Degradation Trajectory Research Articles

A Deep Feature Optimization Fusion Method for Extracting Bearing Degradation Features

Centrifugal pumps with bearings are widely used in nuclear power plants. A challenge in data-driven prognostic technologies for centrifugal pump bearings is to evaluate their degradation features, which can be combined into degradation trajectory; however, the massive data gathered continuously from condition monitoring systems has created challenges to extracting degradation features effectively. The traditional degradation feature extraction methods are highly reliant on prior knowledge and diagnostic expertise, have limited capacities for learning the complex relationships between the degradation features and the massive amounts of measurement data, and their feature design processes are not automated and require intensive human labor. Deep neural networks offer remarkable abilities to extract features from massive data, and they can be used to automatically extract highly abstracted features that correlate well with bearing degradation. Therefore, to extract centrifugal pump bearing degradation features from massive amounts of vibration data, this paper proposes a deep feature optimization fusion method. First, data from the vibration-frequency-domain are mapped to a nonlinear spatial domain using an enhanced autoencoder. Second, the neural nodes in the last hidden layer of the enhanced autoencoder are divided into several child modules. The minimum quantization errors of each child module are used as the candidate degradation features. Finally, the optimal degradation trajectory is obtained via a weighted fusion of the candidate degradation features. The optimal weighting coefficients are calculated using the grey wolf optimizer algorithm. In this paper, experiments were performed using the IEEE PHM2012 bearing prognostic data set and a centrifugal pump bearing condition-monitoring data set. The results demonstrate that the degradation trajectory obtained using the proposed method offers stronger predictive capabilities than do those obtained using other methods, thereby improving the accuracy of predictions of the bearings’ remaining useful life.

Estimating Remaining Useful Life for Degrading Systems with Large Fluctuations

Remaining useful life (RUL) prediction method based on degradation trajectory has been one of the most important parts in prognostics and health management (PHM). In the conventional model, the degradation data are usually used for degradation modeling directly. In engineering practice, the degradation of many systems presents a volatile situation, that is, fluctuation. In fact, the volatility of degradation data shows the stability of system, so it could be used to reflect the performance of system. As such, this paper proposes a new degradation model for RUL estimation based on the volatility of degradation data. Firstly the degradation data are decomposed into trend items and random items, which are defined as a stochastic process. Then the standard deviation of the stochastic process is defined as another performance variable because standard deviation reflects the system performance. Finally the Wiener process and the normal stochastic process are used to model the trend items and random items separately, and then the probability density function (PDF) of the RUL is obtained via a redefined failure threshold function that combines the trend items and the standard deviation of the random items. Two practical case studies demonstrate that, compared with traditional approaches, the proposed model can deal with the degradation data with many fluctuations better and can get a more reasonable result which is convenient for maintenance decision.

Connecting tropical river DOM and POM to the landscape with lignin

Tropical rivers account for two thirds of global fluxes of terrigenous organic matter to the oceans, yet because of their remote locations relative to most industrialized countries, they are poorly studied compared to temperate and even Arctic rivers. Further, most tropical river research has focused on large rivers like the Amazon or Congo, yet more than half of organic matter fluxes from tropical rivers comes from much smaller rivers. This study focuses on two such rivers in the Luquillo Experimental Forest of Puerto Rico, namely the Rio Mameyes and Rio Icacos, and uses time-series measurements of lignin biomarkers to put them in context with much bigger tropical rivers in the literature. Although lignin concentrations and carbon-normalized yields offer some distinction between mountainous vs. floodplain tropical river reaches, compositional differences appear to offer greater potential, including S:V vs. C:V plots that may capture the poorly-studied influence of palm trees, and (Ad:Al)s vs. (Ad:Al)v plots that may reflect differences in underlying mineralogy and degradation in soils. Even though dissolved and particulate lignin ultimately come from the same vegetation sources, comparison of dissolved and particulate lignin parameters within the two Puerto Rican rivers indicate that the pathways by which they end up in the same parcel of river water are largely decoupled. Across several particulate lignin studies in tropical rivers, mineral composition and concentration appears to exert a strong control on particulate lignin compositions and concentrations. Finally, the time-series nature of this study allows for new ways of analyzing dissolved lignin endmember compositions and degradation within the catchment. Plots of dissolved lignin parameters vs. lignin concentration reveal both the composition of “fresh” DOM that is likely mobilized from organic-rich soil surface layers along with the extent and trajectory of degradation of that signature that is possible within the lower mineral layers of the soil. Establishing connectivity between river chemistry and catchment sources and processes in this manner is the only way to realize the full potential of river chemistry as a diagnostic tool for changing sources and processes within the catchment.

