Kriging response surface reliability analysis of a ship-stiffened plate with initial imperfections

Since the prediction of the seismic response of structures is highly uncertain, the need for the probabilistic approach is clear, especially for the estimation of critical seismic response parameters. Considering the uncertainties present in the material and geometric form of reinforced concrete (RC) structures, reliability analyses using the Finite Element Method (FEM) were performed in the context of Performance-Based Earthquake Engineering (PBEE). This study presented and compared the possibilities of nonlinear modelling of the reinforced concrete (RC) planar frame and its reliability analysis using different numerical methods, Mean-Value First-Order Second-Moment (MVFOSM), First-Order Reliability Method (FORM), Second-Order Reliability Method (SORM) and Monte Carlo simulation (MCS). The calibrated numerical models used were based on the previous experimental test of a planar RC frame subjected to cyclic horizontal load. Numerical models were upgraded by random variable (RV) parameters for reliability analysis purposes and, using implicit limit state function (LSF), pushover analyses were performed by controlling the horizontal inter-storey drift ratio (IDR). Reliability results were found to be sensitive to the reliability analysis method. The results of reliability analysis reveal that, in a nonlinear region, after exceeding the yield strength of the longitudinal reinforcement, the cross-sectional geometry parameters were of greater importance compared to the parameters of the material characteristics. The results also show that epistemic (knowledge-based) uncertainties significantly affected dispersion and on the median estimate parameter response. The MCS sampling method is recommended, but the First-Order Reliability Method (FORM) applied on a response model can be used with good accuracy. Reliability analysis using the FEM proved to be suitable for the direct implementation of geometric and material nonlinearities to cover epistemic (knowledge-based) uncertainties.

Structural reliability analysis based on probabilistic response modelling using the Maximum Entropy Method

Since the prediction of the seismic response of structures is highly uncertain, the need for the probabilistic approach is clear, especially for the estimation of critical seismic response parameters. Considering the uncertainties present in the material and geometric form of reinforced concrete (RC) structures, reliability analyses using the Finite Element Method (FEM) were performed in the context of Performance-Based Earthquake Engineering (PBEE). This study presented and compared the possibilities of nonlinear modelling of the reinforced concrete (RC) planar frame and its reliability analysis using different numerical methods, Mean-Value First-Order Second-Moment (MVFOSM), First-Order Reliability Method (FORM), Second-Order Reliability Method (SORM) and Monte Carlo simulation (MCS). The calibrated numerical models used were based on the previous experimental test of a planar RC frame subjected to cyclic horizontal load. Numerical models were upgraded by random variable (RV) parameters for reliability analysis purposes, and, using implicit limit state function (LSF), pushover analyses were performed by controlling the horizontal inter-storey drift ratio (IDR). Reliability results were found to be sensitive to the reliability analysis method. The results of reliability analysis reveal that, in a nonlinear region, after exceeding the yield strength of the longitudinal reinforcement, the cross-sectional geometry parameters were of greater importance compared to the parameters of the material characteristics. The results also show that epistemic (knowledge-based) uncertainties significantly affected dispersion and the median estimate parameter response. The MCS sampling method is recommended, but the First-Order Reliability Method (FORM) applied to a response model can be used with good accuracy. Reliability analysis using the FEM proved suitable for directly implementing geometric and material nonlinearities to cover epistemic (knowledge-based) uncertainties.

