Reliability Sensitivity Analysis Research Articles

Global reliability sensitivity analysis of cradle-type double rotary table

The rotary table is a crucial component of the machine tool, and its accuracy and reliability have an important impact on the machining accuracy and machining efficiency of the machine tool. In this paper, a global reliability sensitivity analysis method of the rotary table is proposed considering the random uncertainty for material parameters of each component. Firstly, the mechanical model of the rotary table is established based on the finite element method. Subsequently, the functional relationship between the parameters of each component and the deformation of the rotary table is reconstructed using the adaptive Kriging surrogate model. Finally, a global reliability sensitivity analysis of the rotary table is performed based on the Bayesian formulation. The results show that the proposed global reliability sensitivity analysis method of the rotary table demonstrates satisfactory efficiency and can provide theoretical guidance for the design and optimization of the rotary table.

An Efficient Integral Approach for Kinematic Reliability Sensitivity Analysis of Industrial Robots

Abstract Assessment of the reliability and reliability sensitivity of positioning accuracy for industrial robots subject to aleatoric and epistemic uncertainties registers a challenging task. This study proposes a new optimized moment-based method for kinematic reliability analysis and its sensitivity analysis, which incorporates the sparse grid (SPGR) technique and the saddlepoint approximation (SPA) method. To start with, the positioning accuracy reliability and its sensitivity models of industrial robots are established via computational optimization techniques and kinematic criteria. The kinematic accuracy reliability and its sensitivity are then calculated. Specifically, the sparse grid technique is adopted to approach the positioning error statistical moments and moment sensitivities. On this basis, positioning accuracy reliability bounds and reliability sensitivity bounds are obtained by the saddlepoint approximation method and optimization techniques. Finally, two practical examples are implemented to demonstrate the proficiency of the currently proposed method against Monte Carlo simulation (MCS) results. The results show that the currently proposed method exhibits superior computational accuracy and efficiency in kinematic reliability and its sensitivity analyses for industrial robots.

Reliability analysis and sensitivity analysis of retrial machine repair problems with multiple vacations and the recovery policy

Reliability analysis and sensitivity analysis of retrial machine repair problems with multiple vacations and the recovery policy

An efficient single-loop strategy for time-variant reliability sensitivity analysis based on Bayes’ theorem

Time-variant reliability sensitivity analysis aims to measure the effect of input variables on the time-variant failure probability, which can then be used to guide structural design and optimization. The traditional methods for calculating the sensitivity index require a nested sampling procedure and their computational complexity depends on the number of input variables, making them computationally the most expensive. To address the above limitations, an efficient single-loop strategy is developed for time-variant reliability sensitivity (TRS) analysis. Based on Bayes' theorem, the TRS index is represented by the difference between the probability density function (PDF) and failure-conditional PDF of the variable. This derivation enables TRS analysis to be implemented using only a single set of samples, with computational costs that don’t depend on the number of input variables. Then, the sensitivity index is normalized to identify influential variables effectively. Several case studies involving numerical and engineering problems are employed to verify the feasibility and effectiveness of the proposed strategy. The direct Monte Carlo simulation is introduced to assess the accuracy of the obtained results. The results indicate that the proposed strategy provides acceptable sensitivity analysis for time-variant events, while greatly conserving computational resources and enhancing efficiency.

Reliability sensitivity analysis for set pressure tolerance of the direct-operated relief valve in a vibration environment

Reliability sensitivity analysis for set pressure tolerance of the direct-operated relief valve in a vibration environment

Reliability-Based Robust Design Optimization with Fourth-Moment Method for Ball Bearing Wear

Ball bearings operating at low speeds and under heavy loads are susceptible to wear failure, leading to significant economic losses. The existing reliability-based robust design optimization method of the fourth-moment method has high accuracy and does not need to determine the random distribution of the input variables, but it is not possible to apply it to ball bearing wear due to the complexity of the bearing wear state function that cannot be characterized as an explicit form. To address this issue, this paper proposes a novel design method for ball bearing wear. Firstly, a surrogate model is constructed using the Kriging model method to establish a relationship between the bearing design parameters and the mechanical response. Subsequently, a wear reliability model is developed on the basis of the fourth-moment method, and reliability sensitivity analysis is conducted. Finally, the ball bearing wear reliability-based robust design optimization is accomplished through the use of a genetic algorithm. The results of the case calculations demonstrate that the proposed method effectively calculates the ball bearing wear reliability and analyzes the impact of design parameter randomness on reliability. Furthermore, optimizing the design parameters reduces the sensitivity of wear reliability to parameter randomness.

