Reliability Sensitivity Analysis Research Articles

Reliability and reliability-based sensitivity analysis of self-centering buckling restrained braces using meta-models

This paper aims to carry out sensitivity analyses to study how the effect of each design variable on the performance of self-centering buckling restrained brace (SC-BRB) and the corresponding buckling restrained brace (BRB) without shape memory alloy (SMA) rods. Furthermore, the reliability analyses of BRB and SC-BRB are performed in this study. Considering the high computational cost of the simulation methods, three Meta-models including the Kriging, radial basis function (RBF), and polynomial response surface (PRSM) are utilized to construct the surrogate models. For this aim, the nonlinear dynamic analyses are conducted on both BRB and SC-BRB by using OpenSees software. The results showed that the SMA area, SMA length ratio, and BRB core area have the most effect on the failure probability of SC-BRB. It is concluded that Kriging-based Monte Carlo Simulation (MCS) gives the best performance to estimate the limit state function (LSF) of BRB and SC-BRB in the reliability analysis procedures. Considering the effects of changing the maximum cyclic loading on the failure probability computation and comparison of the failure probability for different LSFs, it is also found that the reliability indices of SC-BRB were always higher than the corresponding reliability indices determined for BRB which confirms the performance superiority of SC-BRB than BRB.

Thermal error prediction and reliability sensitivity analysis of motorized spindle based on Kriging model

A large amount of heat is generated by motorized spindles during the machining process of CNC machine tools, and it is the main factor restricting the further improvement of machining accuracy. Furthermore, physical properties and material parameters of the motorized spindle are uncertain in practical engineering. Therefore, it is necessary to evaluate the reliability and reliability sensitivity of the motorized spindle system. In this paper, a new thermal error estimation model of motorized spindle is established based on multi-physical field coupling theory. The Quasi-Monte Carlo (QMC) method is introduced to calculate the reliability of the motorized spindle system. An accurate and efficient surrogate model, called Kriging, is used to calculate the reliability and reliability sensitivity of the motorized spindle system to further improve computational efficiency. Moreover, the experimental platform for measuring the temperature and thermal error of the motorized spindle is built to verify the applicability of the proposed model. The analytical framework proposed in this paper provide a guidance for the reliability design and robustness evaluation of motorized spindle.

Reliability and Reliability-based Sensitivity Analyses of Steel Moment-Resisting Frame Structure subjected to Extreme Actions

The ground external columns of buildings are vulnerable to the extreme actions such as a vehicle collision. This event is a common scenario of buildings' damages. In this study, a nonlinear model of 2-story steel moment-resisting frame (SMRF) is made in OpenSees software. This paper aims investigating the reliability analysis of aforementioned structure under heavy vehicle impact loadings by Monte Carlo Simulation (MCS) in MATLAB software. To reduce computational costs, meta-model techniques such as Kriging, Polynomial Response Surface Methodology (PRSM) and Artificial Neural Network (ANN) are applied and their efficiency is assessed. At first, the random variables are defined. Then, the sensitivity analyses are performed using MCS and Sobol's methods. Finally, the failure probabilities and reliability indices of studied frame are presented under impact loadings with various collision velocities at different performance levels and thus, the behavior of selected SMRF is compared by using fragility curves. The results showed that the random variables such as mass and velocity of vehicle and yield strength of used materials were the most effective parameters in the failure probability computation. Among the meta-models, Kriging can estimate the failure probability with the least error, sample number with minimum computer processing time, in comparison with MCS.

Reliability Sensitivity Analysis of Turning Error for Slender Shaft

Reliability Sensitivity Analysis of Turning Error for Slender Shaft

Component based reliability prediction

Software components are measured in off the shelf at a great rate to develop reliable software applications. In component based systems, reliability estimation models are developed based on reliability of individual components and their transition probabilities. In this paper, we consider Scenario based Reliability Estimation using the hierarchical model (Discrete Time Markov Chain). In hierarchical model, variance of the number of visits to each component makes the system reliability closer to the estimated reliability value. We propose a reliability estimation model for the whole application. Component Dependency Graph of the systems, Reliability of individual components and transition probabilities between two components are considered as input for the estimation. Discrete Time Markov Chain is used to generate the mean and variance of the number of visits of the individual component from the initial component. This paper illustrates the reliability prediction and sensitivity analysis with examples.

