A Nonlinear Prognostic Model Based on the Wiener Process with Three Sources of Uncertainty

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Huifang Niu ◽  
Jianchao Zeng ◽  
Hui Shi ◽  
Bin Wang ◽  
Tianye Liu
Keyword(s):  
Measurement Errors ◽  
Prognostic Model ◽  
Health Management ◽  
Real Data ◽  
Remaining Useful Life ◽  
Model Fit ◽  
Model Parameters ◽  
Lifetime Estimation ◽  
Practical Applications ◽  
Sources Of Uncertainty

Estimation of the remaining useful life (RUL) is an important component of prognostics and health management (PHM). The accuracy of the RUL estimation for complex systems is mainly affected by three sources of uncertainty, i.e., the temporal uncertainty, the product-to-product uncertainty, and measurement errors. To improve PHM and account for the effects of the three sources of uncertainty, a nonlinear prognostic model with three sources of uncertainty is presented here. An approximated analytical expression for the probability density function (PDF) of the RUL is obtained based on the concept of first hitting time (FHT). Model parameters are then obtained by the expectation maximization (EM) algorithm, and the drift parameter is estimated adaptively using a Bayesian procedure. Finally, in order to illustrate the practical applications of the presented approach, a comparative study of real data on fatigue crack propagation is presented. Results demonstrate that our method improves model fit and increases the accuracy of the lifetime estimation.

Uncertainty in debris flow rainfall thresholds

2021 ◽  
Author(s):  
Matteo Berti ◽  
Alessandro Simoni
Keyword(s):  
Debris Flow ◽  
Debris Flows ◽  
Measurement Errors ◽  
Critical Conditions ◽  
Model Parameters ◽  
Average Intensity ◽  
Rainfall Thresholds ◽  
Sources Of Uncertainty ◽  
Time Space ◽  
Physically Based

<p>Rainfall is the most significant factor for debris flows triggering. Water is needed to saturate the soil, initiate the sediment motion (regardless of the mobilization mechanism) and transform the solid debris into a fluid mass that can move rapidly downslope. This water is commonly provided by rainfall or rainfall and snowmelt. Consequently, most warning systems rely on the use of rainfall thresholds to predict debris flow occurrence. Debris flows thresholds are usually empirically-derived from the rainfall records that caused past debris flows in a certain area, using a combination of selected precipitation measurements (such as event rainfall P, duration D, or average intensity I) that describe critical rainfall conditions. Recent years have also seen a growing interest in the use of coupled hydrological and slope stability models to derive physically-based thresholds for shallow landslide initiation.</p><p>In both cases, rainfall thresholds are affected by significant uncertainty. Sources of uncertainty include: measurement errors; spatial variability of the rainfall field; incomplete or uncertain debris flow inventory; subjective definition of the “rainfall event”; use of subjective criteria to define the critical conditions; uncertainty in model parameters (for physically-based approaches). Rainfall measurement is widely recognized as a main source of uncertainty due to the extreme time-space variability that characterize intense rainfall events in mountain areas. However, significant errors can also arise by inaccurate information reported in landslide inventories on the timing of debris flows, or by the criterion used to define triggering intensities.</p><p>This study analyzes the common sources of uncertainty associated to rainfall thresholds for debris flow occurrence and discusses different methods to quantify them. First, we give an overview of the various approaches used in the literature to measure the uncertainty caused by random errors or procedural defects. These approaches are then applied to debris flows using real data collected in the Dolomites (Northen Alps, Itay), in order to estimate the variabilty of each single factor (precipitation, triggering timing, triggering intensity..). Individual uncertainties are then combined to obtain the overall uncertain of the rainfall threshold, which can be calculated using the classical method of “summation in quadrature” or a more effective approach based on Monte Carlo simulations. The uncertainty budget allows to identify the biggest contributors to the final variability and it is also useful to understand if this variability can be reduced to make our thresholds more precise.</p><p> </p>

A recursive Bayesian approach to small fatigue crack propagation and detection modeling

2018 ◽  
Vol 232 (6) ◽  
pp. 738-753 ◽  
Author(s):  
Reuel Smith ◽  
Mohammad Modarres ◽  
Enrique López Droguett
Keyword(s):  
Acoustic Emission ◽  
Fatigue Crack ◽  
Measurement Errors ◽  
Crack Detection ◽  
Life Support ◽  
Health Management ◽  
Fatigue Crack Initiation ◽  
Fatigue Cracking ◽  
Remaining Useful Life ◽  
Dog Bone