A single-loop reliability sensitivity analysis strategy for time-dependent rare events with both random variables and stochastic processes

To deal with the time-dependent reliability sensitivity (TDRS) analysis of rare events with both random variables and stochastic processes, a single-loop sampling procedure combined with the cross entropy-based importance sampling strategy (CEIS), namely SCEIS, is derived to lighten the computational burden without loss of precision. Firstly, the TDRS indices are derived to make them implementable by a single-loop importance sampling (IS) procedure. Then, the quasi-optimal IS density is obtained through the extension of the cross-entropy method, which is an adaptive procedure that overcomes the challenges of determining the position and number of design points in traditional IS. Furthermore, the SCEIS can be easily implemented to estimate the TDRS indices for problems with small failure probability. Three examples involving numerical and engineering problems are analyzed to demonstrate the performance of the proposed method. The results obtained from comparing with other existing methods reveal that the proposed method provides satisfactory TDRS analysis for rare events while significantly reducing computational costs.

Global Sensitivity Analysis of Structural Reliability Using Cliff Delta

This paper introduces innovative sensitivity indices based on Cliff’s Delta for the global sensitivity analysis of structural reliability. These indices build on the Sobol’ method, using binary outcomes (success or failure), but avoid the need to calculate failure probability Pf and the associated distributional assumptions of resistance R and load F. Cliff’s Delta, originally used for ordinal data, evaluates the dominance of resistance over load without specific assumptions. The mathematical formulations for computing Cliff’s Delta between R and F quantify structural reliability by assessing the random realizations of R > F using a double-nested-loop approach. The derived sensitivity indices, based on the squared value of Cliff’s Delta δC2, exhibit properties analogous to those in the Sobol’ sensitivity analysis, including first-order, second-order, and higher-order indices. This provides a framework for evaluating the contributions of input variables on structural reliability. The results demonstrate that the Cliff’s Delta method provides a more accurate estimate of Pf. In one case study, the Cliff’s Delta approach reduces the standard deviation of Pf estimates across various Monte Carlo run counts. This method is particularly significant for FEM applications, where repeated simulations of R or F are computationally intensive. The double-nested-loop algorithm of Cliff’s Delta maximizes the extraction of information about structural reliability from these simulations. However, the high computational demand of Cliff’s Delta is a disadvantage. Future research should optimize computational demands, especially for small values of Pf.

Seismic topology optimization considering first-passage probability by incorporating probability density evolution method and bi-directional evolutionary structural optimization

This contribution focuses on addressing the challenging problem of dynamic-reliability-based topology optimization (DRBTO) of engineering structures involving uncertainties by synthesizing the probability density evolution method (PDEM) and the bi-directional evolutionary structural optimization (BESO) approach. The considered optimization problem aims at minimizing the first-passage probability under the constraint of material volume. Generally, the double-loop essence of DRBTO involving dynamic reliability evaluation and topology searching makes the computational efforts prohibitively large. To this end, the PDEM is adopted to efficiently assess the first-passage probability of structures under earthquake actions. In particular, by reformulating the first-passage probability under the framework of the PDEM, the sensitivity of the first-passage probability is derived. To further improve the efficiency, a strategy taking advantage of important representative points (IRPs) is employed to achieve a robust estimate of sensitivity of the first-passage probability. The adjoint variable method (AVM) for the sensitivity analysis of transient response considering given modal damping ratios is incorporated to considerably improve the computational efficiency when the reliability sensitivity analysis in terms of multiple design variables is needed. To drive the topology towards the optimum, the above highly efficient reliability assessment and sensitivity analysis are embedded into BESO. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed method, illustrating significant improvement in computational efficiency compared to direct implementation. Additionally, the necessity of introducing seismic reliability in topology optimization is also discussed based on the numerical results.