Perspective approach in using anti-oxidation and anti-wear particles from oil to estimate residual technical life of a system

Abstract Indirect diagnostic measures have big potential for estimating a system condition. One of these are oil data. Since the oil is in direct contact with the observed system, oil data are of great importance and value. Usually the authors analyse its physio-chemical properties, or the concentration of selected wear particles. In our article, however, we take into account a completely novel attitude towards anti-oxidation and anti-wear particles (AOWP). Their great importance lies in the fact that the AOWP concentration depends on both an operation time and a calendar time. Due to the extensive oil field data the dependence on an operation time and a calendar time is available. The development of the AOWP particles concentration is modelled stochastically with the use of the Wiener process with drift, or generally with a diffusion process. The aim is to set the trajectory of oil or engine degradation, and set the probability of an engine soft failure. In order to compare our results obtained by using the diffusion process of Wiener type we apply the Fuzzy Inference System (FIS). The results are expected to help us to estimate the residual technical life of a system, optimize the maintenance and make life cycle costs more effective. The system is meant to be the oil itself and the combustion engine where the oil is used.

Seagrass ecosystem trajectory depends on the relative timescales of resistance, recovery and disturbance

Seagrass ecosystems are inherently dynamic, responding to environmental change across a range of scales. Habitat requirements of seagrass are well defined, but less is known about their ability to resist disturbance. Specific means of recovery after loss are particularly difficult to quantify. Here we assess the resistance and recovery capacity of 12 seagrass genera. We document four classic trajectories of degradation and recovery for seagrass ecosystems, illustrated with examples from around the world. Recovery can be rapid once conditions improve, but seagrass absence at landscape scales may persist for many decades, perpetuated by feedbacks and/or lack of seed or plant propagules to initiate recovery. It can be difficult to distinguish between slow recovery, recalcitrant degradation, and the need for a window of opportunity to trigger recovery. We propose a framework synthesizing how the spatial and temporal scales of both disturbance and seagrass response affect ecosystem trajectory and hence resilience.

Remaining useful life prediction of degrading systems subjected to imperfect maintenance: Application to draught fans

Abstract Current degradation modeling and remaining useful life prediction studies share a common assumption that the degrading systems are not maintained or maintained perfectly (i.e., to an as-good-as new state). This paper concerns the issues of how to model the degradation process and predict the remaining useful life of degrading systems subjected to imperfect maintenance activities, which can restore the health condition of a degrading system to any degradation level between as-good-as new and as-bad-as old. Toward this end, a nonlinear model driven by Wiener process is first proposed to characterize the degradation trajectory of the degrading system subjected to imperfect maintenance, where negative jumps are incorporated to quantify the influence of imperfect maintenance activities on the system’s degradation. Then, the probability density function of the remaining useful life is derived analytically by a space-scale transformation, i.e., transforming the constructed degradation model with negative jumps crossing a constant threshold level to a Wiener process model crossing a random threshold level. To implement the proposed method, unknown parameters in the degradation model are estimated by the maximum likelihood estimation method. Finally, the proposed degradation modeling and remaining useful life prediction method are applied to a practical case of draught fans belonging to a kind of mechanical systems from steel mills. The results reveal that, for a degrading system subjected to imperfect maintenance, our proposed method can obtain more accurate remaining useful life predictions than those of the benchmark model in literature.

Remaining Useful Life Prediction Based on a General Expression of Stochastic Process Models

In remaining useful life (RUL) prediction, stochastic process models are widely used to describe the degradation processes of systems. For age-dependent stochastic process models, the RUL probability density function (PDF) can be calculated using a closed-form solution. For state-dependent models, however, it is difficult to calculate such a closed-form solution. Therefore, the RUL is always approximately estimated using a sequential Monte Carlo-based method, but this method has some limitations. First, it only provides a numerical approximation result whose accuracy highly relies on the quality and quantity of the simulated degradation trajectories. Second, the time interval is unable to be adjusted during the state transition process, resulting in too few discrete probability densities in the result near the end-of-life. This paper describes the degradation processes using a general expression of age- and state-dependent models. The analytical solution of the RUL PDF is derived from the general expression. After that, a new RUL prediction method is proposed. In this method, a series of degradation trajectories are generated through degradation process simulation. The RUL PDF is estimated by inputting the state values of the degradation trajectories into the analytical solution. The validity of the proposed method is verified using fatigue-crack-growth data.

