Reliability Sensitivity Analysis Research Articles

Reliability optimization design of a planar multi-body system with two clearance joints based on reliability sensitivity analysis

A general method for reliability sensitivity analysis and reliability optimization design of planar slider crank mechanism with two clearance joints was presented. A continuous contact force model considering energy dissipation was employed to estimate the contact force acting on the clearance joint. The Monte Carlo method was used to analyze the reliability sensitivity. In addition, based on the Kriging method, a surrogate model was constructed with consideration of explicit function expression. The precision and reliability of the presented method have been successfully demonstrated by numerical simulation. The results show that the number and position of clearance joint considered have a great influence on the maximum allowable displacement of the slider. The changing of the reliability sensitivity for the mean and variance of several random variables has certain regularity. Compared with the determinacy optimization design, the reliability optimization design presented here shows better dynamical performances.

Computational-experimental approaches for fatigue reliability assessment of turbine bladed disks

In the present study, a computational-experimental framework is developed for fatigue reliability assessment of turbine bladed disks. Within the framework, the overspeed testing is innovatively combined with stochastic finite element (FE) analysis for quantifying uncertainties in the experimental data, material properties and loads. Meanwhile, two schemes are elaborated based on probabilistic S-N curves and stochastic FE simulation coupling with sampling technique. The stochastic FE simulation incorporates the Chaboche constitutive model with Fatemi–Socie criterion for fatigue behavior modeling and life prediction. Moreover, experimental deformation and numerical FE analysis are conducted with regard to the full-scale bladed disk test with increased step-stress overloading. Reliability sensitivity analysis is performed to provide an importance ranking of random variables for fatigue design of the bladed disk. Results indicate that stochastic FE analysis-based scheme provides more conservative predictions than the probabilistic S-N curves-based one.

An efficient global reliability sensitivity analysis algorithm based on classification of model output and subset simulation

The global reliability sensitivity analysis measures the effect of each model input variable on the failure probability, which is very useful for reliability-based optimization design. The aim of this paper is to propose an alternative method to estimate the global reliability sensitivity indices by one group of model input–output samples. Firstly, Bayes formula is used to convert the original expression of global reliability sensitivity index into an equivalent form where only the unconditional failure probability and the failure-conditional probability density function (PDF) of each model input variable are required. All global reliability sensitivity indices can be simultaneously estimated by this new equivalent form, and the computational cost of the process is independent of the dimensionality of model input variables. Secondly, to improve the efficiency of sampling which aims at calculating the unconditional failure probability and estimating the failure-conditional PDF of every model input simultaneously, subset simulation method is extended to achieve these two aims. In the proposed procedure, subset simulation is used to estimate the unconditional failure probability, and Metropolis-Hastings algorithm is employed to convert the samples in failure domain from the current PDF in subset simulation to the PDF corresponding to the original PDF of model inputs for estimating the failure-conditional PDF of each model input variable. Thirdly, Edgeworth expansion is employed to approximate the failure-conditional PDF of each model input variable. Finally, the global reliability sensitivity index can be easily computed as byproducts using the unconditional failure probability and the failure-conditional PDF of each model input in failure probability analysis, and this process does not need any extra model evaluations after the unconditional failure probability analysis is completed by subset simulation. A headless rivet model, a roof truss structure and a composite cantilever beam structure are analyzed, and the results demonstrate the effectiveness of the proposed method in global reliability sensitivity analysis.

Reliability analysis for highly non-linear and complex model using ANN-MCM simulation

To predict reliability for highly non-linear and complex model efficiently and accurately, an artificial neural network (ANN) based Monte Carlo method (MCM) is proposed. In this method, ANN trained by backpropagation (BP) algorithm is developed to establish the relationship between inputs and outputs. The trained ANN model is then connected to MCM to predict reliability and reliability sensitivity of structure. To examine the accuracy and efficiency of the proposed method, results obtained by polynomial-FOSM (first-order second moment) method and ANN-AFOSM (advanced first-order second moment) method are provided. Compared with the traditional Monte Carlo method, the time consumed by ANN-MCM, polynomial-FOSM and ANN-AFOSM methods only accounts for 0.14% of the traditional MCM. The reliability analysis and reliability sensitivity analysis results of ANN-MCM method are very close to traditional MCM, polynomial-FOSM method yields large errors, ANN-AFOSM is in between. It shows that the proposed method is of high accuracy and efficiency.

