Parameters Of Degradation Model Research Articles

Mechanical performance degradation modelling and prognosis method of high‐voltage circuit breakers considering censored data

AbstractDue to the untimely deployment of sensors and the early retirement of high‐voltage circuit breakers, life‐cycle data is missing, leading to an inability to accurately predict the mechanical performance degradation trend. A new modelling and prediction method of mechanical performance degradation of high‐voltage circuit breakers considering censored data was proposed. Firstly, multiple imputation by chained equations was used to impute the missing values in the dataset of circuit breaker closing time, creating an interpolated dataset. Secondly, the Nadaraya–Watson kernel regression method was employed to smoothly estimate the interpolated dataset and eliminate data measurement errors. Then, the functional principal component analysis method was utilized to extract the common degradation trend component and deviation component to construct the degradation model. Finally, Bayesian inference was applied to dynamically update the degradation model parameters and predict the degradation trend of the high‐voltage circuit breaker. The results showed that the proposed method was capable of achieving better interpolation accuracy under the condition of different closing time censored data of high‐voltage circuit breakers. Moreover, as the degradation progressed, the dynamic prediction effect improved. The research can be used to provide an effective decision‐making basis for the operation and maintenance strategy of high‐voltage circuit breakers.

Finite Element and Density Functional Theory Modeling Effectively Predict Pitting Degradation of Hydroxyapatite-Coated Pure Magnesium.

The emergence of degradable orthopedic implants for fracture fixation may abrogate the need for implant removal surgery and minimize pain associated with permanent implants. Magnesium (Mg) and its alloys are being explored as a biomaterial for degradable implants due to mechanical properties similar to those of bone. Previous invitro studies have determined the degradation rate of pure Mg to be relatively fast when compared to bone regeneration. Hydroxyapatite (HA), the mineral component of bone, may serve as a surface coating on Mg-based implants to effectively slow and control the degradation rate. The objective of this work was to develop and implement a finite element (FE) model that utilizes a damage evolution law for pitting corrosion to predict the degradation of pure Mg (non-coated) and HA-coated pure Mg (coated) materials simulated in physiological conditions. Finite element analysis (FEA) was performed on a cylindrical Mg specimen (25.4 mm diameter, 8 mm height) through Abaqus/Standard software to incrementally monitor the damage value of each Mg element and subsequently delete fully-degraded elements from the simulation. A Fortran user-material (UMAT) subroutine assigned each element a pitting parameter, controlling the rate of degradation throughout the simulation and providing necessary inputs of elastic material properties and degradation model parameters for pure Mg and HA into Abaqus. The simulations allowed for the visualization of both pure Mg and HA-coated pure Mg degradation over a 120-day period, displaying expected degradation trends such as lower corrosion rates for HA-coated Mg and degradation propagating from the edges inward. Simulation results were calibrated with our prior results from a 30-day experimental degradation study via direct comparison with mass loss over time. Additionally, lower length scale, density functional theory (DFT) simulations were performed to provide physical meaning for the model pitting parameter. The FE simulation was extended to model resin-enclosed pure Mg and HA-coated pure Mg degradation, where only the top surface of the specimen was exposed to the corrosion surface, for investigating changes in Mg surface roughness (height) over time. The impacts of this work include the establishment of a computational model of pure Mg and HA-coated pure Mg degradation calibrated using invitro degradation data to advance the use of Mg-based biomaterials, and more broadly, to predict degradation rates of next-generation orthopedic implants.

A hybrid prognostic framework: Stochastic degradation process with adaptive trajectory learning to transfer historical health knowledge

Remaining useful life (RUL) prediction is crucial to supporting intelligent maintenance and health management of safety–critical products. Although advanced data-driven approaches such as deep neural networks are effective in processing high-dimensional non-linear health features, their application to field RUL prediction confronts with two challenges: (a) adaptivity of the lifetime parameter learning process is often restricted, and (b) prediction of multi-source uncertainties is almost analytically intractable. This paper addresses such challenges by devising a tractable, global adaptive model-data-interaction prognostic framework, where a non-linear stochastic degradation model governed by self-adaptive trajectory pattern is constructed to transfer historical health knowledge. In particular, a joint parameter learning framework is established under the structure of a multi-branch Bayesian network, such that to simultaneously learn: (a) degradation model parameters, and (b) network hyper-parameters. Additionally, the key control parameters of the degradation process are updated adaptively leveraging multi-dimensional sequential Bayesian learning. An efficient interpolation algorithm is further proposed to alleviate computation burden of RUL distributions. Case studies conducted on both turbofan engines degradation data and field train bearing vibration data demonstrate the superior model performance compared to existing methodologies.

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 merits of model-based and data-driven methods have garnered significant attention. However, the effective integration of the two methods to address the randomness in rolling bearing full life cycle 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 strategies. First, a convolutional stacked bidirectional long short-term memory network with temporal attention mechanism is established to construct Health Index (HI). The RUL prediction is achieved based on HI and polynomial model. Second, a three-phase degradation model based on the Wiener process is developed by considering the evolutionary pattern of different degradation phases. Then, two synergy strategies 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 life cycle 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.

Reliability analysis of piston pump based on gamma process with random effects

This paper proposes a reliability analysis method for piston pumps based on degradation data and considering individual differences. Based on the application of the Gamma process to build a model of degradation data, the random-effects model was introduced to the model of the Gamma process for the individual differences that exist in the degradation process. On this basis, the basic framework of reliability analysis based on Bayesian approach is studied in this paper, and also the estimation of degradation model parameters is investigated, which contains the establishment of a performance degradation analysis model using Bayesian approach, the estimation of model parameters, the acquisition of posterior distribution and the analysis of reliability of piston pumps.The proposed reliability analysis method is verified by carrying out reliability analysis work on the piston pumps.

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.