Reliability Assessment on Pile Foundation Bearing Capacity Based on the First Four Moments in High-Order Moment Method

In this paper, the high-order moment method (HOMM) was developed for estimating pile foundation bearing capacity reliability assessment. Firstly, after the performance function was established, the first four moments (viz. mean, variance, skewness, and kurtosis) were suggested to be determined by a point estimate method based on two-dimensional reduction integrations. Then, the probability distribution of the performance function for the pile foundation bearing capacity was then approximated by a four-parameter cubic normal distribution, in which its distribution parameters are the first four moments. Meanwhile, the quantile of the probability distribution for the performance function and its reliability index was capable to be obtained through this distribution. In order to examine the efficiency of this method in engineering application, four pile foundations with different length-diameter radios were investigated in detail. The results demonstrate that the reliability analysis based on HOMM is greatly improved to the computational efficiency without loss precision compared with Monte Carlo simulation (MCS) and does not require complex partial derivative solving, checking point sought, and large numbers of iteration comparing with first-order reliability method (FORM). Moreover, the probability distribution function (PDF) approximated by the four-parameter cubic normal distribution was found to be consistent with that obtained by MCS. Eventually, the effects of parameter sensitivity for relative soil layer of the certain pile on reliability index were illustrated using the above-mentioned method. It indicated that the HOMM is an effective and simple approach for reliability assessment of the pile foundation bearing capacity.

Research on Bridge Structure Reliability Evaluation due to Vessels Collison Based on a Statistical Moment Method

Damage to bridge structures caused by vessel collision is a risk for bridges crossing water traffic routes. Therefore, safety around vessel collision of existing and planned bridges is one of the key technical problems that must be solved by engineering technicians and bridge managers. In the evaluation of the reliability of the bridge structure, the two aspects of vessel-bridge collision force and structural resistance need to be considered. As there are many influencing parameters, the performance function is difficult to express by explicit function. This paper combines the moment method theory of structural reliability with finite element analysis and proposes a statistical moment method based on finite element analysis for the calculation of vessel-bridge collision reliability, which solves the structural reliability problem with a nonlinear implicit performance function. According to the probability model based on current velocity, vessel velocity, and vessel collision tonnage, the estimate points in the standard normal space are converted into estimate points in the original state space through the Rosenblatt reverse transform. According to the estimate points in the original state space and the simplified dynamic load model of vessel-bridge collision, the sample time-history curve of random vessel-bridge collision force is generated, the dynamic response of the bridge structure and the structural resistance of the bridge are calculated by establishing a finite element model, and the failure probability and reliability index of the bridge structure is calculated according to the fourth-moment method. The statistical moment based on the finite element analysis is based on the finite element analysis and the moment method theory of structural reliability. The statistical moment of the limited performance function is calculated through a quite small amount of confirmatory finite element analysis, and the structural reliability index and failure probability are obtained. The method can be widely used in existing finite element analysis programs, greatly reducing the number of finite element analyses needed and improving the efficiency of structural reliability analysis.

Evaluation of flood risk as a step in determining the “Acceptable Risk” criteria. Case study: Dengkeng River, Klaten, Central Java

The planning of a flood control system in Indonesia is based on the planning criteria issued by the Ministry of Public Works. Flood control planning is based on flood discharge with a specific return period depending on the order of the river and the number of protected populations. Flood events in areas where the flood control system has been planned continue to occur almost every year, meaning that the probability of being exceeded is not as planned. This study is intended to evaluate the criteria for the magnitude of the designed flood discharge in flood control planning that considers the acceptable risk. Potential risks are evaluated against system reliability. The probability of failure of the flood control system occurs if the resistance is smaller than the load expressed as a performance function. By knowing the performance function associated with the level of flood risk, then the flood discharge can be selected with the appropriate return period according to the acceptable risk.

Structural Reliability Analysis via the Multivariate Gegenbauer Polynomial-Based Sparse Surrogate Model

Structural reliability analysis is usually realized based on a multivariate performance function that depicts failure mechanisms of a structural system. The intensively computational cost of the brutal-force Monte-Carlo simulation motivates proposing a Gegenbauer polynomial-based surrogate model for effective structural reliability analysis in this paper. By utilizing the orthogonal matching pursuit algorithm to detect significant explanatory variables at first, a small number of samples are used to determine a reliable approximation result of the structural performance function. Several numerical examples in the literature are presented to demonstrate potential applications of the Gegenbauer polynomial-based sparse surrogate model. Accurate results have justified the effectiveness of the proposed approach in dealing with various structural reliability problems.

Fuzzy reliability analysis based on support vector machine

For a structure with implicit performance function structure and less sample data, it is difficult to obtain accurate probability distribution parameters by traditional statistical analysis methods. To address the issue, the probability distribution parameters of samples are often regarded as fuzzy numbers. In this paper, a novel fuzzy reliability analysis method based on support vector machine is proposed. Firstly, the fuzzy variable is converted into an equivalent random variable, and the equivalent mean and equivalent standard deviation are calculated. Secondly, the support vector regression machine with excellent small sample learning ability is used to train the sample data. Subsequently, and the performance function is approximated. Finally, the Monte Carlo method is used to obtain fuzzy reliability. Numerical examples are investigated to demonstrate the effectiveness of the proposed method, which provides a feasible way for fuzzy reliability analysis problems of small sample data.