Global Reliability Sensitivity Analysis Based on Maximum Entropy and 2-Layer Polynomial Chaos Expansion.

To optimize contributions of uncertain input variables on the statistical parameter of given model, e.g., reliability, global reliability sensitivity analysis (GRSA) provides an appropriate tool to quantify the effects. However, it may be difficult to calculate global reliability sensitivity indices compared with the traditional global sensitivity indices of model output, because statistical parameters are more difficult to obtain, Monte Carlo simulation (MCS)-related methods seem to be the only ways for GRSA but they are usually computationally demanding. This paper presents a new non-MCS calculation to evaluate global reliability sensitivity indices. This method proposes: (i) a 2-layer polynomial chaos expansion (PCE) framework to solve the global reliability sensitivity indices; and (ii) an efficient method to build a surrogate model of the statistical parameter using the maximum entropy (ME) method with the moments provided by PCE. This method has a dramatically reduced computational cost compared with traditional approaches. Two examples are introduced to demonstrate the efficiency and accuracy of the proposed method. It also suggests that the important ranking of model output and associated failure probability may be different, which could help improve the understanding of the given model in further optimization design.

Reliability sensitivity analysis of coherent systems based on survival signature

The reliability sensitivity can be used to rank distribution parameters of system components concerning their impacts on the system’s reliability. Such information is essential to purposes such as component prioritization, reliability improvement, and risk reduction of a system. In this article, we present an efficient method for reliability sensitivity analysis of coherent systems using survival signature. The survival signature is applied to calculate the reliability of coherent systems. The reliability importance of components is derived analytically to evaluate the relative importance of the component with respect to the overall reliability of the system. The closed-form formula for the reliability sensitivity of the system with respect to component’s distribution parameters is derived from the derivative of lifetime distribution of a component to further investigate the impacts of the distribution parameters on the system’s reliability. The effectiveness and feasibility of the proposed approaches are demonstrated with two numerical examples.

Analysis of wind turbine Gearbox's environmental impact considering its reliability

Abstract Wind turbines transform wind energy into electricity and it has a negative environmental impact during manufacturing or transportation. Gearbox is one of the most important components of wind turbine and its reliability is of great concern in industry. So this study performed a Life Cycle Assessment (LCA) to evaluate the environmental impact of wind turbine gearbox considering its reliability, with a “cradle-to-grave” approach. To quantify the influence of wind turbine gearbox's reliability on its environmental impact and provide a more realistic and accurate result, reliability analysis was integrated into LCA model. The reliability of gearbox determines not only the required amount of gearbox to achieve its design life but also the number of components which can be reused in next gearbox, both of which affect the environmental performance. First, the method to calculate these two parameters was described, afterwards, these two parameters would be used in the LCA model. Then, a 2 MW wind turbine gearbox with two recycling scenarios was used as the case study. The results show that the life cycle assessment of the gearbox is dominated by the manufacture process, and the reuse of components can reduce the impact around 10%. The reliability sensitivity analysis indicates that the environmental impact increases 25.25% as gearbox's reliability is reduced from 78.25% to 40.03%. Therefore, by taking reliability information into consideration when evaluating its environmental impact, a more accurate and realistic assessment result can be achieved.

