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• An analytical parameters estimation results by the MLE method for the Wiener process with random effects is obtained. • The comparative study between different MLE methods is implemented. • An unbiased parameters estimation method is proposed and applied to other types of Wiener process-based degradation models. • An empirical unbiased parameters estimation results when the degradation data is measured at different times is developed. • Mis-specification issue about whether considering the random effects is analyzed in theory. Accurate parameters estimation is one of the most crucial components in remaining useful life (RUL) prediction. This paper proposes an unbiased parameters estimation method and analyzes the impact of model mis-specification of Wiener process-based degradation model with random effects. First, we obtain an analytical expression of parameters estimation for the linear Wiener process. Then, by analyzing the natures of parameters estimation, an unbiased parameters estimation method is proposed and applied to other types of Wiener process-based degradation models. This unbiased estimation method is very similar to the sample variance of normal distribution. Since the sample size of degradation data is typically small, hence the proposed unbiased estimation method is suggested. After that, we present an empirical unbiased parameters estimation method with a closed-form solution when the degradation data is measured at different times. The proposed unbiased estimation method could increase computational speed and avoid falling into local minimum. In addition, based on parameters estimation results, the mis-specification issue about whether the random effects should be considered in the degradation modeling is analyzed in theory. Finally, several numerical examples and case studies are used for experimental verification. The experimental results demonstrate that the proposed unbiased parameters estimation method is superior to other parameters estimation methods and the random effects are suggested to be considered. [ABSTRACT FROM AUTHOR]

In this paper, we provide a construction of two algorithms for approximation of the system of the jump-diffusion SDEs. Both methods are based on the classical Milstein steps and use equidistant discretization points. We construct implementable algorithm and their derivative-free version. We show that constructed methods are asymptotically optimal in the class of methods that use equidistant discretization of the interval [ 0 , T ]. Moreover, we report numerical experiments performed for some test equations, which confirm theoretical properties. [ABSTRACT FROM AUTHOR]

Real-time monitoring has received considerable attention recently due to its potential in automatic driving, tele-surgery, and factory automation in the 6G era. In remote estimation or reconstruction of stochastic processes, the statistical properties of stochastic processes to be monitored play a central role. Among the stochastic processes interested by real-time applications, the Brownian motion, also known as the Wiener processes is a typical one. In this paper, we are interested in how to monitor Brownian motions efficiently, timely, and reliably. To achieve this goal, we reveal that the real-time estimation error is jointly determined by the quantization error and freshness of data samples. Based on this observation, we present an optimal joint sampling and quantization scheme that efficiently balances the quantization distortion and the age-of-information (AoI). Furthermore, we find that the error accumulation will lead to infinite distortion as monitoring time increases. To overcome this, a multi-layer error correction method is presented for infinite-time monitoring, in which bounded distortion can be achieved with limited data rate. Finally, to conquer the accumulation of transmission errors in unreliable channels, we present an error correction mechanism based on periodic feedback. Diffusion approximation is then adopted to determine the optimal feedback rate and interval. [ABSTRACT FROM AUTHOR]

Traditionally, in reliability acceptance sampling plans, the decision to accept or reject a lot is made by performing the life tests of items. However, when the item's deterioration is described by a degradation process, it can be made based on the observed deterioration levels of the items obtained from degradation tests. In this paper, two acceptance sampling plans are developed, based on the observation of the deterioration of the items, accumulated on a given period of time. To model the degradation of the items over time, the Wiener process with positive drift is employed. Algorithms to find the parameters of the proposed sampling plans are suggested. Conditionally on the acceptance in the test, the developed sampling plans are shown to improve the reliability performance of the items in the sense that the lifetimes of the items after the reliability sampling test are stochastically larger than those before the test. Also, we compare the two sampling plans both from a technical and economical points of view. [ABSTRACT FROM AUTHOR]

The analysis of record-breaking events is of interest in fields such as climatology, hydrology or anthropology. In connection with the record occurrence, we propose three distribution-free statistics for the changepoint detection problem. They are CUSUM-type statistics based on the upper and/or lower record indicators observed in a series. Using a version of the functional central limit theorem, we show that the CUSUM-type statistics are asymptotically Kolmogorov distributed. The main results under the null hypothesis are based on series of independent and identically distributed random variables, but a statistic to deal with series with seasonal component and serial correlation is also proposed. A Monte Carlo study of size, power and changepoint estimate has been performed. Finally, the methods are illustrated by analyzing the time series of temperatures at Madrid, Spain. The R package RecordTest publicly available on CRAN implements the proposed methods. [ABSTRACT FROM AUTHOR]

