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• A novel trajectory accuracy reliability model evaluates the impact of mixed uncertainties on the motion performance of robot manipulators. • A new analytical algorithm combines the SGQ derives statistical moments of maximum positional error distribution. • A novel reliability analysis method calculates the failure probability of trajectory accuracy efficiently and accurately. This paper proposes a novel trajectory accuracy reliability analysis method with random and interval variables to evaluate the impact of mixed uncertainties on the motion performance of robot manipulators. To effectively and accurately solve the hybrid reliability model, the interval analysis is first conducted on the positional error model established by differential kinematics, and a maximum positional error searching algorithm is developed based on geometric transformation and cell enumeration. Then, the trajectory accuracy reliability model is reconstructed by the eigen-decomposition technique, which further incorporates the adaptive weight vector-based anisotropic sparse-grid quadrature approach to derive the statistical moments of maximum positional error. Afterward, by matching with the cumulants of the original reliability model, a novel approximation method is proposed based on the Weibull distribution and minimized matching error model to complete the trajectory accuracy reliability analysis. The practicality and advantages of the proposed method are demonstrated by two illustrative examples of 6-degrees-of-freedom robot manipulators. Comparative results affirm that the proposed method outperforms existing state-of-the-art algorithms in terms of accuracy and efficiency for trajectory accuracy reliability analysis encompassing random and interval uncertainties. Overall, the outcomes of this paper contribute significantly to the design and analysis of safety and reliability in moving machinery. [ABSTRACT FROM AUTHOR]

• A multi-state balanced system with standby components switching mechanism is proposed. • A general degree balance function is proposed. • In case 1, system balance degree is defined based on all components states. • In case 2, system balance degree is defined based on symmetrical components states. • Finite Markov chain imbedding approach is used to get reliability indexes. An increasing attention has been paid to the reliability analysis of balanced system. In previous studies, there were three rebalancing strategies for balanced systems: forcing down the unbalanced pair of subsystems, restarting components that have been shut down, and dynamically adjusting the state of the working components. In this paper, a new rebalancing strategy is proposed by switching the standby components for a multi-state balanced system. The system consists of m subsystems, each with one working component and n -1 standby components. The system is balanced when the working components do not fail and the system's balanced degree doesn't exceed a threshold. Two cases of system balance conditions are considered: one is based on component states and the other is based on symmetric component states. If the system is imbalanced or fails, the system needs to adjust the state of the working component by switching switches to let the system operate normally. The switching rules for each case are given separately. In this paper, the finite Markov chain imbedding approach (FMCIA) is used to derive the system reliability. Finally, numerical examples and sensitivity analysis are given. [ABSTRACT FROM AUTHOR]

• Developed a novel temporal Noisy-adder structure for analysing scalable C(k,n:F). • Performed comparison experiments to showcase the novel model's effectiveness. • Revealed computation range of 4 algorithms, shown advantage of the novel model. · Provided an effective BN-based route for analyzing Consecutive-k models. The Bayesian network(BN) is a powerful tool for modeling and analyzing reliability, safety, and risk in various engineering systems. Although there have been studies that incorporate it into the modeling of Consecutive- k -out-of- n : F systems(C(k,n :F)), these applications are limited to naive mode and cannot tackle scalable systems (e.g., n>2000,k>40). By introducing temporal Noisy-adder structure, named NaCkoon model, the number of nodes in equivalent C(k,n :F) BN model is significantly reduced, and the Conditional Probability Table (CPT) of temporary nodes can be controlled to linear complexity. The correctness of the proposed algorithm is validated by the comparison of literature case. Through numerical experiments, the novel algorithms proposed in this paper were compared with existing ones, including BN construction and inference computation time, was found to be the most optimal solution. Finally, the computable ranges of novel and existing algorithms are obtained through the capability computation. The test results show that NaCkoon model proposed in this paper has great advantages over existing algorithms and proposed NaA+NaO model based BN. [ABSTRACT FROM AUTHOR]

In constructing the Bayesian network (BN) reliability model, too many components will make the memory storage requirements of the conditional probability table (CPT) exceed the computer random access memory (RAM), especially for the complex multistate system with common cause failure (CCF). However, the existing methods cannot solve the BN modeling's large memory storage requirements problem of the complex multistate system with CCF. Thus, this paper proposes a BN block to process the nodes with CCF, converting CPT to a super multistate node's joint probability table, based on which a multistate BN compression modeling algorithm under CCF is proposed to reduce the memory storage requirements of BN reliability modeling. By deriving the intermediate inference factor constructing rules, this paper proposes a multistate BN compression inference algorithm under CCF to perform the compressed BN reliability inference. Finally, two engineering cases validate the proposed algorithms' performance. The results show that the proposed algorithms can significantly decrease the BN modeling's memory storage requirements and accurately analyze the reliability of the complex multistate system with CCF. • Proposing BN block to process CCF of complex multistate systems. • Deriving the constructing rules of intermediate inference factors with CCF. • Proposing the multistate BN compression inference algorithm under CCF. [ABSTRACT FROM AUTHOR]

Polynomial chaos expansion (PCE) is an efficient surrogate modeling method that can be used for reliability analysis. However, the existing methods generally require sufficient labeled data to build a high-precision surrogate model and cannot use much-unlabeled data. Thus, this paper proposes a parameterized coefficient fine-tuning-based PCE (PCFT-PCE) method. Based on limited labeled data, the PCFT-PCE method first uses the traditional PCE method to initialize the parameterized expansion coefficients of a single-layer neural network. Then based on abundant unlabeled data, the single-layer neural network parameters are fine-tuned by adopting two properties of PCE to construct an unsupervised loss function. Based on the PCFT-PCE method, this paper builds a sphere-biconic reentry vehicle reliability-based design optimization (SBRV-RBDO) framework to minimize the mass and the highest temperature considering geometric and material parameters' uncertainties, where a combination penalty method is proposed to adjust and balance the mass and the highest temperature constraints. Finally, a numerical example and an engineering case validate the proposed methods. The results show that the proposed PCFT-PCE method builds a more accurate PCE model with a little extra calculation time. The SBRV-RBDO framework helps engineers to find reliable optimization schemes for SBRV conceptual design. • Proposing parameterized coefficient fine-tuning-based PCE method. • PCFT-PCE makes much-unlabeled data available for building a PCE model. • Building a more accurate PCE model with a little extra calculation time. • Constructing a SBRV reliability-based design optimization framework. [ABSTRACT FROM AUTHOR]

• A new reliability analysis method for electromechanical system considering varying working conditions was presented. • A new digital-twin-based dynamic Bayesian network was proposed to for reliability analysis using historical operation data. • The reliability of a subsea control module was analyzed, revealing the most probable failure mode and vulnerable components. The reliability evaluation of the subsea control module(SCM) is the key to ensure the safety and stability of subsea oil-gas production. The failure probability and reliability of SCM components are dependent on time and working conditions. To analyze the SCMs' reliability considering varying working conditions, this paper proposed a new digital twin and dynamic Bayesian network(DBN) based model utilizing historical working condition data in reliability analysis. In the proposed framework, critical working condition data is obtained by sensor-based Digital Twin(DT) simulation and used for dynamically updating the parameters in the DBN reliability analysis model. The reliability evaluation of an actual SCM electric system was carried out. The results revealed the most probable failure mode and the most vulnerable components in the system. Finally, the fault prediction based on the back-forward analysis capacity of the proposed method was conducted to predict the probability of the faulty device when unexpected failures occur. [ABSTRACT FROM AUTHOR]