Engineers have witnessed much advancement in the study of fatigue crack detection and propagation modeling. More recently, the use of certain damage precursors such as acoustic emission signals to assess the integrity of structures has been proposed for application to prognosis and health management of structures. However, due to uncertainties associated with small crack detection of damage precursors and crack size measurement errors of the detection technology used, applications of prognosis and health management assessments have been limited. In this article, a methodology is developed for the purpose of assessment of crack detection and propagation parameters and the minimization of uncertainties including detection and sizing errors associated with a series of known crack detection and propagation models that use acoustic emission as the precursor to fatigue cracking. The methodology is facilitated by the Bayesian inference of a joint-likelihood model which includes sizing and detection models. Examples where several dog-bone Al 7075T6 specimens are tested to produce fatigue crack initiation and propagation data and estimates based on remaining useful life support the effectiveness and usefulness of the proposed methodology.

scholarly journals Deep wavelet sequence-based gated recurrent units for the prognosis of rotating machinery

2020 ◽  
pp. 147592172093315
Author(s):  
Meng Ma ◽  
Zhu Mao
Keyword(s):  
Prognostic Model ◽  
Health Management ◽  
Experimental Studies ◽  
Remaining Useful Life ◽  
Vibration Signals ◽  
Useful Life ◽  
Multi Level ◽  
Gated Recurrent Units ◽  
Gated Recurrent Unit ◽  
Domain Information

Prognostics and health management (PHM) is an emerging technique which aims to improve the reliability and safety of machinery systems. Remaining useful life (RUL) prediction is the key part of PHM which provides operators how long the machine keeps working without breakdowns. In this study, a novel prognostic model is proposed for RUL prediction using deep wavelet sequence-based gated recurrent units (GRU). This proposed wavelet sequence-based gated recurrent unit (WSGRU) specifically adopts a wavelet layer and generates wavelet sequences at different scales. Since vibration signals exhibit non-stationary characteristics, wavelet analysis is thereby needed to capture both the time and frequency domain information to fully identify the degradation of the rotating components. In the proposed WSGRU, the vibration signals are decomposed into different frequency sub-bands via wavelet transformation, and then a deep GRU architecture is designed to predict the RUL taking advantage of the temporal dependencies that naturally exist in the waveforms. Experimental studies have been performed for RUL prediction of bearings with collection of vibration signals during the run-to-failure tests. The prediction results show that deep WSGRU outperforms traditional models due to the multi-level feature extraction on the transformed multiscale wavelet sequences.

scholarly journals Estimating the Parameters of Degradation Models when Error Terms are Autocorrelated

2016 ◽  
Vol 40 (3) ◽  
Author(s):  
Jehad Al-Jararha ◽  
Mohammed Al-Haj Ebrahem ◽  
Abedel-Qader Al-Masri
Keyword(s):  
Measurement Errors ◽  
Real Data ◽  
Degradation Process ◽  
Model Parameters ◽  
Ambient Conditions ◽  
Data Set ◽  
Degradation Data ◽  
Error Terms ◽  
The Times ◽  
Cyclic Changes

The need of autocorrelation models for degradation data comes from the facts that the degradation measurements are often correlated, since such measurements are taken over time. Time series can exhibit autocorrelation caused by modeling error or cyclic changes in ambient conditions in the measurement errors or in degradation process itself. Generally, autocorrelation becomes stronger when the times between measurements are relativelyshort and becomes less noticeable when the times between process are longer. In this paper, we assume that the error terms are autocorrelated and have an autoregressive of order one, AR(1). This case is a more general case of the assumption that the error terms are identically and independently normally distributed. Since when the error terms are uncorrelated over the time, the estimate of the parameter of AR(1) is approximately zero.If the parameter of AR(1) is unknown, one can estimate it from the data set. Using two real data sets, the model parameters are estimated and compared with the case when the error terms are independent and identically distributed. Such computations are available by using procedures AUTOREG and model in SAS. Computations show that an AR(1) can be used as a useful tool to remove the autocorrelation between the residuals.

scholarly journals Uncertainty in PHM

2020 ◽  
Vol 6 (4) ◽  
Author(s):  
Shankar Sankararaman ◽  
Sankaran Mahadevan ◽  
Marcos E. Orchard
Keyword(s):  
Health Management ◽  
Research Work ◽  
Remaining Useful Life ◽  
Prognostics And Health Management ◽  
Engineering Systems ◽  
Sources Of Uncertainty ◽  
Arduous Task ◽  
Operational Decision Making ◽  
Inaccurate Estimation ◽  
The Impact