Reliability sensitivity analysis of thermal protection system

This paper carries on a reliability sensitivity analysis on the non-ablative thermal protection system (TPS) of spacecraft during the conceptual design. In the previous work on probabilistic estimation of TPS, the temperature dependency of material properties has not yet been investigated. In this paper, however, the temperature dependency of material properties is characterized and considered during the thermal analysis and reliability sensitivity analysis. Compared to general black-box problems, three special challenges of uncertainty analysis for TPS in real practice are a generally high dimension and multiple outputs on massive meshing nodes, a high level of reliability design target, and a fast evaluation process due to the requirement of the conceptual design. In order to cope with these challenges, a unified reliability sensitivity analysis methodology including multi-input and multi-output support vector machines (MIMO-SVMs), a space-partition (SP) method, and a generalized subset simulation (GSS) is proposed for the conceptual design of TPS with temperature-dependent materials. MIMO-SVMs are used to approximate the thermal responses to save calculation costs. The variance-based global sensitivity indices are calculated by SP to make full use of the information within samples. Based on the sensitivity indices, a dimension reduction process is introduced. In the reduced space, GSS is used to simultaneously evaluate all the failure probabilities by fully exploring the correlation among all the LSFs. Two application examples including a lifting body vehicle model and a spacecraft model are used to demonstrate the performance of the proposed methodology.

Probabilistic analyses of structural dynamic response with modified Kriging-based moving extremum framework

Mechanical system is usually composed of multiple complex structures, which endure the combine action of multi-physical fields (e.g., flow field, thermal field, structural field, and so forth) during operation. Structural response, for instance, deformation, stress, strain, fatigue life, etc., have dynamic and time-varying attributes, their values play an important role in safeguarding function properly, and affects the safety of entire system. Probabilistic analyses (including reliability evaluation and sensitivity analysis) can effectively identify potential risk and improve the reliability level. The traditional way is to use Monte Carlo (MC) simulation to achieve probabilistic analyses of complex structures. However, the MC simulation needs to perform a large amount of calculations to complete the specified task analysis, the computational burden is too heavy for the reliability evaluation and sensitivity analysis of structural dynamic response. To efficiently perform probabilistic analyses of structural dynamic response, we therefore developed a surrogate model method, namely modified Kriging-based moving extremum framework (MKMEF, short for), absorbing extremum thought, moving least squares (MLS) technique, Kriging model and collaborative evolution genetic algorithm (CEGA). For this proposed MKMEF, the extremum thought is used to transform dynamic output response into extremum values within a time domain, and the MLS method is applied to obtain efficient samples to derive Kriging model. Besides, the CEGA is employed to replace gradient descent method to resolve maximum likelihood equation (MLE) and find the optimal hyperparameters of Kriging model. Furthermore, an aeroengine high-pressure turbine blisk is treated as a case study, the probabilistic analyses of radial running deformation is executed to validate the effectiveness of the proposed method by considering the fluid-thermal-solid interaction. The analytical results show that the reliability degree of turbine blisk is 99.78%, when the allowable value of radial running deformation is 2.5071 × 10−3 m (determined by 3 sigma levels), and the highest impact on the turbine blisk radial running deformation is gas temperature, followed by inlet velocity, rational speed, material density and outlet pressure. The comparison of methods including direct simulation, response surface method-based extremum thought (ERSM) and traditional Kriging model, shows that the developed MKMEF holds high-efficiency and high-accuracy for the probabilistic analyses of turbine blisk radial running deformation. The presented efforts provide a useful insight for assessing probabilistic analyses of structural dynamic response and enrich mechanical reliability theory.