Surrogate model-based reliability analysis aims at building a cheap-to-evaluate mathematical model as a substitute for the original performance function to enhance computational efficiency. Data-driven surrogate models have been popularly studied from a perspective of active learning. On the other hand, Physics-informed Neural Networks, called PINNs, have recently gained much attention as a physics-informed surrogate model to directly solve partial differential equations. Building on the capability of avoiding the simulation of traditional numerical solvers such as the finite element analysis, the PINN-based reliability analysis can achieve highly efficient simulation-free uncertainty quantification. This paper focuses on the development of the PINN-based reliability analysis method and its application in practical engineering applications. Reliability analysis with Importance Sampling-based Adaptive Training Physics-informed Neural Networks (IAT-PINN-RA) is proposed in this work. Compared with the existing PINN-based reliability analysis methods, IAT-PINN-RA introduces a pre-training stage for the establishment of the importance sampling distribution, and therefore achieves better performance when handling rare events. The modeling and reliability analysis of chloride penetration, which can pose serious challenges to the durability of concrete structures, are investigated. A practical example demonstrates the feasibility of using PINNs to model this physical phenomenon and the performance of the proposed method to achieve accurate and efficient reliability analysis results. [ABSTRACT FROM AUTHOR]

• The proposed ADSVM can implement the efficiency and accuracy of turbine blade reliability analysis. • Considering soft and hard boundaries can suppress the overfitting and improve boundary samples accuracy. • AST can extract high quality samples for reliability modeling and analysis. • The developed DSVM can improve the stability and efficiency of adaptive sampling process. • DSVM can improve the modeling accuracy of SVM by introducing the penalty coefficients. Machine learning methods have been widely applied to structural reliability analysis, due to the excellent performance in modeling precision and efficiency. In this paper, an adaptive directed support vector machine model (ADSVM) is proposed by integrating the adaptive sampling technology (AST) and the developed directed support vector machine (DSVM), to improve the efficiency and accuracy of turbine blade reliability analysis. In the developed method, the AST is adopted to extract high quality samples, in respect of distributed probability density and the distances between sample values and response values. The DSVM was developed by introducing the penalty coefficients for all the slack variables, to improve the modeling accuracy of SVM approach. One numerical example and the reliability analysis of aeroengine high-pressure turbine blade were performed to validate the developed methods. As illustrated in this numerical investigation, the modeling precision of DSVM is improved by alleviating the lag effect of support vector regression. From the comparison of methods, it is demonstrated that the ADSVM has higher accuracy, efficiency and stability in reliability simulations, which are improved by ∼20 % and ∼46.2 %, respectively. The main efforts of this study are to propose a promising approach, ADSVM, for the reliability analysis of complex structures besides turbine blades, which hold the academical significance in enriching and developing mechanical reliability theory. [ABSTRACT FROM AUTHOR]

• Propose a new method to estimate the reliability of the rare event with high dimensional problem. • The proposed method combines the active subspace method with adaptive two-stage Kriging model. • A new learning function is proposed to construct the first stage Kriging model to provide the gradient information of the performance function. For the high dimensional and small failure probability events widely existing in engineering, structural reliability analysis method still faces challenges at present. Since active subspace (AS) method can effectively reduce the dimension of input vector space, and metamodel-based importance sampling (IS) can efficiently estimate small failure probability, this paper combines AS with IS to propose an adaptive two-stage Kriging model method (AS-IS-AK 2) for rare failure event with high dimensional problem. The proposed AS-IS-AK 2 includes two stages. In the first stage, a new learning function is proposed to construct the Kriging model for roughly estimating the performance function values of all IS samples, and the gradient information is provided as a by-product for AS. In the second stage, an adaptive Kriging method is constructed in the reduced dimension space to accurately judge the states of all IS samples. Since AS reduces the dimension of input vector space, and IS reduces the required size of candidate sample pool for obtaining the convergent failure probability estimation, the computational complexity is reduced in reconstructing the Kriging model to judge the states of IS samples. The results of three examples verify the advantage of the proposed method for high dimensional problem with small failure probability. [ABSTRACT FROM AUTHOR]

• A dynamic pruning strategy of the candidate sample pool. • An adaptive learning algorithm integrating the U function and the sparsity of training samples. • A formulated convergence condition combining the U function and the number of reduced samples. Adaptive surrogate-based reliability analysis methods have garnered significant attention due to their potential to enhance computational efficiency in accurately estimating failure probability. However, the candidate sample pool remains constant for most surrogate-based reliability methods, and traversing the candidate sample pool one by one will reduce the efficiency of surrogate modeling. More importantly, maintaining a static sample pool may lead to the inclusion of samples that contribute minimally to the construction of the surrogate modeling, thereby impacting the accuracy and efficiency of the reliability analysis. Accordingly, this paper leverages the robust performance of Bayesian support vector regression to propose a dynamic pruning strategy for the candidate sample pool to estimate failure probability efficiently. A dynamic pruning strategy is presented to streamline the process further, iteratively reducing the candidate sample pool. An adaptive learning algorithm is then introduced, integrating the U function and the sparsity of training samples. This is complemented by a formulated convergence condition, contributing to an ideal surrogate model. The proposed approaches showcase superior efficiency and accuracy through illustrations using well-known benchmark problems and complex reliability analysis problems involving small failure probability and high-dimensional limit state function. [ABSTRACT FROM AUTHOR]

• A CSP-free adaptive surrogate model method combining Kriging model and MCS is proposed for reliability analysis. • Particle swarm optimization algorithm is used to identify representative samples for construction of surrogate model. • Penalty intensity control and density control are introduced to achieve an optimal balance between accuracy and efficiency. • Numerical examples are conducted to exhibit the computational performance of the proposed method. In the field of reliability engineering, the active learning reliability method that amalgamates Kriging model and Monte Carlo simulation has been devised and proven to be efficacious in reliability analysis. Nevertheless, the performance of this method is sensitive to the magnitude of candidate sample pool, particularly for systems with small failure probabilities. To surmount these limitations, this paper proposes an active learning method that obviates the need for candidate sample pools. The proposed method comprises two stages: construction of surrogate model and Monte Carlo simulation for failure probability estimation. During the surrogate model construction stage, the surrogate model is iteratively refined based on the representative samples selected by solving the optimization problem facilitated by the particle swarm optimization algorithm. To achieve an optimal balance between solution accuracy and efficiency, the penalty intensity control and the density control for the experimental design points are incorporated to modify the objective function in optimization. The performance of the proposed method is evaluated using numerical examples, and results indicate that by leveraging an optimization algorithm to select representative samples, the proposed method overcomes the limitations of traditional active learning methods based on candidate sample pool and exhibits exceptional performance in addressing small failure probabilities. [ABSTRACT FROM AUTHOR]

Surrogate models have been widely used in structural reliability analysis to improve the computational efficiency and the accuracy of failure probability. Recently, several multi-kernel relevance vector regression (MKRVR) models have been studied to evaluate the failure probability. However, existing multiple kernel functions for relevance vector regression models are fixed choices, which increases the number of calls to the limit state function (LSF) and leads to inaccurate results. To address the problem, this paper presents a new adaptive MKRVR model combined with Monte Carlo simulation (MCS). Firstly, a stepwise kernel selection strategy is developed to adaptively select better-performing kernel functions and eliminate redundant kernel functions for constructing the MKRVR model. Secondly, a new active learning function is proposed by considering the probability of mis-prediction and spatial locations of the existing sampling point to identify the new training sample points. Thirdly, a hybrid efficient stopping criterion is adopted to terminate the learning process automatically. Three benchmark examples and one practical engineering example are introduced to demonstrate the effectiveness of the proposed method. Results show that the proposed method can provide accurate failure probability by less number of calls to the LSF than existing fixed kernel-based methods. • Development of a new adaptive kernel stepwise selection strategy to select potential superior kernel functions. • An automatic selection procedure is proposed to examines the significance of kernel functions. • Integrates the stepwise selection strategy, the new learning function, and the convergence criterion into the AMKRVR-MCS framework. • This method provides accurate and efficient estimates for reliability analysis. [ABSTRACT FROM AUTHOR]

