Reliability Sensitivity Analysis Research Articles

Global reliability sensitivity analysis based on state dependent parameter method and efficient sampling techniques

In order to efficiently assess the influence of input variables on the failure of the structural systems, an improved global reliability sensitivity analysis (SA) method is proposed in this paper. The new method is based on the state dependent parameter (SDP) method and the efficient sampling techniques. In the new method, the efficient sampling techniques are first used to generate samples that are more efficient for reliability analysis, and then the SDP method is further employed to estimate the global reliability sensitivity index by using the same set of samples as the reliability analysis. Two efficient sampling methods, e.g., importance sampling (IS) and truncated importance sampling (TIS), are employed in this paper, and the strategies of combining these methods with the SDP method for global reliability SA are discussed. Compared with the existing SDP method, the new method is more efficient for global reliability SA of structural systems. Three examples are used in the paper to demonstrate the efficiency and precision of the new methods.

Reliability Model and Sensitivity Analysis for General Electronic Systems with Failure Types based on Non-identical Correlated Components

Reliability is the most important qualitative properties of products and industrial electronic systems. Today, industrial electronic systems need to produce products with maximum reliability. In every industry, when a system fails, it becomes harmful in various aspects such as economic, human and political; therefore, accurate estimation of system reliability is very important. Previous methods to calculate system reliability assumed that a large number of components failures are statistically independent. Considering such a hypothesis makes it possible to calculate probability and mathematical computation, but it does not provide perfect system reliability. This paper presents a simple and new technique for reliability analysis by considering unequal reliability and non-identical distribution of correlated components for k-out-of-n and coherent systems. The efficiency of our proposed method is demonstrated by computing the reliability of Bridge system. The results show that the function of existing components correlation has a major impact, and that ignoring it has a significant effect on system safety.

Performance Margin Modeling and Reliability Analysis for Harmonic Reducer Considering Multi-Source Uncertainties and Wear

The harmonic reducer of the space drive mechanism is one of the critical components of the satellite remote sensing system and its reliability is always required strictly in practice. During the manufacturing and usage processes of the harmonic reducer, uncertainties are ubiquitous and performance degradation is inevitable, which is mainly caused by the wear between the meshed tooth surfaces. They influence the reliability of harmonic reducer. In this paper, a performance margin modeling and reliability analysis for harmonic reducer considering multi-source uncertainties and wear is proposed. Firstly, based on the functional principle and the influence of wear, the performance margin model is established using hysteresis and transmission errors as key performance parameters. Then multi-source uncertainties are analyzed and quantified, including manufacturing errors, uncertainties in operational and environmental conditions, and uncertainties in performance thresholds. Finally, the reliability model is constructed based on the performance margin. A case study of a harmonic reducer is applied and the reliability sensitivity analysis is implemented to show the practicability of the proposed method. The results show that the proposed method can provide some suggestions to the design and manufacturing phases of the harmonic reducer.

Capacity Reliability Calculation and Sensitivity Analysis for a Stochastic Transport Network

A major performance index for analyzing a stochastic transport network is the two-terminal capacity reliability R d , defined as the probability that d units of goods can be successfully transported via stochastic arc capacities from the source to the destination. This paper presents an efficient d-minimal path method to calculate R d based on some newly obtained results. The proposed method uses a simple method to check d-minimal path candidates and a more efficient approach to remove duplicate d-minimal paths that are the biggest obstacle in solving d-minimal paths, along with an indication of the advantage over the existing methods. Besides, sensitivity analysis is adopted to explore the most important arc whose reliability change affects the network reliability most significantly, which helps supervisor identify and enhance the critical arcs for improving the network reliability more effectively. Computational and application examples demonstrate the efficiency and utility of the method, respectively.

Hybrid PSO-TS Based Distribution System Expansion Planning for System Performance Improvement Considering Energy Management

Energy management (EM) has become very attractive in smart grid era for both industry and academia. EM in a power distribution system (PDS) can reduce the system losses, operational costs and emissions, and increases system’s reliability, voltage stability and efficiency. This article expands the PDS using different distributed energy resources (DERs) and observes their impacts on EM success, operational costs, system losses, and emissions. Moreover, the impacts of integrating reactive sources (RSs), energy storage systems (ESSs), and electric vehicles (EVs) on the system’s operational performance is investigated. An index is defined to measure the energy management success rate (EMSR) and several case studies are created for investigating variety of system expansion options individually and collectively. Furthermore, a new reliability index, namely reliability index success rate (RISR), is defined and sensitivity analysis are presented to investigate the DERs impacts on system’s voltage controllability and the defined reliability index. A new hybrid PSO-TS optimization algorithm is developed, and the well-known PG&E 69-bus distribution network is selected for the simulations. Several case studies presented in the paper provide a clear understanding of the impacts of integrating different resources on the EM as well as other operational aspects of a PDS. The results reveal that the system expansion using DERs with different capacities along with EM strategies could have significant impacts on PDS performance depending on the DERs types’ and capacities. Due to their availability and low operational costs, gas turbine further improves the performance indices comparing to the renewables that have uncertain availability and to diesel generators with their high operational costs.

