ReliabIlity analysis of containment building subjected to earthquake load using response surface method

Prestressed Concrete Containment Building for the Gentilly Nuclear Power Station

원전 구조물 및 주요기기의 지진 안전성 평가에서는 내진성능을 정량화하는 방법으로 취약도 분석이 사용되고 있다. 지진취약도 분석은 격납건물의 설계 시 반영된 보수성을 배제한 실질적인 내진성능을 평가하는 것으로 이러한 보수성을 성능 및 응답에 관련된 확률론적 변수로 고려하여 평가하게 된다. 본 연구에서는 비선형 지진 해석으로부터 얻은 구조물의 변위응답을 기초로 한 지진취약도 분석 방법을 제시하였다. 또한 원전부지에서 선정된 발생가능한 근거리지진, 원거리지진, 설계지진 및 확률론적 시나리오지진을 시나리오지진으로 선정하고 이들 지진동에 대한 비선형 지진해석을 통하여 한국 표준형 원전 격납건물의 지진취약도를 평가하였다. The seismic fragility analysis method has been used as a quantitative seismic safety evaluation method for the NPP(Nuclear Power Plant) structures and equipments. The seismic fragility analysis gives a realistic seismic capacity excluding the convertism included in the design stage. The conservatism is considered as the probabilistic parameters related to the response and capacity in the seismic fragility analysis. In this study, the displacement based seismic fragility analysis method was proposed based on the nonlinear dynamic analysis results. In this study, the seismic safety of the prestressed concrete containment building of KSNP(Korean Standard Nuclear Power Plant) was evaluated for the scenario earthquakes, neat-fault, far-fault, design earthquake and probability based scenario earthquake, which can be occurred in the NPP sites.

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.

This paper focuses on a reliability analysis of an offshore wind turbine support structure which is part of an assessment and monitoring framework for wind turbines in operation. The reliability analysis builds upon structural, loading, limit state and uncertainty models comprising design, production and erection data. This model basis facilitates the reliability analysis of the ultimate, the fatigue and the serviceability limit states utilizing stochastic finite elements. The complexity of the individual models dictates an efficient solution scheme for the reliability analysis. Such an algorithm is developed in the present paper consisting of an adaptive response surface algorithm and an importance sampling Monte-Carlo algorithm. The response surface algorithm is based on predetermined experimental designs and facilitates the adjustment of design parameters for an optimized prediction variance in the design point region. Approaches for the consideration of multiple design points and the augmentation of the design for reduction of the prediction variance are introduced. In this paper, a reliability analysis for a tripod support structure of a Multibrid M5000 wind turbine is performed. A comparison with the target reliabilities specified in DIN EN 1990 (2002) shows that the requirements are fully met. However, the consideration of system reliability leads to the conclusion that at the end of the service life there is a significant probability of fatigue damages. The quantification of the reliability for the individual structural components for all limit states facilitates an identification of sensitive components. The results of this study can support the targeted application of monitoring systems, the optimization of the support structures and additionally highlight the need for criteria to the systems reliability.

Seismic Fragility of a Typical Containment under Bidirectional Earthquake Excitations

As engineering applications become increasingly complex, they are often characterized by implicit response functions that are both expensive to evaluate and nonlinear in their behavior. Reliability assessment given this type of response is dicult with available methods. Current reliability methods focus on the discovery of a single most probable point of failure, and then build a low-order approximation to the limit state at this point. This creates inaccuracies when applied to engineering applications for which the limit state has a higher degree of nonlinearity or is multimodal. Sampling methods, on the other hand, do not rely on an approximation to the shape of the limit state and are therefore generally more accurate when applied to problems with nonlinear limit states. However, sampling methods typically require a large number of response function evaluations, which can make their application infeasible for computationally expensive problems. This paper describes the application of ecient global optimization to reliability assessment to provide a method that eciently characterizes the limit state throughout the uncertain space. The method begins with a Gaussian process model built from a very small number of samples, and then intelligently chooses where to generate subsequent samples to ensure the model is accurate in the vicinity of the limit state. The resulting Gaussian process model is then sampled using multimodal adaptive importance sampling to calculate the probability of exceeding (or failing to exceed) the response level of interest. By locating multiple points on or near the limit state, more complex limit states can be modeled, leading to more accurate probability integration. By concentrating the samples in the area where accuracy is important (i.e. in the vicinity of the limit state), only a small number of true function evaluations are required to build a quality surrogate model. The resulting method is both accurate for any arbitrarily shaped limit state and computationally ecient even for expensive response functions. This new method is applied to a collection of example problems that currently available methods have diculty

In this study, the probabilistic internal pressure fragility analysis was performed by using the non-linear finite element analysis method. The target structure is one of the containment buildings of typical domestic pressurized water reactors(PWRs). The 3-dimensional finite element model of the containment building was developed with considering the large equipment hatches. To consider uncertainties in the material properties and structural capacities, we performed the sensitivity analysis of the ultimate pressure capacity with respect to the variation of four important uncertain parameters. The results of the sensitivity analysis were used to the selection of the probabilistic variables and the determination of their probabilistic parameters. To reflect the present condition of the tendon pre-stressing force, the data of the pre-stressing force acquired from the in-service inspections of tendon forces were used for the determination of the median value. Two failure modes(leak, rupture) were considered and their limit states were defined to assess the internal pressure fragility of target containment building. The internal pressure fragilities for each failure mode were evaluated in terms of median internal pressure capacity, high confidence low probability of failure(HCLPF) capacity, and fragility curves with respect to the confidence levels. The HCLPF capacity was 115.9 psig for leak failure mode, and 125.0 psig for rupture failure mode.

