Application of deterministic resampling particle filter to fatigue prognosis

The method based on a particle filter for a fatigue crack growth prognosis has proved to be a powerful and effective tool for developing prognostics and health management (PHM) technology. However, the widely used basic particle filter have the unavoidable particle impoverishment problem, which will make particles unable to approximate the true posterior probability density function of the system state and lead to a prognosis result with a large error. This paper proposes a fatigue crack growth prognosis method based on a deterministic resampling particle filter. The active structural health monitoring based on the Lamb wave is used for on-line crack length monitoring with piezoelectric transducers. With the on-line crack measurement, the crack state and crack growth model parameters are estimated for a fatigue crack growth prognosis. In addition, the deterministic resampling procedure is employed to overcome the particle impoverishment problem. The result shows the proposed crack growth prognosis method based on deterministic resampling particle filter can provide more satisfactory results than the basic particle filter

A BAYESIAN FRAMEWORK FOR STRUCTURAL HEALTH MANAGEMENT USING ACOUSTIC EMISSION MONITORING AND PERIODIC INSPECTIONS

Many aerospace and civil infrastructures currently in service are at or beyond their design service-life limit. The ability to assess and predict their state of damage is critical in ensuring the structural integrity of such aging structures. The empirical models used for crack growth prediction suffer from various uncertainties; these models are often based on idealized theories and simplistic assumptions and may fail to capture the underlying physics of the complex failure mechanisms. The other source of uncertainty is the scarcity of relevant material-level test data required to estimate the parameters of empirical models. To avoid in-service failure, the structures must be inspected routinely to ensure no damage of significant size is present in the structure. Currently, the structure has to be taken off line and partly disassembled to expose the critical areas for nondestructive inspection (NDI). This is an expensive and time-consuming process. Structural health monitoring (SHM) is an emerging research area for online assessment of structural integrity using appropriate NDI technology. SHM could have a major contribution to the structural diagnosis and prognosis. Empirical models, offline periodic inspections and online SHM systems can each provide an independent assessment of the structural integrity; in this research, a novel structural health management framework is proposed in which the Bayesian knowledge fusion technique is used to combine the information from all sources mentioned above in a systematic manner. This work focuses on monitoring fatigue crack growth in metallic structures using acoustic emission (AE) technology. Fatigue crack growth tests with real-time acoustic emissions monitoring are conducted on CT specimens made of 7075 aluminum. Proper filtration of the resulting AE signals reveals a log-linear relationship between fracture parameters (da/dN and ΔK ) and select AE features; a flexible statistical model is developed to describe the relationship between these parameters. Bayesian regression technique is used to estimate the model parameters using experimental data. The model is then used to calculate two important quantities that can be used for structural health management: (a) an AE-based instantaneous damage severity index, and (b) an AE-based estimate of the crack size distribution at a given point in time, assuming a known initial crack size distribution. Finally, recursive Bayesian estimation is used for online integration of the structural health assessment information obtained from various sources mentioned above. The evidence used in Bayesian updating can be observed crack sizes and/or crack growth rate observations. The outcome of this approach is updated crack size distribution as well as updated model parameters. The model with updated parameters is then used for prognosis given an assumed future usage profile

A Fast Monte Carlo Method for Model-Based Prognostics Based on Stochastic Calculus

This work proposes a fast Monte Carlo method to solve differential equations utilized in model-based prognostics. The methodology is derived from the theory of stochastic calculus, and the goal of such a method is to speed up the estimation of the probability density functions describing the independent variable evolution over time. In the prognostic scenarios presented in this paper, the stochastic differential equations describe variables directly or indirectly related to the degradation of a monitored system. The method allows the estimation of the probability density functions by solving the deterministic equation and approximating the stochastic integrals using samples of the model noise. By so doing, the prognostic problem is solved without the Monte Carlo simulation based on Euler's forward method, which is typically the most time consuming task of the prediction stage. Three different prognostic scenarios are presented as proof of concept: (i) life prediction of electrolytic capacitors, (ii) remaining time to discharge of Lithium-ion batteries, and (iii) prognostic of cracked structures under fatigue loading. The paper shows how the method produces probability density functions that are statistically indistinguishable from the distributions estimated with Euler's forward Monte Carlo simulation. However, the proposed solution is orders of magnitude faster when computing the time-to-failure distribution of the monitored system. The approach may enable complex real-time prognostics and health management solutions with limited computing power

