Reliability Analysis of the Light Truck Frame Based on Statics Structure and Response Surface Methodology

This chapter introduces reliability methods to give approximate and inexpensive methods to estimate the probability of failure of a system. It begins with the definition of the reliability and the simple first-order second-moment method, which relies heavily on a host of assumptions about the underlying QoI. Then the advanced first-order second-moment method is presented and applied to several problems.

The limit state function (LSF) is implicit to many structure reliability analysis problems, which may make some classical reliability method complicated to be applied. One of the surrogate methods-support vector classification (SVC) was applied in the structural reliability analysis herein which has not been applied to structure reliability analysis until recent years. Then the advanced first order second moment method (AFOSM) can be applied. The expressions of structure system reliability sensitivity to basic variable were deduced. The flow of how to call the SVC program was presented. An example was shown to compare the SVC based method with some other classical reliability analysis methods. The results are accurately accepted and the advantages of SVC are analyzed.

In this paper, the mean-centered first-order second-moment (FOSM) method is employed to perform probabilistic push-over analysis (POA) of structural and/or soil-structure systems. Approximations of first and second statistical moments (FSSMs) of engineering demand parameters (EDPs) of structural and/or geotechnical systems with random material parameters are computed based on finite-element (FE) response and response sensitivity analysis (RSA) results. The FE RSA is performed accurately and efficiently by using the direct differentiation method (DDM) and is employed to evaluate the relative importance (RI) of the various modeling material parameters in influencing the variability of the EDPs. The proposed approximate methodology is illustrated through probabilistic POA results for nonlinear inelastic FE models of: (1) a three-story reinforced-concrete (RC) frame building and (2) a soil-foundation-structure interaction system consisting of a RC frame structure founded on layered soil. FSSMs of EDPs computed through the FOSM method are compared with the corresponding accurate estimates obtained via Monte Carlo simulation. Results obtained from exact (or local) and averaged (or global) response sensitivities are also compared. The RI of the material parameters describing the systems is studied in both the deterministic and probabilistic sense, and presented in the form of tornado diagrams. Effects of statistical correlation between material parameters are also considered and analyzed by the FOSM method. A simple approximation of the probability density function and cumulative distribution function of EDPs due to a single random parameter at a time (while all the other parameters are fixed to their mean values) is also proposed. Conclusions are drawn on both the appropriateness of using local RSA for simplified probabilistic POA and on the application limits of the FOSM method. It is observed that the FOSM method combined with the DDM provides accurate estimates of FSSMs of EDPs for low-to-moderate level of inelastic structural or system behavior and useful qualitative information on the RI ranking of material parameters on the structural or system response for high level of inelastic behavior.

Dynamic interactions of groundwater flow and soil deformation in randomly heterogeneous porous media

The seismic safety of reinforced concrete containment building can be evaluated by probabilistic analysis considering randomness of earthquake, which is more rational than deterministic analysis. In the safety assessment of earthquake-resistant structures by the deterministic theory, it is not easy to consider the effects of random variables but the reliability theory and random vibration theory are useful to assess the seismic safety with considering random effects. The reliability assessment of reinforced concrete containment building subjected to earthquake load includes the structural analysis considering random variables such as load, resistance and analysis method, the definition of limit states and the reliability analysis. The reliability analysis procedure requires much time and labor and also needs to get the high confidence in results. In this study, random vibration analysis of containment building is performed with random variables as earthquake load, concrete compressive strength, modal damping ratio. The seismic responses of critical elements of structure are approximated at the most probable failure point by the response surface method. The response surface method helps to figure out the quantitative characteristics of structural response variability. And the limit state is defined as the failure surface of concrete under multi-axial stress, finally the limit state probability of failure can be obtained simply by first-order second moment method. The reliability analysis for the multiaxial strength limit state and the uniaxial strength limit state is performed and the results are compared with each other. This study concludes that the multiaxial failure criterion is a likely limit state to predict concrete failure strength under combined state of stresses and the reliability analysis results are compatible with the fact that the maximum compressive strength of concrete under biaxial compression state increases.

Variation of reliability-based seismic analysis of an electrical cabinet in different NPP location for Korean Peninsula

A methodology is presented for probabilistic design optimization of aircraft structures subject to a set of multidisciplinary constraints including reliability, manufacturability, and manufacturing cost. Using the advanced firstorder second-moment method, reliability of each structural component is evaluated by considering its primary static failure mode. Metrics-based analytical models are used in manufacturability analysis, and semi-empirical models are used for manufacturing cost estimation. The described design methodology is developed into a software tool and applied to probabilistic sizing optimization of a moderately loaded built-up wing spar. Using two alternative web design concepts, one limited by buckling and the other by diagonal semitension field action, the spar model is optimized for weight considering uncertainties in the material properties, structural sizing, and loading parameters. The optimization problem is solved using the method of sequential quadratic programming for different values of target reliability, with or without any limit on manufacturing cost. The optimization results are used to highlight the interactions between reliability, weight, and cost, whereas the probabilistic sensitivities are used to examine the influence of each random variable on structural reliability.