Surrogate model-based reliability analysis methods, especially the adaptive Kriging model, have received increasing attention due to their high accuracy and efficiency for reliability analysis. In the context of the practical engineering and a design target of high reliability, the adaptive Kriging is combined with more efficient sampling techniques such as the spherical decomposition-based Monte Carlo simulation (SDMCS). In this paper, a new stopping criterion is tailored for the adaptive Kriging model with SDMCS (AKSDMCS). The relative error of the failure probability obtained by AKSDMCS is first derived. Then, the effect of samples with high probabilities of wrong classification on the relative error of failure probability is quantified. In each sub-region of SDMCS, it can be found that the number of points in wrong classification follows a binomial distribution. The expected upper bound of the relative error of the failure probability is subsequently formulated. Finally, a new stopping criterion designed for AKSDMCS is developed. Three applications are used to validate the performance of the proposed stopping criterion and the results showcase that the adaptive Kriging with the proposed stopping criterion can stop the active training process at an appropriate stage and significantly mitigate the computational effort of rare event estimation. • The relative error of failure probability by AKSDMCS is derived. • The effect of dangerous points on the failure probability estimation is quantified. • A new error-based stopping criterion is proposed for AKSDMCS. • Three numerical examples are utilized to validate the efficiency and accuracy. [ABSTRACT FROM AUTHOR]

• An anisotropic RBF is proposed with high generalization and accuracy. • A fast cross-validation method is proposed for efficient reliability analysis. • A novel weighted clustering method is developed to sampling in parallel. Reliability analysis is crucial to ensure the safety and reliability of a system with uncertainty. In reliability analysis, the metamodeling method is usually engaged to reduce the related computation. The metamodel-based reliability analysis methods need to continuously improve the accuracy of important areas, which is often accompanied by an increase in the sample number. Therefore, to improve the metamodel's accuracy while ensuring its calculation efficiency, an RBF-based reliability analysis method is presented in this paper. Firstly, an anisotropic technology is proposed to further improve the local accuracy of RBF. Secondly, a fast cross-validation method is developed to construct the model variance, which can also significantly reduce the computation intensity in model training. Furthermore, a novel weighted clustering method is contrived to sample in parallel when proceeding with reliability analysis to effectively reduce the number of iterations. Calibrated against the currently prevailing methods, the superior efficiency and accuracy of the proposed methods are demonstrated by exemplifications with popular benchmark problems and a complex reliability analysis problem of a pintle nozzle. [ABSTRACT FROM AUTHOR]

• Surrogate modeling approach (SMA) based on XGboost technique to enhance efficiency. • SMA-assisted creep-fatigue (CF) reliability assessment for turbine disc application. • Multi-source uncertainty analysis at bottom groove having maximum CF damage value. • Additional geometric tolerance uncertainty making more conservative reliability. • Optimized clearance fit in the groove structure enhancing structural reliability. This paper proposes a surrogate modeling approach based on XGboost machine learning technique, in order to establish a data-driven mapping relationship between input and output abstracted from practical finite element analysis (FEA) results. It facilitates novel insights into an efficient application of creep-fatigue reliability assessment in low-pressure turbine disk without a large amount of high-fidelity FEA cases. In detail, a general technical route is proposed for the probabilistic estimations of creep-fatigue lifetimes, where the multi-source uncertainties in the sequenced levels are synchronously considered. Subjected to typical creep-fatigue load spectrum, precise weakness hotspot is identified at the 1st bottom fir-tree groove of the turbine disk. Based on hotspot-based strategy, it is found that XGboost-involved surrogate modeling approach significantly improves the computational efficiency. The common results show that logarithmic creep-fatigue lifetimes roughly obey the normal distributions with the present of uncertainty sources, regardless of the multi-source combinations. Specifically, geometric tolerance plays an important role in reliability assessment results, which not only makes conservative gap but also shows high sensitivity in the reliability assessments. [ABSTRACT FROM AUTHOR]

• Establish a more realistic reliability analysis model for multi-mode time-dependent structural system. • Propose a new efficient extremum learning function when constructing the Kriging model. • Propose a new initial sampling method when generating the initial training set. For the widely existing time-dependent structural system (TDSS), the current model ignores the interaction among multiple modes in the minimum transformation of the performance function of each mode w.r.t. the time, it may misjudge the state of the system at some instants and result in the error of estimating the reliability. To avoid this possible mistake, this paper proposes an improved reliability analysis model for the TDSS. In the proposed model, the TDSS performance function is transformed into the single-mode time-dependent performance function firstly according to the relationship of multiple modes. Then the failure probability of the TDSS can be estimated by the single-mode time-dependent performance function. The relationship of multiple modes is strictly considered in the proposed model. On the basis of the improved model, this paper also presents the Kriging surrogate model combined with the Monte Carlo simulation method to estimate the failure probability of the TDSS. In this Kriging method, the initial training samples are uniformly selected in the sample space and a new extremum learning function is proposed. Theoretical analysis verifies the rationality of the proposed reliability analysis model, and the efficiency of the proposed method is illustrated by the results of numerical examples. [ABSTRACT FROM AUTHOR]

As a protective device for vehicles, shock absorbers are designed to maintain the safety and stability of vehicles. However, the constantly changing road conditions along with various dependent failure mechanisms pose challenges to their performance stability and maintenance strategy formulation. This paper investigates a linearly degraded system subject to both a dynamically changing operating environment and a series of external shocks, where an N-critical shock model is utilized to describe the limited shock resistance of shock absorbers and a continuous-time Markov process is employed to characterize the random evolution of environments. Explicit formulas for computing system reliability functions are proposed, along with a simulation algorithm as the alternative method. Furthermore, a novel shock-dependent preventive maintenance policy is developed to fully take advantage of the information on shock arrivals, which is observable and measurable, for degraded systems operating in a dynamic environment. Valuable conclusions are drawn that increasing the critical or shock failure threshold can enhance system performance while reducing maintenance costs; an increase in corrective maintenance costs indicates a need for earlier replacement, while an increase in preventive maintenance costs leads to postponed replacement. • Degraded systems subject to dynamic environments and N-critical shocks are studied. • Analytical formulas and simulation algorithms for reliability indexes are given. • Both corrective maintenance and shock arrival information is utilized. • New shock-dependent preventive maintenance policy is designed. • A case study is provided to illustrate the developed models and methods. [ABSTRACT FROM AUTHOR]

• Build a performance-based system including subsystems with protective devices (PDs). • Propose a new triggering condition of PDs based on units' internal degradation rate. • Consider the degradation of PDs of load-sharing subsystems before running firstly. • Study the real case that the PDs in poor states may fail to function. • Formulate an efficient method of MPIA and UGF to get the system reliability. Existing studies on the systems with protective devices (PDs) all consider that the components are independent, and the PDs are activated to work in a perfect state and always realize their functions successfully until failures. However, it can be found that the above assumptions have some limitations, motivated by actual engineering cases. To fill the research gaps, this paper proposes a new system which contains multiple load-sharing subsystems with PDs. The PDs are subject to internal degradation with a lower rate before working, and may be unable to protect the components in poor states. The PD in each subsystem is triggered when the internal degradation rate of the working components reaches the preset value. The PDs can decrease the probability of the valid shocks and the internal degradation rate of the components. Each subsystem has multiple states, determined by the number of failed components and the subsystem in each state takes certain performance. The state of entire system is divided into multiple levels according to the total performance of subsystems. The Markov process imbedding approach and universal generating function technique is combined to analyze the system reliability. Finally, the applicability of the proposed model is validated using numerical examples. [ABSTRACT FROM AUTHOR]