Optimization design of gear reducer based on multi-attribute decision making and reliability sensitivity

In order to solve the complexity and implicitness of lightweight optimization of the gear reducer, this paper constructs a multi-objective reliability optimization mathematical model of the gear reducer. and to obtain multi-objective Pareto solution, artificial intelligence algorithm is used to optimize structural parameters. Then, through repeatedly changing the structural parameters of the reducer, the experimental simulation analysis is carried out to obtain the maximum working stress. Based on the idea of the weight reduction and miniaturization, the stress state and reliability index values under different structural parameters are compared and analyzed. In order to determine the optimal solution of structural parameters, multi-attribute decision theory is used to determine the solution. Finally, in order to effectively reveal the inherent variation of attribute values and decision results and quantitatively reflect the impact of various structural parameters on system reliability, reliability sensitivity analysis of the gear reducer is carried out by the response surface-Monte Carlo and DPS methods. Thereby, an optimized structure that meets the safety reliability and the appropriate economy is obtained, and this study produces a balanced and improved optimized design that is coordinated with cost, quality, volume, safety and stability.

A Fast Product of Conditional Reduction Method for System Failure Probability Sensitivity Evaluation

System reliability sensitivity analysis becomes difficult due to involving the issues of the correlation between failure modes whether using analytic method or numerical simulation methods. A fast conditional reduction method based on conditional probability theory is proposed to solve the sensitivity analysis based on the approximate analytic method. The relevant concepts are introduced to characterize the correlation between failure modes by the reliability index and correlation coefficient, and conditional normal fractile the for the multi-dimensional conditional failure analysis is proposed based on the two-dimensional normal distribution function. Thus the calculation of system failure probability can be represented as a summation of conditional probability terms, which is convenient to be computed by iterative solving sequentially. Further the system sensitivity solution is transformed into the derivation process of the failure probability correlation coefficient of each failure mode. Numerical examples results show that it is feasible to apply the idea of failure mode relevancy to failure probability sensitivity analysis, and it can avoid multi-dimension integral calculation and reduce complexity and difficulty. Compared with the product of conditional marginal method, a wider value range of correlation coefficient for reliability analysis is confirmed and an acceptable accuracy can be obtained with less computational cost.

Hazard recognition and reliability analysis of CTCS-3 on-board subsystem

This paper presents an investigation of hazard sources identification and reliability sensitivity analysis of CTCS-3 on-board subsystem. Traditional quantitative and qualitative safety and reliability analysis generally used static analysis methods, such as Fault Tree. When device redundancy, dynamic logic and dynamic mechanism are taken into consideration, dynamic analysis methods are preferred, such as Dynamic Fault Tree (DFT). In this paper, the methods of Hazards and Operability (HAZOP), DFT and Monte Carlo Simulation (MCS) are used for quantitative and qualitative analysis. Firstly, to reflect the structure and functions of on-board subsystem, two models (i.e reference model and function hierarchical model) are built. HAZOP is applied to identify hazard sources of on-board subsystem according to above models. Secondly, DFT is put forward within which the top event is CTCS-3 on-board subsystem failure event and the basic events are from results of HAZOP analysis. Then, both MCS and Maximum Likelihood Estimation (MLE) are adopted to estimate the reliability parameters of the CTCS-3 on-board subsystem and components. Reliability sensitivity analysis is observing the variations in components’ reliability parameter contributing to the changes of Mean Time to Failure (MTTF) of CTCS-3 on-board subsystem. Finally, a failure density curve of CTCS-3 on-board subsystem and a table of MTTF sensitivity parameters are presented. According to the sensitivity table, it is knowledgeable for decision makers to take effective measures to improve the reliability of CTCS-3 on-board subsystem.