Kinematic reliability and sensitivity analysis of the modified Delta parallel mechanism

In order to improve the kinematic reliability, it is crucial to find out the influence of each error source on the kinematic reliability of the mechanism. Reliability sensitivity analysis is used to find the changing rate in the probability of reliability in relation to the changes in distribution parameters. Based on the structural response surface function method, the functional relation between the kinematic reliability of a modified Delta parallel mechanism and the original input-error vectors is described using the quadratic function with cross terms. Moreover, the partial derivatives of the functional relation with respect to the means and variances of the original input errors are derived, which can efficiently evaluate kinematic reliability sensitivity of the mechanism. The advantages of this method are as follows: First, the response surface function, which can be easily set up by the position-error model of the mechanism, is convenient for calculating the variance, partial derivative, and reliability sensitivity. Second, in this case (unlike in the traditional error-mapping model), although the input-error values are unknown, pseudorandom variables used as random input-error sources can be generated by MATLAB software. Furthermore, the kinematic reliability of the mechanism can be assessed using the Monte Carlo method.

Dynamic Reliability Design of Multicomponent Structure with Improved Weighted Regression Distributed Collaborative Surrogate Model Method

For dynamic reliability design of complex structures with multiple components, an improved weighted regression distributed collaborative surrogate model method (IWRDCSMM) is developed from the extremum response surface method (ERSM), decomposed‐coordinated thought, and improved weighted regression principle. The ERSM is used to address the dynamic reliability and sensitivity analyses of multicomponent structures and enhance the computing efficiency. The decomposed‐coordinated thought is applied to handle the relationship among multiple components. The improved weighted regression method is used to find the efficient samples with smaller errors to improve the modeling accuracy. The proposed method is first introduced for dynamic probabilistic analysis (including reliability analysis and sensitivity analysis) of multicomponent structures. The method is then mathematically modeled by adopting the efficient samples selected based on the improved weighted regression method. Finally, the radial deformation dynamic probabilistic analysis of an aeroengine turbine blisk assembled by blade and disk is accomplished, in respect of the IWRDCSMM, fluid‐thermal‐structure interaction, and the randomness of input parameters within the time domain [0, T]. The results illustrate that the reliability degree of turbine blisk radial deformation is 0.9951 when the allowable value uallow is 2.30 × 10−3 m, and all the input parameters affecting the turbine blisk radial deformation are gas temperature, angular speed, inlet velocity, outlet pressure, material density, and inlet pressure, successively. As revealed by the comparison of different methods, the IWRDCSMM has high fitting speed and simulation efficiency with the guarantee of accuracy. The efforts of this study provide a promising dynamic probabilistic analysis technique for complex structures with multiple components and enrich mechanical reliability theory.

Fatigue reliability analysis of mooring system for fish cage

Fish cages in the open sea are exposed to cycle loads due to irregular wave climate during their service life, and thus the fatigue reliability assessment of mooring system should be conducted to ensure the safe operation. The aim of this study is to evaluate the fatigue failure probability of mooring system for fish cage. Numerical simulation of net cage in random waves is performed and the time dependent approach is applied to conduct the fatigue reliability analysis of shackle chains based on S-N curve method. The sensitivity analysis of fatigue reliability of mooring line to the uncertainty of random variables in the fatigue limit state is conducted. In addition, the system reliability for mooring system is analyzed and the effect of the initial pretension and safety factor on system reliability is investigated. The results indicate that a case without the initial pretension on anchor lines is helpful to decrease the failure probability of mooring system and the safety factor of mooring lines in the current regulation is conservative for the system reliability against fatigue damage.

A modified importance sampling method for structural reliability and its global reliability sensitivity analysis

The importance sampling method is an extensively used numerical simulation method in reliability analysis. In this paper, a modification to the importance sampling method (ISM) is proposed, and the modified ISM divides the sample set of input variables into different subsets based on the contributive weight of the importance sample defined in this paper and the maximum super-sphere denoted by β-sphere in the safe domain defined by the truncated ISM. By this proposed modification, only samples with large contributive weight and locating outside of the β-sphere need to call the limit state function. This amelioration remarkably reduces the number of limit state function evaluations required in the simulation procedure, and it doesn’t sacrifice the precision of the results by controlling the level of relative error. Based on this modified ISM and the space-partition idea in variance-based sensitivity analysis, the global reliability sensitivity indices can be estimated as byproducts, which is especially useful for reliability-based design optimization. This process of estimating the global reliability sensitivity indices only needs the sample points used in reliability analysis and is independent of the dimensionality of input variables. A roof truss structure and a composite cantilever beam structure are analyzed by the modified ISM. The results demonstrate the efficiency, accuracy, and robustness of the proposed method.

