Modified Schemes of Sequential Probability Ratio Test for Incipient Failure Detection in Dynamic Systems

This paper determines the theoretical limits of failure detectability in systems with modeling errors. Such errors are the main obstacle to accurate failure detection in aircraft, jet engines, power generation systems, and most other systems that include mechanical components and/or thermofluid processes. The paper then introduces the reachable measurement intervals (RMI) failure detection method that performs at the limit of detectability. RMI is capable of detecting the smallest theoretically detectable failures in systems with modeling errors, and is implementable in real time on microprocessors. The method is illustrated on a jet engine example. Nomenclature a — entry of the matrix A A = system matrix b = entry of the matrix B B = input matrix Bj = input matrix equal to the identity matrix C = output matrix C{ = output matrix for additional measurements D = direct transmission matrix H = Pontryagin's function K — matrix of gains for additional measurements L = vector of Lagrange multipliers m = entry of the matrix M M = matrix of Lagrange multipliers associated with uncertain entries of A n = entry of the matrix N N = matrix of Lagrange multipliers associated with uncertain entries of B p = discrete-time index corresponding to current time P = performance index for optimization q - vector of system parameters / = time t0 — current time ts = length of the processing window T - sampling time u = input vector x = state vector y = output vector z - vector of additional measurements Subscripts d = discrete e = uncertain and uncorrelated n = nominal v = uncertain

Effects of indicating failure odds and smoothed outputs on human failure detection in dynamic systems∗

Effects of indicating failure odds and smoothed outputs on human failure detection in dynamic systems : Tzelgov, J., Tsach, U., and Sheridan, T.B.Ergonomics, 1985, 28.2, 449–462

Robust Detection and Estimation in Dynamic Systems and Statistical Signal Processing: Intersections, Parallel Paths and Applications

Robust probabilistic predictable feature analysis and its application for dynamic process monitoring

The model-based approach to fault detection in dynamic systems has been receiving more and more attention over the last two decades, in the contexts of both research and real plant application.KeywordsFuzzy LogicFault DetectionFault DiagnosisResidual EvaluationResidual GenerationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

A time series Kalman filter (TSKF) is proposed that successfully handles outlier detection in dynamic systems, where normal process changes often mask the existence of outliers. The TSKF method combines a time series model fitting procedure with a modified Kalman filter to deal with additive outlier and innovational outlier detection problems in dynamic process dataset. Compared with current outlier detection methods, the new method enjoys the following advantages: (a) no prior knowledge of the process model is needed; (b) it is easy to tune; (c) it can be applied to both univariate and multivariate outlier detection; (d) it is applicable to both on‐line and off‐line operation; (e) it cleans outliers while maintains the integrity of the original dataset. © 2014 American Institute of Chemical Engineers AIChE J, 61: 419–433, 2015

Robust Change Detection in Dynamic Systems with Model Uncertainties

In statistics and engineering the problem of change point detection in dynamical systems can be addressed using the class of sequential detection rules called limited generalized likelihood ratio (GLR) schemes. In this paper, some open problems concerning the statistical theory and practical implementation of these procedures are discussed. A method to select the window size and the threshold value, based on the joint use of Monte Carlo simulation and theoretical results, is proposed and illustrated through an example.

Conditional frequentist tests of a precise hypothesis versus a composite alternative have recently been developed, and have been shown to be equivalent to conventional Bayes tests in the very strong sense that the reported frequentist error probabilities equal the posterior probabilities of the hypotheses. These results are herein extended to sequential testing, and yield fully frequentist sequential tests that are considerably easier to use than are conventional sequential tests. Among the interesting properties of these new tests is the lack of dependence of the reported error probabilities on the stopping rule, seeming to lend frequentist support to the stopping rule principle. Keywords:Bayes factor; Composite hypothesis; Conditional test; Error probability; Likelihood ratio; Sequential probability ratio test; Sequential test.

A non-parametric sequential rank-sum probability ratio test method for binary hypothesis testing

In medical, health, and sports sciences, researchers desire a device with high reliability and validity. This article focuses on reliability and validity studies with n subjects and m ≥2 repeated measurements per subject. High statistical power can be achieved by increasing n or m, and increasing m is often easier than increasing n in practice unless m is too high to result in systematic bias. The sequential probability ratio test (SPRT) is a useful statistical method which can conclude a null hypothesis H0 or an alternative hypothesis H1 with 50% of the required sample size of a non-sequential test on average. The traditional SPRT requires the likelihood function for each observed random variable, and it can be a practical burden for evaluating the likelihood ratio after each observation of a subject. Instead, m observed random variables per subject can be transformed into a test statistic which has a known sampling distribution under H0 and under H1. This allows us to formulate a SPRT based on a sequence of test statistics. In this article, three types of study are considered: reliabilityof a device, reliability of a device relative to a criterion device, and validity of a device relative to a  criterion device. Using SPRT for testing the reliability of a device, for small m, results in an average sample size of about 50% of the fixed sample size for a non-sequential test. For comparing a device to criterion, the average sample size approaches to 60% approximately as m increases. The SPRT tolerates violation of normality assumption for validity study, but it does not for reliability study.

In this article the problem of a sequential test for the model of independent non-identically distributed observations is considered. Based on recursive calculation a new numerical approach to approximate test characteristics for a sequential probability ratio test (SPRT) and a truncated SPRT (TSPRT) is constructed. The problem of robustness evaluation is also studied when the contamination is presented by the distortion of the distributions of all increments of the log-likelihood ratio statistics. The two-side truncated functions are proposed to be used for constructing the robustified SPRT. An algorithm to choose the thresholds of these truncated functions is indicated. The results are applied for a sequential test on parameters of time series with trend. Some kinds of the contaminated models of time series with trend are used to study the robustness of the truncated SPRT. Numerical examples confirming the theoretical results mentioned above are given.

In this paper, we introduce a sequential procedure for the Multi-Objective Ranking and Selection (MOR&S) problems that identifies the Pareto front with a guaranteed probability of correct selection (PCS). In particular, the proposed procedure is fully sequential using the test statistics built upon the generalized sequential probability ratio test (GSPRT). The main features of the new proposed procedure are: 1) a unified framework, the new procedure treats the multi-objective problems in the same way as the single-objective problems; 2) an indifference-zone-free formulation, the new procedure eliminates the necessity of indifference-zone parameter; 3) asymptotically optimality, the GSPRT achieves asymptotically the shortest expected sample size among all sequential tests; 4) general distribution, the procedure uses the empirical likelihood for generally distributed observation. A numerical evaluation demonstrates the efficiency of the new procedure.

This paper presents the application of multivariate state estimation technique (MSET) and sequential probability ratio test (SPRT) for early damage detection of low speed slew bearing. This paper also investigates the appropriate and reliable features for slew bearing condition monitoring. It is found that largest Lyapunov exponent (LLE), approximate entropy, margin factor (MF) and impulse factor (IF) are able to monitor the slew bearing condition. The aim of present study is to calculate single condition monitoring parameter from multiple features. Combined MSET and SPRT were used to analyse the recorded reliable features obtained from a previous work. The result shows that the method can clearly picked up the sign of early bearing damage.