Parameters Of Degradation Model Research Articles

Data and model synergy-driven rolling bearings remaining useful life prediction approach based on deep neural network and Wiener process

Abstract Various Remaining Useful Life (RUL) prediction methods, encompassing model-based, data-driven, and hybrid methods, have been developed and successfully applied to prognostics and health management for diverse rolling bearing. Hybrid methods that integrate the advantages of model-based and data-driven approaches have garnered significant attention. However, the effective integration of the two methods to address the randomness in rolling bearing full lifecycle processes remains a significant challenge. To overcome the challenge, this paper proposes a data and model synergy-driven RUL prediction framework that includes two data and model synergy approaches. Firstly, a convolutional stacked bidirectional long and short-term memory network with temporal attention mechanism is established to construct health index. The RUL prediction is achieved based on HI and polynomial model. Secondly, a three-phase prediction model based on the Wiener process is established by considering the evolution law of different degradation phases. Then, two synergy methods are designed. Strategy 1: HI is adopted as the observation value for online updating of physics degradation model parameters under Bayesian framework, and the RUL prediction results are obtained from the physics degradation model. Strategy 2: The RUL prediction results from the data-driven and physics-based model are weighted linearly combined to improve the overall prediction accuracy. The effectiveness of the proposed model is verified using two bearing full lifecycle datasets. The results indicate that the proposed approach can accommodate both short-term and long-term RUL predictions, outperforming state-of-the-art single models.

A remaining useful life prediction method of aluminum electrolytic capacitor with adaptive degradation model selection

The degradation process of aluminum electrolytic capacitors(AECs) usually exhibits characteristics such as non-linearity and multi-stage. These degradation features lead to the difficulty to accurately predict the remaining useful life(RUL) of the whole degradation process of AECs. To address this, by dividing the capacitor degradation process into two stages, a two-stage RUL prediction method for AECs considering multiple degradation models is proposed in this paper.In the offline parameter estimation phase, the initial degradation model parameters of two stages are estimated using two-step maximum likelihood estimation combined with particle swarm optimization(PSO) algorithm. In the dynamic parameter updating phase, a sequential Bayesian method is used to update the model parameters. To select the optimal degradation model, an evaluation method based on historical RUL similarity is proposed to calculate the fitness of each model. Finally, the effectiveness of the method is verified on NASA’s accelerated degradation data set and several widely used methods are used for comparison. The experimental results show that the proposed method has higher accuracy, which proves the superiority of the method.

A remaining useful life prediction algorithm incorporating real-time and integrated model for hidden actuator degradation

This paper proposed a prediction algorithm for the degraded actuator taking into account the impact of estimation error of hidden index in the closed-loop system. To this end, a unified prediction framework is established to evaluate the hidden degradation information and recursively update the degradation model parameters simultaneously. The advantage is that the prediction framework can comprehensively compensate the estimation error of hidden degradation index caused by system uncertainty. To jointly estimate the degradation information in avoidance of the impact of system uncertainty, a modified adaptive Kalman filter is designed, and the proof of stability is provided. With the priori estimate from the filter, the degradation model parameters are updated by the inverse filtering probability based on Bayes’ theorem. It is followed by the computation of the remaining useful life (RUL) prediction utilizing aforementioned hidden degradation information and the latest degradation model. The effectiveness of the proposed RUL prediction algorithm is demonstrated by the degraded actuator in the continuous casting process.

Degradation Modelling of and Optimising the Timing of Replacements for Batch Vacuum Pans

Replacing a pan involves the expenditure of significant capital for a sugar mill. Replacing a pan too late may result in excessive downtime, maintenance costs, and risk of catastrophic failure. On the other hand, replacing a pan too early will lead to wasting residual life and an unnecessary allocation of capital funds that may have been spent better elsewhere in the mill. This paper reports on the development of a replacement policy for batch vacuum pan components based on a stochastic model of degradation. Degradation data, principally wall-thickness measurements, were collected from the vacuum pans of an Australian sugar factory and used to develop component degradation models. Unlike the conventional approach of using a line of best fit to identify the end of life of the pan, the methods adopted account for the uncertainties due to seasonal operating conditions and inherent uncertainty in the degradation model parameters. The quantification of the uncertainty in identifying the end of life of a vacuum pan has shown that there is significant risk of a pan failing earlier than the straight-line prediction. Employing this quantification of the risk, a component replacement plan was developed by optimising the replacement of each component individually and subsequently optimising the replacement plan for the entire pan. This strategy is demonstrated using a case study with and without parametric uncertainty to evaluate its impact on maintenance optimisation. Including parametric uncertainty leads to the determination of greater risk earlier, proposing the replacement of components earlier than when parameters are considered as ‘known’. It is, therefore, important to consider parametric uncertainty in the planning of pan component replacements to better manage risk.