Probabilistic modeling of excavation-induced damage depth around rock-excavated tunnels

Abstract The cracked zones caused by tunnel excavations are among the major reasons for structural instability in mechanized tunnel projects. Thus, various methods have been proposed to evaluate such cracks in terms of size and depth. However, deterministic estimations have been associated with a margin of error due to the inherent uncertainties of the respective problems as well as the approximation nature of the existing methods. Therefore, in this study, a probabilistic approach was adopted to assess the depth of a cracked zone induced around a tunnel. For this purpose, the problem was formulated as a reliability model, and the Monte Carlo method was utilized to calculate the exceedance probability for the crack depth around the tunnel. The exceedance probability was then calculated for any different depths of crack and presented as probability contours around the excavation zone. It was demonstrated that the exceedance probability is reduced sharply with an increase in the crack depth such that it fell below 5% for the cracks deeper than 2.28 times the tunnel radius. Effects of the maximum tangential stress at excavation boundary and crack initiation threshold on the exceedance probability were further calculated using the reliability sensitivity analysis. Eventually, the influence of in-plain stress ratio on the failure probability was investigated, and the results were reported for three rock types, including limestone, granite, and mudstone.

A framework for global reliability sensitivity analysis in the presence of multi-uncertainty

In reliability analysis with numerical models, one is often interested in the sensitivity of the probability of failure estimate to changes in the model input. In the context of multi-uncertainty, one whishes to separate the effect of different types of uncertainties. A common distinction is between aleatory (irreducible) and epistemic (reducible) uncertainty, but more generally one can consider any classification of the uncertain model inputs in two subgroups, type A and type B. We propose a new sensitivity measure for the probability of failure conditional on type B inputs. On this basis, we outline a framework for multi-uncertainty-driven reliability sensitivity analysis. A bi-level surrogate modelling strategy is designed to efficiently compute the new conditional reliability sensitivity measures. In the first level, a surrogate is constructed for the model response to circumvent possibly expensive evaluations of the numerical model. By solving a sequence of reliability problems conditional on samples of type B random variables, we construct a level 2-surrogate for the logarithm of the conditional probability of failure, using polynomial bases which allow to directly evaluate the variance-based sensitivities. The new sensitivity measure and its computation are demonstrated through two engineering examples.

Probability based global sensitivity analysis of fatigue reliability of steel structures

This article focuses on reliability-oriented global sensitivity analysis of the fatigue limit state of a steel member stressed by many times repeated loading. The fatigue limit state is associated with fatigue failure, which is caused by brittle fracture due to propagation of a fatigue crack from initial to critical size. The fatigue crack propagation is analysed using linear fracture mechanics. The fundamental question in terms of structural reliability is how significant is the effect of input random quantities on the probability of failure. A new type of global sensitivity analysis subordinated to a contrast identified the equivalent stress range and initial edge crack length as random quantities that most significantly influence the failure probability. The new findings obtained using the contrast-based global sensitivity analyses show interaction effects that are unusually strong in comparison with some results of Sobol’s sensitivity analysis aimed at the reliability of structures. The sensitivity indices are estimated using double-nested-loop simulation of the Latin Hypercube Sampling method.

Architecture-Based Reliability-Sensitive Criticality Measure for Fault-Tolerance Cloud Applications

The widespread adoption of service computing allows software to be developed by outsourcing open cloud services (i.e., SOAP-based or RESTful Web APIs) through mashup or service composition techniques. Fault tolerance for the purpose of assuring the stable execution for cloud-based software (or CBS) application has attracted great attention in coping with a loosely coupled CBS operating under dynamic and uncertain running environments. It is too expensive to rent massively redundant cloud services for CBS fault tolerance application. To reduce budget but guarantee the effectiveness of CBS fault tolerance, identifying critical components within a CBS composite system is of significant importance. We integrate CBS composite system architecture analysis and reliability sensitivity analysis approaches and propose an Architecture-based Reliability-sensitive Criticality Measure (or ARCMeas) method in this paper. We verify ARCMeas application through a cost-effective fault tolerance CBS by presenting a particle swarm optimization (PSO)-based cost-effective fault tolerance strategy determination (or PSO-CFTD) algorithm. Experimental results suggest the effectiveness of the approach.

