(53b) An Adaptive Framework for State-Based Prediction of Rotating Equipment Failures

Motivation and Problem Statement

Rising global demand is motivating the manufacturing industry to implement maintenance strategies that minimize operational downtime. The field of prognostics and health management (PHM) research seeks to develop methods and frameworks that minimize downtime by avoiding both equipment failure and unnecessary preventative maintenance [1]. A key aspect of PHM research is the development of predictive maintenance (PdM) models, which detect ongoing equipment degradation and predict system failures. Because rotating equipment (such as pumps, turbines, and compressors) is widely used in process manufacturing operations, much of the recent PdM research has focused on this class of equipment.

Two limitations of existing PdM models have hindered their efficacy when applied to industrial rotating equipment. The first is a reliance on instantaneous (snapshot) analysis, which involves using only the most recent measurements from a system to detect degradation and predict failure. PdM models that take this approach are often unable to recognize the early stages of degradation in rotating equipment, which can be characterized by gradual trends in machine signals. An alternative to snapshot analysis is state-based analysis, where a PdM model uses histories of recent system measurements to classify the current state of equipment health and generate predictions about future health states. The second limitation of existing PdM models is treating system health models as static entities. While the shape and direction of degradation generally remains consistent across different machines, the value of healthy signal baselines and the speed of degradation can vary significantly, even throughout the life of a single machine.

PdM models that do not detect and adapt to variances in degradation behavior can generate inaccurate modeling outputs and quickly become obsolete.

This work addresses these limitations by proposing an adaptive framework for

predicting failures in industrial rotating equipment with state-based PdM models. The work here is an extension of the methods developed in [2] and [3], which use static, state-based models to make repair quality assessments, and the adaptive modeling framework proposed in [4], which is specific to rolling element bearing degradation. The proposed framework relies on equipment and reliability experts to specify a set of degradation modes to which a system is susceptible, along with templates for models describing the general behavior of machine signals as a function of time. Soliciting this input increases the resources necessary to implement the framework but allows it to be applied across a wide range of systems and degradation modes and results in modeling outputs that can easily be interpreted by end-users.

Approach

1. Modeling Architecture

This framework relies on equipment and reliability experts to define a set of degradation modes to which a machine is susceptible, and a predictive model class for each degradation mode. As in object-oriented programming, predictive model classes act as a template for creating model instances that describe the degradation behavior of one or more features derived from machine signals. Predictive model classes consist of a set of fixed parameters, with values that remain constant across different machines and failure events, as well as a set of variable parameters, with values that are allowed to vary across machines and failure events. Additionally, a predictive model class must include a method that maps the duration of degradation to a probability density function describing the value of one or more system features. For example, a predictive model class may describe a linear increase in a vibration feature () over time () using the function , where the slope parameter () is fixed, the variance of a Gaussian random variable () is fixed, and the offset parameter () is variable. Finally, a predictive model class must include a method to re-estimate the local parameters of a model based on a training dataset.

During online monitoring, a system health statechart describes the degradation modes that a system may experience. These statecharts consist of a state and a set of states that are each associated with a predictive model, instantiated from a pre-existing model class, describing the expected degradation behavior in that state. The state is associated with a model instance that describes steady-state behavior in machine features, which is referred to as a stationary model. Once a system's potential degradation modes and associated predictive model classes have been defined, the adaptive methodology described in the following section can be implemented to perform state estimation and failure prediction.

1. Adaptive Failure Prediction Methodology

This methodology defines four computational stages that are used to monitor the health of a system during operation and adapt existing modeling resources when system measurements deviate from expected behavior. The first stage of the methodology, routine monitoring, involves two processes: state estimation and anomaly detection, that are repeated whenever new measurements are collected. The goal of state estimation is to determine the recent state history of a system based on the current structure of the system health statechart. This is implemented by adapting the Viterbi algorithm, a common method for estimating the state histories of systems represented by hidden Markov models (HMMs) [5], to be compatible with the time-varying feature distributions provided by predictive models. State estimation results provide estimates about the current degradation mode of a system based on recent measurement histories along with an estimate of the degradation onset time, defined as the time at which a system transitions from the state to the most-likely state. Well-established Monte Carlo methods can then be used to estimate a time-to-failure distribution for the system based on the predictive model associated with the most-likely degradation mode [6].

Anomaly detection seeks to identify when system measurements start to deviate from the behavior described by the state's stationary model or any of the predictive models included in a system's health statechart. To achieve this, the system health statechart is again considered to be an HMM () and a Markov chain Monte Carlo sampling method is used to generate samples from the observation probability distribution of the HMM, . The probability of the most recent observation is then compared with these samples to determine whether the observation is anomalous or expected. When several consecutive anomalous observations are detected, the subsequent stages of the methodology provide mechanisms to adapt the predictive signal models and system health statechart in response.

The second stage of the methodology, model localization, involves re-estimating each model's variable parameters based on recent system measurements. Anomaly detection is then repeated with the updated models and, if the anomalies are not resolved, an automated statechart update stage is triggered. This process provides a mechanism to modify the degradation stages included in a system's health statechart. The PCA similarity factor [7] between recent measurements and the entire set of available model classes is computed to quantify whether any models capture the general direction of degradation. If any model classes demonstrate a sufficiently high similarity factor, the current statechart is augmented with a state for each of these model classes, and anomaly detection is repeated. In the case that anomalies are still not resolved, records of recent measurements and the results of the PCA similarity analysis are reported to system experts to inform the creation of a new model class to describe this unexpected degradation behavior as part of the final stage, SME-informed statechart update.

Concluding Remarks

The framework developed here enables state-based failure prediction with degradation models defined by experts and provides a methodology for adapting these models when anomalous degradation behavior emerges. These capabilities provide transparent modeling results to inform maintenance decisions and facilitates the deployment of robust PdM strategies in industry. Case studies in [3] and [4] demonstrate the value of an adaptive, state-based modeling approach, and the full presentation for this project contains a case study implementing the framework described here.

References

[1] J. Lee, F. Wu, W. Zhao, M. Ghaffari, L. Liao, and D. Siegel, “Prognostics and health management design for rotary machinery systems reviews, methodology, and applications,” Me-

chanical Systems and Signal Processing, vol. 42, no. 1-2, pp. 314–334, 2014.

[2] M. Toothman, K. Barton, B. Braun, S. J. Bury, M. Dessauer, K. Henderson, J. Moyne, and R. Wright, “Trend-based assessment of industrial rotating equipment health,” in 2020 Virtual AIChE Annual Meeting. AIChE, 2020.

[3] M. Toothman, B. Braun, S. J. Bury, M. Dessauer, K. Henderson, D. M. T. Ray Wright, J. Moyne, and K. Barton, “Trend-based repair quality assessment for industrial rotating

equipment,” IEEE Control Systems Letters, vol. 5, no. 5, pp. 1675–1680, 2020.

[4] Y. Zhao, M. Toothman, J. Moyne, and K. Barton, “An adaptive modeling framework for bearing failure prediction,” Electronics, vol. 11, no. 2, p. 257, 2022.

[5] L. R. Rabiner, “A tutorial on hidden markov models and selected applications in speech recognition,” Proceedings of the IEEE, vol. 77, no. 2, pp. 257–286, February 1989.

[6] C. J. Lu and W. O. Meeker, “Using degradation measures to estimate a time-to-failure distribution,” Technometrics, vol. 35, no. 2, pp. 161–174, 1993.

[7] W. Krzanowski, “Between-groups comparison of principal components,” Journal of the American Statistical Association, vol. 74, no. 367, pp. 703–707, 1979.