Deterministic and reliability analysis of prestressed concrete bridge girders: comparison of the Chinese, Hong Kong and AASHTO LRFD Codes

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

This paper summarizes the results of a research program conducted during 1980–1985 to develop probability‐based analysis and design procedures for structures in nuclear plants. Limit states of concrete containments and shear walls are formulated. Probabilistic models for static and dynamic loads and structural resistance variables are established. Reliability analysis methods are established for estimating limit state probabilities for nuclear plant structures subjected to combinations of static and dynamic loads. Practical probability‐based design criteria are developed for concrete containments and shear walls in a load and resistance factor design format. The load and resistance factors are illustrated for several limit states and target limit state probabilities.

In order to analyze the reliability and failure probability of the repaired shaft engineering, this article makes fail-safe analysis and instability risk prediction of the shaft engineering. A reliability analysis method was applied combining the improved response surface method which has improved sample points’ selection based on the traditional response surface method to decreasing the number of the structural analysis under the premise of the accuracy of the calculated results with numerical simulation. The limit state whose failure criteria was safe factor was constructed to analyze the reliability of the repaired shaft engineering, the reliability index of the repaired shaft engineering was computed by JC method. The results show the reliability index value of the repaired shaft engineering is 3.1127 slight fewer than design objective value and it’s failure probability value is 0.0929%, which show that the repaired shaft is stable and it’s deformation should be monitored to ensure it is safety application because of it is reliability index value slight fewer than design objective value.

Recent research has focused on assessing the effectiveness of response surface methodology (RSM), a non-machine learning technique, and artificial neural networks (ANN), a machine learning approach, for predicting concrete performance. This research aims to predict and simulate the compressive strength of concrete that replaces cement and fine aggregate with waste materials such as eggshell powder (ESP) and waste glass powder (WGP) for sustainable construction materials. In order to ensure concrete’s durability and structural integrity, a compressive strength evaluation is essential. Precise predictions maximize efficiency and advance sustainability, particularly when dealing with waste materials like ESP and WGP. The response surface methodology (RSM) and artificial neural network (ANN) techniques are used to accomplish this for practical applications in the built environment. A dataset comprising previously published research was used to assess ANN and RSM’s predictive and generalization abilities. To model and improve the model, ANN used seven independent variables, while three variables, cement, waste glass powder, and eggshell powder, improved the RSM. Both the ANN and RSM techniques are effective instruments for predicting compressive strength, according to the statistical results, which include mean squared error (MSE), determination coefficient (R2), and adjusted coefficient (R2 adj). RSM was able to achieve the R2 by 0.8729 and 0.7532 for compressive strength, while the accuracy of the results for ANN was 0.907 and 0.956 for compressive strength. Moreover, the correlation between ANN and RSM models and experimental data is high. The artificial neural network model, however, exhibits superior accuracy.

Automobile plays an indispensable role in people's daily life, and the frame, as the main bearing part of the automobile, always affects the performance of the automobile and people's driving safety. The reliability of the truck frame is an important part of the inspection of the automotive quality. Because the frame of light truck is a complex structure, the general reliability analysis methods such as first-order second-moment method and second-order second-moment method cannot accurately solve the reliability index of complex systems, while Monte Carlo simulation has a large amount of computation and low efficiency. Therefore, this paper proposes a technique for the reliability of the truck frame combining response surface methodology and advanced first-order second-moment method. In this method, the response surface methodology is employed to obtain the performance function of the truck frame and advanced first-order second-moment method is used to obtain the reliability of the truck frame. The reliability analysis results of the light truck frame show the feasibility and effectiveness of the proposed method.

To improve the efficiency and accuracy of traditional least squares method–based polynomial response surface method (RSM) for reliability analysis of structure, the application of various adaptive metamodeling approaches is notable. The moving least squares method (MLSM)–based RSM is the simplest one and found to be effective in this regard. But, its performance in reliability analysis of structure largely depends on the proper choice of the parameter of weight function involved. In the present study, a generalized scheme to appropriately obtain the hyper-parameter of the MLSM-based RSM to approximate implicit responses of structure for reliability analysis is proposed. The algorithm is hinged on the fact that for reliability analysis, one is interested in the sign of the approximated limit state function (LSF) rather than its magnitude. Thereby, it is sufficient to obtain the hyper-parameter for which the first derivative of the probability of failure as obtained from the approximated LSF with respect to the hyper-parameter is zero. The effectiveness of the proposed algorithm is elucidated through three numerical examples. The improvement achieved by the proposed MLSM-based RSM has been compared with the reliability results obtained by the MLSM-based RSM considering the commonly recommended value of the hyper-parameter and also by the approach where the parameters are obtained by leave one out cross-validation procedure.

The Support Vector Machine (SVM) response surface method (RSM) is proposed on fast Markov chain simulation for the problem with implicit limit state function usually encountered in engineering reliability analysis and design. In the proposed method, Markov chain is used to generate the samples in the important region of the limit state function, and the SVM is employed to construct the response surface by use of these samples. Since Markov chain can adaptively simulate the samples in the important region, and the candidate state but not Markov state is used as the training samples for SVM, the proposed method can well approximate the limit state equation in the zone surrounding the design point, and can make full use of information provided by Markov chain simulation. In addition, the iterative strategy is adopted to improve the convergence speed of the failure probability. Moreover, the proposed method uses the SVM regression method to construct the response surface, which can automatically apply the Structural Risk Minimization (SRM) inductive principle in approximating the limit state equation, thus it can approximate the failure probability with high accuracy. Finally applications in a numerical example and an engineering example indicate that the proposed method owns good performance in calculating efficiency and accuracy.