Fault Detection, Isolation and Quantification from Gaussian Residuals with Application to Structural Damage Diagnosis

International audienceDespite the general acknowledgment in the Fault Detection and Isolation (FDI) literature that FDI are typically accomplished in two steps, namely residual generation and residual evaluation, the second step is by far less studied than the first one. This paper investigates the residual evaluation method based on the local approach to change detection and on statistical tests. The local approach has the remarkable ability of transforming quite general residuals with unknown or non Gaussian probability distributions into a standard Gaussian framework, thanks to a central limit theorem. In this paper, the ability of the local approach for fault quan-tification will be exhibited, whereas previously it was only presented for fault detection and isolation. The numerical computation of statistical tests in the Gaussian framework will also be revisited to improve numerical efficiency. An example of vibration-based structural damage diagnosis will be presented to motivate the study and to illustrate the performance of the proposed method

Fault Isolation and Quantification from Gaussian Residuals with Application to Structural Damage Quantification

International audienceFault detection for structural health monitoring has been a topic of much research during the last decade. Localization and quantification of damages, which are linked to fault isolation, have proven to be more challenging, and at the same time of higher practical impact. While damage detection can be essentially handled as a data-driven approach, localization and quantification require a strong connection between data analysis and physical models. This paper builds upon a hypothesis test that checks if the mean of a Gaussian residual vector – whose parameterization is linked to possible damage locations – has become non-zero in the faulty state. It is shown how the damage location and extent can be inferred and robust numerical schemes for their estimation are derived based on QR decompositions and minmax approaches. Finally, the relevance of the approach is assessed in numerical simulations of two structures

Fault Diagnosis Via Univariate Frequency Analysis Monitoring: A Novel Technique Applied to a Simulated Integrated Drive Generator

The purpose of this research was to develop a fault detection and diagnostic method that would be able to detect and isolate seeded faults in data that was generated from a simulated integrated drive generator. The approach to the solution for this problem is summarized below. A novel approach for the detection and diagnoses of an anomaly due the occurrence of a fault within a system has been developed. This innovative technique uses specific characteristics of the frequency spectrum of a univariate signal to monitor system health for abnormal behavior due to previously characterized component failure. A fault detection and diagnostic scheme was developed that used dual heteroassociative kernel regression models. The first of these empirical models estimates selected features from the analytical redundant spectrum characteristic profile of the exciter current using power demand, a stressor, placed on the system as input query. The predicted spectrum features were compared to the actual characteristic features, which resulted in the generation of a residual signal. This signal was then analyzed in order to determine if they were the result of normal system disturbances or a predefined fault. If a fault was detected, the residual signal was passed to the second model, which isolated, and given enough information, identified the specific component of components causing the anomaly. Two case studies are presented to illustrate the capability to detect, isolate, and identify a system anomaly. As demonstrated, the monitoring of the frequency spectrum of a single variable can provide adequate indication of equipment health. With the availability of the appropriate data, as in the first case, it is possible for the development of three-layer detection and diagnostic systems that provides fault detection, isolation, and identification. A three-layer detection and diagnostic system is essential in the development of more advance health monitoring and prognostic systems. Despite some shortcomings in the simulated data made available for this work, this method is believed to be applicable to data that more realistically captures real-world relationships, including sensor noise and faults that grow with time