• A novel generalized shock model with multiple change points is firstly built. • The reliability of coherent systems under the proposed shock model is analyzed. • Two new shock impact mechanisms are proposed for the two shock environments. • A multi-stage FMCIA is constructed to derive the system reliability. The operating environment of some industrial systems is complex and may change several times. However, the latest literature about shock models only considered the case that the shock environment may change only one time at most, which cannot accord with the reality of shock environment changing multiple times. To bridge the research gaps, this paper evaluates the reliability of two coherent systems, series-parallel and parallel-series systems, which operate under a generalized mixed shock model with multiple change points. Two distinct shock environments are considered, where the shock impact mechanisms on two coherent systems are completely different. The cases that the system initially runs in environment I or II are both investigated. The shock environment may change multiple times. After one successful shift of the environment, the system continues to run in the other environment. The proposed shock model is a generalization of many existing shock models, and when the parameters of the proposed model take specific values, some previous shock models can be obtained. Reliability indices of two coherent systems are derived by a multi-phase finite Markov chain imbedding approach. An application of target system is presented to demonstrate validity of the proposed model and the effectiveness of the method. [ABSTRACT FROM AUTHOR]

• A systematic reliability analysis method for subsea wellhead systems is proposed. • Multiple risk factors and component degradation are taken into consideration in system reliability modeling. • A multistate transition model of wellhead components is established to analyze system degradation. • The proposed method is validated using a hybrid structural reliability analysis model. Subsea wellhead systems play a critical role in ensuring the safe exploitation of offshore oil and gas during offshore drilling and production operation stages. However, due to the complexity of the marine environment and operating condition, this kind of structure is prone to the failure caused by cumulative effects of the fatigue and degradation of components. This paper presents a Markov- Monte Carlo-DBN-based approach to comprehensively predict the reliability of subsea wellhead systems and diagnose the underlying root cause during its service life. Multi-factor impacts on system performance are considered for modeling. A multistate transition model of wellhead components is proposed to analyze system degradation. Reliability evaluation of the critical component is performed and verified by employing the Monte Carlo simulation-based method which is also used to address the issue of insufficient data for subsea wellhead fatigue prediction. By embedding multi-factor effects and multistate transition into DBN, the system state can be effectively updated. An example of a subsea wellhead system demonstrates the application of this approach, through which the system reliability during its service life is predicted, and the most important factors that affect the system's reliability and deserve special attention are identified. [ABSTRACT FROM AUTHOR]

• A novel optimal tolerance design approach with positioning accuracy reliability is presented. • A tolerance optimization model balances failure probability and manufacturing cost is proposed. • A novel reliability analysis method and an improved genetic algorithm to solve the tolerance design model. This paper proposes a novel tolerance design method for robot manipulators to select the optimal tolerances of kinematic parameters. A tolerance optimization model is presented to minimize the failure probability of positioning accuracy with the constraint of manufacturing cost. First, the performance function of positioning accuracy is constructed by performing the differential kinematics and eigen-decomposition concepts, which further combines the chi-square approximation and numerical integration methodologies to calculate the positioning accuracy reliability. An improved genetic algorithm is then presented based on the diversity crossover and differential mutation strategies to optimally and efficiently solve the tolerance design model. The applicability and performance of the proposed method are validated by the tolerance design of a 6-degree-of-freedom robot manipulator. The comparison with the existing techniques illustrates that the proposed method (i) processes better accuracy and efficiency in positioning accuracy reliability analysis; (ii) obtains a tolerance combination of kinematic parameters with a higher positioning accuracy reliability. The proposed method contributes to the optimal tolerance range selection and design of robot manipulators and other moving parts of machinery. [ABSTRACT FROM AUTHOR]

Non-coherent systems represent a specific group of systems in context of reliability analysis. These systems are characteristic by existence of situations in which degradation of a system component can result in improvement of the whole system. Non-coherent systems are mostly investigated in case of Binary-State Systems (BSSs) that admit two performance levels for modeling system as well as its components. Properties of these systems have been studied and algorithms for calculation of most of reliability measures have been developed. However, in case of Multi-State Systems (MSSs), the situation is completely different. Non-coherent MSSs have been studied only marginally with focus on homogeneous MSSs. In this paper, we deal with heterogeneous non-coherent MSSs, generalize existing definitions for them and develop a new approach for computation of their critical system states, which play a key role in importance analysis. The analysis of non-coherent MSSs considered in this paper is implemented based on its representation in a form of time independent structure function. • Non-coherent Multi-State System (MSS) analysis. • The analysis of different definitions of component relevancy for MSSs. • The definition of critical system states for non-coherent MSSs. • The development of logical derivatives for analysis of non-coherent MSSs. • The computation of critical system states for non-coherent MSSs. [ABSTRACT FROM AUTHOR]

This paper addresses the challenge of performing importance sampling in high-dimensional space (several hundred inputs) in order to estimate the failure probability of a physical system subject to randomness. It is assumed that the failure domain defined in the input space can possibly include multiple failure regions. A new approach is developed to construct auxiliary importance sampling densities sequentially for each failure region identified as part of the failure domain. The search for failure regions is achieved through optimization. A stochastic decomposition of the elliptically distributed inputs is exploited in the structure of the auxiliary densities, which are expressed as the product of a parametric conditional distribution for the radial component, and a parametric von Mises–Fisher distribution for the directional vector. The failure probability is then estimated by multiple importance sampling with a mixture of the densities. To demonstrate the efficiency of the proposed method in high-dimensional space, several numerical examples are considered involving the multivariate Gaussian and Student distributions, which are commonly used elliptical distributions for input modeling. In comparison with other simulation methods, the numerical cost of the proposed approach is found to be quite low when the gradient of the performance function defining the failure domain is available. • Importance sampling in high-dimensional space for elliptical distributions. • Auxiliary distribution based on a stochastic decomposition of the inputs. • Failure probability estimated by multiple importance sampling. • Adaptive search for the multiple failure regions of the failure domain. [ABSTRACT FROM AUTHOR]

• An accurate and robust approach is proposed for reliability analysis. • The exact dimension-reduction model is obtained by contribution-degree analysis. • A sample points selection strategy is proposed for evaluating coefficients of PCE. • A convergence criterion of PCE approximation is proposed based on information entropy. • The proposed method is applied to reliability analysis of industrial robots. Polynomial chaos expansion (PCE) is considered an excellent method for accurately and efficiently reliability analysis in various engineering problems. However, it becomes practically infeasible in scenarios characterized by high-dimensional input random variables and thousands of training data. To solve this problem, this paper proposes a new PCE-based surrogate-assisted method. To start with, the interacting variables are screened out from original high-dimensional input random variables by contribution-degree analysis (CDA). The original high-dimensional performance function is decomposed into a lower-dimensional component function composed of the interacting variables and multiple one-dimensional component function containing only one non-interacting variable. Then, PCE combined with a sample points selection strategy is used to fit the lower-dimensional component function, and a full PCE is utilized for fitting each one-dimensional component function. Three methods, namely the Hadamard's inequality of the design matrix, the rank revealing QR factorization of the design matrix and the maximum entropy, are implemented to realize sample point selection. Four examples are investigated to demonstrated the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

• Reliability analysis of a BWR plant system at startup stage. • Analysis has been performed by the GO-FLOW methodology. • An actual loop structured engineering system has been solved in reliability analysis. • The GO-FLOW chart suggests us how to model logical loop relations without any loop structure in the chart. • Phased mission problem appeared in BWR system is also solved by the GO-FLOW. A reliability analysis of a boiling water reactor (BWR) system at startup stage has been performed. This paper is a useful attempt at a reliability analysis of a phased mission system (PMS) with loop structures in a real engineering system. The system startup schedule has been set based on typical BWR system. During startup, phased mission problem occurs, and loop structures are formed in the system. The solution of Boolean expression for a reliability of loop structure has been explained. Reliability analysis has been performed by the GO-FLOW methodology; a brief explanation of the GO-FLOW has been given. The system has been modeled on a GO-FLOW chart. The loop structured parts have been modeled corresponding to the solution of the Boolean equations. The chart suggests a way to model logical loop relations in a diagram without loop structure. The PMS of a BWR system has been also modeled on the same GO-FLOW chart by using the phased mission operator. An exact analytical approach for loop structured system has been selected and both the logic of loop structures and the logic of PMS have been modeled on the same GO-FLOW chart. This allows PMS with loop structures to be easily solved. The mission success probabilities of the system have been obtained in a single computation by a single GO-FLOW chart. The proposed modeling method for logical loop structures and phased mission problem is useful in evaluating reliability and/or availability of large complex engineering systems. [ABSTRACT FROM AUTHOR]

