David W. Allen

Structural damage classification using extreme value statistics

The first and most important objective of any damage identification algorithm is to ascertain with confidence if damage is present or not. Many methods have been proposed for damage detection based on ideas of novelty detection founded in pattern recognition and multivariate statistics. The philosophy of novelty detection is simple. Features are first extracted from a baseline system to be monitored, and subsequent data are then compared to see if the new features are outliers, which significantly depart from the rest of population. In damage diagnosis problems, the assumption is that outliers are generated from a damaged condition of the monitored system. This damage classification necessitates the establishment of a decision boundary. Choosing this threshold value is often based on the assumption that the parent distribution of data is Gaussian in nature. While the problem of novelty detection focuses attention on the outlier or extreme values of the data, i.e., those points in the tails of the distribution, the threshold selection using the normality assumption weights the central population of data. Therefore, this normality assumption might impose potentially misleading behavior on damage classification, and is likely to lead the damage diagnosis astray. In this paper, extreme value statistics is integrated with the novelty detection to specifically model the tails of the distribution of interest. Finally, the proposed technique is demonstrated on simulated numerical data and time series data measured from an eight degree-of-freedom spring-mass system.

Statistical Damage Classification Using Sequential Probability Ratio Tests

The primary objective of damage detection is to ascertain with confidence if damage is present or not within a structure of interest. In this study, a damage classification problem is cast in the context of the statistical pattern recognition paradigm. First, a time prediction model, called an autoregressive and autoregressive with exogenous inputs (AR-ARX) model, is fit to a vibration signal measured during a normal operating condition of the structure. When a new time signal is recorded from an unknown state of the system, the prediction errors are computed for the new data set using the time prediction model. When the structure undergoes structural degradation, it is expected that the prediction errors will increase for the damage case. Based on this premise, a damage classifier is constructed using a sequential hypothesis testing technique called the sequential probability ratio test (SPRT). The SPRT is one form of parametric statistical inference tests, and the adoption of the SPRT to damage detection problems can improve the early identification of conditions that could lead to performance degradation and safety concerns. The sequential test assumes a probability distribution of the sample data sets, and a Gaussian distribution of the sample data sets is often used. This assumption, however, might impose potentially misleading behavior on the extreme values of the data, i.e. those points in the tails of the distribution. As the problem of damage detection specifically focuses attention on the tails, the assumption of normality is likely to lead the analysis astray. To overcome this difficulty, the performance of the SPRT is improved by integrating extreme values statistics, which specifically models behavior in the tails of the distribution of interest into the SPRT.

Coupling sensing hardware with data interrogation software for structural health monitoring

The process of implementing a damage detection strategy for aerospace, civil and mechanical engineering infrastructure is referred to as structural health monitoring (SHM). The authors approach is to address the SHM problem in the context of a statistical pattern recognition paradigm. In this paradigm, the process can be broken down into four parts: (1) Operational Evaluation, (2) Data Acquisition and Cleansing, (3) Feature Extraction and Data Compression, and (4) Statistical Model Development for Feature Discrimination. These processes must be implemented through hardware or software and, in general, some combination of these two approaches will be used. This paper will discuss each portion of the SHM process with particular emphasis on the coupling of a general purpose data interrogation software package for structural health monitoring with a modular wireless sensing and processing platform. More specifically, this paper will address the need to take an integrated hardware/software approach to developing SHM solutions.

Damage detection in mechanical structures using extreme value statistics

The first and most important objective of any damage identification algorithms is to ascertain with confidence if damage is present or not. Many methods have been proposed for damage detection based on ideas of novelty detection founded in pattern recognition and multivariate statistics. The philosophy of novelty detection is simple. Features are first extracted from a baseline system to be monitored, and subsequent data are then compared to see if the new features are outliers, which significantly depart from the rest of population. In damage diagnosis problems, the assumption is that outliers are generated from a damaged condition of the monitored system. This damage classification necessitates the establishment of a decision boundary. Choosing this threshold value is often based on the assumption that the parent distribution of data is Gaussian in nature. While the problem of novelty detection focuses attention on the outlier or extreme values of the data i.e. those points in the tails of the distribution, the threshold selection using the normality assumption weighs the central population of data. Therefore, this normality assumption might impose potentially misleading behavior on damage classification, and is likely to lead the damage diagnosis astray. In this paper, extreme value statistics is integrated with the novelty detection to specifically model the tails of the distribution of interest. Finally, the proposed technique is demonstrated on simulated numerical data and time series data measured from an eight degree-of-freedom spring-mass system.

