Kai Goebel

Prognostics Methods for Battery Health Monitoring Using a Bayesian Framework

This paper explores how the remaining useful life (RUL) can be assessed for complex systems whose internal state variables are either inaccessible to sensors or hard to measure under operational conditions. Consequently, inference and estimation techniques need to be applied on indirect measurements, anticipated operational conditions, and historical data for which a Bayesian statistical approach is suitable. Models of electrochemical processes in the form of equivalent electric circuit parameters were combined with statistical models of state transitions, aging processes, and measurement fidelity in a formal framework. Relevance vector machines (RVMs) and several different particle filters (PFs) are examined for remaining life prediction and for providing uncertainty bounds. Results are shown on battery data.

Metrics for evaluating performance of prognostic techniques

Prognostics is an emerging concept in condition based maintenance (CBM) of critical systems. Along with developing the fundamentals of being able to confidently predict Remaining Useful Life (RUL), the technology calls for fielded applications as it inches towards maturation. This requires a stringent performance evaluation so that the significance of the concept can be fully exploited. Currently, prognostics concepts lack standard definitions and suffer from ambiguous and inconsistent interpretations. This lack of standards is in part due to the varied end-user requirements for different applications, time scales, available information, domain dynamics, etc. to name a few issues. Instead, the research community has used a variety of metrics based largely on convenience with respect to their respective requirements. Very little attention has been focused on establishing a common ground to compare different efforts. This paper surveys the metrics that are already used for prognostics in a variety of domains including medicine, nuclear, automotive, aerospace, and electronics. It also considers other domains that involve prediction-related tasks, such as weather and finance. Differences and similarities between these domains and health maintenance have been analyzed to help understand what performance evaluation methods may or may not be borrowed. Further, these metrics have been categorized in several ways that may be useful in deciding upon a suitable subset for a specific application. Some important prognostic concepts have been defined using a notational framework that enables interpretation of different metrics coherently. Last, but not the least, a list of metrics has been suggested to assess critical aspects of RUL predictions before they are fielded in real applications.

Comparison of prognostic algorithms for estimating remaining useful life of batteries

The estimation of remaining useful life (RUL) of a faulty component is at the centre of system prognostics and health management. It gives operators a potent tool in decision making by quantifying how much time is left until functionality is lost. RUL prediction needs to contend with multiple sources of errors, like modelling inconsistencies, system noise and degraded sensor fidelity, which leads to unsatisfactory performance from classical techniques like autoregressive integrated moving average (ARIMA) and extended Kalman filtering (EKF). The Bayesian theory of uncertainty management provides a way to contain these problems. The relevance vector machine (RVM), the Bayesian treatment of the well known support vector machine (SVM), a kernel-based regression/classification technique, is used for model development. This model is incorporated into a particle filter (PF) framework, where statistical estimates of noise and anticipated operational conditions are used to provide estimates of RUL in the form of a probability density function (pdf). We present here a comparative study of the above-mentioned approaches on experimental data collected from Li-ion batteries. Batteries were chosen as an example of a complex system whose internal state variables are either inaccessible to sensors or hard to measure under operational conditions. In addition, battery performance is strongly influenced by ambient environmental and load conditions.

Damage propagation modeling for aircraft engine run-to-failure simulation

This paper describes how damage propagation can be modeled within the modules of aircraft gas turbine engines. To that end, response surfaces of all sensors are generated via a thermo-dynamical simulation model for the engine as a function of variations of flow and efficiency of the modules of interest. An exponential rate of change for flow and efficiency loss was imposed for each data set, starting at a randomly chosen initial deterioration set point. The rate of change of the flow and efficiency denotes an otherwise unspecified fault with increasingly worsening effect. The rates of change of the faults were constrained to an upper threshold but were otherwise chosen randomly. Damage propagation was allowed to continue until a failure criterion was reached. A health index was defined as the minimum of several superimposed operational margins at any given time instant and the failure criterion is reached when health index reaches zero. Output of the model was the time series (cycles) of sensed measurements typically available from aircraft gas turbine engines. The data generated were used as challenge data for the prognostics and health management (PHM) data competition at PHMpsila08.

Uncertainty Management for Diagnostics and Prognostics of Batteries using Bayesian Techniques

Uncertainty management has always been the key hurdle faced by diagnostics and prognostics algorithms. A Bayesian treatment of this problem provides an elegant and theoretically sound approach to the modern Condition-Based Maintenance (CBM)/Prognostic Health Management (PHM) paradigm. The application of the Bayesian techniques to regression and classification in the form of Relevance Vector Machine (RVM), and to state estimation as in Particle Filters (PF), provides a powerful tool to integrate the diagnosis and prognosis of battery health. The RVM, which is a Bayesian treatment of the Support Vector Machine (SVM), is used for model identification, while the PF framework uses the learnt model, statistical estimates of noise and anticipated operational conditions to provide estimates of remaining useful life (RUL) in the form of a probability density function (PDF). This type of prognostics generates a significant value addition to the management of any operation involving electrical systems.

