Reliability-based Sensitivity Analysis 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.

REINFORCED CONCRETE BEAM AT ULTIMATE LIMIT STATE CONSIDERING VARIABILITY IN THE CONCRETE MIX DESIGN PARAMETERS

Variability in design parameters of Civil Engineering infrastructure is inevitable at implementation in most practical situations, the effect of which can best be determined at design stage using reliability concepts. This study used First Order Reliability Method (FORM) to determine the effect of variation in Nano Engineered Concrete (NEC) mix design parameters on structural safety of Nano Engineered Reinforced Concrete (NERC) beams at ultimate limit state using reliability based sensitivity analysis. The variability in NEC mix design parameters was incorporated into EN1992-1-1(2008) design formulations using predictive models of NEC characteristic compressive strength developed on the basis of experimental data with the aid of DataFit statistical package. FORTRAN based subroutines of the NERC beam performance functions were developed and used for the reliability sensitivity analysis at ultimate limit state. Results indicate that variability in NEC mix design parameters affect structural safety of NERC beams in accordance with how the mix design parameter contributes to characteristic compressive strength development. Moreover, increase in nanosilica dosage beyond optimal value was found to have negative effect on structural safety of NERC beams. The study found that compressive strength contributes to tensile strength of NERC beams through composite action. Furthermore, the study suggested that the effect of variability in concrete mix design parameters be incorporated in design formulations of Civil Engineering Codes of Practice to aid estimation of safety of structural elements to be designed and produced with NEC for improved safety, sustainability and resilience of Civil Engineering infrastructure.

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.

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 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.

An approach for reliability-based sensitivity analysis based on saddlepoint approximation

Reliability-based sensitivity analysis quantifies the effects of input random variables on model outputs. It is an integral part of reliability-based design and robust optimal design. An efficient reliability sensitivity method is developed in this article by combining the stochastic perturbation technique and the moment-based saddlepoint approximation. The main advantage of the presented method is that only the first three moments of the structural response are needed and the cumulant generating functions of input random variables are not strictly required. Several examples are illustrated, and the analysis procedure shows that the method is convenient to be applied to parameter sensitivity analysis of structural reliability.

A structural reliability-based sensitivity analysis method using particles swarm optimization: relative convergence rate

This paper proposes a novel reliability-based sensitivity analysis (SA) method, namely relative convergence rate of random variables using particles swarm optimization (PSO). The convergence rate of a random variable during the optimum evolution process reflects the sensitivity of the objective function with respect to the random variables. An optimized group strategy is proposed to consider the fluctuation of the convergence rate of a variable during the optimum process. The coefficient of variation (COV) for candidate particles and the relative convergence rate of a random variable can be calculated using the particles in the optimized group. The smaller the COV for candidate particles, i.e., the larger the relative convergence rate, the more sensitive the objective function with respect to the variable. Three examples are available for the application of this method, and the results indicate that the sensitivity of the reliability index with respect to the variable obtained using the PSO technique and gradient of limit-state function is the same in the quantitative sense.

Reliability-based sensitivity analysis for prestressed concrete girder bridges

In this paper, the authors calculate the reliability indices for prestressed concrete girders using new statistical parameters for materials and load components. Various types of girders are considered, with spans ranging from 80 to 200 feet and girder spacings from 8 to 10 feet. The paper also presents a derivation of sensitivity functions for parameters affecting prestressed concrete girder performance, focusing in particular on bending capacity.

Reliability-based robust optimization design of automobile components with non-normal distribution parameters

In the reliability designing procedure of the vehicle components, when the distribution styles of the random variables are unknown or non-normal distribution, the result evaluated contains great error or even is wrong if the reliability value R is larger than 1 by using the existent method, in which case the formula is necessary to be revised. This is obviously inconvenient for programming. Combining reliability-based optimization theory, robust designing method and reliability based sensitivity analysis, a new method for reliability robust designing is proposed. Therefore the influence level of the designing parameters’ changing to the reliability of vehicle components can be obtained. The reliability sensitivity with respect to design parameters is viewed as a sub-objective function in the multi-objective optimization problem satisfying reliability constraints. Given the first four moments of basic random variables, a fourth-moment technique and the proposed optimization procedure can obtain reliability-based robust design of automobile components with non-normal distribution parameters accurately and quickly. By using the proposed method, the distribution style of the random parameters is relaxed. Therefore it is much closer to the actual reliability problems. The numerical examples indicate the following: (1) The reliability value obtained by the robust method proposed increases (>0.04%) comparing to the value obtained by the ordinary optimization algorithm; (2) The absolute value of reliability-based sensitivity decreases (>0.01%), and the robustness of the products’ quality is improved accordingly. Utilizing the reliability-based optimization and robust design method in the reliability designing procedure reduces the manufacture cost and provides the theoretical basis for the reliability and robust design of the vehicle components.

Reliability-Based Sensitivity Analysis for Machining Precision by Saddle-Point Approximation

Based on the saddle-point approximation theory, the reliability sensitivity formula is derived systematically. Then, combining the reliability theory with the sensitivity analysis method, the reliability-based sensitivity of machining precision for ball-end milling cutter is analyzed. Based on the premise that the probability distribution of random parameters is known, firstly, the saddle-point approximation theory is employed to solve the reliability of machining precision for ball-end milling cutter and, as a result, the saddle-point approximation method is proved accurate with higher speed in comparison with the Monte-Carlo method. Secondly, the reliability-based sensitivity is calculated. Finally, the effect of changes in machining parameters on the reliability of machining precision is analyzed.

Reliability sensitivity based on first-order reliability method

A new efficient and accurate method for reliability sensitivity analysis of mechanical components is proposed based on the first-order reliability method (FORM). This method provides very close approximate solutions for strongly non-linear limit state functions with independent normal random variables. But most probable point should be searched at first. Three methods are presented and investigated for reliability-based sensitivity analysis. They are, respectively, based on three different reliability analysis methods which are mean-value first-order reliability method, Monte Carlo method, and FORM. Numerical results of the three methods are calculated out by three examples. The accuracy and efficiency of the new method are demonstrated by the comparison of the numerical results.

Reliability-based sensitivity analysis of vehicle components with non-normal distribution parameters

Techniques from the perturbation method, fourth moment method, reliability-based design theory, and sensitivity analysis approach are employed to present a practical and efficient method for testing the reliability sensitivity of vehicle components with non-normal distribution parameters. With the condition that the first four moments of original random variables are known, the reliability sensitivity theory and cases are researched using the presented numerical method. The variation regularities of reliability sensitivity are obtained and the effects of design parameters on reliability of the vehicle components are studied. The sophisticated formulation provided in this paper is easily amenable to computational procedures. The respective program can be used to obtain the reliability sensitivity of vehicle components with non-normal distribution parameters accurately and quickly. The results obtained are perfect and the solutions compared very well with those from Monte Carlo simulation. The method presents a theoretic basis for the reliability design of the vehicle components.