Prognostics of Li(NiMnCo)O2-based lithium-ion batteries using a novel battery degradation model

Some lithium-ion battery materials show two-phase degradation behavior with evident inflection points, such as lithium nickel manganese cobalt oxide (Li(NiMnCo)O2 or NMC) cells. A model-based Bayesian approach is proposed in this paper to predict remaining useful life (RUL) for these types of batteries. First, a two-term logarithmic model is developed to capture the degradation trends of NMC batteries. By fitting the battery degradation data, it is experimentally demonstrated that the developed model is superior to existing empirical battery degradation models. A particle filtering–based prognostic method is then incorporated into the model to estimate the batteries' possible degradation trajectories. Correspondingly, the RUL values of NMC batteries are expressed in terms of probability density function. The effectiveness of the developed method is verified with our collected experimental data. The results indicate that the proposed prognostic method can achieve higher predictive accuracy than the existing two-term exponential model.

Remaining useful life prediction for an adaptive skew-Wiener process model

Predicting the remaining useful life for operational devices plays a critical role in prognostics and health management. As the models based on the stochastic processes are widely used for characterizing the degradation trajectory, an adaptive skew-Wiener model, which is much more flexible than traditional stochastic process models, is proposed to model the degradation drift of industrial devices. To make full use of the prior knowledge and the historical information, an on-line filtering algorithm is proposed for state estimation, a two-stage algorithm is adopted to estimate unknown parameters as well. For remaining useful life prediction, a novel result is presented with an explicit form based on the closed skew normal distribution. Finally, sufficient Monte Carlo simulations and an application for ball bearings in rotating electrical machines are used to validate our approach.

Hydrologic controls on aperiodic spatial organization of the ridge–slough patterned landscape

Abstract. A century of hydrologic modification has altered the physical and biological drivers of landscape processes in the Everglades (Florida, USA). Restoring the ridge–slough patterned landscape, a dominant feature of the historical system, is a priority but requires an understanding of pattern genesis and degradation mechanisms. Physical experiments to evaluate alternative pattern formation mechanisms are limited by the long timescales of peat accumulation and loss, necessitating model-based comparisons, where support for a particular mechanism is based on model replication of extant patterning and trajectories of degradation. However, multiple mechanisms yield a central feature of ridge–slough patterning (patch elongation in the direction of historical flow), limiting the utility of that characteristic for discriminating among alternatives. Using data from vegetation maps, we investigated the statistical features of ridge–slough spatial patterning (ridge density, patch perimeter, elongation, patch size distributions, and spatial periodicity) to establish more rigorous criteria for evaluating model performance and to inform controls on pattern variation across the contemporary system. Mean water depth explained significant variation in ridge density, total perimeter, and length : width ratios, illustrating an important pattern response to existing hydrologic gradients. Two independent analyses (2-D periodograms and patch size distributions) provide strong evidence against regular patterning, with the landscape exhibiting neither a characteristic wavelength nor a characteristic patch size, both of which are expected under conditions that produce regular patterns. Rather, landscape properties suggest robust scale-free patterning, indicating genesis from the coupled effects of local facilitation and a global negative feedback operating uniformly at the landscape scale. Critically, this challenges widespread invocation of scale-dependent negative feedbacks for explaining ridge–slough pattern origins. These results help discern among genesis mechanisms and provide an improved statistical description of the landscape that can be used to compare among model outputs, as well as to assess the success of future restoration projects.

Gas turbine engine prognostics using Bayesian hierarchical models: A variational approach

Prognostics is an emerging requirement of modern health monitoring that aims to increase the fidelity of failure-time predictions by the appropriate use of sensory and reliability information. In the aerospace industry it is a key technology to reduce life-cycle costs, improve reliability and asset availability for a diverse fleet of gas turbine engines.In this work, a Bayesian hierarchical model is selected to utilise fleet data from multiple assets to perform probabilistic estimation of remaining useful life (RUL) for civil aerospace gas turbine engines. The hierarchical formulation allows Bayesian updates of an individual predictive model to be made, based upon data received asynchronously from a fleet of assets with different in-service lives and for the entry of new assets into the fleet.In this paper, variational inference is applied to the hierarchical formulation to overcome the computational and convergence concerns that are raised by the numerical sampling techniques needed for inference in the original formulation. The algorithm is tested on synthetic data, where the quality of approximation is shown to be satisfactory with respect to prediction performance, computational speed, and ease of use. A case study of in-service gas turbine engine data demonstrates the value of integrating fleet data for accurately predicting degradation trajectories of assets.