Hybrid soft computing systems: industrial and commercial applications

Soft computing (SC) is an association of computing methodologies that includes as its principal members fuzzy logic, neurocomputing, evolutionary computing and probabilistic computing. We present a collection of methods and tools that can be used to perform diagnostics, estimation, and control. These tools are a great match for real-world applications that are characterized by imprecise, uncertain data and incomplete domain knowledge. We outline the advantages of applying SC techniques and in particular the synergy derived from the use of hybrid SC systems. We illustrate some combinations of hybrid SC systems, such as fuzzy logic controllers (FLCs) tuned by neural networks (NNs) and evolutionary computing (EC), NNs tuned by EC or FLCs, and EC controlled by FLCs. We discuss three successful real-world examples of SC applications to industrial equipment diagnostics, freight train control, and residential property valuation.

Precursor Parameter Identification for Insulated Gate Bipolar Transistor (IGBT) Prognostics

Precursor parameters have been identified to enable development of a prognostic approach for insulated gate bipolar transistors (IGBT). The IGBT were subjected to thermal overstress tests using a transistor test board until device latch-up. The collector-emitter current, transistor case temperature, transient and steady state gate voltages, and transient and steady state collector-emitter voltages were monitored in-situ during the test. Pre- and post-aging characterization tests were performed on the IGBT. The aged parts were observed to have shifts in capacitance-voltage (C-V) measurements as a result of trapped charge in the gate oxide. The collector-emitter ON voltage VCE(ON) showed a reduction with aging. The reduction in the VCE(ON) was found to be correlated to die attach degradation, as observed by scanning acoustic microscopy (SAM) analysis. The collector-emitter voltage, and transistor turn-off time were observed to be precursor parameters to latch-up. The monitoring of these precursor parameters will enable the development of a prognostic methodology for IGBT failure. The prognostic methodology will involve trending precursor data, and using physics of failure models for prediction of the remaining useful life of these devices.

An integrated approach to battery health monitoring using bayesian regression and state estimation

The application of the Bayesian theory of managing uncertainty and complexity to regression and classification in the form of relevance vector machine (RVM), and to state estimation via particle filters (PF), proves to be a powerful tool to integrate the diagnosis and prognosis of battery health. Accurate estimates of the state-of-charge (SOC), the state-of-health (SOH) and state-of-life (SOL) for batteries provide a significant value addition to the management of any operation involving electrical systems. This is especially true for aerospace systems, where unanticipated battery performance may lead to catastrophic failures. Batteries, composed of multiple electrochemical cells, are complex systems whose internal state variables are either inaccessible to sensors or hard to measure under operational conditions. In addition, battery performance is strongly influenced by ambient environmental and load conditions. Consequently, inference and estimation techniques need to be applied on indirect measurements, anticipated operational conditions and historical data, for which a Bayesian statistical approach is suitable. Accurate models of electro-chemical processes in the form of equivalent electric circuit parameters need to be combined with statistical models of state transitions, aging processes and measurement fidelity, need to be combined in a formal framework to make the approach viable. The RVM, which is a Bayesian treatment of the support vector machine (SVM), is used for diagnosis as well as for model development. The PF framework uses this model and statistical estimates of the noise in the system and anticipated operational conditions to provide estimates of SOC, SOH and SOL. Validation of this approach on experimental data from Li-ion batteries is presented.

Advances in uncertainty representation and management for particle filtering applied to prognostics

Particle filters (PF) have been established as the de facto state of the art in failure prognosis. They combine advantages of the rigors of Bayesian estimation to nonlinear prediction while also providing uncertainty estimates with a given solution. Within the context of particle filters, this paper introduces several novel methods for uncertainty representations and uncertainty management. The prediction uncertainty is modeled via a rescaled Epanechnikov kernel and is assisted with resampling techniques and regularization algorithms. Uncertainty management is accomplished through parametric adjustments in a feedback correction loop of the state model and its noise distributions. The correction loop provides the mechanism to incorporate information that can improve solution accuracy and reduce uncertainty bounds. In addition, this approach results in reduction in computational burden. The scheme is illustrated with real vibration feature data from a fatigue-driven fault in a critical aircraft component.

Model-Based Prognostics With Concurrent Damage Progression Processes

Model-based prognostics approaches rely on physics-based models that describe the behavior of systems and their components. These models must account for the several different damage processes occurring simultaneously within a component. Each of these damage and wear processes contributes to the overall component degradation. We develop a model-based prognostics methodology that consists of a joint state-parameter estimation problem, in which the state of a system along with parameters describing the damage progression are estimated, followed by a prediction problem, in which the joint state-parameter estimate is propagated forward in time to predict end of life and remaining useful life. The state-parameter estimate is computed using a particle filter and is represented as a probability distribution, allowing the prediction of end of life and remaining useful life within a probabilistic framework that supports uncertainty management. We also develop a novel variance control algorithm that maintains an uncertainty bound around the unknown parameters to limit the amount of estimation uncertainty and, consequently, reduce prediction uncertainty. We construct a detailed physics-based model of a centrifugal pump that includes damage progression models, to which we apply our model-based prognostics algorithm. We illustrate the operation of the prognostic solution with a number of simulation-based experiments and demonstrate the performance of the approach when multiple damage mechanisms are active.