Reliability, maintainability and sensitivity analysis of physical processing unit of sewage treatment plant

India is facing radical change in perspective of inadequate water resources which can reduce by using treated water. In this direction, sewage treatment plants play a key role. Sewage treatment plant comprises three units namely physical processing, chemical processing and biological process. The physical process is the most important part and it has five component arranged in series configuration. It becomes necessary to perform this process with high efficiency and reliability, availability, maintainability, and dependability (RAMD) is the methodology to analyze the performance. The failure and repair rates of the subsystems has been considered exponentially distributed. Chapman–Kolmogorov differential equations are derived using Markovian birth–death process and several measures like mean time between failures, mean time to repair and dependability ratio are derived. The sensitivity analysis of reliability of the plant has also been performed. RAMD investigation shows that: availability of system is 0.952177, reliability of the system after 20 days is 0.2018 and after 60 days 0.00823, maintainability of the plant is 0.999948, dependability ratio is 0.9541 and raw sewage sump is the most sensitive subsystem of the plant with reliability 0.382893. This work is projected to support as an informative exertion in steering a RAMD analysis of physical processing unit and vary few work is available in literature related to the performance features of physical processing units of the sewage treatment plants. The main findings may be very useful for sewage treatment plants designers.

Reliability model and sensitivity analysis for wind turbine with failure types based on non-identical correlated components

ABSTRACT Today, wind turbines have a high cost of maintenance. Therefore, designing them with reliable and efficient systems is essential for longer lifespans. When wind turbine components fail, it becomes harmful in various aspects such as economic and environmental pollution, therefore, accurate estimation of wind turbine components reliability is very important. Previous methods to calculate wind turbine reliability assumed that components failures are statistically independent. This paper presents a new technique for the reliability of wind turbine with dependent components failures. The results show that existing components correlation has a major impact, and ignoring it has a significant effect on wind turbine safety.

Reliability sensitivity analysis with subset simulation: application to a carbon dioxide storage problem

Reliability sensitivity analysis (RSA) is a sensitivity analysis to measure the effect of modelling parameters on the predicted reliability of a system. It can be used for reliability-based design, safety management, etc. The output-classification-based version of RSA compares the failure-conditional probability density function (PDF) of model parameters with their unconditional PDF to measure sensitivity. The main challenge is to estimate failure-conditional PDFs. Usually, these PDFs can be estimated through the failure samples obtained by Monte Carlo simulation. However, practical systems usually have a small failure probability. For such cases, the brute-force Monte Carlo simulation requires a larger number of samples to obtain enough failure samples. Therefore, the computational cost is very high. In this paper, we propose to use subset simulation to estimate the output-classification-based reliability sensitivity index. Subset simulation introduces a series of intermediate failure events which are easier to sample from, and then iteratively samples in each constrained failure region until the target failure event is reached. Compared to brute-force Monte Carlo simulation, subset simulation samples in a direction towards the target failure domain. Therefore, the failure samples can be obtained more efficiently. We apply subset simulation to perform RSA for a carbon dioxide storage benchmark problem. We show that subset simulation can estimate the output-classification-based reliability sensitivity index more efficiently compared to brute-force Monte Carlo simulation.

Reliability and sensitivity analysis for bearings considering the correlation of multiple failure modes by mixed Copula function

The correlation between contact fatigue failure and wear failure of rolling bearing is analyzed, and the reliability model of rolling bearing based on multi-correlation failure mode is established. Based on the improved linear fatigue cumulative damage theory and wear theory, the limit state equations of two failure modes are established, and the correlation of state functions of contact fatigue and wear failure modes is described by the mixed Copula function. The random sample data are generated by Monte Carlo method, and the unknown parameters are estimated by genetic algorithm based on the minimum deviation square criterion, then the dynamic reliability model of rolling bearing is established. The quadratic polynomial without cross-term is used as the implicit functional proxy model, then the Latin hypercube sampling method and least squares theory are employed to estimate parameters of mixed Copula function and finally, the reliability sensitivity analysis of multi-failure modes of bearing is presented by fourth-order moment estimation method. Taking a certain type of spherical roller bearing as an example, the bearing reliability analysis considering the correlation of failure modes is carried out. The results show that compared with the bearing reliability model based on the assumption of independent failure modes and the weakest link theory, the bearing reliability model based on multi-correlation failure is more consistent with the practical application.

Dynamic Reliability and Global Sensitivity Analysis for Hydraulic Pipe Based on Sparse Grid Integral Method

Abstract Due to the extremely rough working environment, aero-hydraulic pipes face serious dynamic failure problems in applications for practical engineering. This paper proposes a dynamic reliability and moment-independent global sensitivity analysis (GSA) method to evaluate the dynamic reliability and the effects of random input variables on the dynamic reliability of aero-hydraulic pipes. Based on the Miner criterion for the cumulative damage of structural fatigue, this paper establishes the dynamic reliability analysis method under the condition of double random vibration. In order to further analyze the influence of the uncertainty of each random variable of pipe on its dynamic reliability, a moment-independent global sensitivity index for dynamic reliability based on cumulative distribution function is proposed in this paper. The index can reflect the effects of random variables on dynamic reliability quantitatively. Based on the proposed GSA method of dynamic reliability, a sparse grid integral (SGI) method is introduced to solve the dynamic reliability and moment-independent global sensitivity index, with high computational efficiency. Finally, the effects of clamp supports, diameters, and curvature of curved pipe on the dynamic reliability and GSA are analyzed through a hydraulic piping example.