Identification of Important Random Field Domain in Foundation Engineering through Reliability Sensitivity Analysis

Identification of Important Random Field Domain in Foundation Engineering through Reliability Sensitivity Analysis

Adaptive design of experiments to fit surrogate Gaussian process regression models allows fast sensitivity analysis of the input waveform for patient-specific 3D CFD models of liver radioembolization

Background and objectivePatient-specific 3D computational fluid dynamics (CFD) models are increasingly being used to understand and predict transarterial radioembolization procedures used for hepatocellular carcinoma treatment. While sensitivity analyses of these CFD models can help to determine the most impactful input parameters, such analyses are computationally costly. Therefore, we aim to use surrogate modelling to allow relatively cheap sensitivity analysis. As an example, we compute Sobol's sensitivity indices for three input waveform shape parameters. MethodsWe extracted three characteristic shape parameters from our input mass flow rate waveform (peak systolic mass flow rate, heart rate, systolic duration) and defined our 3D input parameter space by varying these parameters within 75 %-125 % of their nominal values. To fit our surrogate model with a minimal number of costly CFD simulations, we developed an adaptive design of experiments (ADOE) algorithm. The ADOE uses 100 Latin hypercube sampled points in 3D input space to define the initial design of experiments (DOE). Subsequently, we re-sample input space with 10,000 Latin Hypercube sampled points and cheaply estimate the outputs using the surrogate model. In each of 27 equivolume bins which divide our input space, we determine the most uncertain prediction of the 10,000 points, compute the true outputs using CFD, and add these points to the DOE. For each ADOE iteration, we calculate Sobol's sensitivity indices, and we continue to add batches of 27 samples to the DOE until the Sobol indices have stabilized. ResultsWe tested our ADOE algorithm on the Ishigami function and showed that we can reliably obtain Sobol's indices with an absolute error <0.1. Applying ADOE to our waveform sensitivity problem, we found that the first-order sensitivity indices were 0.0550, 0.0191 and 0.407 for the peak systolic mass flow rate, heart rate, and the systolic duration, respectively. ConclusionsAlthough the current study was an illustrative case, the ADOE allows reliable sensitivity analysis with a limited number of complex model evaluations, and performs well even when the optimal DOE size is a priori unknown. This enables us to identify the highest-impact input parameters of our model, and other novel, costly models in the future.

Efficient reliability assessment of slope stability with insightful sensitivity analysis concerning the safety factor

The limit state functions (LSFs) of slope stability are nonlinear, implicit, or derived from numerical simulations, and additional surrogate models are usually used for its reliability problems. Alternatively, an efficient numerical procedure using a variant of the HLRF-BFGS algorithm is proposed to address this issue without additional surrogate models. This proposed procedure simultaneously conducts reliability assessment and sensitivity analysis concerning the safety factor by suggested calculations of partial derivatives using the finite difference method (FDM). Two highly nonlinear numerical examples are presented to validate its convergence and to investigate the step length of the FDM. Results show that the proposed procedure can get considerable accuracy while the HLRF algorithm cannot converge, and its required iterations are about 30% and 81% less than those of the limited step-size iteration algorithm. In addition, a step length not greater than 0.1 is suggested after investigations. Application to a classical two-layered slope is illustrated. Reliability results show that the proposed procedure can get the same accuracy as those of surrogate models after only 5 iterative steps. Sensitivity results show that the cohesion of the upper soil is the only sensitivity factor, and the most possible potential slide surface lies in the upper soil.

Dynamic reliability analysis of angular contact ball bearing based on maximum entropy quadratic fourth moment method*

ABSTRACT Bearing failure occurs when the dynamic contact stress exceeds the yield strength of the bearing material during operation. To minimise the risk of bearing failure, a new reliability theory method is proposed based on the stress-strength model of bearings, incorporating random input variables to analyse the reliability of angular contact ball bearings (ACBBs) and quantify their dynamic performance. The maximum entropy quadratic fourth moment method is used to calculate the probability distribution of maximum orthogonal shear stress-strength of bearing, and the maximum entropy principle is used to obtain the approximation of the minimum human error factors. Additionally, reliability-based sensitivity indices are derived to investigate the parametric significance of random input variables. Using B218 bearing as an example, the engineering application of this method in dynamic reliability and reliability-based sensitivity analysis is illustrated. Monte Carlo simulation is performed to verify the accuracy and effectiveness of the method to provide benchmark results. The results show that the Poisson’s ratio have a greater influence on the dynamic reliability of ACBBs than other parameters. Improving parameters such as ball diameter, raceway groove curvature radius and contact angle can also improve the reliability of bearings to some extent.