The Nadaraya-Watson kernel-type nonparametric estimate of Poisson regression function is studied. The uniform consistency conditions are established and the limit theorems are proved for continuous functionals on C[a, 1 - a], 0 < a < 1/2. [ABSTRACT FROM AUTHOR]

In the field of reliability analysis, the constant-stress accelerated degradation test is one of the most commonly used methods to evaluate a product's reliability as degradation data are provided. In this paper, a constant-stress accelerated degradation test model of the Wiener process with random effects is proposed. First, the generalized confidence intervals of the model parameters are developed by constructing generalized pivotal quantities. Second, utilizing the substitution method, the generalized confidence intervals for the reliability function of lifetime, mean time to failure and the generalized prediction intervals for the degradation characteristic at the normal operating condition are also developed. Simulation studies are conducted to investigate the performances of the proposed generalized confidence intervals and prediction intervals. The simulation results reveal that the proposed generalized confidence intervals and prediction intervals work well in terms of the coverage percentage. In particular, a comparative analysis is made with the traditional bootstrap confidence intervals. At last, the proposed procedures are used for a real data analysis. [ABSTRACT FROM AUTHOR]

In this paper, the numerical solution of stochastic FitzHugh–Nagumo equation (SFNE) has been obtained by Chebyshev spectral collocation. Semi-implicit Euler–Maruyama scheme has been used for temporal variable to discretize the stochastic FitzHugh–Nagumo equation. A detailed stability analysis for stochastic FitzHugh–Nagumo equation has also been discussed. Graphical representations of obtained results of the stochastic FitzHugh–Nagumo equation have been discussed to provide a clear idea about the behavior of the solutions. [ABSTRACT FROM AUTHOR]

From the key composite quantum system made of a two-level system (qubit) and a harmonic oscillator (photon) with resonant or dispersive interactions, one derives the corresponding quantum Stochastic Master Equations (SME) when either the qubits or the photons are measured. Starting with an elementary discrete-time formulation based on explicit formulae for the interaction propagators, one shows how to include measurement imperfections and decoherence. This qubit/photon quantum system illustrates the Kraus-map structure of general discrete-time SME governing the dynamics of an open quantum system subject to measurement back-action and decoherence induced by the environment. Then, on the qubit/photon system, one explains the passage to a continuous-time mathematical model where the measurement signal is either a continuous real-value signal (typically homodyne or heterodyne signal) or a discontinuous and integer-value signal obtained from a counter. During this derivation, the Kraus map formulation is preserved in an infinitesimal way. Such a derivation provides also an equivalent Kraus-map formulation to the continuous-time SME usually expressed as stochastic differential equations driven either by Wiener or Poisson processes. From such Kraus-map formulation, simple linear numerical integration schemes are derived that preserve the positivity and the trace of the density operator, i.e. of the quantum state. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Harbin Institute of Technology. Social Sciences Edition / Haerbin Gongye Daxue Xuebao. Shehui Kexue Ban is the property of Harbin Institute of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Revista de Ciencias Sociales (13159518) is the property of Revista de Ciencias Sociales de la Universidad del Zulia Venezuela and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we investigate the application of the probabilistic method (PM) for the numerical solution of the Dirichlet generalized harmonic problem in axisymmetric finite homogeneous and isotropic bodies with a right circular cylindrical hole. The term "generalized" indicates that a boundary function has a finite number of first kind discontinuity curves. The suggested algorithm for the numerical solution of boundary problems consists of the following main stages: a) application of the PM, which in turn is based on the computer modeling of the Wiener process; b) finding the intersection point of the trajectory of the simulated Wiener process and the surface of the problem domain; c) development of a code for the numerical implementation and checking the reliability of obtained results; d) finding the probabilistic solution of generalized problems at any fixed points in the considered domains. The algorithm does not require the approximation of a boundary function. The PM is tested on an explicit analytical solution from the literature. To illustrate the effectiveness and simplicity of the proposed method several examples are considered. Numerical results are presented and discussed. [ABSTRACT FROM AUTHOR]