REAL-TIME RELIABILITY ASSESSMENT AND LIFETIME PREDICTION FOR BEARINGS USING THE INDIVIDUAL STATE DEVIATION BASED ON THE MANIFOLD DISTANCE

In recent years, the real-time reliability evaluation and life prediction for rolling bearings has attracted more attention. Most of the existing methods employ real-time transformation of traditional reliability indices, performance degradation trajectory or distribution analysis, which usually have certain limitations in terms of accuracy and applicability. This paper proposes a method for bearing real-time reliability evaluation and life prediction to avoid the negligence of real-time transformation of the monitored individual, as well as reduce the errors caused by the randomness from individual bearing operational process. The individual state deviation of a running rolling bearing geometrically measured by manifold distance is normalized into a state deviation degree, which is used to formulate a modified real-time reliability model for realtime reliability evaluation and lifetime prediction. Finally, the feasibility and efficiency of this method is validated by bearing run-to-failure experiments.

Remaining Useful Life Prediction for a Nonlinear Heterogeneous Wiener Process Model With an Adaptive Drift

Nonlinear degradation trajectories are encountered frequently, and not all of them evolve homogeneously in practical systems. To take nonlinearity, heterogeneity, and the entire historical degradation data into account, we propose a nonlinear heterogeneous Wiener process model with an adaptive drift to characterize degradation trajectories. A state-space based method is employed to delineate our model. Due to the introduction of the adaptive drift, it is difficult to directly apply Kalman filter methods to update the distribution of the estimated degradation drift. To address this issue, we develop an online filtering algorithm based on Bayes' theorem. The expectation-maximization (EM) algorithm, as well as a novel Bayes'-theorem-based smoother, are adopted to estimate the unknown parameters in our model. Moreover, the distribution of the predicted remaining useful life (RUL) incorporating the complete distribution of the estimated degradation drift is achieved analytically. Finally, a simulation, and a case study are provided to validate the proposed approach.

A Prognostic-Information-Based Order-Replacement Policy for a Non-Repairable Critical System in Service

This paper proposes a prognostic-information-based joint order-replacement policy for a non-repairable critical system in service. The primary difference from existing work is to take the online condition monitoring data into consideration during the joint decision-making process. Towards this end, the system’s degradation trajectory is modeled by a Wiener process whose parameters are real-time estimated based on the newly obtained condition monitoring data by utilizing the expectation maximization algorithm and Bayesian inference. By doing so, the remaining useful life distribution of the system of interest can be predicted in real-time, which is then used as the prognostic information to dynamically update the optimal ordering and replacement times jointly. This process makes the jointly obtained order-replacement decisions rely on the prognostic information available from the system’s degradation monitoring. Finally, a practical case study of the inertial navigation system in aircraft is provided to validate the proposed joint decision policy.

Real-Time Reliability Evaluation and Life Prediction for Bearings Based on Normalized Individual State Deviation

Most of the existing methods for bearing real-time reliability evaluation employ real-time transformation of traditional reliability indices, performance degradation trajectory analysis, and performance degradation distribution, which are usually limited in terms of accuracy and applicability. A method for real-time reliability evaluation and life prediction for bearings based on normalized individual state deviation is proposed in this study. First, a self-organizing map neural network is utilized to obtain the individual state deviation of a running rolling bearing. Second, individual state deviation is normalized into a state deviation degree, which is used to formulate a modified real-time reliability model for the realization of real-time reliability evaluation and residual life prediction. The proposed method combines population information with real-time monitoring information of individual bearings, and thus avoids the negligence of the real-time transformation of the monitored individual. The errors caused by the randomness of the individual bearing operational process are also reduced. Finally, the feasibility and efficiency of the proposed method is validated by performing run-to-failure experiments on bearings.

Degradation prediction model based on a neural network with dynamic windows.

Tracking degradation of mechanical components is very critical for effective maintenance decision making. Remaining useful life (RUL) estimation is a widely used form of degradation prediction. RUL prediction methods when enough run-to-failure condition monitoring data can be used have been fully researched, but for some high reliability components, it is very difficult to collect run-to-failure condition monitoring data, i.e., from normal to failure. Only a certain number of condition indicators in certain period can be used to estimate RUL. In addition, some existing prediction methods have problems which block RUL estimation due to poor extrapolability. The predicted value converges to a certain constant or fluctuates in certain range. Moreover, the fluctuant condition features also have bad effects on prediction. In order to solve these dilemmas, this paper proposes a RUL prediction model based on neural network with dynamic windows. This model mainly consists of three steps: window size determination by increasing rate, change point detection and rolling prediction. The proposed method has two dominant strengths. One is that the proposed approach does not need to assume the degradation trajectory is subject to a certain distribution. The other is it can adapt to variation of degradation indicators which greatly benefits RUL prediction. Finally, the performance of the proposed RUL prediction model is validated by real field data and simulation data.