Prognostics and Health Management of Industrial Equipment

ISBN13: 9781466620957Prognostics and health management (PHM) is a field of research and application which aims at making use of past, present and future information on the environmental, operational and usage conditions of an equipment in order to detect its degradation, diagnose its faults, predict and proactively manage its failures. The present paper reviews the state of knowledge on the methods for PHM, placing these in context with the different information and data which may be available for performing the task and identifying the current challenges and open issues which must be addressed for achieving reliable deployment in practice. The focus is predominantly on the prognostic part of PHM, which addresses the prediction of equipment failure occurrence and associated residual useful life (RUL)

Interacting multiple-models, state augmented Particle Filtering for fault diagnostics

International audienceParticle Filtering (PF) is a model-based, filtering technique, which has drawn the attention of the Prognostic and Health Management (PHM) community due to its applicability to nonlinear models with non-additive and non-Gaussian noise. When multiple physical models can describe the evolution of the degradation of a component, the PF approach can be based on Multiple Swarms (MS) of particles, each one evolving according to a different model, from which to select the most accurate a posteriori distribution. However, MS are highly computational demanding due to the large number of particles to simulate. In this work, to tackle the problem we have developed a PF approach based on the introduction of an augmented discrete state identifying the physical model describing the component evolution, which allows to detect the occurrence of abnormal conditions and identifying the degradation mechanism causing it. A crack growth degradation problem has been considered to prove the effectiveness of the proposed method in the detection of the crack initiation and the identification of the occurring degradation mechanism. The comparison of the obtained results with that of a literature MS method and of an empirical statistical test has shown that the proposed method provides both an early detection of the crack initiation, and an accurate and early identification of the degradation mechanism. A reduction of the computational cost is also achieved.

Model-based prognosis of fatigue crack growth under variable amplitude loading

International audienceIn this paper, a model-based prognosis method using a particle filter that takes model uncertainty, measurement uncertainty and future loading uncertainty into account is proposed. A nonlinear analytical model of the degradation that depends on loading parameters is established, and then a particle filter is used to estimate and forecast these unknown inputs at the same time as the degradation state. Moreover, adding to this joint input-state estimation, a two-sided CUSUM algorithm is implemented to detect load variations. This would help the prognosis module to adapt to a change in the degradation state evolution, in order to correct the remaining useful life prediction. Real data from fatigue tests on fiber-reinforced metal matrix composite materials are used to demonstrate the efficiency of the proposed methodology for crack growth prognosis

Particle filter-based damage prognosis using online feature fusion and selection

Damage prognosis generally resorts to damage quantification functions and evolution models to quantify the current damage state and to predict the future states and the remaining useful life (RUL). The former typically consists of a function describing the relationship between the damage state and a statistical feature extracted from the measured signals, thus the prognostic performance will strongly depend on the selection of a proper feature. Given the best feature may vary for different specimens or even at each time instant for the same specimen during damage progression, such selection is a challenging task but has received little investigation so far. In this context, this paper proposes a particle filter-based damage prognosis framework, which involves an online feature fusion and selection scheme. A prognostic model is considered for each feature, with a multivariate process equation, formulated using both a damage degradation function and a bias parameter, and a measurement equation linking the damage state and that feature considering a data-driven model and the bias. One PF is used to estimate the damage state, its evolution parameters, and the bias for each model. Then, at each step, the feature with the smallest estimated bias is selected as the best feature providing the most likely state vectors and is used to select the most likely samples of the damage state and growth parameters for predicting the RUL and for calculating the prior at the next step. The proposed prognostic framework is demonstrated by an experimental study, where an aluminum lug structure subject to fatigue crack growth is monitored by a Lamb wave measurement system