DEVELOPMENT OF DIAGNOSTIC AND PROGNOSTIC METHODOLOGIES FOR ELECTRONIC SYSTEMS BASED ON MAHALANOBIS DISTANCE

Diagnostic and prognostic capabilities are one aspect of the many interrelated and complementary functions in the field of Prognostic and Health Management (PHM). These capabilities are sought after by industries in order to provide maximum operational availability of their products, maximum usage life, minimum periodic maintenance inspections, lower inventory cost, accurate tracking of part life, and no false alarms. Several challenges associated with the development and implementation of these capabilities are the consideration of a system's dynamic behavior under various operating environments; complex system architecture where the components that form the overall system have complex interactions with each other with feed-forward and feedback loops of instructions; the unavailability of failure precursors; unseen events; and the absence of unique mathematical techniques that can address fault and failure events in various multivariate systems. The Mahalanobis distance methodology distinguishes multivariable data groups in a multivariate system by a univariate distance measure calculated from the normalized value of performance parameters and their correlation coefficients. The Mahalanobis distance measure does not suffer from the scaling effect--a situation where the variability of one parameter masks the variability of another parameter, which happens when the measurement ranges or scales of two parameters are different. A literature review showed that the Mahalanobis distance has been used for classification purposes. In this thesis, the Mahalanobis distance measure is utilized for fault detection, fault isolation, degradation identification, and prognostics. For fault detection, a probabilistic approach is developed to establish threshold Mahalanobis distance, such that presence of a fault in a product can be identified and the product can be classified as healthy or unhealthy. A technique is presented to construct a control chart for Mahalanobis distance for detecting trends and biasness in system health or performance. An error function is defined to establish fault-specific threshold Mahalanobis distance. A fault isolation approach is developed to isolate faults by identifying parameters that are associated with that fault. This approach utilizes the design-of-experiment concept for calculating residual Mahalanobis distance for each parameter (i.e., the contribution of each parameter to a system's health determination). An expected contribution range for each parameter estimated from the distribution of residual Mahalanobis distance is used to isolate the parameters that are responsible for a system's anomalous behavior. A methodology to detect degradation in a system's health using a health indicator is developed. The health indicator is defined as the weighted sum of a histogram bin's fractional contribution. The histogram's optimal bin width is determined from the number of data points in a moving window. This moving window approach is utilized for progressive estimation of the health indicator over time. The health indicator is compared with a threshold value defined from the system's healthy data to indicate the system's health or performance degradation. A symbolic time series-based health assessment approach is developed. Prognostic measures are defined for detecting anomalies in a product and predicting a product's time and probability of approaching a faulty condition. These measures are computed from a hidden Markov model developed from the symbolic representation of product dynamics. The symbolic representation of a product's dynamics is obtained by representing a Mahalanobis distance time series in symbolic form. Case studies were performed to demonstrate the capability of the proposed methodology for real time health monitoring. Notebook computers were exposed to a set of environmental conditions representative of the extremes of their life cycle profiles. The performance parameters were monitored in situ during the experiments, and the resulting data were used as a training dataset. The dataset was also used to identify specific parameter behavior, estimate correlation among parameters, and extract features for defining a healthy baseline. Field-returned computer data and data corresponding to artificially injected faults in computers were used as test data

Clustering of Redundant Parameters for Fault Isolation with Gaussian Residuals

International audienceFault detection and isolation in stochastic systems is typically model-based, meaning fault-indicating residuals are generated based on measurements and compared to equivalent mathematical system models. The residuals often exhibit Gaussian properties or can be transformed into a standard Gaussian framework by means of the asymptotic local approach. The e_ectiveness of the fault diagnosis depends on the model quality, but an increasing number of model parameters also leads to redundancies which, in turn, can distort the fault isolation. This occurs, for example, in structural engineering, where residuals are generated by comparing structural vibrations to the output of digital twins. This article proposes a framework to _nd the optimal parameter clusters for such problems. It explains how the optimal solution is a compromise, because with an increasing number of clusters, the fault isolation resolution increases, but the detectability in each cluster decreases, and the number of false alarms changes. To assess these factors during the clustering process, criteria for the minimum detectable change and the false-alarm susceptibility are introduced and evaluated in an optimization scheme

Change detection and isolation in mechanical system parameters based on perturbation analysis

International audienceThe monitoring of mechanical systems aims at detecting damages at an early stage, in general by using output-only vibration measurements under ambient excitation. In this paper, a method is proposed for the detection and isolation of small changes in the physical parameters of a linear mechanical system. Based on a recent work where the multiplicative change detection problem is transformed to an additive one by means of perturbation analysis, changes in the eigenvalues and eigenvectors of the mechanical system are considered in the first step. In a second step, these changes are related to physical parameters of the mechanical system. Finally, another transformation further simplifies the detection and isolation problem into the framework of a linear regression subject to additive white Gaussian noises, leading to a numerically efficient solution of the considered problems. A numerical example of a simulated mechanical structure is reported for damage detection and localization

Statistical model-based optimization for damage extent quantification

International audienceDamage localization and quantification constitute different aspects of structural damage diagnosis, which are of particular interest in the Structural Health Monitoring field. Therein, a classical solution is model updating, where the parameters of a finite element model of the possibly damaged structure are optimized to match with the corresponding parameters estimated from its vibration responses. To avoid ill-posedness of the classical finite element updating problem, damage localization and quantification can be treated separately. First, the information about regions or clusters of possibly damaged elements in the structure is obtained by a damage localization method. Then, this information is used to reduce the number of parameters for damage quantification. A framework combining the advantages of methods for damage localization with model optimization is proposed in this paper. For the exploration of the clustered physical model space, a stochastic optimization algorithm is coupled with the evaluation of the statistical properties of the MAC and frequency differences between the numerical model and the estimated modes for an adequate treatment of the data-based uncertainties. Herein, the development of the statistical properties of the MAC estimate is an important step, which is based on a recent quadratic framework that is adapted to the context of the inner product between an estimated mode shape and a numerical mode shape. This statistical information is used in the formulation of the objective function as well as in a data-driven stopping criterion for the optimization search. The proposed framework is validated on numerical simulations of a beam model, where damage at multiple locations is quantified up to the clustering precision