Evidence-Theory-Based Reliability Analysis Through Kriging Surrogate Model

It is generally understood that intractable computational intensity stemming from repeatedly calling performance function when evaluating the contribution of joint focal elements hinders the application of evidence theory in practical engineering. In order to promote the practicability of evidence theory for the reliability evaluation of engineering structures, an efficient reliability analysis method based on the active learning Kriging model is proposed in this study. To start with, a basic variable is selected according to basic probability assignment (BPA) of evidence variables to divide the evidence space into sub-evidence spaces. Intersection points between the performance function and the sub-evidence spaces are then determined by solving the univariate root-finding problem. Sample points are randomly identified to enhance the accuracy of the subsequently established surrogate model. Initial Kriging model with high approximation accuracy is subsequently established through these intersection points and additional sample points generated by Latin hypercube sampling. An active learning function is employed to sequentially refine the Kriging model with minimal sample points. As a result, belief (Bel) measure and plausibility (Pl) measure are derived efficiently via the surrogate model in the evidence-theory-based reliability analysis. The currently proposed analysis method is exemplified with three numerical examples to demonstrate the efficiency and is applied to reliability analysis of positioning accuracy for an industrial robot.

Reliability Analysis of Loess Cave Dwellings Based on Fuzzy Failure Criterion

The reliability of loess cave dwellings based on fuzzy failure criterion is researched to analyze the influence of fuzzy set, membership function, and different combinations of random variables. Due to the strength reduction method, the basic failure criterion is established, the fuzzy property of failure criterion is characterized by fuzzy set and membership function, and the performance function of loess cave dwellings is expressed by a quadratic polynomial without cross terms. Reliability is analyzed with different random variable combinations. The reliability research of loess cave dwellings in Shan Plateau, Henan province, China, shows that the loess property in this area is suitable for loess cave dwelling construction and the reliability index of loess cave dwellings is high, which will be decreased when considering the fuzzy failure criterion and will be increasing sharply when the small cave leg width is improved to average value.

Optimizing Disruption Tolerance for Rail Transit Networks Under Uncertainty

In this paper, we develop a distributionally robust optimization model for the design of rail transit tactical planning strategies and disruption tolerance enhancement under downtime uncertainty. First, a novel performance function evaluating the rail transit disruption tolerance is proposed. Specifically, the performance function maximizes the worst-case expected downtime that can be tolerated by rail transit networks over a family of probability distributions of random disruption events given a threshold commuter outflow. This tolerance function is then applied to an optimization problem for the planning design of platform downtime protection and bus-bridging services given budget constraints. In particular, our implementation of platform downtime protection strategy relaxes standard assumptions of robust protection made in network fortification and interdiction literature. The resulting optimization problem can be regarded as a special variation of a two-stage distributionally robust optimization model. In order to achieve computational tractability, optimality conditions of the model are identified. This allows us to obtain a linear mixed-integer reformulation that can be solved efficiently by solvers like CPLEX. Finally, we show some insightful results based on the core part of Singapore Mass Rapid Transit Network.

PENILAIAN RISIKO KEGAGALAN BENDUNGAN KEDUNGOMBO SEBAGAI DASAR PRIORITAS PEMELIHARAAN BENDUNGAN

A dams must always be maintained for their performance, function, and safety, so it is necessary to carry out various maintenance, repairs, and rehabilitation on dams that have been built and operating. Priority systems for the implementation of repair and rehabilitation of dams can be arranged based on the status of safety hazards or the level of risk of failure due to natural disasters or other consequences. Based on this, it is necessary to carry out an assessment of the dam to estimate the magnitude of the risk to the dam. According to the Risk Analysis Guidelines, the estimation of the probability of failure can be done using two methods, namely the traditional method and the event tree method. Based on the results of assessment analysis, the risk probability of the Kedungombo Dam with the traditional method and the event tree method is 4,010 x 10-1 and 1,548 x 10-3 where the acceptable limit conditions for the existing dam are a maximum of 1,000 x 10-5. The risk probability value of the Kedungombo Dam does not meet the requirements of an acceptable risk value. Therefore, it is necessary to recommend risk reduction for the risk assessment results. ABSTRAKBendungan harus selalu dijaga kinerja operasi, fungsi, dan keamanannya, sehingga perlu dilakukan berbagai kegiatan pemeliharaan, perbaikan, dan rehabilitasi pada bendungan yang sudah terbangun dan beroperasi. Sistem prioritas pada pelaksanaan kegiatan perbaikan dan rehabilitasi pada bendungan dapat disusun berdasarkan status bahaya bendungan dari segi keamanan atau besarnya risiko terhadap kegagalan bendungan akibat bencana alam maupun akibat lain. Berdasarkan hal tersebut, maka perlu dilakukan penilaian risiko pada bendungan untuk memperkirakan besarnya risiko bahaya pada bendungan. Berdasarkan Pedoman Analisis Risiko, perkiraan probabilitas kegagalan dapat dilakukan dengan dua metode yaitu metode tradisional dan metode pohon kejadian (event tree). Berdasarkan hasil analisis penilaian risiko, probabilitas risiko Bendungan Kedungombo metode tradisional dan metode pohon kejadian sebesar 4,010 x 10-1 dan 1,548 x 10-3 dimana syarat batas yang dapat diterima untuk bendungan eksisting maksimum 1,000 x 10-5. Nilai probabilitas risiko Bendungan Kedungombo tidak memenihi syarat nilai risiko yang dapat diterima. Dengan demikian, diperlukan rekomendasi tindakan pengurangan risiko untuk risiko hasil penilaian tersebut.