With its extensive use in industry, assessing the reliability of the micro inertial measurment unit (MIMU) has become a pressing need. Unfortunately, the MIMU is made up of several components, and the degradation processes of each are intertwined, making it difficult to assess the MIMU’s reliability and remaining useful life. In this research, we offer a reliability assessment approach for the MIMU, which has long-lifetime and multiple performance characteristics (PCs), based on accelerated degradation data and copula theory.Each PC model of MIMU is constructed utilizing drift Brownian motion to depict accelerated degradation process. The copula function is used to model the multivariate dependent accelerated degradation test data and to describe the dependency between multiple MIMU performance parameters. The particle swarm optimization algorithm is used to estimate the unknown parameters in the multi-dependent ADT model. Finally, the storage test and simulation example on MIMU’s accelerated degradation data verify the feasibility and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Due to the high reliability of present meters, it is difficult to obtain the failure time of meters through accelerated life tests. Based on the failure data of the accelerated life test, this paper studies the mathematical model based on the Wiener process and establishes the degradation model of the instrument by the maximum likelihood to estimate the parameters of the Wiener model. With full consideration of the possible nonlinear effects in modeling, the time scale transformation method is used to study and obtain the reliability life prediction model of smart meters based on nonlinear data. Finally, the reliability life prediction model of meters is verified and evaluated through the example data of the accelerated life test of smart meters. Compared with the conventional method, this method has less error in calculating the reliability, greatly saves test time, and has a higher accuracy than estimating the lifetime model using the Wiener process directly. [ABSTRACT FROM AUTHOR]

In this paper we study a class of impulsive systems of stochastic differential equations with infinite Brownian motions. Sufficient conditions for the existence and uniqueness of solutions are established by mean of some fixed point theorems in vector Banach spaces. An example is provided to illustrate the theory.

Given the problem of three-sources uncertainty in aero engine degradation process and the assumption of normal distribution of measurement error in existing research, a Wiener process aero engine residual useful life time(RUL) prediction method with logistic distribution of measurement error was proposed. Firstly, the performance degradation model was established when the measurement error obeys the logistics distribution, and the accurate mathematical expression of the RUL distribution was given under the first arrival time. Secondly, in order to improve the utilization of monitoring parameters, a key parameter screening method based on Spearman coefficient was given. Lastly, in view of the lack of historical data and prior information, a parameter estimation method based on maximum entropy unscented particle filtering and conditional expectation maximization algorithm was adopted. Meanwhile after new performance degradation data was obtained, the model parameters could be adaptively updated. With MSE as the evaluation index, the experimental results show that the MSE value of this method is 13.25, and the MSE value is 16.12 lower than that of traditional method, which can effectively improve the prediction accuracy and the engine utilization and safety.

The Wiener process was used to explore the (2 + 1)-dimensional chiral nonlinear Schrödinger equation (CNLSE). This model outlines the energy characteristics of quantum physics’ fractional Hall effect edge states. The sine-Gordon expansion technique (SGET) was implemented to extract stochastic solutions for the CNLSE through multiplicative noise effects. This method accurately described a variety of solitary behaviors, including bright solitons, dark periodic envelopes, solitonic forms, and dissipative and dissipative–soliton-like waves, showing how the solutions changed as the values of the studied system’s physical parameters were changed. The stochastic parameter was shown to affect the damping, growth, and conversion effects on the bright (dark) envelope and shock-forced oscillatory wave energy, amplitudes, and frequencies. In addition, the intensity of noise resulted in enormous periodic envelope stochastic structures and shock-forced oscillatory behaviors. The proposed technique is applicable to various energy equations in the nonlinear applied sciences.

The proton exchange membrane fuel cell (PEMFC) is a promising power source, but the short lifespan and high maintenance cost restrict its development and widespread application. Performance degradation prediction is an effective technique to extend the lifespan and reduce the maintenance cost of PEMFC. This paper proposed a novel hybrid method for the performance degradation prediction of PEMFC. Firstly, considering the randomness of PEMFC degradation, a Wiener process model is established to describe the degradation of the aging factor. Secondly, the unscented Kalman filter algorithm is used to estimate the degradation state of the aging factor from monitoring voltage. Then, in order to predict the degradation state of PEMFC, the transformer structure is used to capture the data characteristics and fluctuations of the aging factor. To quantify the uncertainty of the predicted results, we also add the Monte Carlo dropout technology to the transformer to obtain the confidence interval of the predicted result. Finally, the effectiveness and superiority of the proposed method are verified on the experimental datasets.

In the sense of a conformable fractional operator, we consider a generalized fractional–stochastic nonlinear wave equation (GFSNWE). This equation may be used to depict several nonlinear physical phenomena occurring in a liquid containing gas bubbles. The analytical solutions of the GFSNWE are obtained by using the F-expansion and the Jacobi elliptic function methods with the Riccati equation. Due to the presence of noise and the conformable derivative, some solutions that were achieved are shown together with their physical interpretations.

