Reliability analysis of nonlinear structural systems using response surface method

Modified subset simulation method for reliability analysis of structural systems

In this work, a novel framework is proposed for the risk based design optimization of engineering systems by minimizing the demand on the system components’ accuracy (which directly relates to their cost). The fundamental development of this work is an analytical upper bound for calculating the probability of failure. This is in contrast with First Order Reliability Method (FORM), where a lower bound is used in calculating the probability of failure. FORM is one of the most popular methods for reliability analysis of engineering systems. In this paper, we show that FORM results in an optimistic measure of risk, hence potentially catastrophic in engineering design. A more accurate measure of failure is proposed by utilizing an analytical upper bound for the distribution of reliability index (the length of the most probable point vector to origin). This distribution is a function of the eigenvalues of the linearized limit state function in the normal space which results in a better understanding of failure phenomenon. The proposed formulation is computationally efficient and straightforward to solve, since it only involves finding eigenvalues in each iteration. This algorithm is applicable to any linearizable continuous limit state function with any type of distribution for the design variables. The method is applied to two examples and its accuracy is compared with the Monte Carlo simulation and FORM, demonstrating its effectiveness and value.

Hybrid probabilistic interval analysis of bar structures with uncertainty using a mixed perturbation Monte-Carlo method

In this paper, a sampling-based RBDO method using a classification method is presented. The probabilistic sensitivity analysis is used to compute sensitivities of probabilistic constraints with respect to random variables. Since the probabilistic sensitivity analysis requires only the limit state function, and not the response surface or sensitivity of the response, an efficient classification method can be used for a sampling-based RBDO. The proposed virtual support vector machine (VSVM), which is a classification method, is a support vector machine (SVM) with virtual samples. By introducing virtual samples, VSVM overcomes the deficiency in existing SVM that uses only classification information as their input. In this paper, the universal Kriging method is used to obtain locations of virtual samples to improve the accuracy of the limit state function for highly nonlinear problems. A sequential sampling strategy effectively inserts new samples near the limit state function. In sampling-based RBDO, Monte Carlo simulation (MCS) is used for the reliability analysis and probabilistic sensitivity analysis. Since SVM is an explicit classification method, unlike implicit methods, computational cost for evaluating a large number of MCS samples can be significantly reduced. Several efficiency strategies, such as the hyper-spherical local window for generation of the limit state function and the Transformations/Gibbs sampling method to generate uniform samples in the hyper-sphere, are also applied. Examples show that the proposed sampling-based RBDO using VSVM yields better efficiency in terms of the number of required samples and the computational cost for evaluating MCS samples while maintaining accuracy similar to that of sampling-based RBDO using the implicit dynamic Kriging (D-Kriging) method.

An optimization method for learning statistical classifiers in structural reliability

The seismic reliability analysis of complex structure is carried out based on the response surface method and finite element method. Firstly, the appropriate design points are selected based on the mean values and standard deviations of the basic random variables. Secondly, the finite element method is employed to obtain the values of the limit state function of the complex structure. Thirdly, with selected design points and the obtained values of the limit state function of the complex structure, a polynomial function is constructed to approximate the original implicit limit state function. Then, with the established explicit polynomial limit state function and available methods of structural reliability analysis, the seismic reliability of the complex structure is estimated. Numerical analyses show that the established method is simple to use for the evaluation of the reliability analysis of complex structure.

In this paper a torque estimation model for induction machines is studied. The model requires several machine parameters as input. Since the input parameters are deduced from measurements burdened with inaccuracy, it is necessary to take into account uncertainty in the input of the model. A first order and second order reliability method are performed to evaluate the probability of failure of the system under the uncertain inputs. The system failure is defined through the limit state function and occurs when the calculated value of the torque differs significantly from the rated torque at rated conditions. Monte Carlo simulations are performed for validation and importance sampling is discussed to reduce the Monte Carlo simulation error. The probability of failure is also derived from the torque probability density function by means of a stochastic response surface method. The analysis includes current and speed measurement uncertainties as well.

Reliability analysis of pipe whip impacts

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.

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

The reliability of a simple turbomachinery model was calculated to demonstrate the application of a newly developing system integration tool, Probabilistic Design and Analysis Framework(PRODAF), along with efficient probabilistic methods using a response surface method. The model represents a system consisting of hypothetical turbine components. The parts include a blade, disk, and shaft with an applied angular velocity. All the components were modeled with the properties of the nickel alloy, Inconel 718. A response surface was calculated for the system of components to improve probabilistic computational efficiency. In addition, a fast probability integration method, Advanced First Order Reliability Method (AFORM), was used for the probabilistic analysis in order to provide an efficient analysis as possible. Geometric dimensions, the applied load, and material yield strength were varied for this study. The probability of failure was determined using the maximum first principal stress response and the material yield strength. A simple G function using the difference between strength and loading stress was used to determine failure limits. The probabilistic sensitivity of the failure response relative to the individual variables was determined also with material yield strength having the greatest influence. The model was recreated with every iteration of the probabilistic analysis in order to vary the geometry. As a result, the response surface method has a significant impact on improving computational efficiency and enabling reliability analysis with rapid turnaround.

Application of the homotopy analysis method to determine the analytical limit state functions and reliability index for large deflection of a cantilever beam subjected to static co-planar loading

An efficient quasi-Newton approximation-based SORM to estimate the reliability of geotechnical problems

Reliability assessment of a subsea pipe-in-pipe system for major failure modes

PurposeBecause of the high computational efficiency, response surface method (RSM) has been widely used in structural reliability analysis. However, for a highly nonlinear limit state function (LSF), the approximate accuracy of the failure probability mainly depends on the design point, and the result is that the response surface function composed of initial experimental points rarely fits the LSF exactly. The inaccurate design points usually cause some errors in the traditional RSM. The purpose of this paper is to present a hybrid method combining adaptive moving experimental points strategy and RSM, describing a new response surface using downhill simplex algorithm (DSA-RSM).Design/methodology/approachIn DSA-RSM, the operation mechanism principle of the basic DSA, in which local descending vectors are automatically generated, was studied. Then, the search strategy of the basic DSA was changed and the RSM approximate model was reconstructed by combining the direct search advantage of DSA with the reliability mechanism of response surface analysis.FindingsThe computational power of the proposed method is demonstrated by solving four structural reliability problems, including the actual engineering problem of a car collision. Compared to specific structural reliability analysis methods, the approach of modified DSA interpolation response surface for structural reliability has a good convergent capability and computational accuracy.Originality/valueThis paper proposes a new RSM technology based on proxy model to complete the reliability analysis. The originality of this paper is to present an improved RSM that adjusts the position of the experimental points judiciously by using the DSA principle to make the fitted response surface closer to the actual limit state surface.