Reliability Sensitivity-based Correlation Coefficient Calculation in Structural Reliability Analysis

The correlation coefficients of random variables of mechanical structures are generally chosen with experience or even ignored,which cannot actually reflect the effects of parameter uncertainties on reliability.To discuss the selection problem of the correlation coefficients from the reliability-based sensitivity point of view,the theory principle of the problem is established based on the results of the reliability sensitivity,and the criterion of correlation among random variables is shown.The values of the correlation coefficients are obtained according to the proposed principle and the reliability sensitivity problem is discussed.Numerical studies have shown the following results：（1） If the sensitivity value of correlation coefficient ρ is less than（at what magnitude 0.000 01）,then the correlation could be ignored,which could simplify the procedure without introducing additional error.（2） However,as the difference between ρs,that is the most sensitive to the reliability,and ρR,that is with the smallest reliability,is less than 0.001,ρs is suggested to model the dependency of random variables.This could ensure the robust quality of system without the loss of safety requirement.（3） In the case of ｜Eabs｜ρ0.001 and also ｜Erel｜ρ0.001,ρR should be employed to quantify the correlation among random variables in order to ensure the accuracy of reliability analysis.Application of the proposed approach could provide a practical routine for mechanical design and manufactory to study the reliability and reliability-based sensitivity of basic design variables in mechanical reliability analysis and design.

Reliability and sensitivity analyses of HPT blade-tip radial running clearance using multiply response surface model

To reasonably design the blade-tip radial running clearance(BTRRC) of high pressure turbine and improve the performance and reliability of gas turbine, the multi-object multi-discipline reliability sensitivity analysis of BTRRC was accomplished from a probabilistic prospective by considering nonlinear material attributes and dynamic loads. Firstly, multiply response surface model(MRSM) was proposed and the mathematical model of this method was established based on quadratic function. Secondly, the BTRRC was decomposed into three sub-components(turbine disk, blade and casing), and then the single response surface functions(SRSFs) of three structures were built in line with the basic idea of MRSM. Thirdly, the response surface function(MRSM) of BTRRC was reshaped by coordinating SRSFs. From the analysis, it is acquired to probabilistic distribution characteristics of input-output variables, failure probabilities of blade-tip clearance under different static blade-tip clearances δ and major factors impacting BTRRC. Considering the reliability and efficiency of gas turbine, δ=1.87 mm is an optimally acceptable option for rational BTRRC. Through the comparison of three analysis methods(Monte Carlo method, traditional response surface method and MRSM), the results show that MRSM has higher accuracy and higher efficiency in reliability sensitivity analysis of BTRRC. These strengths are likely to become more prominent with the increasing times of simulations. The present study offers an effective and promising approach for reliability sensitivity analysis and optimal design of complex dynamic assembly relationship.

Matrix description of differential relations of moment functions in structural reliability sensitivity analysis

In a structural system reliability analysis that lacks probabilistic information, calculating the numerical characteristics of the state functions, especially the first four moments of the state functions, is necessary. Based on that, the structural system reliability is analyzed with a fourth-order moment method. The reliability sensitivity is required to conduct the differential operation of the numerical characteristic functions. A reliability sensitivity analysis formula is then derived in combination with the relation of the differential operation. Based on the matrix theory and Kronecker algebra, this paper systematically derives a matrix expression of the first four moments of the state functions, and establishes the matrix relation between the first four moments of the state functions and those of the basic random variables. On this basis, a differential operation formula of the first four moments of the state functions is further derived against the first four moments of the basic random variables. The vector relation between the state functions and the multidimensional basic random variables is described by means of the matrix operation to extend the operation method. Finally, a concise and intuitive formula is obtained to explore the inherent essential relation between the numerical characteristics of the state functions and those of the basic random variables, leading to a universal equation for the two kinds of numerical characteristics.

Reliability Sensitivity Analysis for Drum Brake on Modal Stress

A reliability sensitivity analysis based on modal stress is presented and applied to predict the influence factors of parameters on drum brake.Firstly,the first 10 modes of prestress of the brake drum are performed in the software ANSYS Workbench.According to the results of brake noise research,it can be detected whether the drum brake meets the results that the noise frequency range of 500-1000 Hz.The reliability sensitivity design of mechanical parts based on the normal distribution parameters for complex mechanical system is discussed.Secondly,according to the first order second moment(FOSM)theory on reliability,the reliability sensitivity of drum brake is analyzed and calculated,and compared with the Monte Carlo(MC)numerical simulation results,The variation rules of reliability sensitivity is given,which provides a theoretical basis for the design of drum brake.

Reliability Analysis of Flexure Hinge Based on Kriging Method

The uncertainty widely exists in the engineering practice.Therefore,it is necessary to research the effect of uncertainty on the structural system. In this paper,the reliability and sensitivity of the flexure hinge, which is the key component of the compliant mechanisms,are investigated. The results of the reliability analysis can effectively guide the engineer to design and optimize the flexure hinge. In order to improve the calculating efficiency,the kriging method is introduced to estimate the failure probability and reliability sensitivity.

Reliability Sensitivity Algorithm Based on Stratified Importance Sampling Method for Multiple Failure Modes Systems

Combining the advantages of the stratified sampling and the importance sampling, a stratified importance sampling method （SISM） is presented to analyze the reliability sensitivity for structure with multiple failure modes. In the presented method, the variable space is divided into several disjoint subspace by n-dimensional coordinate planes at the mean point of the random vec- tor, and the importance sampling functions in the subspaces are constructed by keeping the sampling center at the mean point and augmenting the standard deviation by a factor of 2. The sample size generated from the importance sampling function in each subspace is determined by the contribution of the subspace to the reliability sensitivity, which can be estimated by iterative simulation in the sampling process. The formulae of the reliability sensitivity estimation, the variance and the coefficient of variation are derived for the presented SISM. Comparing with the Monte Carlo method, the stratified sampling method and the importance sampling method, the presented SISM has wider applicability and higher calculation efficiency, which is demonstrated by numerical examples. Finally, the reliability sensitivity analysis of flap structure is illustrated that the SISM can be applied to engineering structure.

Analytical Calculation Method of Reliability Sensitivity Indexes for Distribution Systems Based on Fault Incidence Matrix

An analytical calculation method for the reliability sensitivity indexes of distribution systems is proposed to explicitly quantify the impact of various influence factors on system reliability.Firstly,the analytical calculation formulas for the reliability indexes of distribution systems are derived based on the fault incidence matrix(FIM).Secondly,the factors that affect system reliability are divided into two categories:quantifiable parameter factors and non-quantifiable network structure factors.The sensitivity indexes for the quantifiable parameter factors are derived using the direct partial derivation of the reliability calculation formulas.The sensitivity indexes for the nonquantifiable network structure factors are derived using the transformation of FIMs.Finally,the accuracy and efficiency of the proposed sensitivity calculation method are verified by applying them to an IEEE 6-bus RBTS system.This paper sums up the factors that influence system reliability in detail and gives the explicit analytical calculation method for the sensitivity of each factor.Repetitive calculation of the reliability index can be avoided during the sensitivity analysis.The bottleneck that affects the reliability level of distribution systems can be identified efficiently,and valuable information and guidance can be provided to enhance the reliability of distribution systems.

A reliable and sensitive closing gear

The model QQCplankton net closing gear is a device designed to control the stratifiedsampling of the plankton net by means of a messenger. The device in its fie1d use has met with98% success in 766 times of strtified sampling of plankton at 157 stations during separatesurveys of Fujian coast zone, the Taiwan Strait, and the central section of the South China Sea,