A recursive inference method based on invertible neural network for multi-level model updating using video monitoring data

Likelihood-free inference methods have been widely adopted, but they face significant challenges in updating multi-level computational models that have hierarchically embedded sub-models. This difficulty arises from the lack of direct observations of the quantities of interest of the sub-models. In addition, recent advancements in sensing and image processing technologies allow for the collection of a substantial amount of video monitoring data through non-contact sensing techniques. The implicit and very complicated relationship between the uncertain model parameters and video monitoring data adds an additional layer of challenge to the updating of multi-level models. This paper overcomes these challenges by proposing an innovative Recursive Inference method based on Invertible Neural Networks (RINN) for multi-level models. The proposed RINN framework first compresses the high-dimensional video monitoring data into low-dimension latent-space data using a convolutional autoencoder. Using synthetic video monitoring data generated by considering various uncertainty sources in the computational simulation models, a likelihood-free inference model is then trained through a conditional invertible neural network (cINN) and a summary neural network. This model efficiently approximates the posterior distributions of uncertain model parameters without evaluating the computationally intractable likelihood function, given any latent-space data obtained from the autoencoder. To facilitate continuous monitoring and model updating over an extended monitoring period, this paper further proposes a recursive model updating strategy that integrates the cINN-based likelihood-free inference with the particle filtering method. The updating of a degradation model of a miter gate application is employed as an example throughout this paper to explain and demonstrate the efficacy of the proposed RINN framework. The results of the case study show that the RINN is able to effectively reduce uncertainty in the degradation model parameters through strain video monitoring data of a miter gate, and thereby increase the confidence in the remaining useful life (RUL) estimation using the updated degradation model.

A Hybrid Health Monitoring Approach for Aircraft Flight Control Systems With System-Level Degradation

This paper proposes a novel hybrid health monitoring approach to monitor the system-level degradation of aircraft flight control systems (FCSs). The idea derives from observing the nonlinear hysteresis phenomenon in FCS. First, a health FCS model is developed to implement the nonlinear degradation signal extraction of FCS by building an adaptive-network-based fuzzy inference system, a data-driven method. Subsequently, the Jump Markov autoregressive exogenous (JMARX) system with time delays is adopted to establish the FCS system-level degradation model. An expectation maximum-convex optimization algorithm is innovatively proposed to identify the model parameters. After that, three health indicators associated with the degradation model parameters are utilized for FCS system-level health monitoring. Finally, a practical flight experiment is conducted by a civil aircraft. The obtained experimental data is used to validate the effectiveness of the proposed FCS monitoring approach. The model of the time-delay JMARX system gets good modeling evaluation results on mean absolute error, standard deviation, etc. Besides, each of the three health indicators shows a clear FCS degradation tendency, which indicates that the proposed method successfully extracts the degradation information and monitors the health states of FCS. This approach is potential for practical and effective engineering applications in the aviation industry.

The Remaining Useful Life Prediction Method of a Hydraulic Pump under Unknown Degradation Model with Limited Data.

This study proposes a remaining useful life (RUL) prediction method using limited degradation data with an unknown degradation model for hydraulic pumps with long service lives and no failure data in turbine control systems. The volumetric efficiency is calculated based on real-time monitoring signal data, and it is used as the degradation indicator. The optimal degradation curve is established using the degradation trajectory model, and the optimal probability distribution model is selected via the K-S test. The above process was repeated to optimize the degradation model and update parameters in different performance degradation stages of the hydraulic pump, providing quantification of the prediction uncertainty and enabling accurate online prediction of the hydraulic pump's RUL. Finally, an RUL test bench for hydraulic pumps is built for verification. The results show that the proposed method is convenient, efficient, and has low model complexity. The method enables online accurate prediction of the RUL of hydraulic pumps using only limited degradation data, with a prediction accuracy of over 85%, which meets practical application requirements.

