Reliability-based Sensitivity Research Articles

Reliability analysis for 5G industrial network with application and dynamic coupling

The analysis of reliability is vital in ensuring the operation of 5G industrial networks (5GIN). With 5GIN are no longer merely chains of physical components, they consist of different applications that are dynamically deployed on base platform. Such a sharing of infrastructure between applications complicates the fault logic and greatly impacts their operation. Current reliability analysis tends to treat system as static, fail to take applications and dynamic coupling into accounts. This paper proposes a model consisting of network evolution model of 5GIN (NEM5G) and reliability-based sensitivity analysis (SA). NEM5G depicts the interaction of physical components and applications, which provides a description of dynamic coupling within system and its effect on reliability. Furthermore, SA helps identify influential parameters within 5GIN to support reliability optimization. The simulation results show that, our model achieves steady-state reliability aligned with that of the Continuous Time Markov Chain (CTMC) model in a simplified intelligent optical network case. When facing complex steel processing scenario, simulation results illustrate the variation trend of 5GIN reliability, further presents an importance ranking of parameters and analyzes available design strategies.

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.

Regional reliability sensitivity analysis based on dimension reduction technique

Reliability sensitivity analysis is crucial for efficient design optimisation based on parametric modelling. A common fact in applications is that reliability shows different degrees of sensitivity to changes in the ranges of design parameters within a design space. Therefore, a regional reliability sensitivity analysis (RRSA) is proposed to study how the reliability-based sensitivity indexes change when the local ranges of the design parameters are modified. In this study, a method combining the Bayesian formula and the sampling simulation method is utilised to obtain the derivative of the failure probability in an augmented space without the need to fit a function. Based on the idea of averaging the square of the local gradients in the entire parameter space, a covariance matrix is constructed using the average outer product of the gradient of the failure probability function (FPF) for the RRSA. As an emerging dimension-reduction technique, the active subspace method (ASM) is employed to identify the important directions of design variables to perform a reliability-based sensitivity analysis. The covariance matrix for the high-dimensional reliability analysis is estimated using the dynamic propagation sampling (DPS) method. Finally, we demonstrate the effectiveness and efficiency of the proposed RRSA through a numerical example wherein a Monte Carlo simulation (MCS) is employed for comparison.

Machine learning-based sensitivity of steel frames with highly imbalanced and high-dimensional data

The machine learning-based feature selection approach is presented to estimate the effect of uncertainties and identify failure modes of structures that incorporate a low failure probability and high-dimensional uncertainties. As structures are designed to have few failures, a dataset classified based on the failure status becomes imbalanced, which poses a challenge for the predictive modeling of machine learning classifiers. Moreover, in order to improve the accuracy and efficiency of the model performance, it is necessary to determine the critical factors and redundant factors, especially for a large feature set. This study benchmarks the novel method for sensitivity analysis by using datasets that exacerbate the problems involved in class imbalance and large number of input features. This study investigates two planar steel frames with spatially uncorrelated properties between structural members. Geometric and material properties are considered as uncertainties, such as material yield stress, Young’s modulus, frame sway, and residual stress. Six feature importance techniques including ANOVA, mRMR, Spearman’s rank, impurity-based, permutation, and SHAP are employed to measure the feature importance and identify parameters germane to the prediction of structural failures. Logistic regression and decision tree models are trained on the important feature set, and the predictive performance is evaluated. The use of the feature importance approach for structures with a low probability of failure and a large number of uncertain parameters is validated by showing identical results with the reliability-based sensitivity study and appropriate predictive accuracy.

Reliability Analysis of Pyrotechnic Igniter for Hydrogen-Oxygen Rocket Engine with Low Temperature Combustion Instability Failure Mode

To evaluate the functional reliability of the pyrotechnic igniter in the failure mode of unstable combustion at low temperature, a reliability and reliability sensitivity analysis method based on the combination of an interior ballistic model and Kriging reliability method is proposed. Through the deterministic interior ballistic simulation, the failure mode of low temperature unstable combustion of the pyrotechnic igniter is examined, while the random variables are introduced to establish the ignition nonlinear implicit function of the pyrotechnic igniter. The ignition display function of the pyrotechnic igniter is established by the Kriging model, which avoids the repeated calculation of true limit state function values. This study provides an efficient approach to evaluate the ignition reliability of the pyrotechnic igniter and compared with the traditional Monte Carlo method to verify the accuracy of the results. Finally, reliability-based sensitivity indices are presented to quantify the significance of random parameters. It is shown that the influence of the uncertainties can be precisely described, and the diameter of the nozzle plays a dominant role in ignition reliability. Additionally, ignition experiments of nozzles with different diameters were performed to verify the result of sensitivity. This can further support the detailed design of the pyrotechnic igniter.