Structural reliability theory stems from the nature of randomness, fuzziness, characteristic and some other uncertainties in the process of engineering structural design, construction and employment. With the rapid development of science technology and industry, many departments have realized the importance of structural reliability problem and its potential economic benefits. Solving the problem of structural reliability has quickly become an important issue in the field of academic research. Because of the complexity of the structure and the harsh working environment which lead to a complex structural reliability problem, the traditional quality analysis method can’t explain the failure problems in practical engineering. How to solve the problem of large-scale complex structural reliability, improve the accuracy and efficiency of reliability analysis method, and further obtain great economic benefits, have become one of the most important exploration areas for the enterprises and scholars at home and abroad. The response surface method, which can replace the implicit limit state function by small amount of computation arises at this time. Through a series of deterministic response surface method, it uses polynomial function to approximate implicit limit state function. By reasonably selecting sites and iteration strategy, it ensures that the polynomial function on the failure probability can converge to the failure probability of the implicit limit state function. Response surface method, with high efficiency of clarity and precision, strong operability, combined with finite element advantage, is a reliability method widely used at present. In the process of the implementation of the response surface method, it uses three key steps of selecting the response surface function forms, obtaining sample points by the experiment design and using the regression fitting model, which has direct impact on the degree of the response surface method approximating limit state function and determines the performance of the response surface method. This is a problem that the response surface method must solve. It is the paper’s original intention to conduct the research work based on the response surface method of structural reliability optimization, improving the above three steps and the efficiency of engineering structure .The paper aims at the implicit limit state function problem, studying the structural reliability analysis of the weighted response surface method, combining the advantage of obtaining better sites by vector projection method and increases weighted coefficient by weighted response surface method. The improved weighted response surface method based on vector projection sampling is proposed. It uses the vector of the gradient projection method to get new design point and sample points, giving the actual limit state function of sample points more weights to construct the quadratic response surface function, updating the iterative response surface function, and solves the problem of the structural reliability of the implicit limit state function. Example analysis shows the characteristics of the proposed method, a steady design point can be found, and the calculation of stability has been improved considerably. The classical response surface method is optimized and reduces the defects that the calculation results are seriously affected by the interpolation coefficient. To some extent, it improves the calculation accuracy and can get relatively better results. Improved weighted response surface method based on vector projection sampling combines the advantages of obtaining test sample points by vector projection and weighted regression method, which is effective, feasible and can operate directly. It extends the application field of the response surface method to some degree and gets better approximate fitting limit state function at design point. It has better stability and robustness and provides new approach and ideas to solve the implicit limit state function.

Probabilistic investigation of piezoelectric application for reliability enhancement of composite laminates under edge delamination

Structural reliability analysis for implicit performance functions using artificial neural network

Probabilistic evaluation for the implicit limit-state function of stability of a highway tunnel in China

This paper examines the complementary roles and interconnections among the first-order reliability method (FORM) for single failure modes, the system FORM for correlated multiple failure modes, the second-order reliability method (SORM) for curved limit state surfaces, and the response surface methods as a link between reliability methods and stand-alone numerical packages. Geotechnical examples of reliability-based design and analysis will be provided to illustrate the principles, merits and limitations of each, and to explain the connections and evolutionary relationships among FORM, system-FORM and SORM. Comparisons will be made with other probabilistic methods in recent geotechnical literature. Apart from elucidating efficient and practical procedures for reliability-based design and analysis with the hope of engaging more practitioners to consider the probabilistic approach, the paper also aims to provide some discussions and a more balanced perspective of other probabilistic approaches (different from FORM, system-FORM, SORM, RSM) published by various researchers in recent geotechnical papers.

Since the performance functions of large complex structures can not be expressed explicitly in the process of reliability analysis, support vector machines (SVM) with good ability of generalization are used as the response surface function based on the small training samples. The uniform design method was adopted in selecting the training data. The least support vector machines (LS-SVM) were used to find the support vectors. The limit state function was expressed by the LS-SVM regression. Reliability analysis was then performed by the usual reliability method (e.g., the first-order reliability method, the second-order reliability method or Monte Carlo) on the response surface. The results of calculations of numerical examples and a typical cable-stayed bridge show that LS-SVM using the uniform design method can well approximate the real response of complex structures which has a good efficiency and accuracy and can be applied in complex structures.

Data-driven reduced order model and simplicial homology global optimization for reliability analysis and application

Protecting steel pipeline systems from failure due to corrosions defects is a crucial issue in pipeline industry. Reliability models that use the rate of corrosion growth combined with closed form solutions for the failure pressure are often used to estimate the time periods before excavation and repair. A methodology is presented for the assessment of predicted failure pressure based on finite element analysis (FEA) and reliability analysis. Deterministic failure equations are transformed to probabilistic limit state models. The failure mode is considered to be controlled by the stresses due to internal pressure and the presence of corrosion. A response surface method (RSM) is utilized to build a surrogate model of the limit state function. A comparison between closed-form and the surrogate model approach is discussed. A stochastic model is assumed to match the uncertainty inherent in both loads and strength. Simulation-based approaches and asymptotic methods for probability of failure evaluation are used, namely, Monte Carlo simulation, importance sampling, First Order Reliability Method (FORM) and Second Order Reliability Method (SORM). An adaptive building of the numerical experimental design for the surrogate limit state is proposed. A new artificial neural network (ANN) is developed in order to reduce the computational cost of experimental design scheme’s evaluation. The outcomes obtained from such an approach are useful as a decision-making tool for the maintenance, repair or optimization of pipelines systems.