Fusing Conflicting Multisource Imprecise Information for Reliability Assessment of Multistate Systems: A Two-Stage Optimization Approach

Expert knowledge is an important information source for system reliability assessment, especially when historical data are limited. However, when elicited, expert knowledge is often imprecise with large uncertainty. Moreover, as experts usually own different expertise and knowledge, the elicited knowledge from different experts might be conflicting. In this article, a two-stage optimization model is put forth to fuse the imprecise and conflicting information from multiple sources to assess reliability of multistate systems. The degradation of the components in the multistate system is modeled via imprecise Markov models. Then, in the first-stage optimization, upper and lower bounds of the degradation model parameters are determined by minimizing the conflict between the prediction of the model and the multisource imprecise information elicited from experts. A particle swarm optimization algorithm is tailored to solve the computational problems brought by the presence of high-dimensional decision variables and resolve the optimization problem. The second-stage optimization is, then, conducted to identify the upper and lower bounds of the system reliability function given that the degradation model parameters are constrained in the bounds obtained from the first-stage optimization. A numerical example, along with a radar display and control system, is used to demonstrate the effectiveness and applicability of the proposed method.

A health state prediction method of traction converter IGBT based on optimized particle filter

Insulated gate bipolar transistor (IGBT), as the most critical and vulnerable power electronic component in the field of rail transportation, its reliability has become a research hotspot in recent years. To improve the safe and reliable operation of rail transportation and to reduce the maintenance cost by rationalizing system maintenance, it is critical to monitor the health of the traction converter IGBTs. This paper first reviews the failure mechanism of the IGBT, then analyzes the health state characterization parameters of the IGBT by the accelerated aging test, selects thermal resistance as the health state characterization parameter of the IGBT, and establishes the degradation model of the IGBT. On this basis, a health state prediction method of IGBT based on the genetic algorithm unscented particle filter (GA-UPF) is proposed. This method uses an unscented Kalman filter to generate important proposal density distribution for each particle, estimates, and updates the parameters of the degradation model, alleviates the particle degradation problem, and uses a genetic algorithm to solve the particle impoverishment problem introduced by the traditional resampling method, which improves the particle diversity and prediction accuracy. Mahalanobis distance is used to monitor the abnormal state of the thermal resistance. After the abnormal occurs, the value of the thermal resistance is predicted according to the degradation model and updated parameters. The degradation trend of the thermal resistance is predicted to reflect the health state of the IGBT. Experiments on IGBT degradation data show that the proposed method can provide higher health state prediction accuracy than the traditional particle filter method.

A deep neural network and Bayesian method based framework for all-terminal network reliability estimation considering degradation

Most research on network reliability has considered links to have a binary state, i.e., functioning or failed, whereas nodes are considered flawless. In a more realistic scenario, both links and nodes might fail or may exhibit degradation behavior before failing. This study develops a framework to estimate the all-terminal reliability of a network that considers the degradation and probability of failure of all nodes and links in a network. Unlike previous works on network reliability that considered constant reliability for links, this paper considers the reliability of links, nodes, and the network as functions of time. In the proposed framework, the Bayesian methods (BM) are employed to estimate the reliability of links and nodes as functions of time considering degradation data. Due to the complexity of the all-terminal reliability problem, and to get fast estimations of the reliability of a network, an integration of Monte Carlo (MC) and Deep Neural Networks (DNNs) is proposed. The proposed MC algorithm can estimate the network reliability for given nodes and links reliability values. To speed up the calculation, a DNN model is integrated into the framework, thus enabling accurate and fast estimation of network reliability for given link and node reliability values. The DNN accuracy, based on the RMSE (0.01460), outperforms previous traditional artificial neural network (ANN) approaches. Moreover, the DNN model takes 0.3 ms to compute the reliability for any given links and reliability values. The proposed framework can provide not only reliability point estimates but also credible intervals. Finally, we take advantage of Bayesian methods to integrate new data into the framework as they become available. The framework uses the new data to refine and further update the degradation model parameters and the prediction of the reliability of links, nodes, and the network. The proposed methodology has been demonstrated with the real-world network topology Ion (125 nodes, 150 links) with actual degradation data.