Development of a Prognostic Method for the Production of Undeclared Enriched Uranium

As global demand for nuclear energy and threats to nuclear security increase, the need for verification of the peaceful application of nuclear materials and technology also rises. In accordance with the Nuclear Nonproliferation Treaty, the International Atomic Energy Agency is tasked with verification of the declared enrichment activities of member states. Due to the increased cost of inspection and verification of a globally growing nuclear energy industry, remote process monitoring has been proposed as part of a next-generation, information-driven safeguards program. To further enhance this safeguards approach, it is proposed that process monitoring data may be used to not only verify the past but to anticipate the future via prognostic analysis. While prognostic methods exist for health monitoring of physical processes, the literature is absent of methods to predict the outcome of decision-based events, such as the production of undeclared enriched uranium. This dissertation introduces a method to predict the time at which a significant quantity of unaccounted material is expected to be diverted during an enrichment process. This method utilizes a particle filter to model the data and provide a Type III (degradation-based) prognostic estimate of time to diversion of a significant quantity. Measurement noise for the particle filter is estimated using historical data and may be updated with Bayesian estimates from the analyzed data. Dynamic noise estimates are updated based on observed changes in process data. The reliability of the prognostic model for a given range of data is validated via information complexity scores and goodness of fit statistics. The developed prognostic method is tested using data produced from the Oak Ridge Mock Feed and Withdrawal Facility, a 1:100 scale test platform for developing gas centrifuge remote monitoring techniques. Four case studies are considered: no diversion, slow diversion, fast diversion, and intermittent diversion. All intervals of diversion and non-diversion were correctly identified and significant quantity diversion time was accurately estimated. A diversion of 0.8 kg over 85 minutes was detected after 10 minutes and predicted to be 84 minutes and 10 seconds after 46 minutes and 40 seconds with an uncertainty of 2 minutes and 52 seconds

Damage Precursor Based Structural Health Monitoring and Prognostic Framework Using Dynamic Bayesian Network

Structural health monitoring (SHM), as an essential tool to ensure the health integrity of aging structures, mostly focus on monitoring conventional observable damage markers such as fatigue crack size. However, degradation starts and progressively evolves at microstructural levels much earlier than detection of such indicators. This dissertation goes beyond classical approaches and presents a new SHM framework based on evolution of Damage Precursors, when conventional direct damage indicator, such as crack, is unobservable, inaccessible or difficult to measure. Damage precursor is defined in this research as “any detectable variation in material/ physical properties of the component that can be used to infer the evolution of the hidden/ inaccessible/ unmeasurable damage during the degradation”. Accordingly, the degradation process is to be expressed based on progression of damage precursor through time and the damage state assessment would be updated by incorporating multiple different evidences. Therefore, this research proposes a systematic integration approach through Dynamic Bayesian Network (DBN) to include all the evidences and their relationships. The implementation of augmented particle filtering as a stochastic inference method inside DBN enables estimating both model parameters and damage states simultaneously in light of various evidences. Incorporating different sources of information in DBN entails advance techniques to identify and formulate the possible interaction between potentially non-homogenous variables. This research uses the Support Vector Regression (SVR) in order to define generally unknown nonparametric and nonlinear correlation between some of the variables in the DBN structure. Additionally, the particle filtering algorithm is studied more fundamentally in this research and a modified approach called “fully adaptive particle filtering” is proposed with the idea of online updating not only the state process model but also the measurement model. This new approach improves the ability of SHM in real-time diagnostics and prognostics. The framework is successfully applied to damage estimation and prediction in two real-world case studies of 1) crack initiation in a metallic alloy under fatigue and, 2) damage estimation and prognostics in composite materials under fatigue. The proposed framework is intended to be general and comprehensive such that it can be implemented in different applications