The stochastic fractional (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation (SFHFSCE), which is driven in the Stratonovich sense by a multiplicative Wiener process, is considered here. The analytical solutions of the SFHFSCE are attained by utilizing the Jacobi elliptic function method. Various kinds of analytical fractional stochastic solutions, for instance, the elliptic functions, are obtained. Physicists can utilize these solutions to understand a variety of important physical phenomena because magnetic solitons have been categorized as one of the interesting groups of non-linear excitations representing spin dynamics in semi-classical continuum Heisenberg systems. To study the impact of the Wiener process on these solutions, the 3D and 2D surfaces of some achieved exact fractional stochastic solutions are plotted. [ABSTRACT FROM AUTHOR]

The Half-Plane Half-Comb walk is a random walk on the plane, when we have a square lattice on the upper half-plane and a comb structure on the lower half-plane, i.e., horizontal lines below the x-axis are removed. We prove that the probability that this walk returns to the origin in 2N steps is asymptotically equal to 2 / (π N). As a consequence, we prove strong laws and a limit distribution for the local time. [ABSTRACT FROM AUTHOR]

The accelerated aging process is incorporated into the design and development of intravascular catheters to assess their reliability assuring that this medical device is safe and effective for the intended use during their shelf life. The accelerated aging process is based on a common approach that assumes that the rate of aging increases by a factor of 2A(AT/l0), where AT is the temperature increment. However, with the life data obtained from this empirical method is difficult to do inferences about reliability. This paper presents an accelerated destructive degradation test using thermal stress to obtain degradation data directly relates reliability to critical performance characteristic, which is the tensile strength in the intravascular catheter tip considered as a critical concern in patients' safety. The degradation data model is given by a stochastic Wiener process with the drift parameter being represented as Arrhenius function. The parameters of the Wiener process and Arrhenius function are estimated using maximum likelihood; these parameters are used to estimate the first-passage time (time to failure) distribution when the intravascular catheters degradation path reaches a tensile strength critical value in each thermal stress level. Based on this, a complete product reliability assessment is performed and presented. [ABSTRACT FROM AUTHOR]

Product fault diagnosis has always been the focus of quality and reliability research. However, a failure–rate curve of some products is a symmetrical function, the fault analysis result is not true because the failure period of the products cannot be judged accurately. In order to solve the problem of fault diagnosis, this paper proposes a new Takagi-Sugeno (T-S) dynamic fault tree analysis method based on a Bayesian network accompanying the Wiener process. Firstly, the top event, middle event, and bottom event of the product failure mode are determined, and the T-S dynamic fault tree is constructed. Secondly, in order to form the Bayesian network diagram of the T-S dynamic fault tree, the events in the fault tree are transformed into nodes, and the T-S dynamic gate is also transformed into directed edges. Then, the Wiener process is used to model the performance degradation process of the stationary independent increment of the symmetric function distribution, and the maximum likelihood estimation method is applied to estimate the unknown parameters of the degradation model. Next, the product residual life prediction model is established based on the concept of first arrival time, and a symmetric function of failure–rate curve is obtained by using the product failure probability density function. According to the fault density function derived from the Wiener process, the reverse reasoning algorithm of the Bayesian network is established. Combined with the prior probability of the bottom event, the posterior probability of the root node is calculated and sorted as well. Finally, taking the insufficient braking force of electromagnetic brakes as an example, the practicability and objectivity of the new method are proved. [ABSTRACT FROM AUTHOR]

We establish the global existence of weak martingale solutions to the simplified stochastic Ericksen–Leslie system modeling the nematic liquid crystal flow driven by Wiener-type noises on the two-dimensional bounded domains. The construction of solutions is based on the convergence of Ginzburg–Landau approximations. To achieve such a convergence, we first utilize the concentration-cancellation method for the Ericksen stress tensor fields based on a Pohozaev type argument, and then the Skorokhod compactness theorem, which is built upon uniform energy estimates. [ABSTRACT FROM AUTHOR]

The Gierer–Meinhardt system occurs in morphogenesis, where the development of an organism from a single cell is modelled. One of the steps in the development is the formation of spatial patterns of the cell structure, starting from an almost homogeneous cell distribution. Turing proposed different activator–inhibitor systems with varying diffusion rates in his pioneering work, which could trigger the emergence of such cell structures. Mathematically, one describes these activator–inhibitor systems as coupled systems of reaction-diffusion equations with different diffusion coefficients and highly nonlinear interaction. One famous example of these systems is the Gierer–Meinhardt system. These systems usually are not of monotone type, such that one has to apply other techniques. The purpose of this article is to study the stochastic reaction-diffusion Gierer–Meinhardt system with homogeneous Neumann boundary conditions on a one or two-dimensional bounded spatial domain. To be more precise, we perturb the original Gierer–Meinhardt system by an infinite-dimensional Wiener process and show under which conditions on the Wiener process and the initial conditions, a solution exists. In dimension one, we even show the pathwise uniqueness. In dimension two, uniqueness is still an open question. [ABSTRACT FROM AUTHOR]