• Probabilistic life model is established by three-point bending fatigue tests. • Cantilever bending fatigue tests under different internal pressure are conducted. • Successive AK-MCS is proposed for reliability analysis of pipelines. • The efficiency of successive AK-MCS is improved by sharing training information. Fatigue failure caused by high pressure of fluid and external vibration seriously affects the performance and reliability of hydraulic pipelines. Probabilistic fatigue life assessment can quantify failure probability and fully utilize the performance of pipeline. The objective of this paper is to develop an effective reliability method to analyze the bending fatigue life of hydraulic pipeline combining with fatigue tests. Firstly, three-point bending fatigue experiments of pipelines are conducted to establish probabilistic-based life models by linear variance regression analysis. Then the established formulas are further verified by the combined results of deterministic finite element analysis and cantilever bending fatigue experiment of hydraulic pipelines. Successive AK-MCS based on ESC is proposed for the fatigue reliability analysis of hydraulic pipelines. The main novelty of successive AK-MCS is that a training information sharing strategy is designed to estimate the failure probabilities under different load cycles. The effectiveness and feasibility of the proposed method is verified by comparing the results of fatigue reliability analysis on cantilever pipeline under an internal pressure of 28 MPa with traditional AK-MCS. Lastly, the influence of internal pressure and survival probability on the relationship between load cycle and failure probability of the cantilever hydraulic pipeline are further discussed. [ABSTRACT FROM AUTHOR]

• A hybrid data-driven model is proposed to quantify risk under uncertain parameters.during a tunnel's excavation process. • A real case is used to evaluate the effectiveness and feasibility of our proposed approach. • A Markov-Chain-based importance sampling is used to analyze settlement reliability. Tunnel boring machines are widely used to construct underground rail networks in urban areas. However, ground settlement due to complex geological conditions is an ever-present reality requiring continuous monitoring and management of risks. This paper addresses the following research question: How can we predict tunnel-induced ground settlement with engineering parameters, improve its predictive ability, and quantify its risks under uncertain parameters in complex geological conditions ? To this end, we develop a hybrid data-driven model that considers prior domain knowledge to effectively and accurately quantify risk under uncertain parameters during a tunnel's excavation process. Our model comprises: (1) a deep neural network (DNN) to construct a ground settlement prediction model; (2) the incorporation of physical knowledge into the DNN-based prediction model; and (3) a Markov-chain-based importance sampling to analyze settlement reliability. We use the San-yang Road tunnel project in Wuhan, China, to evaluate the effectiveness and feasibility of our proposed approach. The results demonstrate that our hybrid data-driven model can accurately predict tunnel-induced ground settlement and quantify failure probability for geotechnical reliability under uncertain parameters during a tunnel's excavation process. [ABSTRACT FROM AUTHOR]

• BUS-SSAK, a deep integration of adaptive Kriging-based subset simulation and Bayesian updating with structural reliability (BUS), is proposed. • Conditional Acceptance Rate Curve (CARC) and Dynamic Learning Function (DLF) are introduced. • CARC and DLF facilitate precise identification of intermediate failure thresholds in subset simulation with limited realizations. • BUS-SSAK enables Bayesian updating of complex, computationally demanding models. The well-known BUS algorithm (i.e., Bayesian Updating with Structural reliability) transforms Bayesian updating problems into structural reliability to address challenges of updating with equality information and improve computational efficiency. However, as the number of observations increases, the resulting failure probability or acceptance ratio becomes exceedingly small, requiring a formidable number of evaluations of the likelihood function. To overcome this limitation especially for complex computational models, this paper presents a new approach where the probability estimation problem of the very rare event associated with updating is decomposed into a set of sub-reliability problems with uncertain failure thresholds. Two concepts of Conditional Acceptance Rate Curve (CARC) and Dynamic Learning Function (DLF) are proposed to enable precise identification of the intermediate failure thresholds and to train Kriging surrogate models for the established limit state functions. Two benchmark numerical examples and a practical corrosion problem in marine environments are investigated to analyze the efficiency of the proposed method relative to BUS and other state-of-the-art methods. Results indicate that the proposed method can reduce computational costs by about an order of magnitude while maintaining high accuracy; therefore, enabling Bayesian updating of complex computational models. [ABSTRACT FROM AUTHOR]

Recovering the probability distribution of the performance function with an arbitrary shape is still a difficult task for structural reliability analysis. Since working with the characteristic function curve provides an alternative and frequently much simpler route than working directly with the probability distribution, this paper proposes a generalized density reconstruction method based on the inversion of characteristic function, which is estimated based on the complex fractional moments. First, the complex fractional moments of the limit state function are numerically evaluated by using the sample estimator. Then, the characteristic function is numerically determined in terms of complex fractional moments. Since inverting the numerical version of characteristic function to be the corresponding probability distribution is not an easy task, two analytical expressions of characteristic function are proposed according to its different features, where the undetermined parameters are obtained via fitting an analytical expression based on the data estimated by complex fractional moments. Then, the probability distribution of the limit state function is obtained by using the inverse Fourier transform of characteristic function, where a one-to-one mapping relationship is involved. Finally, the failure probability can be readily obtained. Several analytical distributions and numerical examples are extensively investigated to validate the proposed method. • The proposed method is applicable to both unimodal and multimodal distributions. • Analytical expressions are proposed for CF fitting according to different characteristics. • The proposed method outperforms the conventional Mellin transform. • Numerical examples validate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

• Definition of new type 18 operator to enhance the model ability of GO methodology for MC(k,n) system. • Optimization of BN structure corresponding to large-scale MC(k,n) system. • Mapping procedure transforming GO model of MC(k,n) system to corresponding BN. • Fault diagnosis and improvement guidance of MC(k,n) system based on extended GO model and BN. As a success-oriented system reliability and safety analysis technique, GO methodology is widely used in the modeling and analysis scenarios of critical safety engineering systems with signal flow, such as nuclear, chemical industry, electric power transportation, wireless network and microwave communication network. Consecutive- k -out-of- n systems are also widely applied in these fields, but due to their relatively complex logic, there are no corresponding graphical modeling and calculation methods. In this paper, the basic GO methodology is extended to support the modeling and analysis of multi-state linear and circular consecutive- k -out-of- n : F system (MLC(k,n) &MCC(k,n)) models. Two new operators are defined in graphical modeling to represent the two types of complex system logic. The multi-state logic semantics of the new operators and mapping rules to Bayesian networks (BN) are given. And the programmable process is presented to transform the extended GO model into BN, and the reliability of the MLC(k,n)/MCC(k,n) is calculated. Finally, three cases are used to verify i) the correctness of the method supporting multi-state model, ii) the efficiency and ability of the algorithm, and iii) the forward calculation and reverse diagnosis of the MLC(k,n) and MCC(k,n) systems with external shared components. [ABSTRACT FROM AUTHOR]