Failure-based sealing reliability analysis considering dynamic interval and hybrid uncertainties

In the reliability analysis of a sealing structure, radial clearance of the contact surface is usually regarded as a failure criterion, and the sample size is usually quite small, which brings great challenges to uncertainty quantification. Therefore, this paper proposes a reliability analysis method based on the leakage mechanism of the sealing. With the application of dynamic interval, the proposed method can be used to deal with problem of degradation in small sample to evaluate reliability. Moreover, the dynamic reliability with the mixture of the probabilistic and non-probabilistic variables can be obtained using the proposed method. An illustrative numerical case study of a spool valve is conducted in order to validate the proposed method and the implemented reliability sensitivity analysis. The proposed method is of great help in evaluating and predicting reliability with small degradation sample and hybrid uncertainties.

Failure-based sealing reliability analysis considering dynamic interval and hybrid uncertainties

In the reliability analysis of a sealing structure, radial clearance of the contact surface is usually regarded as a failure criterion, and the sample size is usually quite small, which brings great challenges to uncertainty quantification. Therefore, this paper proposes a reliability analysis method based on the leakage mechanism of the sealing. With the application of dynamic interval, the proposed method can be used to deal with problem of degradation in small sample to evaluate reliability. Moreover, the dynamic reliability with the mixture of the probabilistic and non-probabilistic variables can be obtained using the proposed method. An illustrative numerical case study of a spool valve is conducted in order to validate the proposed method and the implemented reliability sensitivity analysis. The proposed method is of great help in evaluating and predicting reliability with small degradation sample and hybrid uncertainties.

Variance-based reliability sensitivity analysis and the FORM [formula omitted]-factors

In reliability assessments, it is useful to compute importance measures that provide information on the influence of the input random variables on the probability of failure. Classical importance measures are the α-factors, which are obtained as a by-product of the first-order reliability method (FORM). These factors are the directional cosines of the most probable failure point in an underlying independent standard normal space. Alternatively, one might assess sensitivity by a variance decomposition of the indicator function, i.e., the function that indicates membership of the random variables to the failure domain. This paper discusses the relation of the latter variance-based sensitivity measures to the FORM α-factors and analytically shows that there exist one-to-one relationships between them for linear limit-state functions of normal random variables. We also demonstrate that these relationships enable a good approximation of variance-based sensitivities for general reliability problems. The derived relationships shed light on the behavior of first-order and total-effect indices of the failure event in engineering reliability problems.

Global reliability sensitivity analysis index and its efficient numerical simulation solution in presence of both random and interval hybrid uncertainty

In the presence of both random and interval hybrid uncertainty (RI-HU), investigating global reliability sensitivity (GRS) can identify the effect of random input on the structural safety globally. To this end, this work establishes the GRS index model and its corresponding efficient solution, and the innovation includes three aspects. Firstly, the GRS of the random input is defined by the average absolute difference between the failure probability upper bound (FP-UB) and the conditional FP-UB on the fixed random input under the RI-HU, and it can reflect the effect of the fixed random input on the structural safety. Secondly, the conditional FP-UB on fixing the random input at the realization is approximated by the conditional FP-UB on fixing the random input in a differential interval. Then the conditional probability theorem can be employed to convert estimating the GRS into the state recognition of the samples, which is the by-product of estimating the FP-UB by the numerical simulation. Finally, by the strategy of surrogating the performance function twice, the meta-importance sampling method is developed to efficiently estimate the GRS in presence of the RI-HU. The rationality of the proposed GRS index model and the efficiency of the developed estimation method are fully verified by the numerical and engineering examples.