Uncertainty plays an important role in diagnostics, prognostics, and health management of engineering systems. The presence of uncertainty leads to an imprecise understanding of the behavior of such systems; as a result, this may adversely affect the results of diagnostics and prognostics. In particular, this may lead to an inaccurate estimation of the remaining useful life, which in turn affects operational decision-making. While several researchers have recognized the importance of uncertainty in prognostics and health management (PHM), there has not been a significant amount of research work that addresses the impact of uncertainty in different PHM activities. This is challenging because there are various sources of uncertainty that affect PHM, their interactions are not fully understood, and therefore, it is an arduous task to perform different PHM activities by systematically accounting for these sources of uncertainty. However, when this can be accomplished, it would be possible to estimate the uncertainty and confidence in the results of diagnostics and prognostics, and quantify the risk involved in prognostics-based decisionmaking.

EXPONENTIATED HALF-LOGISTIC LOMAX DISTRIBUTION WITH PROPERTIES AND APPLICATION

2019 ◽  
Vol XVI (2) ◽  
pp. 1-11
Author(s):  
Farrukh Jamal ◽  
Hesham Mohammed Reyad ◽  
Soha Othman Ahmed ◽  
Muhammad Akbar Ali Shah ◽  
Emrah Altun
Keyword(s):  
Real Data ◽  
Continuous Model ◽  
Model Parameters ◽  
Data Set ◽  
Lomax Distribution ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Probability Weighted Moment ◽  
Record Statistics ◽  
Maximum Likelihood Criterion

A new three-parameter continuous model called the exponentiated half-logistic Lomax distribution is introduced in this paper. Basic mathematical properties for the proposed model were investigated which include raw and incomplete moments, skewness, kurtosis, generating functions, Rényi entropy, Lorenz, Bonferroni and Zenga curves, probability weighted moment, stress strength model, order statistics, and record statistics. The model parameters were estimated by using the maximum likelihood criterion and the behaviours of these estimates were examined by conducting a simulation study. The applicability of the new model is illustrated by applying it on a real data set.

Remaining useful life estimation: a review on stochastic process-based approaches

2020 ◽  
Vol 14 ◽  
Author(s):  
Dangbo Du ◽  
Jianxun Zhang ◽  
Xiaosheng Si ◽  
Changhua Hu
Keyword(s):  
Stochastic Process ◽  
Health Management ◽  
Remaining Useful Life ◽  
Future Trends ◽  
Prognostics And Health Management ◽  
Inverse Gaussian ◽  
Life Estimation ◽  
Inverse Gaussian Process ◽  
Pros And Cons ◽  
Useful Life

Background: Remaining useful life (RUL) estimation is the central mission to the complex systems’ prognostics and health management. During last decades, numbers of developments and applications of the RUL estimation have proliferated. Objective: As one of the most popular approaches, stochastic process-based approach has been widely used for characterizing the degradation trajectories and estimating RULs. This paper aimed at reviewing the latest methods and patents on this topic. Methods: The review is concentrated on four common stochastic processes for degradation modelling and RUL estimation, i.e., Gamma process, Wiener process, inverse Gaussian process and Markov chain. Results: After a briefly review of these four models, we pointed out the pros and cons of them, as well as the improvement direction of each method. Conclusion: For better implementation, the applications of these four approaches on maintenance and decision-making are systematically introduced. Finally, the possible future trends are concluded tentatively.

scholarly journals Accommodating Taste and Scale Heterogeneity for Front-Seat Passenger’ Choice of Seat Belt Usage

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 460 ◽  
Author(s):  
Mahdi Rezapour ◽  
Khaled Ksaibati
Keyword(s):  
Mixed Model ◽  
Seat Belt ◽  
Model Fit ◽  
Model Parameters ◽  
Extended Model ◽  
Random Parameters ◽  
Front Seat ◽  
Scale Heterogeneity ◽  
Error Terms ◽  
The Cost