• A systematic approach for analyzing safety barriers in a battery pack. • Investigation on the battery degradation and barriers against cascading failures. • Integration of thermal propagation, thermal simulations, degradation, and reliability analysis. Lithium-ion batteries have been widely employed as the principal power source in electric vehicles and other storage systems. However, some critical issues in a battery pack still exist, such as thermal failures on initial cells that impact the temperatures of the surrounding cells. Such cascading failures may significantly affect battery performance and safety. Thermal barriers, as one kind of safety barrier, are therefore installed to prevent failure propagations. This paper focuses on the situation when the temperature of battery cell increases, but the battery pack still can be used in a degradation mode since the barriers are against cascading failures. An approach is proposed to analyze how the deployment and performance of thermal barriers in a battery pack determine their capabilities against cascading failures. The approach includes thermal propagation models associated with the simulations, degradation models, reliability analysis, and barrier analysis. Its application is illustrated with a practical case study. The battery reliabilities are sensitive to many factors of the barriers, such as temperature differences, failed cells, and performance coefficient. The barriers between parallel cells are found to be more effective in mitigating failure propagation. Such findings can be beneficial for barrier optimization and reliability improvement of battery packs. [ABSTRACT FROM AUTHOR]

• A computational framework for optimal monitoring location of risk tracking of geotechnical structures is proposed. • A novel metric called SOI is proposed to quantify the relative change in updated and prior reliability at a specific location. • An enhanced Subset simulation is proposed to improve the computational efficiency of reliability updating. • Adaptive Kriging is adopted to facilitate the exploration of optimal monitoring location. • The proposed framework facilitates the identification of optimal monitoring location for tunneling-induced settlement to building damage. Structural health monitoring (SHM) technologies offer ever-increasing opportunities to continually observe various responses and states of structures, such as settlement-induced building damage. Recent advances in reliability updating have enabled estimating the probability of failing to meet a prescribed objective for systems using various types of information including those acquired from SHM. However, reliability updates are sensitive to monitoring location, especially when the risks are evolving. Therefore, there may exist optimal locations in a system for monitoring that yield maximum value for reliability updating. This paper proposes a computational framework for optimal monitoring location based on an innovative metric called sensitivity of information (SOI). This metric quantifies the change in unconditional and conditional reliability indexes, which subsequently facilitates fast exploration of optimal monitoring location by parameterizing an optimization function. A state-of-the-practice case related to assessing evolving risks posed by tunneling-induced settlement to buildings is explored in-depth with respect to the progression of tunneling. Simulation results showcase that the proposed framework can successfully find the monitoring location that is the most impactful to the accuracy of the updated reliability. [ABSTRACT FROM AUTHOR]

• An adaptive sparse polynomial chaos expansion is proposed for reliability analysis. • Greedy coordinate descent is fused with a local variance based optimality criterion. • An active learning strategy adaptively shifts training focus to important regions. • Examples of varying complexity and input dimensionality are used for comparison. • This method provides accurate estimates of event probabilities with high efficiency. In this paper, a prediction-oriented active sparse polynomial chaos expansion (PAS-PCE) is proposed for reliability analysis. Instead of leveraging on additional techniques to reduce the problem dimensionality and/or to obtain the local error estimates, which has been done in the majority of existing PCE-based methods, this study first makes use of the Bregman-iterative greedy coordinate descent in effectively solving the least absolute shrinkage and selection operator based regression for sparse PCE approximation with a small set of initial samples. Then, the local variance distribution of the performance function is predicted using the approximated PCE. By maximizing an optimality measure that balances the exploration of design space and exploitation of the PCE characteristics, a recently proposed learning function is subsequently adopted for selecting the optimal samples one by one from a candidate pool to cover the limit state surface regions proportionally to the predicted local variance. The performance of the proposed PAS-PCE is assessed on four numerical examples of varying complexity and input dimensionality through comparison with several state-of-the-art active learning methods based on a variety of surrogate models. Results show that the proposed method is superior to the benchmark algorithms in terms of both accuracy and efficiency for reliability analysis. [ABSTRACT FROM AUTHOR]

• A k -out-of- n : F capability-balanced system subject to multi-source shocks is built. • Concept of system capability balance is proposed based on real engineering cases. • The multi-source shock environment is first considered for balanced systems. • A two-stage FMCIA and P H distributions are combined to evaluate system reliability. Research on balanced systems has sparked intense attentions due to their widespread engineering applications. Previous studies all considered that balanced systems operate in a single-source shock environment and the existing concepts of system balance are limited. Nevertheless, some balanced systems operate in more complex shock environment with multiple sources and new system balance requirements can be explored based on real engineering cases. To make up research gaps, this paper proposes a k -out-of- n : F capability-balanced system working in a multi-source shock environment, where the shock impacts from various sources can differ significantly. The components have multiple states owing to shocks and an operating capability is taken for each component state. The concept of system capability balance is defined based on the largest capability difference between components and a random probability of system to keep capability-balanced within a certain range is considered. System failure can be caused by dissatisfying the capability-balanced conditions and reaching the critical number of failed components. A two-stage finite Markov chain imbedding approach and P H distribution are combined to evaluate the probabilistic quantities of the system. Finally, illustrative examples are provided to validate the proposed model and future studies are discussed. [ABSTRACT FROM AUTHOR]

• Deep PCNN parameterizes the expansion coefficients into the learnable weights. • Deep PCNN makes the abundant unlabeled data available for building a PCE model. • Deep PCNN uses consistency regularization to assist the main model training. • Deep PCNN uses fewer labeled data but builds a more accurate surrogate model. Polynomial chaos expansion (PCE) is a powerful method for building a surrogate model that can be applied to assist reliability analysis. Generally, a PCE model with a higher expansion order is required to obtain an accurate surrogate model for some complex non-linear stochastic systems. However, the high-order PCE increases the number of labeled data necessary for solving the expansion coefficients. To alleviate this problem, this paper proposes a consistency regularization-based deep polynomial chaos neural network (Deep PCNN) method, including the low-order adaptive PCE model (the auxiliary model) and the high-order polynomial chaos neural network (the main model). The expansion coefficients of the main model are parameterized into the learnable weights of the polynomial chaos neural network, realizing iterative learning of expansion coefficients to obtain more accurate high-order PCE models. By unlabeled data, the auxiliary model uses the proposed consistency regularization loss function to assist in training the main model. The consistency regularization-based Deep PCNN method can precisely solve the expansion coefficients with fewer labeled data without reducing the high-order PCE model accuracy compared to the existing PCE methods. Two numerical examples validate the effectiveness of the consistency regularization-based Deep PCNN method, which is then applied to satellite reliability analysis. [ABSTRACT FROM AUTHOR]

In reliability analysis with Monte Carlo simulation, the uncertainty about the probability of failure can be formally quantified through Bayesian statistics. Credible intervals for the probability of failure can be derived analytically. This paper gives a detailed overview of Bayesian post-processing for Monte Carlo simulation. We investigate the influence of different weakly-informative prior assumptions on the resulting credible intervals. On this basis, we recommend to use a prior distribution on the probability of failure that follows from the principle of maximum information entropy. We also show that even if no failure sample occurs in a Monte Carlo simulation, Bayesian post-processing still allows to deduce useful information about the probability of failure. The presented Bayesian post-processing strategy can also be applied if Monte Carlo simulation is used for reliability updating; i.e., to evaluate the probability of failure conditional on data or observations. We derive expectations for credible intervals for this case. • Credible intervals are an intuitive and practical manner of representing sampling uncertainty in reliability analysis. • The influence of different prior assumptions on credible intervals is studied. • Use of prior distribution based on the principle of maximum information entropy is recommended. • The proposed Bayesian post-processing can also be applied to reliability updating. • Credible intervals are meaningful even if no failure samples were observed during the simulation. [ABSTRACT FROM AUTHOR]