A condition-based prognostic approach for age- and state-dependent partially observable nonlinear degrading system

To deal with age- and state-dependent degradation, unit-to-unit variability and partially observable or hidden degradation in remaining useful life prediction jointly, this paper proposes a condition-based prognostic approach for age- and state-dependent partially observable nonlinear degrading system. The dynamics and nonlinearity of the system degradation process are described by the age- and state-dependent nonlinear diffusion process. The nonlinear relationship between observations and the hidden degradation state is characterized by a state space model. To derive the distribution of the remaining useful life, we apply the extended Kalman filtering and expectation-maximization algorithm to adaptively estimate the degradation states and the unknown model parameters. Based on the estimated degradation states and model parameters, we derive the approximately analytical distribution of remaining useful life in the concept of the first hitting time. Furthermore, the distribution of remaining useful life can be updated according to the newly available data, thereby realizing real-time remaining useful life estimation. An illustrative example is given to explain the application of the proposed approach in the specific age- and state-dependent nonlinear degradation model. Finally, a numerical example and a case study for bearing degradation data are presented to verify the accuracy and effectiveness of the proposed model.

Mechanism equivalence analysis for accelerated degradation tests based on tweedie exponential dispersion process

ABSTRACT Mechanism equivalence analysis, focusing on the underlying quantitative relationship between degradation model parameters under different stress levels when the accelerated failure mechanism remains unchanged, has been developed and adopted widely in accelerated degradation tests (ADTs) over recent years. For a specific degradation process, the mechanism equivalence conditions can be derived based on the acceleration factor invariant principle and further utilized to test whether the accelerated failure mechanism remains unchanged or not under different stress levels. In this paper, a unified form of the mechanism equivalence conditions for commonly-used stochastic process models is derived based on Tweedie exponential dispersion process. The unified form can cover the conditions of Wiener, Gamma and inverse Gaussian processes, etc. Based on this, a complete procedure for mechanism equivalence test of ADT is proposed through the joint application of normality test and parameter hypothesis tests. In this way, the availability of the ADT data can be distinguished before using them for lifetime prediction of products. In addition, the effects caused by degradation model mis-specification and ADT data misuse are further analyzed from the perspective of relative error. A simulation example and two real-world case studies are used to demonstrate the effectiveness of the proposed methods.

Reliability-Box of Systems Under Model Parameter Uncertainty Based on Evidential Variable and Evidential Network

Advanced engineering systems possess a large number of components with complicated failure dependencies. To accurately assess the system reliability, the degradation models of components should be known in advance and the model parameters should be accurately estimated via a large quantity of historical time-to-failure data. In real-world situations, due to limited data, lack of knowledge, and vague judgments from experts, components’ degradation model parameters are, however, inevitably encountered with epistemic uncertainty and oftentimes quantified as evidential variables. In this article, upper and lower bounds of system reliability, termed as reliability-box, are estimated when components’ degradation model parameters are elicited from experts and quantified by evidential variables. In the first place, the constrained optimization model is leveraged to assess the reliability-box of each component by giving the evidential variable of the component’s degradation model parameters. Next, based on the system structure, the evidential network of the system is constructed to propagate the epistemic uncertainty from the component level to the system level. Therefore, the focal elements of the evidential variable of system reliability, i.e., the system reliability bounds, can be assessed via the belief and plausibility functions to the mass function of the leaf node of the evidential network. The effectiveness of the proposed methods is demonstrated by a rolling system in the chip cutting detection module.

Model correction and updating of a stochastic degradation model for failure prognostics of miter gates

Understanding the degradation of the quoin block is vital for failure prognostics in miter gates. Due to the complicated degradation mechanism, degradation models based on simplifications and assumptions cannot accurately describe the damage evolution. It is observed that small errors in a simplified degradation model can lead to a large discrepancy in the remaining useful life estimation attributed to error accumulation over time. Aiming to address this issue in failure prognostics, this paper presents a dynamic model correction framework for a simplified degradation model using strain measurements. In the proposed framework, a polynomial chaos expansion (PCE) model is employed to compensate the missing physics in a simplified stochastic degradation model. A maximum likelihood estimation method is developed to estimate the uncertain parameters of the simplified physics-based degradation model along with the unknown PCE model parameters using strain measurements as the observables. The updated damage degradation model is then applied to failure prognostics of a miter gate. Results of a case study show that the proposed approach can effectively improve the accuracy of failure prognostics in miter gates.