Sequentially Quadratic Surrogate Algorithm for Time-dependent Reliability and Reliability Sensitivity Analysis

Time-dependent reliability and reliability sensitivity analysis in presence of random uncertainty is widespread in equipment structures. To this end, this paper establishes a sequentially quadratic surrogate method. Firstly, the global reliability sensitivity analysis (GRS) is transformed into the classification problem of the time-dependent performance function outputs by means of conditional probability formula. Secondly, referring to the strategy of the Meta-IS method, the Kriging model of time-dependent performance function is employed to construct the importance sampling function to generate the importance sampling (IS) samples of failure domain efficiently. Furthermore, the Kriging model is updated in the IS samples set through the single-loop adaptive Kriging method to realize the accurate identification of the failure indicator function of IS samples, as well as simulation of time-dependent failure probability. Finally, utilize the information of the failure samples obtained by the estimation of time-dependent reliability to evaluate GRS. The proposed algorithm has excellent computational efficiency and applicability due to the conversion of the conditional probability formula, which enables the computational consumption of the time-dependent reliability and GRS analysis independent of the dimensions of the inputs, as well as the Meta-IS method, which improves the sampling efficiency and is applicable to the case of complex implicit performance function. The given examples fully verify the conclusions.

Sensitivity analysis of aircraft structural fatigue reliability under mixed uncertainty

Fatigue is the main failure mode of the structure. The aircraft structure is subject to multi-level cyclic loading, which is prone to fatigue damage, reduces reliability, and affects flight safety. Various uncertainties are inevitably associated with the factors related to the fatigue performance of the structure. In particular, for the variables with insufficient information, their uncertainties are hard to describe by the probability density function. In this paper, these variables are treated as interval variables. The sensitivity analysis of the aircraft structure fatigue reliability model under mixed uncertainties is studied. On the basis of the definition of the distance between interval numbers, the interval distance indexes are proposed as a global sensitivity measure for a mixed random-interval model system. To reduce the computational cost, the method combining the space partition with unscented transformation (SP-UT) is used to calculate the proposed indexes. Lastly, the proposed indexes and method are applied to solve the aircraft structure fatigue problem. Compared with the traditional MCS method, the proposed method has proved to be more conducive and efficient.

Optimization of reliability and sensitivity analysis for flange structures

The study delves into the reliability-driven optimization design of the flanges, drawing from reliability design theory, advanced optimization methodologies, and comprehensive sensitivity analysis. Flanges, integral to mechanical systems, demand precise design. Reliability design theory emphasizes consistent operation under diverse conditions. A novel approach to the flange-specific reliability sensitivity analysis method is central to this research. It promises to revolutionize flange design. By understanding the first two moments of core random parameters, we expedite reliability-driven optimization designs for mechanical connections. The programs enhance our approach, streamlining the pursuit of reliability-driven designs and providing rapid, accurate sensitivity analysis data for mechanical connections. This data offers critical insights into parameter influence, enabling targeted design adjustments. In summary, this research represents a significant advancement in mechanical engineering. By integrating reliability design theory with cutting-edge methodologies, it promises to enhance the quality and reliability of mechanical connections, meeting the rigorous demands of contemporary engineering applications. This holistic approach will play a pivotal role in the future of mechanical component design.

High-speed rolling bearing lubrication reliability analysis based on probability box model

An efficient and high-precision method is proposed for the analysis and evaluation of high-speed rolling bearing lubrication reliability based on a probability box (p-box) model. This method expands the application of mixed aleatory and epistemic uncertainties analysis within the realm of bearing lubrication reliability. Initially, the method establishes a reliability model for high-speed rolling bearing lubrication, taking into account the shear thermal effect through the analytical solution of a Γубин-type entrance zone. Subsequently, the uncertainty surrounding lubrication parameters under high-speed conditions is examined, with its mixed aleatory and epistemic uncertainties accurately depicted by using the p-box model. Furthermore, an effective and precise method for analyzing the reliability of rolling bearing lubrication is introduced based on the p-box model, in which the optimization model involved is efficiently solved using a decoupling method. Finally, lubrication reliability analysis and sensitivity analysis of parameter uncertainty levels are conducted for high-speed rolling bearings in this study. The research results demonstrate that the proposed method achieves higher accuracy and efficiency.