Reliability analysis of the traction unit of a shearer mechanism with response surface method

The paper presents a High order stochastic response surface method (HOSRSM) for reliability and reliability-based sensitivity analyses of transmission mechanism of a shearer in heavy and impulsive environments. Dynamic analysis is affected by several sources of uncertainty, and it is important to quantify their combined effect on performance of the mechanism in order to aid risk assessment, risk mitigation, and decision-making. A dynamic transmission model of the traction unit is established under the condition of low speed and impulsive load. A performance function is proposed to evaluate the system transmission accuracy. The effects of basic variables in HOSRSM are investigated on calculation efficiency and computation cost of system precision reliability. The results indicate that structure parameters of a sun gear are more sensitive than others. The tooth width is a more sensitive geometric parameter than the diameter of the center hole. The targets are proposed to manufacture and inspect the sun gear in traction unit for safety.

Structural reliability sensitivity analysis based on classification of model output

In structural reliability analysis, sensitivity analysis can be used to measure how the input variable influences the failure of structure. In this work, a new reliability sensitivity analysis method is proposed. In the proposed method, the model output is separated into two classes (failure domain and safe domain). The basic idea is that if the failure-conditional probability density function of input variable is significantly different from its unconditional probability density function, then the input variable is sensitive to the failure of structure. The proposed reliability sensitivity indices contain both individual sensitivity index and interaction sensitivity index. The individual sensitivity index can measure the individual effect of input variable on the failure of structure. The asymmetrical interaction sensitivity index can measure how one input variable influences the effect of another input variable on the failure of structure. Additionally, the meanings of the proposed reliability sensitivity indices are also interpreted explicitly, and a data-driven estimation method is also proposed to estimate the proposed reliability sensitivity indices. Finally, a numerical example and two engineering examples are presented to illustrate the rationality of the proposed sensitivity indices and the feasibility of the proposed estimation method.

Reliability analysis of random vibration transmission path systems

The vibration transmission path systems are generally composed of the vibration source, the vibration transfer path and the vibration receiving structure. The transfer path is the medium of the vibration transmission. Therefore, the uncertainty of path parameters influences the system reliability greatly. In order to avoid the resonance failure, the transmission reliability analysis and the reliability sensitivity analysis are both very important. Based on the reliability theory, the absolute value difference of natural frequency and excitation frequency of random vibration transmission path system was limited and the reliability pattern of the resonance problem was defined in this paper. Applying the generalized second moment technique of vector-valued functions and the stochastic finite element theory, the theoretical analysis method of the transmission reliability and reliability sensitivity was presented. The corresponding vibration transmission path system with uncertain path parameters including mass, stiffness and path position was analyzed theoretically and computed numerically, and then the correlated mathematical expressions were obtained. Thus, in practical project, most of uncertain factors in the vibration systems can be analyzed so that the effective way can be given to avoid resonance failure.

Extending first-passage method to reliability sensitivity analysis of motion mechanisms

Identifying the parameters that substantially affect the time-dependent reliability is critical for reliability-based design of motion mechanism. The time-dependent local reliability sensitivity and global reliability sensitivity are the two effective techniques for this type of analysis. This work extends the first-passage method and PHI2 method, which are commonly used for estimating the time-dependent reliability, for efficiently estimating the time-dependent local reliability sensitivity and global reliability sensitivity indices of the motion mechanism. Both the local reliability sensitivity and global reliability sensitivity indices are analytically derived based on the Poisson assumption–based first-passage method and the first-order Taylor’s expansion of the motion error function. Compared with the current envelope function method for estimating the time-dependent local reliability sensitivity and global reliability sensitivity indices, the developed method does not need to estimate the second-order derivatives of motion error function, thus is more applicable. The accuracy and effectiveness of the proposed method are demonstrated by a numerical example and a satellite antenna, the direction of which is controlled by a four-bar function generator mechanism.