Global sensitivity analysis of a CaO/Ca(OH)2 thermochemical energy storage model for parametric effect analysis

Simulation models have been widely used for thermochemical energy storage to better understand its behavior and consequently to improve operational control of the device. However, incomplete knowledge of system properties leads to a significant number of uncertain parameters in the simulation models, which in turn cause uncertainties in system predictions. In this work, we perform global sensitivity analysis to identify the effect of uncertain parameters on the outputs of a thermochemical energy storage model, so that we can better understand the predictive uncertainties, proceed with targeted data acquisition or even simplify the corresponding uncertainty quantification. To get reliable sensitivity analysis results, we use both variance-based and regional sensitivity analysis since they focus on different probabilistic features of model outputs. Since the simulation model is computationally expensive, we use model reduction via the (arbitrary) polynomial chaos expansion. Then, to further confirm the results, the regional sensitivity index is also estimated based on the original model with the same given sample set. Based on the results of both sensitivity analysis methods, we can find that there are 8 unimportant parameters among 16 analyzed parameters. Thus, we can focus resources on investigating the important uncertain parameters. Also, we can ignore the uncertainty of unimportant parameters to simplify the corresponding uncertainty quantification.

Reliability sensitivity analysis of ball-end milling accuracy

In the process of milling, the setting of parameters has a significant influence on the milling characteristics. If the selection of cutting parameters is not reasonable, it will be difficult to ensure the machining accuracy of the workpiece. Considering the uncertainty of cutting parameters in the milling process, this paper proposes a reliability sensitivity analysis method for angular ball-end milling precision. First, the cutting edge contact section is determined by the discrete event simulation, based on the Z-map method. Then, the milling cutter is considered equivalent to a cantilever beam, while a flexible prediction model, including the tool deformation in the milling process, is established. In order to improve the calculation efficiency of the tool deflection error, the functional relationship between the parameters and the machining error is reconstructed, using kriging technology. Following, the kriging model is used to replace the dynamic model to analyze the reliability sensitivity of milling precision, based on the Monte Carlo method. Finally, both experimental and simulation results show that the tool deflection error model and the sensitivity calculation method, as proposed in this paper, exhibit high precision.

Failure mechanism and reliability analysis of the rear cargo door lock of transport aircraft

The cargo door lock is a critical component of the rear cargo door system of transport aircraft. Malfunction of the cargo door lock may lead to airdrop mission failure or even catastrophic accident. In the reliability test of the rear cargo door system of a transport aircraft, one of the cargo door locks failed to open. However, the failure cannot be remedied by simply strengthening the failed parts. In this work, we analyze the failure mechanism to find out the root cause. Then, the open function reliability is assessed and the local as well as the global reliability sensitivity analysis are performed to interrogate the impacts of the random influence factors. On this basis, the critical random influence factors are identified and accordingly the improvement measures are proposed. After the failed cargo door lock is improved based on the improvement measures, the open function failure didn’t occur again in the subsequent test, verifying the effectiveness of the proposed improvement measures.

Ramifications of blind adoption of load and resistance factors in building codes: reliability-based assessment

This paper presents a probabilistic approach to reveal the negative consequences of overlooking code calibration when adopting the provisions of nonindigenous building codes in design. A taxonomy of the national building codes of various countries whose provisions are adopted from one or more original standards is first presented. Next, the reliability-based approach to quantify the lack of safety that may arise due to the absence of code calibration is presented. This approach is then applied to the case study of the National Building Code of Iran, whose load and resistance factors are directly adopted from ASCE/SEI 7. To this end, seven steel building archetypes with various structural systems at various regions with different seismicity levels and site classes are designed according to the Iranian loading and steel design codes. Subsequently, 2510 structural elements, including beams, columns, and braces, from these archetypes are subjected to reliability analysis to compute their reliabilities. In this analysis, the uncertainty of material properties are quantified using local laboratory test data and the uncertainties associated with manufacturing tolerances of steel elements are quantified through extensive field surveys. The analysis results in reliability indices that are markedly smaller than the targets set by the original standards the Iranian code has adopted from, which exposes the notable lack of safety in the ensuing designs. Subsequently, the load and resistance factors are calibrated to achieve the target reliabilities. Among other changes, the results indicate the need for a 25% increase in the earthquake load factor, which reveals the lack of safety that is implicit in the current practice. Reliability sensitivity analysis is then employed to determine the sources of uncertainty that are most influential on the resulting reliabilities. The presented approach is immediately applicable to the assessment of the building codes of other countries.