Data-model interactive prognosis for multi-sensor monitored stochastic degrading devices

With advances in sensing and monitoring techniques, real time multi-sensor monitoring data of stochastic degrading devices has become the reality. How to effectively fuse these multi-sensor monitoring data to first construct the composite health index (CHI) and then model its degradation evolving process has become the emerging topic in the field of the remaining useful life (RUL) prediction. However, existing works treat the CHI construction and degradation modeling for prognostics under multi-sensor data as the disjoint problems rather than both though they are closely related in nature. To address this issue, this paper presents a novel data-model interactive RUL prediction method for multi-sensor monitored stochastic degrading devices. In the proposed method, based on the CHI extracted from multi-sensor historical data and the associated lifetime prediction via stochastic degradation modeling, an optimization objective function synthesizing the mean squared error between the predicted life and the actual life as well as the variance of the predicted life is constructed. As such, a closed-loop feedback mechanism is established for the CHI constructing and stochastic degradation modeling. Based on this feedback mechanism, the fusion coefficients for multi-sensor data and the failure threshold of the associated CHI are reversely optimized to realize the collaborative interaction between the CHI constructing and stochastic degradation modeling. To do so, the goal of making the constructed CHI automatically match the adopted stochastic degradation model can be achieved naturally. To make the degradation model accurately reflect the current reality of the in-service device, a sequential Bayesian method is proposed to update the degradation model parameters. Based on the updated model, the RUL distribution can be derived under the concept of the first passage time to achieve the prognosis. Finally, through multi-sensor data of aircraft gas turbine engines, we justify the necessity of applying the proposed method in prognosis and show its advantages in the improvements of the signal quality and prognosis accuracy.

Optimal warranty policy design for deteriorating products with random failure threshold

With the rapid development of technologies and increasing availability of degradation data, the design of appropriate warranty policy for products subject to performance deterioration has hitherto received more attention in boosting profits and improving the competition of enterprises. In most existing works, a product is considered to have failed and trigger a warranty service when the degradation level exceeds the constant failure threshold. However, the stochastic nature of failure threshold exists in many applications. In this study, firstly, two truncated distributions are employed to model the random failure threshold. Then we propose three types of warranty policies-free replacement, full refund and partial refund, that take into account the random failure threshold based on the degradation model. Under the first policy, the manufacturer’s total expected profit is maximized to determine the optimal price and warranty period, besides these, the prescribed maintenance times can also be obtained under the other two policies. We further compare these warranty policies under random failure threshold characterized by different distributions. Finally, a numerical example is presented along with sensitivity analysis to illustrate and compare the proposed warranty policies, showing that the parameters of degradation model and random failure threshold can lead to different expected profits.

Improving Durability of PEMFC by Reducing the Impact of Operating Conditions on Electrode Degradation