We investigate the mixed fractional Brownian motion with trend of the form X t = θ t + σ W t + κ B t H , driven by a standard Brownian motion W and a fractional Brownian motion B H with Hurst parameter H. We develop and compare two approaches to estimation of four unknown parameters θ , σ , κ and H by discrete observations. The first algorithm is more traditional: we estimate σ , κ and H using the quadratic variations, while the estimator of θ is obtained as a discretization of a continuous-time estimator of maximum likelihood type. This approach has several limitations, in particular, it assumes that H < 3 4 , moreover, some estimators have too low rate of convergence. Therefore, we propose a new method for simultaneous estimation of all four parameters, which is based on the ergodic theorem. Finally, we compare two approaches by Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

In this paper, we describe how the probabilistic method (PM) can be applied to numerical solving the Dirichlet generalized harmonic problem in regular n-sided pyramidal domains. The term "generalized" indicates that a boundary function has a finite number of first kind discontinuity curves. In the considered case, the edges of the pyramid represent the curves. Application of the PM consists of the following main stages: a) computer modelling of the Wiener process; b) construction of an algorithm for finding the point of intersection of the trajectory of the simulated Wiener process and the surface of the pyramid; c) checking a scheme and a corresponding calculating program needed for numerical implementation and reliability of the obtained results; d) finding a probabilistic solution of generalized problems at any fixed points of the considered pyramid. The algorithm does not require approximation of a boundary function, which is main of its important properties. For illustration of the effectiveness and simplicity of the suggested method several numerical examples are considered and numerical results are presented. [ABSTRACT FROM AUTHOR]

We consider a linear stochastic Sobolev type equation with relatively p-bounded operator and formulate a multipoint initial–final value condition for the equation. In addition, we prove a theorem on the existence of a unique solution to this problem in the space of K -"noises". Abstract results are used to study a specific multipoint initial–final value problem for linear stochastic Hoff equations on a geometric graph. The model describes the movement of a construction of some I-beams that moves in near-Earth space under random effects. The initial–final value condition require that the projections of the construction onto the surface of the Earth are specified at certain points in time. [ABSTRACT FROM AUTHOR]

Nowadays, systems are more complex and require high reliability for their components, especially critical system components. Therefore, to avoid serious damage, system are often replaced before the actual failure. The replaced parts are considered to have “soft failure”, and the limit in which the parts are replaced is known as the critical level of the degradation process. Determining the appropriate value of the critical level for a product is an important problem in their exploitation, as well as for predicting the Mean Time to Failure (MTTF) or Remaining Useful Lifetime (RUL) of this product based on the degradation data by the mathematical models. In this article, an approach in determining the critical levels based on failure data from an accelerated test is introduced. This approach is applied with the degradation process of Light-Emitting Diodes (LED) in an accelerated test and a type of Wiener process-based model is used to predict the MTTF or RUL of LED based on their degradation data and the found critical level. [ABSTRACT FROM AUTHOR]

With the aim of solving the reliability modeling and calculation of multivariate stochastic degradation systems, two stochastic degradation models based on the bivariate Wiener process are proposed, in which two performance characteristics are composited to one variable. Two different failure modes including the defect-based failure and the duration-based failure are considered. The explicit expressions of the system reliability are derived in the cases that the performance characteristics are not composited or the performance characteristics are composited according to the linear combination of the degradation measurements. An algorithm based on the Monte Carlo simulation is proposed to simulate the degradation process, in which the performance characteristics are composited in arbitrary forms, and the correctness of the analytical results is also verified. Finally, some numerical examples are presented to illustrate the present reliability assessment method。

Bearings play a pivotal role in various mechanical systems, and their health directly impacts the reliability and safety of these systems. Consequently, extensive research has been dedicated to the estimation of Bearing Remaining Useful Life (RUL) through the lens of information fusion theory. The absence of comprehensive life-cycle degradation data for bearings, a common challenge within the information fusion domain, can hinder the accuracy and reliability of RUL prediction models. A novel hybrid data and model approach named GRU-AE-Wiener has been developed to address this limitation. This approach combines the power of Gated Recurrent Unit (GRU) and Wiener process models within the information fusion framework. Firstly, a Loop Generative Adversarial Network (Loop-GAN) is introduced to synthesize pseudo data to enhance the quality of synthetic data. Next, a bidirectional GRU model is structurally integrated with the Wiener process. In this design, the GRU model is configured in an Auto-Encoder-like structure, with the Wiener process serving as the hidden layer within this Auto-Encoder. Importantly, both the GRU and Wiener processes are jointly optimized with the assistance of Loop-GAN, emphasizing the collaborative nature of information fusion in this approach. The effectiveness of the proposed GRU-AE-Wiener is validated using the PHM 2012 dataset and XJTU-SY dataset. Experimental results underscore its superior RUL predictive performance compared to other deep learning models, highlighting the practical application of information fusion principles in bearing health assessment. [ABSTRACT FROM AUTHOR]