Sealing reliability and reliability sensitivity analysis of the piston–cylinder bore friction pair in a hydraulic pump under incomplete probability information

Incomplete probability information makes it impossible to determine the probability distribution of a random variable accurately. Such a lack of probability information is manifested by the fact that the reliability index of engineering products can only be estimated qualitatively and approximately based on the readily available data. In this paper, the sealing reliability of the piston–cylinder bore friction pair in a hydraulic pump is designed and its sensitivity is analyzed under incomplete probability information. A reliability design model that incorporates both the motion and load effects is established. A method for designing the sealing reliability and for analyzing its sensitivity under incomplete probability information is proposed for the piston–cylinder bore friction pair, and the trends of the change in the reliability with the design parameters are determined by a simulation. The influence of the changes in the design parameters on the reliability is clarified. The reliability design problem of the piston–cylinder bore friction pair under the dual effects of motion and load is solved using the available probability information. The reliability of the piston–cylinder bore friction pair is designed and its sensitivity is analyzed using limited probability information through a computer program.

Reliability and global sensitivity analysis for an airplane slat mechanism considering wear degradation

This paper focuses on the issue of reliability and global sensitivity analysis for an airplane slat mechanism considering the uncertainties in the wear process of mechanical components. First, the multi-body kinematic model of the slat mechanism is built in the ADAMS software. The geometrical sizes of the roller wheels after wear degradation are considered as input variables and the angle the slat should turn is considered as the output response. To accurately identify the influential roller wheels to the reliability and robustness of the slat mechanism, the failure probability based sensitivity and variance-based sensitivity indices are introduced. Comprehensive analysis of the results have shown that the reliability analysis and global sensitivity theory can help engineers find significant parts by their contributions, thus provide guidance for mechanical design and maintenance.

Reliability Sensitivity Analysis of Vehicle CAN Bus Message Transmission Based on Second-moment Method

CAN bus, as one of the most successful on-board network systems, is widely used in modern automobiles. The main function of CAN bus is to realize timely and accurate message transmission, so higher and higher requirements are put forward for the reliability of message transmission. In this paper, a typical CAN bus message transmission model was selected for analysis, and the reliability sensitivity of the bus message transmission was analyzed and calculated based on the reliability second-moment theory. The results were consistent with the qualitative analysis, and the reliability sensitivity calculation of the second-moment method is verified. The reliability sensitivity analysis of CAN bus message transmission by this method will provide a reasonable theoretical support for the further study of message transmission reliability in CAN bus system.

Phân tích độ nhạy của độ tin cậy kết cấu - một nghiên cứu áp dụng cho công trình ngầm

This article introduces the results of research on sensitivity analysis of structural reliability. The article has analyzed reliability methods, importance factor (IS), sensitivity index (SI) of random variables and their effects on failure probability and reliability index. The article has also analyzed the reliability, the important factor and the sensitivity index for a specific underground work. From the results received, it is proposed to choose the method of calculating structural reliability and problems related to sensitivity analysis of the structural reliability.

Time-varying reliability and global sensitivity analysis of regenerative chatter stability in turning considering tool wear

Investigating the effect of the uncertainty in the parameters on time-varying chatter stability is critical to refrain from the time-varying regenerative chatter in turning. In this study, the influence of tool wear on the cutting force coefficient (CFC) in turning processing is taken into consideration, and CFC variation during cutting time is described by the Gamma process. The model of the time-varying chatter stability in turning is established based on the motional and mechanical properties of the cutting process in turning. Time-varying reliability (TVR) is estimated based on the uncertain and time-varying characteristics of the turning process parameters. The method of moment-independent time-varying global sensitivity analysis (TV-GSA) based on the cumulative failure probability (CFP) is proposed to measure the effect of parameters on the CFP of the chatter stability in turning. Furthermore, for reducing the computational cost of moment-independent TV-GSA based on CFP, the active learning Kriging model is established to replace the nonlinear and implicit limit state function of the chatter stability in turning. The dynamic model of the turning chatter is validated by an illustrative example. And the results of the proposed method are compared with the results of the Monte Carlo simulation to verify the effectiveness of the proposed method.