Reinforced Concrete Beam under Support Removal-Parametric Analysis.

This paper investigates the behaviour of a reinforced concrete beam under a support removal. A detailed parametric analysis is carried out, covering the effect of support removal rate on dynamic response. The linear elastic and nonlinear inelastic responses are computed and studied in detail. Critical parameters during the structural response are identified. In order to determine the ultimate load, the vertical pushover analysis is performed. The key parameters driving the beam response are assumed as random variables, and respective reliability study makes it possible to check the overall uncertainty of the dynamic response. In particular, the response spectrum measuring the effect of support removal rate has been computed. It has been demonstrated that the critical vertical response occurs when the time of support removal is up to to 17% of the first natural period. The vertical pushover analysis results in obtaining capacity curves and showed the order in which two plastic hinges occur for various load patterns. Finally, the reliability-based sensitivity analysis indicates the geometric cross-section cover and height are the most sensitive parameters of the beam response.

Earthquake-induced economic loss estimation of eccentrically braced frames through roof acceleration-based nonmodel approach

This paper develops a nonmodel-based approach for seismic loss assessment of buildings with eccentrically braced frames (EBFs). An extensive database is utilized to predict engineering demand parameters (EDPs), including, peak and residual story drift ratios, peak story link rotations, and also peak floor absolute accelerations, along with the height of the buildings. The estimated EDPs are used to assess the total economic losses associated with the collapse, demolition, and repair of structural and/or non-structural components. The database includes seismic intensity measure, improved wavelet-based refined damage-sensitive feature (rDSF) assembled only by the roof absolute acceleration response, geometric information, and EDPs of the 4-, 8-, and 16-story prototype models, extracted from incremental dynamic analyses subjected to 44 far-field ground motions. The nonlinear model of the aforementioned structures was already developed by the authors to capture the response of the structures up to collapse. Symbolic and Bayesian regressions are carried out in addition to ordinary least square linear regression to develop the empirical equations. Moreover, a thorough study is performed on the optimal selection of the intensity measures proposed in the literature as the input variable of the predictive equations through reliability-based sensitivity analysis. To estimate the first mode period of the considered structures to compute the improved wavelet-based rDSF and promote a nonmodel-based approach, Auto-Regressive model with exogenous input is employed. The results show that the story-based EDPs and also the corresponding expected economic losses of EBF buildings are accurately predicted compared with those obtained from incremental dynamic analyses. Consequently, the proposed nonmodel-based approach paves the path for rapid earthquake-induced economic loss assessment of EBF buildings in emergency operations.

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.

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.

A priori error estimates for local reliability-based sensitivity analysis with Monte Carlo Simulation

In this work, we present a priori error estimates for local reliability-based sensitivity analysis. The Score Function Method and the Weak Approach using Monte Carlo Simulation are studied. The results are important for practical choice of parameters in local sensitivity analysis. Besides, the results can be employed for development of a posteriori error estimates and adaptive schemes in the future. The theoretical results are obtained for the one dimensional case, but are also useful in the multidimensional context, as confirmed through a set of numerical experiments.

Dynamic reliability analysis of mechanical system with wear and vibration failure modes

The wear and vibration of machine tool system are coupled and time-variant, which have significant influences on the dynamic performance of machine tool feed drive system in different time scales. In this study, the coupling effects between the wear of linear guide and the vibration of machine worktable system are studied based on the infinitesimal method. A nonlinear dynamic model is developed to analyze the wear and vibration failure mechanisms considering the uncertainty of parameters. To evaluate the dynamic reliability of the machine worktable system under multi-failure modes, a time-variant and conditional reliability approach based on the active learning Kriging model and Monte Carlo Simulation is proposed. The approach gets rid of repeated calculating of the real limit state function values and the calculation efficiency is enhanced greatly. Additionally, reliability-based sensitivity indices are presented to investigate the significance of random parameters to the reliability of the system. Besides of the reliability analysis for machine worktable systems, the proposed framework and corresponding method are also suitable for the reliability evaluation of other complex mechanical systems with the conditional multi-failure modes.

