A method for establishing a bearing residual life prediction model for process enhancement equipment based on rotor imbalance response analysis

A rotating packed bed is a typical chemical process enhancement equipment that can strengthen micromixing and mass transfer.During the operation of the rotating packed bed,the nonreactants and products irregularly adhere to the wire mesh packing in the rotor,thus resulting in an imbalance in the vibration of the rotor,which may cause serious damage to the bearing and material leakage.This study proposes a model prediction for estimating the bearing residual life of a rotating packed bed based on rotor imbalance response analysis.This method is used to determine the influence of the mass on the imbalance in the vibration of the rotor on bearing damage.The major influence on rotor vibration was found to be exerted by the imbalanced mass and its distribution radius,as revealed by the results of orthogonal experiments.Through implementing finite element analysis,the imbalance response curve for the rotating packed bed rotor was obtained,and a correlation among rotor imbalance mass,distribution radius of imbalance mass,and bearing residue life was established via data fitting.The predicted value of the bearing life can be used as the reference basis for an early safety warning of a rotating packed bed to effectively avoid accidents.

Residual life estimation based on bivariate Wiener degradation process with measurement errors

An adaptive method of residual life estimation for deteriorated products with two performance characteristics (PCs) was proposed, which was sharply different from existing work that only utilized one-dimensional degradation data. Once new degradation information was available, the residual life of the product being monitored could be estimated in an adaptive manner. Here, it was assumed that the degradation of each PC over time was governed by a Wiener degradation process and the dependency between them was characterized by the Frank copula function. A bivariate Wiener process model with measurement errors was used to model the degradation measurements. A two-stage method and the Markov chain Monte Carlo (MCMC) method were combined to estimate the unknown parameters in sequence. Results from a numerical example about fatigue cracks show that the proposed method is valid as the relative error is small.

Equilibrium Reinsurance Strategy and Mean Residual Life Function

In this paper,we analyze the relationship between the equilibrium reinsurance strategy and the tail of the distribution of the risk.Since Mean Residual Life(MRL)has a close relationship with the tail of the distribution,we consider two classes of risk distributions,Decreasing Mean Residual Life(DMRL)and Increasing Mean Residual Life(IMRL)distributions,which can be used to classify light-tailed and heavy-tailed distributions,respectively.We assume that the underlying risk process is modelled by the classical CramérLundberg model process.Under the mean-variance criterion,by solving the extended Hamilton-Jacobi-Bellman equation,we derive the equilibrium reinsurance strategy for the insurer and the reinsurer under DMRL and IMRL,respectively.Furthermore,we analyze how to choose the reinsurance premium to make the insurer and the reinsurer agree with the same reinsurance strategy.We find that under the case of DMRL,if the distribution and the risk aversions satisfy certain conditions,the insurer and the reinsurer can adopt a reinsurance premium to agree on a reinsurance strategy,and under the case of IMRL,the insurer and the reinsurer can only agree with each other that the insurer do not purchase the reinsurance.

TWO METHODS FOR ASSESSMENT OF RESIDUAL LIFE OF HK-40 FURNACE TUBES

Two methods for predicting residual life of high temperature furnace tubes are studied. One is testanalysis method that is mainly based on the creep rupture tests on postservice specimens. Specimens were taken from the tubes, which had been in service for different times. KachanovRobinsons damage summation concept is employed, however with a modified factor K(ts) to account for prior damage in the specimens. If the foregone total life corresponds with real condition, all of the test data modified by K(ts) should be distributed uniformly nearby the master curve of the new material. The other iscomputer simulation method that considers all of the operating conditions that influence the life. The finite element method (FEM) with iterative calculation is used in the analysis. The variation rates of critical damage element along the wall thickness are determined as a function of the service temperature and current damage. A special program designed based on the method predicts well the residual life of furnace tubes, so long as the maximum depth of critical damage in radius direction of tubes has been detected by ultrasonic techniques.

Residual Life Prediction Based on Nonlinear Fatigue Damage Accumulation Model

When a nonlinear fatigue damage accumulation model based on damage curve approach is used to get better residual life prediction results, it is necessary to solve the problem caused by the uncertain exponent of the model. Considering the effects of load interaction, the assumption that there is a linear dependence between the exponent ratio and the loading ratio is established to predict fatigue residual life of materials. Three experimental data sets are used to validate the rightness of the proposition. The comparisons of experimental data and predictions show that the predictions based on the proposed proposition are in good accordance with the experimental results as long as the parameters that represent the linear correlativity are set an appropriate value. Meanwhile, the accuracy of the proposition is approximated to that of an existing model. Therefore, the proposition proposed in this paper is reasonable for residual life prediction.