There is growing interest in implementation of the mixed model to account for heterogeneity across population observations. However, it has been argued that the assumption of independent and identically distributed (i.i.d) error terms might not be realistic, and for some observations the scale of the error is greater than others. Consequently, that might result in the error terms’ scale to be varied across those observations. As the standard mixed model could not account for the aforementioned attribute of the observations, extended model, allowing for scale heterogeneity, has been proposed to relax the equal error terms across observations. Thus, in this study we extended the mixed model to the model with heterogeneity in scale, or generalized multinomial logit model (GMNL), to see if accounting for the scale heterogeneity, by adding more flexibility to the distribution, would result in an improvement in the model fit. The study used the choice data related to wearing seat belt across front-seat passengers in Wyoming, with all attributes being individual-specific. The results highlighted that although the effect of the scale parameter was significant, the scale effect was trivial, and accounting for the effect at the cost of added parameters would result in a loss of model fit compared with the standard mixed model. Besides considering the standard mixed and the GMNL, the models with correlated random parameters were considered. The results highlighted that despite having significant correlation across the majority of the random parameters, the goodness of fits favors more parsimonious models with no correlation. The results of this study are specific to the dataset used in this study, and due to the possible fact that the heterogeneity in observations related to the front-seat passengers seat belt use might not be extreme, and do not require extra layer to account for the scale heterogeneity, or accounting for the scale heterogeneity at the cost of added parameters might not be required. Extensive discussion has been made in the content of this paper about the model parameters’ estimations and the mathematical formulation of the methods.

scholarly journals Theory and Applications of the Unit Gamma/Gompertz Distribution

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1850
Author(s):  
Rashad A. R. Bantan ◽  
Farrukh Jamal ◽  
Christophe Chesneau ◽  
Mohammed Elgarhy
Keyword(s):  
Stochastic Ordering ◽  
Real Data ◽  
Rate Function ◽  
The Other ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Gompertz Distribution ◽  
Probability And Statistics ◽  
Analytical Behavior

Unit distributions are commonly used in probability and statistics to describe useful quantities with values between 0 and 1, such as proportions, probabilities, and percentages. Some unit distributions are defined in a natural analytical manner, and the others are derived through the transformation of an existing distribution defined in a greater domain. In this article, we introduce the unit gamma/Gompertz distribution, founded on the inverse-exponential scheme and the gamma/Gompertz distribution. The gamma/Gompertz distribution is known to be a very flexible three-parameter lifetime distribution, and we aim to transpose this flexibility to the unit interval. First, we check this aspect with the analytical behavior of the primary functions. It is shown that the probability density function can be increasing, decreasing, “increasing-decreasing” and “decreasing-increasing”, with pliant asymmetric properties. On the other hand, the hazard rate function has monotonically increasing, decreasing, or constant shapes. We complete the theoretical part with some propositions on stochastic ordering, moments, quantiles, and the reliability coefficient. Practically, to estimate the model parameters from unit data, the maximum likelihood method is used. We present some simulation results to evaluate this method. Two applications using real data sets, one on trade shares and the other on flood levels, demonstrate the importance of the new model when compared to other unit models.

Guided image filtering based ℓ0 gradient minimization for limited-angle CT image reconstruction

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Tianyi Wang ◽  
Chengxiang Wang ◽  
Kequan Zhao ◽  
Wei Yu ◽  
Min Huang
Keyword(s):  
Iteration Process ◽  
Real Data ◽  
Image Filtering ◽  
Reconstruction Technique ◽  
Ct Reconstruction ◽  
Imaging Device ◽  
Practical Applications ◽  
Guided Image Filtering ◽  
Simultaneous Algebraic Reconstruction Technique ◽  
Limited Angle

Abstract Limited-angle computed tomography (CT) reconstruction problem arises in some practical applications due to restrictions in the scanning environment or CT imaging device. Some artifacts will be presented in image reconstructed by conventional analytical algorithms. Although some regularization strategies have been proposed to suppress the artifacts, such as total variation (TV) minimization, there is still distortion in some edge portions of image. Guided image filtering (GIF) has the advantage of smoothing the image as well as preserving the edge. To further improve the image quality and protect the edge of image, we propose a coupling method, that combines ℓ 0 {\ell_{0}} gradient minimization and GIF. An intermediate result obtained by ℓ 0 {\ell_{0}} gradient minimization is regarded as a guidance image of GIF, then GIF is used to filter the result reconstructed by simultaneous algebraic reconstruction technique (SART) with nonnegative constraint. It should be stressed that the guidance image is dynamically updated as the iteration process, which can transfer the edge to the filtered image. Some simulation and real data experiments are used to evaluate the proposed method. Experimental results show that our method owns some advantages in suppressing the artifacts of limited angle CT and in preserving the edge of image.

Sign in / Sign up

Export Citation Format

Share Document