Efficient Methods for Reliability Sensitivity Analysis of Distribution Parameters and Their Application

To efficiently evaluate the influence of the distribution parameters of the input variables on the failure probability of engineering structures and improve the reliability and safety of engineering structures in a targeted manner, new methods for the global reliability sensitivity analysis (RSA) of distribution parameters are proposed in this study based on the cubature formula (CF), surrogate sampling probability density function (SSPDF), and quasi-Monte Carlo (QMC) method. By introducing CF, the proposed methods can effectively improve the computational efficiency of the nested expectation and variance operators in the reliability sensitivity indices of the distribution parameters. Based on the concept of SSPDF, a surrogate importance sampling probability density function was developed. This not only overcomes the problem of the computational effort of propagating parameter uncertainty to the failure probability function (FPF), which depends on the dimensionality of the parameters; it also further improves the efficiency of the RSA of the parameters in the case of a small failure probability. Finally, by incorporating the idea of the QMC method, the process of calculating the reliability sensitivity indices of the parameters is reduced from a double-loop to a single-loop one. Three engineering examples are used in this study to demonstrate the efficiency and accuracy of the new algorithms.

Reliability sensitivity analysis for water hammer-induced stress failure of fluid-conveying pipe

The water hammer, resulting from sudden valve closures or similar operations, is a primary cause of leakage and damage in fluid-conveying pipe systems. This work aims to investigate the reliability sensitivity of fluid-conveying pipes under the water hammer. A reliability model for the fluid-conveying straight pipe, involving uncertainty and fluid-structure interaction, is developed based on the stress-strength interference theory. Then the method of characteristics is employed to analyze the nonlinear behaviors of the pipe. To avoid excessive model evaluations, the Kriging surrogate strategy is used to evaluate rapidly the statistics of nonlinear responses. Furthermore, the Kriging model coupled with the single-loop Monte Carlo simulation is presented for estimating reliability sensitivity indices. The accuracy of results is verified by the Monte Carlo simulation. The results reveal that the proposed method is feasible for the reliability sensitivity analysis of fluid-conveying pipe under the water hammer. Moreover, the wall thickness has the most obvious influence on stress failure, followed by the inner radius, while the pipe length, Young's modulus, density of the pipe material, and Poisson ratio show a low effect. This work can not only guide the safety design of pipe but also enrich the theory and application of statistical analysis and reliability sensitivity evaluation for liquid-conveying pipe systems.

Sensitivity evaluation of machine learning-based calibrated transportation mode choice models: A case study of Alexandria City, Egypt

Intelligent methods including Machine Learning (ML) techniques have been increasingly employed in transportation mode choice modeling, which is more complex than other demand models, since it has to reliably and accurately reflect a wide range of related categorical and continuous variables, concerning the travelers, transportation system, and trip characteristics. ML techniques can capture such complex relationships. So that, they can provide a more nuanced understanding of the travelers’ decision process. Most research studies focused mainly on the evaluation of the model accuracy, where little has been done to evaluate the models’ performance toward transport attributes. This research aims to calibrate the transportation choice models using ML techniques, then conduct a comparison with the Multinomial Logit (MNL) model to identify the impact on the model accuracy and performance and quantify to what extent the ML models are sensitive to transport policies compared to the traditional MNL model. To this end, eight ML classifiers were examined. As a case study, the models were calibrated to reflect the choice behavior of trip makers in Alexandria City, Egypt. The models were successfully calibrated with satisfying accuracy; however, the ML models have better calibration results in terms of predictability, outperforming the MNL model, where the GBDT classifier records the best prediction accuracy. Finally, the sensitivity analysis test was performed to quantify the elasticity of the models to transport policies. The results show the ML models’ structure is more comprehensively and accurately built than the MNL model providing better indicative and reliable sensitivity analysis results.