Meeting long-term durability targets with low Pt loading (<0.125 mg/cm2) still poses a significant challenge before wide-scale commercialization of PEM fuel cells is achieved. In our previous work with H2/N2 voltage cycling with single factor studies with the state-of-art (SOA) membrane electrode assembly (MEA), we have reported that electrode degradation rates significantly vary at different operating conditions [1,2]. To study the effect of operating conditions in depth and identify the interactions between the test factors, we have utilized a design of experiments approach. A 20-run design with three levels and temperature, relative humidity, upper potential limit, and upper potential hold time as the test factors was created. Tests were conducted in H2/N2 environment for 60,000 cycles. In-situ electrochemical diagnostics such as electrochemical surface area (ECSA), mass activity (MA), and specific activity (SA) along with polarization curves were measured at beginning-of-life (BOL) and after 30k and 60k voltage cycles. A platinum oxide coverage-based degradation model [3] was developed to predict ECSA loss. In the model, the damage factor is estimated as a function of the oxide current and oxide coverage which are dependent on temperature, relative humidity, and cell potential. Data from 20-run design is fit to the degradation model and fitting parameters are obtained. Simulations are run with drive cycles with varying operating conditions to calculate the damage factor and subsequently ECSA loss for each drive cycle is calculated. Based on the model results, benign operating conditions are identified which enable achieving 5000-hr durability. Figure 1 shows the results of 1000 hours of operation of the MEA with baseline drive cycle and drive cycle with benign operating conditions which were selected from results of the degradation model simulations. The results show that life-limiting electrode degradation rates can be significantly reduced by optimal selection of PEMFC operating conditions.References Kumaraguru, 2019 Annual Progress Report, https://www.hydrogen.energy.gov/pdfs/progress19/fc_fc156_kumaraguru_2019.pdf Ahluwalia, Rajesh K., et al. "Achieving 5,000-h and 8,000-h Low-PGM Electrode Durability on Automotive Drive Cycles." Journal of The Electrochemical Society (2021).Arisetty, Srikanth, et al. "Modeling platinum oxide growth of PEMFC cathode catalysts." ECS Transactions 69.17 (2015): 273. Figure 1

Time-dependent reliability assessment of aging structures considering stochastic resistance degradation process

Reasonable assessment of structural resistance degradation and reliability is the premise of formulating targeted maintenance strategy of aging structures. In this paper, a Gamma-based stochastic resistance degradation model is developed by incorporating the spatial degradation into a non-stationary degradation process. Then, based on the hazard-function-based reliability analysis method, a novel reliability assessment approach of aging structures is proposed considering stochastic degradation process of resistance. In addition, a simple case analysis of concrete bridge is used to illustrate the application of the proposed method. The case analysis results show that the resistance degradation presents great discontinuities in time and large spatial variability in the middle and later service period of structures. After 50 years of service, the resistance degradation coefficient considering the effect of spatial degradation process is 13.8% lower than that without consideration in this case. Parametric analyses show that an increase of the shape and scale parameters of mean resistance degradation model will significantly increase the cumulative failure probability of structures. This conclusion is also applicable to the non-stationary vehicle load effect model of case bridge. Additionally, ignoring the spatial variability of resistance degradation and the non-stationary nature of the vehicle load effect will overestimate the reliability of aging structures.

Nonlinear Doubly Wiener Constant-Stress Accelerated Degradation Model Based on Uncertainties and Acceleration Factor Constant Principle

Although Wiener process models with the consideration of uncertainties, which are nonlinearity, random effects, and measurement errors, have been developed for lifetime prediction in the accelerated degradation test (ADT), they fail to describe the real degradation process because these models assume that the drift parameter correlates with the applied stress, while the diffusion parameter is constant. This paper put forward a nonlinear doubly Wiener constant-stress accelerated degradation model, where both diffusion and drift parameters were compatible with the applied stress according to the acceleration factor constant principle. When degradation data were available, we obtained the unknown parameters by applying a maximum likelihood estimation (MLE) algorithm in the constant-stress ADT (CSADT) model taking uncertainties into account. In addition, the proposed model’s effectiveness was validated through an illustrative example, and an application to the traveling wave tube (TWT) was carried out to demonstrate the superiority of our model in practical applications.

Remaining useful life prediction of lithium battery based on capacity regeneration point detection

Lithium batteries have been widely used in various electronic devices, and the accurate prediction of its remaining useful life (RUL) can prevent the occurrence of sudden equipment failure. Battery capacity is a commonly used indicator to represent the health status of lithium batteries. However, the capacity regeneration is usually unavoidable due to the impact of battery “rest time” between two cycles, which leads to inaccurate prediction of the RUL. To solve this problem, this paper combines the particle filter (PF) and Mann-Whitney U test (PF-U) to detect the capacity regeneration point (CRP). In this light, the autoregressive (AR) model and PF algorithm are adopted for RUL prediction. The predicted capacity through AR model is used to update the degradation model parameters of PF algorithm, and the validation of our approach is verified through the lithium battery dataset of NASA. In comparison, our proposed method exhibits the highest precision and provides a platform to detect the points with capacity regeneration, and further reduce the RUL prediction error.