Variations on the Kalman filter for enhanced performance monitoring of gas turbine engines

Since their advent in the 1940's, gas turbines have been used in a wide range of land, sea and air applications due to their high power density and reliability. In today's competitive market, gas turbine operators need to optimise the dispatch availability (it i.e., minimise operational issues such as aborted take-offs or in-flight shutdowns) as well as the direct operating costs of their assets. Besides improvements in the design and manufacture processes, proactive maintenance practices, based on the actual condition of the turbine, enable the achievement of these objectives. Generating dependable information about the health condition of the gas turbine is a requisite for a successful implementation of condition-based maintenance. In this thesis, we focus on the assessment of the performance of the thermodynamic cycle, also known as Module Performance Analysis. The purpose of module performance analysis is to detect, isolate and quantify changes in engine module performance, described by so-called health parameters, on the basis of measurements collected along the gas-path of the engine. Generally, the health parameters are correcting factors on the efficiency and the flow capacity of the modules while the measurements are inter-component temperatures, pressures, shaft speeds and fuel flow. Module performance analysis can be cast as an estimation problem that is characterised by a number of difficulties such as non-linearity of the system and noise and bias in the measurements. Moreover the number of health parameters usually exceeds the number of gas-path measurements, making the estimation problem underdetermined. This thesis starts with a survey of the state-of-the-art in module performance analysis. We then propose enhancements to a monitoring tool for steady-state data developed by Dr. P. Dewallef during his thesis at the Turbomachinery Group. Specifically, the improvements concern the fault detection and isolation tasks, respectively handled by a hypothesis testing and a sparse estimator. As a complement, we define metrics for the selection and analysis of sensor--health parameter suites based on the Information Theory. In a second step, we investigate the feasibility and the benefit that could be expected from the processing of data collected during transient operation of a gas turbine. We also discuss the impact of modelling errors on the estimation procedure and propose a solution that makes the health assessment robust with respect to modelling errors. The theoretical developments are evaluated on the basis of simulated test-cases through a series of metrics that gauge the estimation accuracy and the performance of the fault detection and isolation modules

An Integrated Fuzzy Inference Based Monitoring, Diagnostic, and Prognostic System

To date the majority of the research related to the development and application of monitoring, diagnostic, and prognostic systems has been exclusive in the sense that only one of the three areas is the focus of the work. While previous research progresses each of the respective fields, the end result is a variable grab bag of techniques that address each problem independently. Also, the new field of prognostics is lacking in the sense that few methods have been proposed that produce estimates of the remaining useful life (RUL) of a device or can be realistically applied to real-world systems. This work addresses both problems by developing the nonparametric fuzzy inference system (NFIS) which is adapted for monitoring, diagnosis, and prognosis and then proposing the path classification and estimation (PACE) model that can be used to predict the RUL of a device that does or does not have a well defined failure threshold. To test and evaluate the proposed methods, they were applied to detect, diagnose, and prognose faults and failures in the hydraulic steering system of a deep oil exploration drill. The monitoring system implementing an NFIS predictor and sequential probability ratio test (SPRT) detector produced comparable detection rates to a monitoring system implementing an autoassociative kernel regression (AAKR) predictor and SPRT detector, specifically 80% vs. 85% for the NFIS and AAKR monitor respectively. It was also found that the NFIS monitor produced fewer false alarms. Next, the monitoring system outputs were used to generate symptom patterns for k-nearest neighbor (kNN) and NFIS classifiers that were trained to diagnose different fault classes. The NFIS diagnoser was shown to significantly outperform the kNN diagnoser, with overall accuracies of 96% vs. 89% respectively. Finally, the PACE implementing the NFIS was used to predict the RUL for different failure modes. The errors of the RUL estimates produced by the PACE-NFIS prognosers ranged from 1.2-11.4 hours with 95% confidence intervals (CI) from 0.67-32.02 hours, which are significantly better than the population based prognoser estimates with errors of ~45 hours and 95% CIs of ~162 hours