The Proportional Mean Residual Life Regression Model with Cure Fraction and Auxiliary Covariate

As biological studies become more expensive to conduct,it is a frequently encountered question that how to take advantage of the available auxiliary covariate information when the exposure variable is not measured.In this paper,we propose an induced cure rate mean residual life time regression model to accommodate the survival data with cure fraction and auxiliary covariate,in which the exposure variable is only assessed in a validation set,but a corresponding continuous auxiliary covariate is ascertained for all subjects in the study cohort.Simulation studies elucidate the practical performance of the proposed method under finite samples.As an illustration,we apply the proposed method to a heart disease data from the Study of Left Ventricular Dysfunction.

Likelihood Ratio Inference for Mean Residual Life of Length-biased Random Variable

In lifetime data analysis, naturally recorded observations are length-biased data if the probability to select an item is proportional to its length. Based on i.i.d, observations of the true distribution, empirical likelihood （EL） procedure is proposed for the inference on mean residual life （MRL） of naturally recorded item. The limit distribution of the EL based log-likelihood ratio is proved to be the chi-square distribution. Under right censorship, since the EL based log-likelihood ratio leads to a scaled chi-square distribution and estimating the scale parameter leads to lower coverage of confidence interval, we propose an algorithm to calculate the likelihood ratio （LR） directly. The corresponding log-likelihood ratio converges to the standard chi-square distribution and the corresponding confidence interval has a better coverage. Simulation studies are used to support the theoretical results.

Nonparametrie Quantile Inference for Cause-specific Residual Life Function Under Length-biased Sampling

This paper considers a competing risks model for right-censored and length-biased survival data from prevalent sampling.We propose a nonparametric quantile inference procedure for cause-specific residual life distribution with competing risks data.We also derive the asymptotic properties of the proposed estimators of this quantile function.Simulation studies and the unemployment data demonstrate the practical utility of the methodology.

Residual Fatigue Life Prediction of Ball Bearings Based on Paris Law and RMS

Paris law can reflect the failure mechanism of materials and is usually used to be a method to predict fatigue life or residual fatigue life.But the variable which can represent the health of machine is hardly measured on line.To a degree,the difficulty of on-line application restricts the scope of application of Paris law.The relationship between characteristic values of vibration signals and the variable in the Paris equation which can describe the health of machine is investigated by taking ball bearings as investigative objects.Based on 6205 deep groove ball bearings as a living example,historical lives and vibration signals are analyzed.The feasibility of describing that variable in the Paris equation by the characteristic value of vibration signals is inspected.After that vibration signals decomposed by empirical mode decomposition（EMD）,root mean square（RMS） of intrinsic mode function（IMF） involving fault characteristic frequency has a consistent trend with the diameter of flaws.Based on the trend,two improved Paris models are proposed and the scope of application of them is inspected.These two Paris Models are validated by fatigue residual life data from tests of rolling element bearings and vibration signals monitored in the process of operation of rolling element bearings.It shows that the first improved Paris Model is simple and plain and it can be easily applied in actual conditions.The trend of the fatigue residual life predicted by the second improved Paris model is close to the actual conditions and the result of the prediction is slightly greater than the truth.In conclusion,after the appearance of detectable faults,these improved models based on RMS can predict residual fatigue life on line and a new approach to predict residual fatigue life of ball bearings on line without disturbing the machine running is provided.

Ensemble Recurrent Neural Network-Based Residual Useful Life Prognostics of Aircraft Engines

Residual useful life(RUL)prediction is a key issue for improving efficiency of aircraft engines and reducing their maintenance cost.Owing to various failure mechanism and operating environment,the application of classical models in RUL prediction of aircraft engines is fairly difficult.In this study,a novel RUL prognostics method based on using ensemble recurrent neural network to process massive sensor data is proposed.First of all,sensor data obtained from the aircraft engines are preprocessed to eliminate singular values,reduce random fluctuation and preserve degradation trend of the raw sensor data.Secondly,three kinds of recurrent neural networks(RNN),including ordinary RNN,long shortterm memory(LSTM),and gated recurrent unit(GRU),are individually constructed.Thirdly,ensemble learning mechanism is designed to merge the above RNNs for producing a more accurate RUL prediction.The effectiveness of the proposed method is validated using two characteristically different turbofan engine datasets.Experimental results show a competitive performance of the proposed method in comparison with typical methods reported in literatures.

Application of time-temperature superposition method in thermal aging life prediction of shipboard cables

The life of shipboard cables will decrease due to the complex aging processes. In terms of the safety perspective, remaining life prediction of the cable is essential to maintain a reliable operation. In this paper, firstly, based on Arrhenius equation, residual life of new styrene-butadiene cable is calculated; result indicates that the degradation rate which changes with time is proportional to thermal temperature. Then second order dynamic model is adopted into the residual life prediction, combined with the time-temperature superposition method(TTSP), and a new residual life model is proposed. According to the accelerated thermal aging experiment data and Arrhenius equation, TTSP method demonstrates to be an efficient way for life prediction, and life at normal temperature can be estimated by this model. In order to monitor the state of styrene-butadiene cable more accurately, an improved residual life model based on equivalent environment temperature of cable is proposed, and life of cable under real operation is analyzed. Result indicates that this model is credible and reliable, and it provides an important theoretical base for residual life of cables.