Prognostics and system health management (PHM) has attracted increasing attention from both scholars and engineers with interests in improving the reliability, availability, and profitability of industrial systems. Recognized as the two prominent challenges in the prognostics of complicated degrading systems, temporal nonlinearity and stochastic dynamics have incentivized numerous research on nonlinear degradation modeling-based prognostic approaches such as diffusion-process-based models. Comparatively, much less research on how to incorporate the corresponding prognosis information into the decision making on health management has been conducted. In this paper, an optimal condition-based maintenance (CBM) policy for stochastic degrading systems characterized by a diffusion-process-based model has been presented. The CBM policy is firstly converted into a Markovian decision process (MDP) based on the expected discounted cost function (EDCF) within the infinite horizon. Then, the structural properties of the optimal CBM policy have been thoroughly investigated, and the value-based iteration algorithm to solve the optimal CBM problem is proposed. It is proved that the optimal CBM policy for a periodically inspected nonlinear degrading system governed by a diffusion process is a control limit policy, which neither increases in the degradation state nor decreases in the age of the system. Finally, the proposed optimal CBM policy has been illustrated and validated by a case study on the gyroscopes. • An optimal CBM policy for a kind of nonlinear stochastic degrading systems is proposed. • The structural properties of the optimal CBM policy have been thoroughly investigated. • A control limit policy has been proved as the optimal CBM policy. • A value-based iteration algorithm to solve the optimal CBM problem is presented. [ABSTRACT FROM AUTHOR]

[Display omitted] • Real-time monitoring with a data-model fusion approach for remaining useful life. • Dynamic hybrid matching between monitoring data and models achieves high accuracy. • Real-time inference for enhanced model interpretability. • Efficient real-time monitoring with minimal data usage. Ensuring the reliable operation of electric vehicles relies on accurate predictions of the remaining useful life (RUL) for lithium batteries. Existing model-based prediction methods face limitations due to insufficient full-life experimental data, while online monitoring data-driven methods lack empirical guidance and interpretability of the training data. To address these challenges, a model-data-fusion prediction method is proposed. Firstly, the degradation process is characterized using a generalized Wiener process model. Secondly, A Whale Optimization Particle Search Filter (WOS-PF) is introduced for real-time parameter updating of the degradation model. This approach ensures that even with a small sample size, parameters can be reliably estimated. Finally, leveraging the continuously updated parameters, a probability density function is derived to predict the RUL of lithium batteries in real-time. Experimental results indicate that this method enhances prediction accuracy compared to other existing methods, leading to better real-time monitoring of lithium battery health. [ABSTRACT FROM AUTHOR]

Quantization has been widely employed in analog-to-digital conversion (ADC) for the acquisition of digital data, which are further utilized for prognostics. However, quantization errors are inevitable during ADC, resulting in bias in the subsequent prognosis results. Compared to the numerous researches on prognosis considering measurement noises, slight attention has been paid on remaining useful life (RUL) for degrading devices incorporating quantization errors. In this study, a Wiener-process-based model incorporating mixed random noise is utilized to describe the degradation process involving quantization errors. In order to mitigate the impact of quantization errors, a parameter identification approach and a degradation state estimation method are proposed, which integrate maximum likelihood estimation, particle filter, and Bayesian inference. Subsequently, the results of RUL prediction with and without considering quantization errors are derived, respectively. Finally, numerical examples and a case study of the control moment gyroscopes (CMG) and batteries are provided to demonstrate the proposed method. • Prognosis for stochastic degrading devices incorporating quantization is investigated. • A prognosis method involving both measurement and quantization errors is proposed. • Offline and online parameters identification methods are presented. • The PDFs of the RUL prediction incorporating quantization are derived. [ABSTRACT FROM AUTHOR]

We use a Riemannian metric as a cost metric when it comes to the optimal decisions that should be made in a multi-agent/Team scenario. The two parameters of interest to us are Team skill and Team interdependence, which are modeled as Wiener process drift and the inverse of Wiener process diffusion, respectively. The underlying mathematics is presented, along with some approximating rules of thumb. It is noteworthy that the mathematics points to, what seems at first, counter-intuitive paradigms for Team performance. However, in reality the mathematics shows a subtle interplay between the factors affecting Team performance.