Utilizing the sequential probability ratio test for building joint monitoring

In this application of the statistical pattern recognition paradigm, a prediction model of a chosen feature is developed from the time domain response of a baseline structure. After the model is developed, subsequent feature sets are tested against the model to determine if a change in the feature has occurred. In the proposed statistical inference for damage identification there are two basic hypotheses; (1) the model can predict the feature, in which case the structure is undamaged or (2) the model can not accurately predict the feature, suggesting that the structure is damaged. The Sequential Probability Ratio Test (SPRT) develops a statistical method that quickly arrives at a decision between these two hypotheses and is applicable to continuous monitoring. In the original formulation of the SPRT algorithm, the feature is assumed to be Gaussian and thresholds are set accordingly. It is likely, however, that the feature used for damage identification is sensitive to the tails of the distribution and that the tails may not necessarily be governed by Gaussian characteristics. By modeling the tails using the technique of Extreme Value Statistics, the hypothesis decision thresholds for the SPRT algorithm may be set avoiding the normality assumption. The SPRT algorithm is utilized to decide if the test structure is undamaged or damaged and which joint is exhibiting the change.

A software tool for graphically assembling damage identification algorithms

At Los Alamos National Laboratory (LANL), various algorithms for structural health monitoring problems have been explored in the last 5 to 6 years. The original DIAMOND (Damage Identification And MOdal aNalysis of Data) software was developed as a package of modal analysis tools with some frequency domain damage identification algorithms included. Since the conception of DIAMOND, the Structural Health Monitoring (SHM) paradigm at LANL has been cast in the framework of statistical pattern recognition, promoting data driven damage detection approaches. To reflect this shift and to allow user-friendly analyses of data, a new piece of software, DIAMOND II is under development. The Graphical User Interface (GUI) of the DIAMOND II software is based on the idea of GLASS (Graphical Linking and Assembly of Syntax Structure) technology, which is currently being implemented at LANL. GLASS is a Java based GUI that allows drag and drop construction of algorithms from various categories of existing functions. In the platform of the underlying GLASS technology, DIAMOND II is simply a module specifically targeting damage identification applications. Users can assemble various routines, building their own algorithms or benchmark testing different damage identification approaches without writing a single line of code.

STATISTICAL DAMAGE CLASSIFICATION USING SEQUENTIAL PROBABILITY RATIO TESTS.

The primary objective of damage detection is to ascertain with confidence if damage is present or not within a structure of interest. In this study, a damage classification problem is cast in the context of the statistical pattern recognition paradigm. First, a time prediction model, called an autoregressive and autoregressive with exogenous inputs (AR-ARX) model, is fit to a vibration signal measured during a normal operating condition of the structure. When a new time signal is recorded from an unknown state of the system, the prediction errors are computed for the new data set using the time prediction model. When the structure undergoes structural degradation, it is expected that the prediction errors will increase for the damage case. Based on this premise, a damage classifier is constructed using a sequential hypothesis testing technique called the sequential probability ratio test (SPRT). The SPRT is one form of parametric statistical inference tests, and the adoption of the SPRT to damage detection problems can improve the early identification of conditions that could lead to performance degradation and safety concerns. The sequential test assumes a probability distribution of the sample data sets, and a Gaussian distribution of the sample data sets is often used. This assumption, however, might impose potentially misleading behavior on the extreme values of the data, i.e. those points in the tails of the distribution. As the problem of damage detection specifically focuses attention on the tails, the assumption of normality is likely to lead the analysis astray. To overcome this difficulty, the performance of the SPRT is improved by integrating extreme values statistics, which specifically models behavior in the tails of the distribution of interest into the SPRT.