A Well-Designed Parameter Estimation Method for Lifetime Prediction of Deteriorating Systems with Both Smooth Degradation and Abrupt Damage

Deteriorating systems, which are subject to both continuous smooth degradation and additional abrupt damages due to a shock process, can be often encountered in engineering. Modeling the degradation evolution and predicting the lifetime of this kind of systems are both interesting and challenging in practice. In this paper, we model the degradation trajectory of the deteriorating system by a random coefficient regression (RCR) model with positive jumps, where the RCR part is used to model the continuous smooth degradation of the system and the jump part is used to characterize the abrupt damages due to random shocks. Based on a specified threshold level, the probability density function (PDF) and cumulative distribution function (CDF) of the lifetime can be derived analytically. The unknown parameters associated with the derived lifetime distributions can be estimated via a well-designed parameter estimation procedure on the basis of the available degradation recordings of the deteriorating systems. An illustrative example is finally provided to demonstrate the implementation and superiority of the newly proposed lifetime prediction method. The experimental results reveal that our proposed lifetime prediction method with the dedicated parameter estimation strategy can get more accurate lifetime predictions than the rival model in literature.

Ant community structure and response to disturbances on coastal dunes of Gulf of Mexico

Coastal dunes are complex and fragile ecosystems. The decrease in environmental stressors from sea to inland creates zonation patterns of habitats, which support high biodiversity. Although coastal dunes have been examined in primary succession studies for more than 100 years, invertebrates have received much less attention than other taxa. In this study, we examined ant community composition and its relationship with vegetation structure on dunes, and used ants as indicators to reveal the influence of anthropogenic disturbances on these habitats. Quadrat sampling, hand collecting, and beating plants were used to sample ants on coastal dunes fringing the northern Gulf of Mexico. Ants representing 44 species were found, with diversity and number of functional groups increasing from foredunes to backdunes. Bush areas of the backdunes supported a unique ant community. Ant diversity was correlated with plant richness, stem number, and plant cover, but the correlation was not consistent among habitats. Ant diversity was lower in degraded, young-planted, and re-built but not in old-planted sites. In addition, different types of disturbance changed the ant community and functional groups in different ways. Our study emphasizes the importance of protecting the whole dune system, especially the backdunes, which support high diversity but are often completely destroyed by urban development. Data from this research provides a benchmark to examine trajectories of coastal dune ecosystem degradation or recovery when exposed to natural or anthropogenic disturbances.

Remaining useful life estimation for mechanical systems based on similarity of phase space trajectory

When evolving from a normal state to failure, mechanical systems undergo a gradual degradation process. Due to the nonlinearity of damage accumulation, degradation data always exhibit a distinctive trend and random fluctuations. It makes the prediction of remaining useful life (RUL) very difficult and inaccurate. The phase space trajectory reconstructed from the time series of degradation data is capable of reliably elucidating the nonlinear degradation behavior. In this paper, a novel method based on the similarity of the phase space trajectory is proposed for estimating the RUL of mechanical systems. First, the reference degradation trajectories are built with historical degradation data using the phase space reconstruction. Second, the similarities between the current degradation trajectory and the reference degradation trajectories are measured with a normalized cross correlation indicator, which is determined solely by the trajectory shape and is not interfered with the scaling and shifting of the trajectory. Trajectory shape and degradation stage matching algorithms are combined to find the optimal segments in the reference degradation trajectories compared with the current degradation trajectory. Finally, the RULs corresponding to the optimal matching segments are subjected to weighted averaging to obtain the RUL of the current degradation process. The proposed method is evaluated utilizing both simulated data in stochastic degradation processes and experimental data measured on an actual pump. The results show that the predicted RULs are very close to the actual RUL.

A particle filtering and kernel smoothing-based approach for new design component prognostics

This work addresses the problem of predicting the Remaining Useful Life (RUL) of components for which a mathematical model describing the component degradation is available, but the values of the model parameters are not known and the observations of degradation trajectories in similar components are unavailable. The proposed approach solves this problem by using a Particle Filtering (PF) technique combined with a kernel smoothing (KS) method. This PF–KS method can simultaneously estimate the degradation state and the unknown parameters in the degradation model, while significantly overcoming the problem of particle impoverishment. Based on the updated degradation model (where the unknown parameters are replaced by the estimated ones), the RUL prediction is then performed by simulating future particles evolutions. A numerical application regarding prognostics for Lithium-ion batteries is considered. Various performance indicators measuring precision, accuracy, steadiness and risk of the obtained RUL predictions are computed. The obtained results show that the proposed PF–KS method can provide more satisfactory results than the traditional PF methods.