The irrelevance coverage model (ICM) is an extension of the imperfect fault coverage model (IFCM), which can reduce the risk of uncovered component failures by isolating irrelevant components in systems. However, the ICM has been limited to static systems so far. To address this issue, we extend the ICM to dynamic systems modeled by dynamic fault trees (DFTs) with Priority-AND (PAND) gates. The component irrelevance is analyzed in the DFTs, which shows a component could become irrelevant due to specific sequence failures of some other components, and the implication of irrelevancy may differ from that in static systems. The definition of minimal irrelevance triggers (MITs) and the reduction rules are introduced based on the temporal algebraic framework. The sum of disjoint products (SDP) method is further applied for the quantitative analysis of system reliability. Case studies demonstrate the effectiveness of our method. Furthermore, the ICM can also play a role in the dynamic systems in terms of reliability improvement compared to the IFCM. • The possible change of component relevancy in the PAND gate is firstly addressed in this paper. • The concept of minimal irrelevance trigger is redefined for dynamic fault trees. • The irrelevance coverage model is extended from static fault trees to dynamic fault trees accordingly by using algebraic structure-functions. [ABSTRACT FROM AUTHOR]

Reliability analysis of a complex system is vital and challenging. The Bayesian theory is widely used to integrate multiple source data for this problem by decomposing the system into multiple levels. However, the data in the component-level are integrated first and then transmitted to system-level in existing methods. This theory involves extensive computation and is easily affected by the setting of combined weights in the data integration of each level. By contrast, a method is proposed based on multi-source data transmitting first and then pooling together with integration in this paper. Firstly, multi-source data are grouped into lifetime, degradation and other data types and used to determine the corresponding distributions. Next, the data of each data type are separately transmitted to higher level of system. If there are data of identical data type in the higher level, then they are pooled with the transmitted data from the lower level. Finally, all the transmitted data are integrated with the native data in the system-level for reliability analysis of system. An illustrative example shows the application of the proposed method on a system in a satellite. The results, sensitivity analysis, and comparison demonstrate the effectiveness and advantages of the proposed method. • A method is proposed for reliability analysis of multi-level system with multi-source data. • All the data below the system-level are transmitted and pooled upward before integration. • The data integration is only required in system-level for reliability analysis. • The proposed method can reduce the computation extensively during the data transmission upward. • The proposed method is effective and superior to the existing methods. [ABSTRACT FROM AUTHOR]

• Third party risk indicators are extended with property damage risk and noise impact. • An integrated cost assessment model is proposed to incorporate various risk types. • An optimization model is developed to tackle risk-based UAV path planning problems. • A hybrid method integrates estimation of distribution algorithm & CostA* algorithm. Various applications of unmanned aerial vehicles (UAVs) in urban environments facilitate our daily life and public services. However, UAV operations bring third party risk (TPR) issues, as UAV may crash to pedestrians and vehicles on the ground. It may also cause property damages to critical infrastructures and noise impacts to the public. Path planning is an effective method to mitigate these risks and impacts by avoiding high-risk areas before flight. However, most of the existing path planning methods focus on minimizing flight distance or energy cost, rarely considered risk cost. This paper develops a novel flight path optimization method that considers an integrated cost assessment model. The assessment model incorporates fatality risk, property damage risk, and noise impact, which is an extension of current TPR indicators at modeling and assessment levels. To solve the proposed integrated cost-based path optimization problem, a hybrid estimation of distribution algorithm (EDA) and CostA* (named as EDA-CostA*) algorithm is proposed, which provides both global and local heuristic information for path searching in cost-based environments. A downtown area in Singapore is selected for the case study. Simulation results demonstrate the effectiveness of the developed cost-based path optimization model in reducing the risk cost. The statistical analysis for 100 sampled environments also shows the reliability of the proposed method, which reduced the cost by [42.64%, 44.15%] at 95% confidence level. [ABSTRACT FROM AUTHOR]

• A combinatorial method for reliability analysis of smart home sensor systems subject to competing failures. • The method is based on an efficient binary decision diagram reduction technique. • The method is applicable to any arbitrary component time-to-failure distribution. • Accuracy and efficiency are verified and compared with the fault tree reduction method. ZigBee and Bluetooth devices (particularly sensors) abound in smart home sensor systems (SHSSs), and they can only be connected to the network through gateways. Therefore, there exists functional dependence between these sensors and the corresponding gateway, where the failure of the gateway makes the connected sensors inaccessible or isolated. Two kinds of sensor failures can be distinguished in the SHSS: local failure that only affects the sensor itself (e.g., hardware failures) and propagated failure that affects other components and even causes the entire SHSS to fail (e.g., jamming attacks). Competitions exist between the gateway failure and propagated failures from the connected sensors in the time domain. Particularly, if the gateway fails before the propagated failures from the connected sensors, the propagated failures can be isolated and no longer affect other devices in the system; otherwise, the SHSS may fail due to the failure propagation effect. To address the influence of such competing failures, this paper proposes a new combinatorial method based on improved binary decision diagrams (BDDs) to analyze the reliability of SHSSs with competing failures. As compared to the existing method that involves generation of multiple reduced fault trees and their conversions to BDDs, the proposed method eliminates the process through an efficient BDD reduction technique. The efficiency and accuracy of the proposed method are discussed through an example SHSS. [ABSTRACT FROM AUTHOR]

In the operating process of multi-component systems, components may interact with each other in a way that the load of a failed component is taken up by its nearby components at varying proportions. As a result, the failure rates of the proximate components are accelerated while distant components are not affected. This paper develops a novel spatial model for estimating the reliability of a load-sharing system considering spatial dependence and proximity effects. The spatial model is applicable to systems with heterogeneous or homogeneous components and is suitable for systems with or without distance information. To investigate the importance and significance of the spatial effect, we compare our spatial model with an equal load-sharing through numerical examples. Our results demonstrate that our model is more accurate than standard load sharing models in evaluating system reliability when spatial effects exist. • Developed a load sharing model considering spatial dependency and proximity effect. • Investigated the spatial effect on load distributions among components. • Investigated the spatial effect when distance information is known and unknown. • Compared our model with standard load sharing models. • Demonstrated that spatial model is more accurate in presence of spatial effect. [ABSTRACT FROM AUTHOR]

• K-L expansion method was adopted to generate random field with different spatial correlation lengths • A critical spatial correlation length existed for predicting time-dependent settlement of soft soils • A single random variable analysis is not always the most conservative analysis in predicting settlement of soft soils • It is essential to perform random field analysis to reduce the risk of the design to be applied in construction. Low embankment strategy is one of the effective methods to control time-dependent settlement of soft soils in infrastructure construction projects. Spatial variability of soil characteristics is a crucial factor, affecting the reliability of predictions of the long-term settlement in soft soils. In this paper, the time-dependent behaviour of soft soils is analysed incorporating spatial variability of elastic visco-plastic model parameters. Standard Gaussian random fields for correlated elastic-plastic model parameter (λ / V) and the initial creep coefficient (ψ 0 / V) are generated adopting Karhunen-Loeve expansion method based on the spectral decomposition of correlation function into eigenvalues and eigenfunctions. Then the generated random fields are incorporated in the proposed non-linear elastic visco-plastic (EVP) creep model. The impacts of spatially variable elastic visco-plastic model parameters (i.e. ψ 0 / V and λ / V) on long-term settlement predictions are evaluated through random field analysis (RF) with different spatial correlation lengths, and results are then compared to a single random variable (SRV) analysis. The probability of failure (PF) is calculated adopting RF and SRV analysis to determine the critical spatial correlation length, resulted in a maximum probability of failure. This study can be employed by design engineers to determine the critical spatial correlation length for safe design in the absence of adequate data to determine the exact spatial correlation length. The results also confirm that SRV analysis is not always the most conservative analysis in predicting time-dependent settlement of soft soils; and it is essential to perform RF analysis considering the spatial correlation length to reduce the risk and increase the reliability of the design to be applied in construction. [ABSTRACT FROM AUTHOR]