SUMMARYA practical and efficient approach of implementing second‐order reliability method (SORM) is presented and illustrated for cases related to foundation engineering involving explicit and implicit limit state functions. The proposed SORM procedure is based on an approximating paraboloid fitted to the limit state surface in the neighborhood of the design point and can be easily carried out in a spreadsheet. Complex mathematical operations are relegated to relatively simple user‐created functions. The failure probability is calculated automatically based on the reliability index and principal curvatures of the limit state surface using established closed‐form SORM formulas. Four common foundation engineering examples are analyzed using the proposed method and discussed: immediate settlement of a flexible rectangular foundation, bearing capacity of a shallow footing, axial capacity of a vertical single pile, and deflection of a pile under lateral load. Comparisons with Monte Carlo simulations are made. In the case of the laterally loaded pile, the friction angle of the soil is represented as a one‐dimensional random field, and pile deflections are computed based on finite element analysis on a stand‐alone computer package. The implicit limit state function is approximated via the response surface method using two quadratic models. Copyright © 2011 John Wiley & Sons, Ltd.

This paper presents the state of the art in Structural Reliability Analysis (SRA) methods with a view of identifying key applications of each method and its proposed variations, qualifying characteristics, advantages, and limitations. Due to the increasing complexity and scale of modern offshore jacket structures, it becomes increasingly necessary to propose an accurate and efficient approach for the assessment of uncertainties in their material properties, geometric dimensions, and operating environments. SRA, as a form of uncertainty analysis, has been demonstrated to be a useful tool in the design of structures because it can directly quantify how uncertainty about input parameters can affect structural performance. Herein, attention was focused specifically on the probabilistic fracture mechanics approach because this accounts accurately for fatigue reliability mostly encountered as being dominant in the design of such structures. The well-established analytical/approximate methods such as the First- and Second-Order Reliability Methods (FORM/SORM) are widely used as they offer a good balance between accuracy and efficiency for realistic problems. They are, however, inaccurate in cases of highly non-linear systems. As a result, they have been modified using methods such as conjugate search direction approach, saddle point approximation, subset simulation, evidence theory, etc. in order to improve accuracy. Initially, direct simulations methods such as the Monte Carlo Simulation Method (MCS) with its various variance reduction techniques such as the Importance Sampling (IS), Latin Hypercube Sampling (LHS), etc. are ideal for structures having non-linear limit states but perform poorly for problems that calculate very low probabilities of failure. Overall, each method has its own merits and limitation, with FORM/SORM being the most commonly used, but recently, simulation methods have increasingly been used due to continuous advances in computation powers. Other relevant methods include the Response Surface Methods (RSM) and the Surrogate Models/Meta-models (SM/MM), which are advanced approximation methods and are ideal for structures with implicit limit state functions and high-reliability indices. Combinations of advanced approximation methods and reliability analysis methods are also found in literature as they can be suitable for complex, highly non-linear problems.

In the present study, the experimental and finite element (FE) analyses are first carried out to investigate the deboning behavior of metal‐composite adhesive joints under modes of I and mode II loading. To conduct an FE on the debonding propagation, cohesive zone method (CZM), as well as maximum nominal stress and energy criteria, is applied. In the reliability analysis, to achieve the probability of debonding growth (PODG), limit state functions are formulated based on the energy release rate. To that end, the first‐order reliability method (FORM), the second‐order reliability method (SORM), and the Monte Carlo simulation (MCS) are used to calculate the PODG. The effect of initial debonding length on the PODG in all mentioned modes is investigated. Results obtained from reliability analysis reveal that the random variables including the initial debonding length, width, and thickness are the most sensitive variables to ascertain the PODG.

The response surface method (RSM) developed in recent years is an effective way to solve the structural reliability problems with implicit performance function. In order to improve the computational efficiency and make RSM suitable well to large and complex engineering structures, the reliability analysis method based on uniform design method (UDM) and support vector machine (SVM) was proposed. UDM is adopted to select training data and SVM is used as response surface. Structural reliability index is calculated in combination with the traditional reliability analysis methods (such as, the first-order reliability method (FORM), the second-order reliability method (SORM) or Monte Carlo simulation method (MCSM)). Numerical examples show that sampled with the UDM can greatly reduce the number of samples required for training by SVM model, and a very good approximation of the limit state surface can be obtained to get the failure probability. The reliability analysis of the under serviceability limit-state of a typical self-anchored suspension bridge——Sanchaji Bridge was carried out with the improved response surface method.