Dynamic Reliability and Reliability-Based Sensitivity of Transmission System in Shearer

Transmission system in shearer, such as traction unit and cutting arm, is the essential mechanism in the mining process, which supports the whole shearer and shock vibration. Considering various uncertainties, the evolving process is established to describe the dynamic system response with uncertain factors. Considering the parametric randomness and material strength. the failure domain is regarded as the dynamic extreme value of transmission system response exceeding the threshold in operation. According to the saddle-point approximation method, the dynamic extreme distribution is investigated to measure the safe probability and parametric sensitivity of transmission system in shearer. The dynamic reliability and reliability-based sensitivity are analysed to evaluate the evolving process of transmission system in shearer. According to the transmission model of traction unit, the influence degree of each parameter’s fluctuation can be quantified based on the indices of dynamic mean-value reliability-based sensitivity and standard deviation reliability-based sensitivity. The crude Monte Carlo simulation is taken as the benchmark to validate the reasonability.

Dynamic Model-based Saddle-point Approximation for Reliability and Reliability-based Sensitivity Analysis

Dynamic reliability analysis must consider both dynamic performance and parametric randomness to evaluate system safety in operation. The saddle-point approximation method is utilized to establish the dynamic probability distribution for known or unknown types of random variables. The cumulative distribution function is used to establish the approximation dynamic reliability model based on a simplified formula with high accuracy. Dynamic reliability analysis is investigated to describe the system safety of the moving operation process. Additionally, dynamic reliability-based sensitivity is used to represent the influence of the parameters on the system's dynamic performance. The fixed-threshold model and load-strength interference model are considered to develop computational formulas of reliability analysis and the degree of effect of each parameter's fluctuation. Finally, the proposed method is evaluated and demonstrated by means of four numerical examples to analyse the system performance and the parameters’ effects. The crude Monte Carlo simulation is performed to provide benchmark results.

A New Method for Reliability-Based Sensitivity Analysis of Dynamic Random Systems

A novel numerical method for investigating time-dependent reliability and sensitivity issues of dynamic systems is proposed, which involves random structure parameters and is subjected to stochastic process excitation simultaneously. The Karhunen–Loève (K-L) random process expansion method is used to express the excitation process in the form of a series of deterministic functions of time multiplied by independent zero-mean standard random quantities, and the discrete points are made to be the same as Legendre integration points. Then, the precise Gauss–Legendre integration is used to solve the oscillation differential functions. Considering the independent relationship of the structural random parameters and the parameters of random process, the time-varying moments of the response are evaluated by the point estimate method. Combining with the fourth-moment method theory of reliability analysis, the dynamic reliability response can be evaluated. The dynamic reliability curve is useful for getting the weakness time so as to avoid breakage. Reliability-based sensitivity analysis gives the importance sort of the distribution parameters, which is useful for increasing system reliability. The result obtained by the proposed method is accurate enough compared with that obtained by the Monte Carlo simulation (MCS) method.

An Effective Approach for Reliability-Based Sensitivity Analysis with the Principle of Maximum Entropy and Fractional Moments.

The reliability-based sensitivity analysis requires to recursively evaluate a multivariate structural model for many failure probability levels. This is in general a computationally intensive task due to irregular integrations used to define the structural failure probability. In this regard, the performance function is first approximated by using the multiplicative dimensional reduction method in this paper, and an approximation for the reliability-based sensitivity index is derived based on the principle of maximum entropy and the fractional moment. Three examples in the literature are presented to examine the performance of this entropy-based approach against the brute-force Monte-Carlo simulation method. Results have shown that the multiplicative dimensional reduction based entropy approach is rather efficient and able to provide reliability estimation results for the reliability-based sensitivity analysis of a multivariate structural model.

Reliability and reliability-based sensitivity analysis of shell and tube heat exchangers using Monte Carlo Simulation

In the present work, the reliability-based sensitivity analysis of a shell and tube heat exchanger has been investigated. Four optimum heat exchanger layouts have been selected among the available layouts in literature as case studies (which optimized based on the GA, PSO, ICA and BBO algorithms). A computer code has been developed based on the Bell-Dellawar method for the hydraulic and thermal modeling of heat exchanger. The shell and tube side inlet flow temperatures, mass flow rates, fouling resistance and the reduction of inner tubes diameter due to sedimentation are considered as uncertain parameters. The Monte Carlo Simulation (MCS) as the most accurate simulation method has been applied to determine the safety level of different layouts. The total cost of heat exchangers are reported 55.1 k€, 53.2 k€, 54.4 k€ and 50.6 k€ for the GA, PSO, ICA and BBO layout respectively, while the corresponding failure probabilities for these cases are 17.2%, 24.9%, 11.6% and 18.2%. The contribution of different parameters on the system failure has been determined. The contribution of shell side mass flow rate, hot and cold flow inlet temperature uncertainties on the system failure are 38–41%, 22–27% and 18–23% respectively for different layouts. Finally, appropriate ranges for variation of operating conditions are determined by using the sensitivity analysis. The present study shows the importance of reliability analysis in the real world applications which opening a new approach for heat exchanger design.

