failure probability on fixing the input in a small interval, in which the conditional probability theorem of the random event can be used to transform FP-S as estimations of a series of probabilities, and they can be simultaneously completed by a numerical simulation for estimating the unconditional failure probability. For ensuring the precision of the approximation introduced by replacing the realization with the small interval, a selection strategy for the small interval is proposed. Comparing with the competitive Bayes theorem-based estimation for FP-S, the proposed method replaces the conditional PDF estimation with the conditional probability estimation, which greatly reduces the computational complexity and improves the accuracy of the FP-S estimation. By combining with the adaptive kriging surrogate model, the efficiency of the proposed method can be drastically improved, and the presented examples demonstrate the efficiency and accuracy of the proposed method.

关键词： Failure-probability-based-sensitivity Bayes theorem-based method conditional probability density function conditional probability theorem Adaptive kriging

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A neural network approach to describing the scatter of S-N curves

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INTERNATIONAL JOURNAL OF FATIGUE 2006年第4期28卷 311-323页

作者： Bucar, T Nagode, M Fajdiga, M Univ Ljubljana Fac Mech Engn SI-1000 Ljubljana Slovenia

For service life prediction of a structural component, the probability distribution of material fatigue resistance should be determined, given that the scatter of loading spectra is known and a proper damage cumulating model is chosen. In the randomness of fatigue resistance of a material, constant amplitude fatigue test results show that at any stress level the fatigue life is a random variable. Fatigue life in this instance is affected by a variety of influential factors, such as stress amplitude, mean stress, notch factor, temperature, etc. The scope of the paper is to prove that the statistical scatter of the fatigue life N-f at various factors' levels of constant values can be described by the Weibull or lognormal conditional probability density function, which is modelled with a multilayer perceptron. In order to estimate the unknown parameters of the conditional distribution, generally composed of an arbitrary but finite number of lognormal or Weibull component distributions, we introduced an algorithm based on neural network modelling. To support the main idea, two examples are presented. It can be concluded that the suggested neural computing method is suitable for describing the fatigue data trends and the statistical scatter of fatigue life under constant loading conditions for an arbitrary set of influential factors, once the optimal neural network is designed and trained. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： S-N curves fatigue life scatter conditional probability density function multilayer perceptron

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Stochastic interpolation of earthquake ground motions under spectral uncertainties

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STRUCTURAL ENGINEERING AND MECHANICS 1997年第6期5卷 839-851页

作者： Morikawa, H Kameda, H Kyoto Univ Dept Civil Engn Syst Kyoto 606 Japan Kyoto Univ Disaster Prevent Res Inst Uji Kyoto Japan

Closed-form solutions are analytically derived for stochastic properties of earthquake ground motion fields, which are conditioned by an observed time series at certain observation sites and are characterized by spectra with uncertainties. The theoretical framework presented here can estimate not only the expectations of such simulated earthquake ground motions, but also the prediction errors which offer important information for the field of engineering. Before these derivations are made, the theory of conditional random fields is summarized for convenience in this study. Furthermore, a method for stochastic interpolation of power spectra is explained.

关键词： conditional random fields power spectrum spectral uncertainties stochastic interpolation numerical simulation conditional probability density function estimation errors Fourier coefficients

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JIE for a class of MD systems

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IET SIGNAL PROCESSING 2017年第6期11卷 647-656页

作者： Feng, Xiaoxue Liang, Yan Jiao, Lianmeng He, Chongyang Beijing Inst Technol Sch Automat Beijing 100081 Peoples R China Northwestern Polytech Univ Key Lab Informat Fus Technol Xian 710072 Shaanxi Peoples R China

In multi-detection (MD) systems including over-the-horizon radar (OTHR) systems, the forward-based receivers systems and passive coherent location systems, resolvable multiple detections of one target due to the multi-path propagation will be received, in which both identification (including measurement association and propagation mode/transmitting origin identification) and estimation (including path-conditional state estimation and multi-path track fusion) are deeply coupled and affect each other. Up to present, all corresponding methods fall into the scope of sequential identification orientated or estimation orientated processing, and hence the solutions are not satisfactory. Here the joint identification and estimation scheme for the MD systems (MD-JIE) is developed based on the generalized Bayes risk considering both identification and estimation performance. The likelihood-ratio function and the conditional probability density function as the identification cost and estimation cost are recursively calculated, respectively. Taking the data-association constraints into consideration, the proposed MD-JIE scheme is implemented via online constrained optimization technology. Compared to the identification-then-estimation (ITE) method and the estimation-then-identification (ETI) method, the proposed MD-JIE method prevails in the joint performance measure with the higher correct identification rate than the ETI method and the smaller root MSE than the ITE method. Besides, the robustness of the proposed method is verified.