Reliability Prediction of Computing Network with Software and Hardware Failures

In this paper, we investigate the reliability and queueing performance indices for the fault-tolerant computing network having a finite number of unreliable operating components with the provision of warm standby components. Operating and standby components are governed by dedicated software which is also prone to random failure. On failure of operating components, available standby component(s) may switch from the standby state to operating state with negligible switchover time. The switchover process may also fail due to some automation hindrance. The computing network is also subjected to common cause failure in lieu of external cause. The studied redundant fault-tolerant computing network is framed as a Markovian machine interference model with exponentially distributed inter-failure times and service times. For the reliability prediction of the computing network, various performance measures, namely, mean-time-to-failure (MTTF), reliability/availability, failure frequency, etc., have been formulated in terms of transient-state probabilities which we have obtained using the spectral method. To show the practicability of the developed model, numerical simulation has been done. Sensitivity analysis of reliability and other indices of the computing network with respect to different network parameters has been presented, and results are summarized in the tables and graphs. Finally, future scope and concluding remarks have been included.

Efficient Driving Plan and Validation of Aircraft NLG Emergency Extension System via Mixture of Reliability Models and Test Bench

The emergence extension system (a mechanical system) of nose landing gear (NLG) seriously influences the reliability, safety and airworthiness of civil aircrafts. To efficiently realize the NLG emergence extension, a promising driving plan of emergence extension is proposed in respect of the reliability sensitivity analyses with a mixture of models. The working principle, fault tree analysis and four reliability models are firstly discussed for NLG emergence extension. In respect of the mixture of models, the reliability sensitivity analyses of emergence extension are then performed under different flight speeds (270 Kts, 250 Kts, 220 Kts, and 180 Kts). We find dimpling torque and aerodynamic torques of forward and after doors are the top three failure factors and the start reliability is the most in emergence extension failures. Regarding the results, feasible driving plans of NLG emergence extension are developed by adjusting the aerodynamic torque of NLG forward door, and are validated by the aerodynamic torque experiment of forward door with regard to strut rotational angle under the flight speed 270 Kts. It is indicated that (1) the adverse torque generated by the new driving mechanism obviously reduces by about 24.8% from 1462.8 N·m to 1099.6 N·m, and the transmission ratio of aerodynamic torque (force) is greatly improved when the NLG strut is lowered near to 100°; (2) under different flight speeds (180 Kts, 220 Kts, 250 Kts, and 270 Kts), the new driving mechanism realizes the lower tasks of emergence extension which cannot be completed by the initial driving mechanism; and (3) the lowering time of the new driving mechanism shortens with the increasing flight speed. The proposed new driving mechanism is verified to be reliable for emergence extension of aircraft NLG besides normal extension and to be a promising feasible driving plan with high lowering reliability. The efforts of the paper provide an efficient driving mechanism for the design of NLG in civil and military aircrafts.

An efficient method for estimating the parameter global reliability sensitivity analysis by innovative single-loop process and embedded Kriging model

Abstract For evaluating the effect of uncertain distribution parameter on the uncertainty of the failure probability function, the parameter global reliability sensitivity index (PGRSI) is researched and the high efficient estimation algorithm is proposed to approximately estimate the PGRSI. The used definition form of the PGRSI is the expectation of absolute differences between the unconditional expectation of failure probability function and the conditional expectation of failure probability function, which involves a triple-loop evaluation. For efficiently estimating the PGRSI, this paper innovatively inducts the Bayes theorem and the law of total expectation in the successive intervals without overlapping in order to convert the triple-loop evaluation to a single-loop one. The number of actual model evaluations of the single-loop Monte Carlo simulation (MCS) is independent of the dimensionality of uncertain distribution parameters, and the single-loop MCS only needs one set of input-output samples. Besides, the single-loop MCS can be regarded as a classification problem which needs to identify the failure or safety states of samples in the one set. To further enhance the computational efficiency of the proposed single-loop process, the adaptive Kriging (AK) model is embedded in the single-loop MCS, where the Kriging model is used to approximate the actual limit state function to classify the samples. The number of actual model evaluations of the Kriging model nested single-loop process only generates in the process of constructing the AK model. The results of case studies illustrate the accuracy and efficiency of the proposed method.