Probability and Sensitivity Nonlinear Analysis of the Hermetic Cover of Main Shut-off Valve under Extreme Pressure and Temperature

Abstract This paper describes the probabilistic nonlinear analysis of the containment hermetic cover of main shut-off valve (MSV) under an extreme internal overpressure and temperature. The scenario of the hard accident in NPP and the methodology of the calculation of the fragility curve of the failure overpressure using the probabilistic safety assessment PSA 2 level are presented. The elasto-plastic behavior of steel material dependent on temperature was considered in software ANSYS. The method of central composite design sampling (CCD) of the response surface methodology (RSM) was used to probability and sensitivity analysis of the hermetic cover reliability.

Weighted Voting System With Unreliable Links

In a weighted voting system (WVS), outputs of voting units are sometimes not properly transferred to a sink unit because of the unreliability of links between the voting units and the sink unit. In this study, a WVS model with unreliable links is established, and two different kinds of unreliable links are introduced. Type I links have two states, which are connection and disconnection, and type II links have one more state (error state) than type I links. An approach based on a universal generating function method is suggested for evaluating a WVS with unreliable links. Two definitions of sensitivity are presented, which reflect the effect of a link's reliability or a system parameter on system reliability. Reliability evaluation and sensitivity analysis are demonstrated by some examples, and a conclusion is given.

Direct cyber-power interdependencies-based reliability evaluation of smart grids including wind/solar/diesel distributed generations and plug-in hybrid electrical vehicles

Smart grid is a so-called “cyber-power system” because the cyber systems (control/monitoring/protection, and communication networks) are integrated to power systems in it. The less effort has been devoted in literature to reliability evaluation based on direct cyber-power Interdependencies (DCPIs) in widespread presence of distributed generations (DGs) and charging load of plug-in hybrid electric vehicles (PHEVs) as supply side uncertainties and demand side ones. The consideration of uncertainty regarding the PHEVs in addition to other uncertain aspects inside the DCPIs is one of the most important contributions of this paper. In addition, the sensitivity analysis of reliability versus the variation of failures in power and cyber elements is essentially analyzed. The introduced method is applied to two realistic case studies. The test results infer that the DCPI-based reliability evaluation of smart grids including DGs and PHEVs is achievable through use of the proposed method. Because of using the Monte Carlo simulation (MCS), it is possible to extend the proposed method by integration of future uncertain and stochastic subjects without any limit. Further, the test results illustrate that the communication failures as direct network-element interdependencies (DNEI) is more important than direct element-element interdependencies (DEEI). The numerical results also imply that the risk level due to DCPIs increases due to inappropriate cyber network configurations.

Reliability Sensitivity Analysis of Vehicle Components and Architecture Optimization

Reliability Sensitivity Analysis of Vehicle Components and Architecture Optimization

Temporal and spatial multi-parameter dynamic reliability and global reliability sensitivity analysis based on the extreme value moments

Aiming at efficiently estimating the dynamic failure probability with multiple temporal and spatial parameters and analyzing the global reliability sensitivity of the dynamic problem, a method is presented on the moment estimation of the extreme value of the dynamic limit state function. Firstly, two strategies are proposed to estimate the dynamic failure probability. One strategy is combining sparse grid technique for the extreme value moments with the fourth-moment method for the dynamic failure probability. Another is combining dimensional reduction method for fractional extreme value moments and the maximum entropy for dynamic failure probability. In the proposed two strategies, the key step is how to determine the temporal and spatial parameters where the dynamic limit state function takes their minimum value. This issue is efficiently addressed by solving the differential equations satisfying the extreme value condition. Secondly, three-point estimation is used to evaluate the global dynamic reliability sensitivity by combining with the dynamic failure probability method. The significance and the effectiveness of the proposed methods for estimating the temporal and spatial multi-parameter dynamic reliability and global sensitivity indices are demonstrated with several examples.