关键词： Bayes methods probability least mean squares methods sensor fusion signal detection receivers multidetection systems over-the-horizon radar systems forward-based receivers systems passive coherent location systems joint identification and estimation scheme generalised Bayes risk likelihood-ratio function conditional probability density function minimum-mean-square-error data-association constraints MD-JIE scheme

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Statistical analysis of monopulse-synthetic aperture radar for constant false-alarm rate detection of ground moving targets

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IET RADAR SONAR AND NAVIGATION 2015年第6期9卷 641-652页

作者： Wu, Di Zhu, Daiyin Shen, Mingwei Li, Yong Nanjing Univ Aeronaut & Astronaut Key Lab Radar Imaging & Microwave Photon Minist Educ Nanjing 210016 Peoples R China Hohai Univ Coll Comp & Informat Nanjing 211100 Jiangsu Peoples R China

An efficient approach to achieve ground moving target indication (GMTI) for synthetic aperture radar (SAR) is to use the monopulse-SAR system. In this kind of SAR system, moving targets are detected over a so called, called monopulse ratio diagram (MRD) generated by a pixel-to-pixel comparison between the two SAR images acquired from the sum and difference channels. The sample derived from this diagram for the pixel under test (PUT), i.e. the value of monopulse ratio (MR), is employed as the test statistic. This paper examines the statistics of MR when complex Gaussian clutter-plus-noise background in considered. The conditional probability density function (pdf) of MR, given the occurrence that the amplitude of the sum signal is greater than a predetermined threshold, is analysed in detail. Especially, the conditional likelihood function of MR under the null hypothesis is given in a closed-form. Based on these results, an automatic constant false-alarm rate (CFAR) detector for moving target detection (MTD) is proposed and extended to a so called multi-MRD form to further improve the final detection performance. Simulations, as well as experimental results obtained from two groups of real dataset, are presented to examine the detection performance and validate the theoretical analysis.

关键词： statistical analysis synthetic aperture radar radar imaging image motion analysis object detection probability Gaussian processes radar clutter statistical analysis monopulse-synthetic aperture radar ground moving target detection monopulse-SAR ΣΔ-SAR system two-dimensional diagram monopulse ratio diagram pixel-to-pixel comparison complex SAR images sum and difference channels conditional probability density function complex Gaussian clutter-plus-noise background conditional likelihood function null hypothesis automatic constant false-alarm rate detector amplitude threshold detector MR threshold detector multiMRD detection performance improvement

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An estimation approach for linear stochastic systems based on characteristic functions

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AUTOMATICA 2017年 78卷 153-162页

作者： Idan, Moshe Speyer, Jason L. Technion Israel Inst Technol Aerosp Engn IL-3200003 Haifa Israel Univ Calif Los Angeles Mech & Aerosp Engn Los Angeles CA 90095 USA

This paper presents an alternative, characteristic function based approach for the Bayesian design of estimators for dynamic linear systems and linear detection problems. For a measurement update, the a posteriori characteristic function of the unnormalized conditional probability density function (ucpdf) of the state given the measurement history is obtained as a convolution of the a priori characteristic function of the ucpdf with the characteristic function of the measurement noise. It is shown that this convolution holds for a general measurement structure. Time propagation involves the product of the updated characteristic function of the ucpdf and the characteristic function of the process noise. Some estimation problems are found to be naturally tractable using only characteristic functions, such as the multivariable linear system with additive Cauchy measurement and process noise. It is shown that even the derivation of the Kalman filter algorithm has advantages when formulated using the characteristic function approach. Finally, in some instances the estimation problem can only be formulated in terms of characteristic functions. This is illustrated by a one-update scalar example for symmetric-alpha-stable distributions. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Estimation conditional probability density function Filtering for non-Gaussian noise Characteristic functions

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