ObjectivesShip collision is one of the main factors threatening the navigation safety of intelligent ships. A calculation model of ship collision risk should identify potential collision risks in time and provide the basic information for the intelligent ship's autonomous collision avoidance decision-making.MethodsThis paper first analyzes the domain-based collision risk parameter calculation model according to the degree of domain violation and other parameters. The navigation scene is divided into a single-ship encounter situation and an encounter between a ship and target ship group, and a new collision risk parameter calculation model for multi-ship encounters is given. Second, based on the Wiener process, the uncertainty of ship position prediction is modeled and obtained according to the Chi-squared distribution. Finally, a calculation method for collision risk parameters which considers the uncertainty of ship position prediction is given.ResultsOn this basis, the influence of ship position prediction uncertainty on ship collision risk is considered. ConclusionsThis method can further guarantee the safety of intelligent ships at sea.

Electronic packaging solder joints are the key parts of mechanical fixation and electrical interconnection between electronic chips and printed circuit boards, which are prone to failure and lead to electronic device failures under the action of vibration environment stress. In regard to the failure characterization and degradation modeling of electronic packaging solder joints under vibration load, this paper adopts environmental stress tests, builds a vibration failure test platform, designs a vibration load excitation spectrum, and obtains solder joint degradation data under vibration stress; it uses the square root amplitude, form factors, and kurtosis factors to characterize the solder joint degradation process, which effectively identify the solder joint degradation node, and improve the data monotonicity of the solder joint degradation process; the Wiener process is used to build a solder joint multi-stage degradation model. Based on the EM algorithm, the hyperparameters of the degradation model have been optimized, and the universal test of the Wiener degradation model with multiple samples is carried out in accordance with the LB index. The analysis shows that the effectiveness of different samples is as high as 87.5%, which verifies the universality of the Wiener degradation model; Based on the crack morphology subject to the solder joint test and the features of the solder joint in the multi-stages, the paper analyzes the crack propagation behavior of the solder joint, and clarifies the failure mechanism of the solder joint.

A warranty product often has an interval structure, resulting in different warranty periods for each component due to their distinct degradation paths. From the manufacturer's perspective, it is reasonable to establish appropriate warranty periods for each part to achieve cost savings. This paper introduces a dependent series configuration consisting of a main component and an auxiliary component. The failure of the main component leads to system failure, while the failure of the auxiliary component only causes a random damage to the main component. These two components follow different Wiener degradation paths, and then their first passage times (FPTs) follow disparate inverse Gaussian distributions. Assuming a pre-deterministic warranty period, W , for the main component, and η W , 0 < η < 1 , for the auxiliary component, the warranty period can be divided into two stages: [ 0 , η W ] and [ η W , W ]. In this context, the paper proposes warranty claim policies for replacement, objective-oriented imperfect repair (OOIR), and refund. The corresponding warranty costs sustained by manufacturer and consumer within these two stages are considered. Finally, a numerical example is presented to illustrate the warranty costs sustained by manufacturer and consumer under different scenarios, as well as the total warranty costs. • The degradation paths, warranty periods and warranty costs of the series system is analyzed. • The warranty costs sustained by manufacturer and consumer under different scenarios is analyzed. • The interdependence between various components is considered. [ABSTRACT FROM AUTHOR]

• Propose a fully numerical iterative process to optimize the maintenance threshold for systems with non-monotonic degradation behavior subject to competing failures. • Consider lead time before maintenance implementation in the numerical framework. • Assess the impact of shock detection threshold on the expected cost. Shocks have attracted considerable interest in reliability and maintenance engineering because of their impact on vulnerable systems. Most industrial systems suffer from both internal degradation caused by fatigue and wear-out, and external shocks that often occur randomly due to harsh weather conditions, overloading, etc. Developing maintenance optimization models without taking these stochastic shocks into account is often ineffective. This paper develops a model to optimize the maintenance alarm threshold for a single-component continuously monitored system which is exposed to both fatal and non-fatal shocks in the presence of lead time for hard time maintenance. The shocks occur randomly according to a homogeneous Poisson process during the whole degradation process and have a stochastic impact on the degradation level, while the system resistance to shocks decreases as the system approaches failure. We propose a new numerical maintenance optimization model to find the solution without Monte-Carlo simulation and the model is compared to the Wiener process. A numerical example and a real-time experimental case study on roller bearings are used to demonstrate the effectiveness of the model. The results show that the model is capable of improving maintenance decision-making in terms of failure probability and risk perspective. [ABSTRACT FROM AUTHOR]