The present study is focused mainly on development of the fragility curves for the sidesway collapse limit state. One important aspect of deriving fragility curves is how uncertainties are blended and incorporated into the model under seismic conditions. The collapse fragility curve is in uenced by di erent uncertainty sources. In this paper, in order to reduce the dispersion of uncertainties, Adaptive Neuro Fuzzy Inference System (ANFIS)based on the fuzzy C-means algorithm is used to derive structural collapse fragility curve, considering e ects of epistemic and aleatory uncertainties associated with seismic loads and structural modeling. This approach is applied to a Steel Moment-Resisting Frame (SMRF) structural model whose relevant uncertainties have not been yet considered by others in particular by using ANFIS method for collapse damage state. The results show the superiority of ANFIS solution in comparison with excising probabilistic methods, e.g., First- Order Second-Moment Method (FOSM) and Monte Carlo (MC)/Response Surface Method (RSM) to incorporate epistemic uncertainty in terms of reducing computational e ort and increasing calculation accuracy. As a result, it can be concluded that, in comparison with the proposed method rather than Monte Carlo method, the mean and standard deviation are increased by 2.2% and 10%, respectively.

In order to evaluate the failure probability of a complicated structure, the structural responses usually need to be estimated by some numerical analysis methods such as finite element method (FEM). The response surface method (RSM) can be used to reduce the computational effort required for reliability analysis when the performance functions are implicit. However, the conventional RSM is time-consuming or cumbersome if the number of random variables is large. This paper proposes a Legendre orthogonal neural network (LONN)-based RSM to estimate the structural reliability. In this method, the relationship between the random variables and structural responses is established by a LONN model. Then the LONN model is connected to a reliability analysis method, i.e. first-order reliability methods (FORM) to calculate the failure probability of the structure. Numerical examples show that the proposed approach is applicable to structural reliability analysis, as well as the structure with implicit performance functions.

An optimization method for learning statistical classifiers in structural reliability

Generally, buried steel pipes are designed for good transverse behavior by neglecting soil–structure interaction effect. Steel pipelines are also usually designed to prevent from the important failure mode of buckling. However, the design of this type of structures does not normally consider the uncertainties in soil and structural properties. To address the above issues, the paper estimates the uncertainties in terms of the coefficient of variation of critical buckling displacement, CVw using subgrade reaction theory (Winkler model) and first-order second-moment (FOSM) method. Two cases of boundary conditions have been considered in this study. In the first case, CVw is calculated within an infinitely thick soil as a function of uncertainty of subgrade reaction modulus (Ks). In the second case, CVw is calculated in a thick soil cylinder as a function of the uncertainty of the effective subgrade reaction modulus ( $$K_{S}^{{\prime }}$$ ). Furthermore, the uncertainty of pipe flexibility (Sf) is also taken into account in the two cases. Uncertainty calculations by the FOSM method are then validated with those obtained from traditional Monte Carlo simulations.

Earthquake motion is a random process, and thus, analyzing the seismic responses and dynamic reliability of cable-stayed bridges based on the random vibration theory is important. In this paper, dynamic reliability is investigated under earthquake loads by applying the stochastic vibration theory to the Sutong Yangtze River Highway Bridge. The response statistics are obtained from random vibration analyses, and the dynamic reliability of the normal stress of several key cross sections in the bridge is analyzed using the first-order second-moment method and the first-passage failure theory. The dynamic reliability analysis shows that the reliability index changes with girder section location and meets the design requirements. The analysis shows that the Sutong Bridge has adequate earthquake resistance ability. The structure’s earthquake resistance is appraised to provide an important theoretical reference for improving the seismic resistance design methods.

Monte Carlo Simulation and Response Surface Method are two very powerful reliability analysis methods. Normally, in the reliability analysis of complex structures, the limit state function often can not be expressed in a closed-form. Usually, the codes for probabilistic analysis need to be combined with finite element models. ANSYS Probabilistic Design System (PDS) has provided a package to conduct probabilistic analysis automatically. This paper is going to compare the performance of these methods through an easy engineering problem in ANSYS. The results are going to be derived to show the feature of applying the corresponding reliability methods.

To ameliorate reliability analysis efficiency for aeroengine components, such as compressor blade, support vector machine response surface method (SRSM) is proposed. SRSM integrates the advantages of support vector machine (SVM) and traditional response surface method (RSM), and utilizes experimental samples to construct a suitable response surface function (RSF) to replace the complicated and abstract finite element model. Moreover, the randomness of material parameters, structural dimension and operating condition are considered during extracting data so that the response surface function is more agreeable to the practical model. The results indicate that based on the same experimental data, SRSM has come closer than RSM reliability to approximating Monte Carlo method (MCM); while SRSM (17.296 s) needs far less running time than MCM (10958 s) and RSM (9840 s). Therefore, under the same simulation conditions, SRSM has the largest analysis efficiency, and can be considered a feasible and valid method to analyze structural reliability.

Improved response surface method and its application to stiffened plate reliability analysis