Model Based Prognostic Techniques

Model-based prognostic schemes include those that employ a dynamic model of the process being predicted. These can include physics-based models, autoregressive moving-average (ARMA) techniques, Kalman/Particle filtering, and empirical-based methods.

In engineering, the development of a model has been used traditionally to understand component failure mode progression. The development of a Physics of Failure (PoF) or Physics based models (PbM), (the two names will be used interchangeably throughout this Thesis), that incorporates the ability to assess damage to a component, taking into account operating conditions and gives a cumulative damage assessment provides a basis to evaluate the distribution of RUL. The results from such model may be used as a basis for real-time failure prognostic predictions with specified confidence bounds. These confidence bounds may be the result of statistical representations of historical operational profiles.

The actual availability of physics of failure models is limited. A model that incorporates the ability to predict damage parameters with an acceptable confidence boundary over steady-state and transient loads, temperatures and other variables are still quite few. PoF models are implemented in three different ways (Sikorska et al., 2011); firstly, dynamic ordinary or partial differential equations that can be solved with approximation approaches (e.g. Lagrangian or Hamiltonian dynamics), secondly, state-space methods (systems of first order differential equations) and thirdly, simulation methods. One such model that has found prevalence in prognostic literature is the Paris Law for crack propagation (Zhao et al, 2013), (Zhao et al, 2015).

𝑑𝛼

𝑑𝑁= 𝐶0(∆𝐾)𝑛 (27)

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N = running cycles

𝐶0, 𝑛 = material dependant constants

ΔK = range of stress-intensity factor over one loading cycle

The crack growth process was simulated to yield normally distributed crack lengths, which were used within a Bayesian framework to update the parameters of the degradation model (e.g., Paris’ law). The degradation model was initially fed by the results of a stress analysis from a gear dynamic model or finite element model. The distributions of the uncertainty factors were updated via Bayesian Inference using the condition monitoring data (simulated crack lengths), and an estimation of the RUL based on the degradation model was provided.

In terms of electronics, (Kulkarni, Chetan S., et al., 2012) proposes first principles based modeling and prognostics approach for electrolytic capacitors. Electrolytic capacitors and MOSFETs are the two major components, which cause degradations and failures in DC-DC converters. The paper studies the effects of accelerated ageing due to thermal stress on sets of capacitors, with the focus on deriving first principles degradation models for thermal stress conditions. The degradation data forms the basis for developing the model based remaining life prediction algorithm. Finally the data is used to derive accurate models of capacitor degradation, and use them to predict performance changes in DC-DC converters.

(Fan,et al., 2011) looked at how to accurately predict the reliability of LED lighting. In this paper, after analyzing the materials and geometries for high-power white LED lighting at all levels, i.e., chip, package and system; Failure Mode Mechanisms and Effects Analysis (FMMEA) was used in the PoF-based PHM approach to identify and rank the potential failures emerging from the design process. The second step in this paper was to establish the appropriate PoF-based damage models for identified failure mechanisms that carry a high risk.

A PoF based prognostic method for power electronic modules was proposed by (Yin, C. Y., et al., 2008). This method allowed the reliability performance of power modules to be assessed in real time. A compact thermal model was firstly constructed to investigate the relationship between the power dissipation and the temperature in the power module. Such relationship can be used for fast calculation of junction temperature and the temperatures at each interface inside power modules. The predicted temperature profile was then analyzed using a rainflow counting method so

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that the number of thermal cycles with different temperature ranges can be calculated. A reduced order thermo-mechanical model was also constructed to enable a fast calculation of the accumulated plastic strain in the solder material under different loading conditions. The information of plastic strains was then used in the lifetime prediction model to predict the reliability of the solder interconnect under each regular loading condition.

Prognosis with physics-based models are best performed based on an operational profile prediction which must be developed using the steady-state and transient loads, temperatures, or other online measurements. Probabilistic critical-component models then can be ‘‘run into the future’’ by creating statistical simulations of future operating profiles from the statistics of past operational profiles or expected future operating profiles (Vachtsevanos, 2006). Unfortunately, physics of failure models are few and far between, as well as being for more complex processes very difficult and costly to develop. In this case, models are often estimated using system identification techniques, usually via a non-linear least square regression method with a forgetting factor (Ljung, 1999).

Model-based approaches to prognosis differ from feature-based approaches in that they can make RUL estimates in the absence of any measurable events, but when related diagnostic information is present, the model often can be calibrated based on this new information.

A fusion of the feature-based and model-based approaches provides full prognostic ability over the entire life of the component. While failure modes may be unique from component to component, this combined model-based and feature-based methodology can remain consistent across different types of critical components or LRUs.

(Baraldi et al., 2012) propose a prognostic method which predicts the RUL of a degrading system by means of an ensemble of empirical models. RUL predictions of the individual models are aggregated through a Kalman filter (KF)-based algorithm. The method is applied to the prediction of the RUL of turbine blades affected by a developing creep. The Kalman filter assumes that the system must be linear, and the process and measurement noise must be white Gaussian and independent, although non-linearity has been dealt with by the Extended Kalman filter (EFK) and Unscented (UFK).

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An Unscented Kalman Filter (UKF) approach is proposed for the purpose of damage tracking and remaining useful life (RUL) prediction of a Polymer electrolyte membrane fuel cells by (Zhang, Xian, and Pierluigi Pisu, 2012). A physics-based, prognostic- oriented catalyst degradation model is developed to characterize the fuel cell damage that establishes the relationship between the operating conditions and the degradation rate of the electro-chemical surface area.