A hybrid approach for reliability-based robust design optimization of structural systems with dependent failure modes

ABSTRACTEstimating system reliability has been recognized as a critical step in reliability-based design optimization for structural systems. The estimation of system reliability entails multi-dimensional integration, which is very difficult and numerically expensive. The proposed hybrid method integrates the concepts of saddlepoint approximation, the dimension reduction method (DRM) and copulas. The moment-based saddlepoint approximation enhanced by the DRM is used to calculate the component reliability. The copula method is adopted to realize the joint failure probability modelling between two failure modes. Reliability-based sensitivity analysis for the reliability-based robust design optimization is carried out as well. The structural system optimization model is established, including the Euclid norm of the reliability sensitivity as an optimization objective and system reliability as a constraint. Examples demonstrate that the optimization results obtained by the proposed approach ensure the maximization of the robustness of the structural system.

Reliability-based sensitivity estimators of rare event probability in the presence of distribution parameter uncertainty

This paper aims at presenting sensitivity estimators of a rare event probability in the context of uncertain distribution parameters (which are often not known precisely or poorly estimated due to limited data). Since the distribution parameters are also affected by uncertainties, a possible solution consists in considering a second probabilistic uncertainty level. Then, by propagating this bi-level uncertainty, the failure probability becomes a random variable and one can use the mean estimator of the distribution of the failure probabilities (i.e. the “predictive failure probability”, PFP) as a new measure of safety. In this paper, the use of an augmented framework (composed of both basic variables and their probability distribution parameters) coupled with an Adaptive Importance Sampling strategy is proposed to get an efficient estimation strategy of the PFP. Consequently, double-loop procedure is avoided and the computational cost is decreased. Thus, sensitivity estimators of the PFP are derived with respect to some deterministic hyper-parameters parametrizing a priori modeling choice. Two cases are treated: either the uncertain distribution parameters follow an unbounded probability law, or a bounded one. The method efficiency is assessed on two different academic test-cases and a real space system computer code (launch vehicle stage fallback zone estimation).

Parameter Sensitivity Analysis and Probabilistic Optimal Design for the Main-Shaft Device of a Mine Hoist

As a key component of a mine hoist system, the main-shaft device bears most of the bending moment and torque. Thus, it is important to quantify the performance of the main-shaft device and ensure the reliability of the device. The paper aims to investigate the impact of uncertain structural parameters on the reliability of the main-shaft device. The probabilistic optimal design is performed based on the parameter sensitivity results. First, the design of experiments is adopted to realize the stochastic response analysis of the main-shaft device. Second, the moment-based saddlepoint approximation method is used to evaluate the strength reliability of the device considering uncertain parameters. Next, the reliability-based sensitivity is derived to investigate the parametric significance of random input variables. Finally, the probabilistic optimal design involving the reliability sensitivity is conducted. The results of the sensitivity indicate that the torque and the contact length of left bearing have relatively greater impact on the structural reliability than other variables of the main-shaft device.

The strength analysis and probabilistic design of a bogie frame with incomplete probabilistic information

A bogie frame is a key component of high-speed rail; higher requirements of the safety and stability of the bogie frame are put forward with the continuous improvement of the train speed. In this study, we first performed a strength analysis of a bogie frame according to the JIS E 4207 standard by using finite element method. Then, we did a reliability analysis of the bogie frame. The reliability problems are defined as strength reliability and resonant frequency reliability, which indicate the structural safety and stability of the bogie frame. The reliability estimation is realized by experimental design, artificial neural network and stochastic perturbation theory. Additionally, reliability- based sensitivity indices were derived to measure the parameter importance of random input variables. An illustrative example of the bogie frame with incomplete probabilistic information was used to demonstrate the applications of the proposed method for reliability and reliability-based sensitivity estimation in terms of strength and resonant frequency reliability. The results indicate that vertical loads and the material density have more of an impact on reliability than other variables of the bogie frame.