• A novel hybrid prognostic method for remaining useful life prediction is presented. • A new nonlinear health indicator is generated for the training bearings. • The condition monitoring interval of health state is determined by the 3σ criterion. • The degradation and RUL forecasting is achieved based on the nonlinear Wiener process with random effects method. This paper proposes a novel hybrid method aiming at the fault prognosis of bearings. A nonlinear health indicator (HI) is first constructed using Complete Ensemble Empirical Mode Decomposition with Adaptive Noise and Kernel Principal Component Analysis to reflect the health state of a bearing accurately and convincingly. Subsequently, multi-domain features are extracted from vibration signals and the Dual-Channel Transformer Network with the Convolutional Block Attention Module is applied for constructing HIs of the rest bearings. Moreover, the 3σ criterion is employed to establish the condition monitoring interval of health state and detect the First Prediction Time, with which degradation modeling and probabilistic Remaining Useful Life (RUL) prediction are conducted with the assistance of nonlinear Wiener process with random effects. The superior performance of the proposed hybrid prognostic method confirms that the method contributes to the accurate RUL prediction and uncertainty quantification. [ABSTRACT FROM AUTHOR]

In this paper, time domain signal and noise behavior of an active CRLH transmission line was investigated in the nonlinear regime at millimeter wave frequencies. In this structure, the transistor is considered as three coupled transmission lines and all three drain,gate and source lines are CRLH transmission lines. The left-handed element values for the active CRLH transmission line are calculated in such a way that the phase cancellation effect and dispersion of the CRLH transmission line are reduced. In order to model this active CRLH transmission line, with the assumption of wave propagation in the form of Quasi-TEM, the distributed modeling method is used to extract stochastic telegraphic equation (STE) in the non-linear regime. To model noise sources in the non-linear regime, the Wiener process and modulation functions have been used to model white noise in the nonlinear regime and in the time domain. By applying the finite integration method to stochastic telegraphic equation, the behavior of the signal and noise of the active structure CRLH has been compared with a line of active structure RH and the obtain results of the numerical method have been verified with the results of the Agilent ADS software. [ABSTRACT FROM AUTHOR]

In the present paper, an algorithm for the numerical solution of the external Dirichlet generalized harmonic problem for a sphere by the method of probabilistic solution (MPS) is given, where “generalized” indicates that a boundary function has a finite number of first kind discontinuity curves. The algorithm consists of the following main stages: (1) the transition from an infinite domain to a finite domain by an inversion; (2) the consideration of a new Dirichlet generalized harmonic problem on the basis of Kelvin’s theorem for the obtained finite domain; (3) the numerical solution of the new problem for the finite domain by the MPS, which in turn is based on a computer simulation of the Weiner process; (4) finding the probabilistic solution of the posed generalized problem at any fixed points of the infinite domain by the solution of the new problem. For illustration, numerical examples are considered and results are presented.

This paper investigates an uncommon technique by using the influence of the random function (Weiner process function), on a two-temperature problem, at the free surface of the semiconducting medium, by using the photo-thermoelasticity theory. Using the Silicon material as an example of a semiconducting medium under the influence of a magnetic field, the novel model can be formulated. To make the problem more logical, the randomness of the Weiner process function is aged to the governing stochastic equation. A combining stochastic process with the boundary of the variables is studied. In this case, the stochastic and deterministic solutions were obtained for all physical quantities. The additional noise is regarded as white noise. The problem is investigated according to a two-dimensional (2D) deformation. The normal mode method can be used mathematically to obtain numerically the deterministic, stochastic, and variance solutions of all physical quantities. Three sample paths are obtained by making a comparison between the stochastic and deterministic distributions of the field variables. The impacts of adding randomization to the boundary conditions are highlighted. The numerical results are shown graphically and discussed in consideration of the two-temperature parameter effect.

A multi-objective optimization method for the accelerated degradation test based on Wiener process is proposed in this article in order to solve the problem that a single objective optimization cannot solve the difficulty or even conflicting test configurations caused by different optimization objective functions. An accelerated degradation model is established based on Wiener process, and the unknown parameters are solved by a two-step maximum likelihood estimation method. Considering both the accuracies of life estimation and the model parameter estimation, a multi-objective optimization model is established with the optimization goals of the minimum asymptotic variance of P-quantile of lifetime and the maximum determinant of Fisher information matrix. The Pareto solutions are set by the multi-objective genetic algorithm, and the test configurations for multi-objectives are obtained. Under the step stress accelerated degradation test and the constant stress accelerated degradation test, the effectiveness of the proposed method is verified by an optimization example of LEDs accelerated degradation test. [ABSTRACT FROM AUTHOR]