• Maximum entropy method from fractional moments with nondimensionalization is given • The 2nd Akaike information criterion is combined with maximum entropy method • Fractional, integral, positive, negative moments are all considered • The method is illustrated in a case study and an example application In probabilistic reliability analysis for geotechnical engineering applications, determining the underlying probability distributions of soil properties and corresponding parameters from observed data is a critical initial step because subsequent risk and reliability analyses depend upon these evaluations. Conventionally, the choice of probability distribution is dictated by subjective familiarity with a classical (e.g., normal or lognormal) distribution. This paper proposes an objective and unbiased method to estimate probability distributions of a soil property using the maximum entropy method from fractional moments of observed data. The probability distribution is based on the concept of maximum entropy and is free from the assumptions of classical distributions. A case study is presented for the undrained shear strength of soil in the Nipigon River landslide area, Ontario, Canada. The maximum entropy distributions of the soil property from fractional moments are compared to the frequency histogram, normal and lognormal distributions, and maximum entropy distributions from integral moments. The maximum entropy distribution with two-order fractional moments, almost equivalent to that with four-order integral moments, is verified with the chi-square goodness-of-fit test. Issues related to overfitting/underfitting, minimum sample size, fractional orders, negative moments, and limitations are discussed. Application of the method to geotechnical reliability analysis is illustrated. [ABSTRACT FROM AUTHOR]

Engineering models are becoming increasingly complex, involving a larger number of variables. As a result, engineers struggle to deeply understand the models and therefore validate and properly use them. Sensitivity analyses (SA) are usually conducted to help with this task. Nonetheless, the knowledge and computational efforts required to conduct SA increases with the complexity of the model. This paper presents a conceptually simple method to conduct the SA of extreme-based engineering problems, that is, those problems whose outcome of interest is their maximum or minimum values. This type of problems is of relevance for reliability-based design. The method requires to iteratively maximize or minimize the model by fixing one input factor at each time. Then, the variation of the optimal surface is evaluated. The method permits the visualization and measure of the input factors' influence on the extreme model response, with no need of defining the probability distribution of the input factors. Both the easiness of application and interpretation, along with a low computational cost for problems dealing with extreme values, make the proposed method very convenient to practitioners. • Method to analyse sensitivity of extreme-based engineering problems. • Practitioner-oriented method that is easy to apply with low computational cost. • Visualization and importance measure of input factors on the extreme model response. • All-minus-one-at-a-time (A-1AT) optimization-based sensitivity analysis. • No need of defining the probability distribution of input factors. [ABSTRACT FROM AUTHOR]

• A new PHM with environmental factors and degradation trend as covariates is built. • The complex integrand in reliability function is solved by the Taylor formula. • A real-time updated reliability prediction method is developed based on the PHM. • Numerical study and real case studies show the superiority of the proposed method. Degradation data and lifetime data have been broadly used for assessing product and system reliability. To utilize the two kinds of data simultaneously, the proportional hazard (PH) model with degradation data as a covariate is proposed for reliability analysis. However, most existing works focus on modeling the PH model with degradation state as a covariate, while the degradation trend is ignored, which makes the PH model unable to carry out reliability prediction directly. Confronted with that, a new PH model with the degradation trend and environmental factor as covariates is developed in this paper. The Wiener process is firstly applied to depict the degradation trend, then the degradation trend and temperature are used as covariates to establish the PH model, and a closed-form of the reliability is derived by the Taylor approximation. Based on the degradation data under actual ambient conditions, the real-time updated reliability prediction is provided to guide the health management of products and systems. The simulation study validates that the proposed model outperforms two existing models in terms of Mean Square Error (MSE). Finally, a real-world example of MOSFET is presented to demonstrate the implementation of the proposed method. [ABSTRACT FROM AUTHOR]

Kriging with active learning has been widely employed to calculate the failure probability of a problem with random inputs. Training a Kriging model for a high-dimensional problem is computationally expensive. This reduces the efficiency of active learning strategies since the training cost becomes comparable to that of the function evaluation itself. Kriging with partial least squares (KPLS) has the advantage of a fast training time but its efficacy on high-dimensional reliability analysis has not yet been properly investigated. In this paper, we assess the potential benefits of KPLS for solving high-dimensional reliability analysis problems. This research aims to identify the potential advantages of KPLS and characterize the problem domain where KPLS can be most efficient and accurate in estimating the failure probability. Tests on a set of benchmark problems with various dimensionalities reveal that KPLS with four principal components significantly reduces the CPU time compared to the ordinary Kriging while still achieving accurate failure probability. In some problems, it is also observed that KPLS with four principal components reduces the number of function evaluations, which will be beneficial for problems with expensive function evaluations. Using too few principal components, however, does not show any evident improvements over ordinary Kriging. • Efficiency of Kriging with partial least squares for reliability analysis is assessed. • The method is combined with active learning and compared to the ordinary Kriging. • Impact of the number of principal components to the accuracy and CPU time is studied. • Four components accurately estimate the failure probability with reduced CPU time. • The speedup factor is around ten times in high-dimensional heat conduction problem. [ABSTRACT FROM AUTHOR]

• A Bayesian network model is developed under the complicated system assumption. • Reliability and MTTF of the MDS and its subsystems are predicted. • Risky failure items of the MDS are identified. • The errors of predictions are 8% and 10.5% at different working stages of the MDS. • Recommendations on improvements of maintenance and inspections are suggested. Early failures occur in the initial operation period of complicated systems such as Main Drive Systems (MDSs) of Computerized Numerical Control machine tools (CNC machine tools). In this paper, a Bayesian network model is developed to conduct a comprehensive reliability analysis of the MDS of a heavy boring and milling CNC machine tool, in which early failures of the MDS is considered. The primary contributions of this study over the existing analyses are: (i) the early failure of the MDS is investigated. (ii) the reliability analysis is conducted under the complicated system assumption, accordingly, multiple working states of the MDS and its subsystems are considered that are working, have a soft failure or a hard failure. (iii) reliability of the MDS in different working stages and for various manufacturing tasks are analysed. With the Bayesian network model, reliability and mean time to failure of the MDS and its subsystems are predicted. Meanwhile, this study identified risky failure items that potentially give rise to malfunctions of the MDS. The error of the predicted results is 8% at the early-wear stage and 10.5% at the stable-working stage when comparison with collected field data. Recommendations on improvements of maintenance and inspection activities are suggested, which may play a role in overall cost saving and guarantee the reliability of the MDS of the heavy boring and milling CNC machine tool. [ABSTRACT FROM AUTHOR]

The Birnbaum importance is one of the measures often used in importance analysis. Many algorithms for the calculation of this measure have been proposed for coherent systems. Several interpretations of the Birnbaum importance for non-coherent systems also exist. These interpretations are usually based on the prime implicants of the structure function of the system. However, identification of the prime implicants is a complex problem. In this paper, we develop a method for computation of Birnbaum importance using Boolean expression (algebraic representation) and truth table (matrix representation). Both of these representations are calculated based on Logical Differential Calculus, in particular, Boolean derivatives. The Boolean expression derived based on Boolean derivatives is equal to known definitions of the Birnbaum importance. The matrix approach for the calculation of the Birnbaum importance based on Boolean derivatives is novel. This approach can be used for calculation of the Birnbaum importance for the structure function represented by truth table and does not need transformation of the structure function into Boolean expression. An important advantage of the proposed approach (in algebraic or matrix form) is a possibility to define the Birnbaum importance for the evaluation of the non-coherent system failure (restore) with respect to simultaneous changes of states of several system components. • The Boolean expression of Birnbaum importance for non-coherent system is proposed. • The Logical Differential Calculus is developed for importance analysis of non-coherent system. • The Birnbaum importance is defined based on Boolean Derivatives. • The Birnbaum importance of several components is defined based on Boolean Derivatives. • The matrix approach for Birnbaum importance is proposed [ABSTRACT FROM AUTHOR]