Health evaluation method for degrading systems subject to dependent competing risks

This paper proposes a health evaluation method for degrading systems subject to competing risks of dependent soft and hard failures. To characterize the time-varying degradation rate, the degradation process is determined by a non-stationary Gamma process and the soft failure is encountered when it exceeds a predefined critical level. For the hard failure, a Cox’s proportional hazard model is applied to describe the hazard rate of the time to system failure. The dependent relationship is modeled by incorporating the degradation process as a time-varying covariate into the Cox’s proportional hazard model. To facilitate the health characteristics evaluation, a discretization technique is applied both to the degradation process and the monitoring time.All health characteristics can be obtained in the explicit form using the transition probability matrix, which is computationally attractive for practical applications. Finally, a numerical analysis is carried out to show the effectiveness and the performance of the proposed health evaluation method.

Representations for reliability functions of conditional coherent systems with INID components and ordered properties

This paper presents several useful mixture representations for the reliability function of the residual live of a coherent system with independent but non-identically distributed components. These presentations are based on order statistics, signatures and mean reliability functions. We then discuss some stochastic comparisons of residual lives between two systems based on the stochastic ordering of coefficient vectors （or components） of the two systems. These results form nice extensions of some known results for the case of independent and identically distributed components.

Failure prognostic of systems with hidden degradation process

Systems with a hidden degradation process are perva- sive in the real world. Degrading critical components will under- mine system performance and pose potential failures in the future. Prognostic aims at predicting potential failures before it evolves into faults. A prognostic procedure based on expectation maxi- mization and unscented Kalman filter is proposed. System state, sensor measurement and hidden degradation process are viewed as data （incomplete or missing） in the expectation maximization method. System state and hidden degradation process are esti- mated by a unscented Kalman filter upon sensor measurements. Component-specific parameters in a degradation process are iden- tified on the estimation of the degradation process. Residual life is measured by the median of estimated residual life distribution. The proposed procedure is verified by simulations on a first-order capacitor-resistance circuit with degrading resistance. Residual life estimation consists conservatively with the trend and is evalu- ated in terms of relative errors. Simulation results are reasonable. The proposed prognostic method expects applications in practice.

A New Logarithmic Family of Distributions: Properties and Applications

In recent years,there has been an increased interest among the researchers to propose new families of distributions to provide the best fit to lifetime data with monotonic(increasing,decreasing,constant)and non-monotonic(unimodal,modified unimodal,bathtub)hazard functions.We further carry this area of research and propose a new family of lifetime distributions called a new logarithmic family via the T-X family approach.For the proposed family,explicit expressions for some mathematical properties along with the estimation of parameters through Maximum likelihood method are discussed.A sub-model,called a new logarithmic Weibull distribution is taken up.The proposed model is very flexible and can be used to model data with increasing,decreasing,modified unimodal or bathtub shaped hazard rates.The maximum likelihood estimators of the model parameters are obtained.To assess the behavior of the maximum likelihood estimators,a comprehensive Monte Carlo simulation study has been carried out.Finally,the potentiality of the new model is shown via analyzing two real data sets taken from reliability engineering and biomedical fields.The comparison of the proposed model is made with the other well-known competitors such as(i)the three parameters exponentiated Weibull and Marshall–Olkin Weibull distributions and(ii)a four-parameter beta Weibull distribution.The practical applications show that the proposed model performs much better than the competitive models and can be used as a good candidate model to analyze data in engineering,medical sciences and other related fields.

Comprehensive rotor service life study for high&intermediate pressure cylinders of high power steam turbines

The paper provides a comprehensive scheme for assessment of the residual service life and extension of operating life of steam turbine rotors with expired fleet service life.The residual service life of high temperature rotors for high&intermediate pressure cylinders of K-200-130-3 steam turbine without heat grooves calculated and it was showed that the residual service life of high&intermediate pressure rotors without grooves has been extended as compared to the K-200-130-1 turbine rotors with grooves.Also residual life management by supplying hot steam to the HPC and 1PC seals was investigated and it was noted their significant impact on the residual service life.

Applications of survival functions to continuous semi-Markov processes for measuring reliability of power transformers

The reliability of power transformers is subject to service age and health condition.This paper proposes a practical model for the evaluation of two reliability indices:survival function(SF)and mean residual life(MRL).In the proposed model,the periodical modeling of power transformers are considered for collecting the information on health conditions.The corresponding health condition is assumed to follow a continuous semi-Markov process for representing a state transition.The proportional hazard model(PHM)is introduced to incorporate service age and health condition into hazard rate.In addition,the proposed model derives the analytical formulas for and offers the analytical evaluation of SF and MRL.SF and MRL are calculated for new components and old components,respectively.In both cases,the proposed model offers rational results which are compared with those obtained from comparative models.The results obtained by the contrast of the proposed analytical method and the Monte Carlo method.The impact of differentmodel parameters and the coefficient of variation(CV)on reliability indices are discussed in the case studies.