Advanced First-order Second-moment Method Research Articles

Modeling probabilistic-based 1D riverbed elevation estimation model due to uncertainties in runoff and sediment-related factors

Abstract This study aims to develop a probabilistic model to quantify the reliability of estimating riverbed elevations due to the uncertainties in the runoff and sediment-related factors (named PM_MBEE_1D); the above uncertainties are quantified by reproducing a considerable number of runoff-related and sediment-related factors via the multivariate Monte Carlo simulation approach. Using a sizeable number of simulated uncertainty factors, the proposed PM_MBEE_1D model is developed by coupling the rainfall–runoff model (SAC-SMA) and 1D sediment transport simulation model (CCHE1D) with the uncertainty/risk analysis advanced first-order second-moment (AFOSM) method as well as the logistic regression analysis. Validated by the historical data in the Jhuosdhuei River watershed, the proposed PM_MBEE_1D model could efficiently and successfully capture the spatial and temporal changes in the estimated riverbed elevations (i.e., scouring and siltation) due to the uncertainties in the river runoff and sediment with a high accuracy (nearly 0.983). Also, using the proposed PM_MBEE_1D model with given runoff and sediment factors under a desired reliability, the probabilistic-based riverbed elevations could accordingly be estimated as a reference to watershed treatment and management plan.

Probabilistic Slope Stability Evaluation Using Hybrid Metaheuristic Approach

This paper develops an efficient evolutionary hybrid optimization technique based on the adaptive salp swarm algorithm (ASSA) and pattern search (PS) for the reliability evaluation of earth slopes considering spatial variability of soils under the framework of the limit equilibrium method. In the ASSA, to improve the salp swarm approach's exploration ability while also avoiding premature convergence, two new equations for the leaders' and followers' position updating procedure are introduced. The proposed hybrid algorithm (ASSPS) benefits from the effective global search ability of the adaptive salp swarm algorithm as well as the powerful local search capability of the pattern search method. The suggested ASSPS algorithm's efficiency is confirmed using mathematical test functions, and its findings are compared with the standard salp swarm algorithm as well as some efficient optimization techniques. Then, the ASSPS is applied for calculation of the lowest safety factor and reliability index of earth slopes. The safety factor is formulated using the Morgenstern and Price approach and the advanced first-order second-moment (AFOSM) method is implemented for the reliability calculation model. The ASSPS's efficacy for the evaluation of the minimum reliability index of slopes is investigated by considering two literature-based case studies. The numerical experiments demonstrate that the new algorithm could generate better optimal solutions and significantly outperform other methods in the literature.

Contact stress reliability analysis based on first order second moment for variable hyperbolic circular arc gear

Aiming at the contact strength reliability of variable hyperbolic circular arc gear, a reliability analysis method for contact strength of variable hyperbolic circular arc gear based on Kriging model and advanced first-order and second-moment algorithm is proposed. Kriging model was used to establish the limit state equation of the contact stress reliability analysis of variable hyperbolic circular arc gear, and the advanced first-order second-moment method was used to analyze the contact stress reliability of variable hyperbolic circular arc gear based on the limit state equation of the contact stress. In order to verify the effectiveness of the proposed algorithm, a Markov Chain Monte Carlo reliability analysis method based on Important Sampling was proposed. Markov Chain and Important Sampling were exploited to improve the accuracy of contact reliability analysis based on Monte Carlo method for variable hyperbolic circular arc gear. The comparison between the analysis results of Markov Chain Monte Carlo with Important Sampling method and first order second moment shows that it is feasible to analyze the reliability of variable hyperbolic circular arc gear by first-order second-moment method.

Research on slope reliability analysis using multi-kernel relevance vector machine and advanced first-order second-moment method

To increase the efficiency and accuracy in slope stability analysis, a reliability analysis method based on machine learning and the advanced first-order second-moment (AFOSM) method was proposed, and the partial derivative of the machine-learning algorithm was derived. First, a multi-kernel was introduced to establish the multi-kernel relevance vector machine (MKRVM). Then, the kernel parameters of the MKRVM were optimized by the harmony search (HS) method to use the high-precision MKRVM method instead of the traditional methods for determining the factor of safety. It was necessary to obtain the partial derivative of the performance function, which was explicitly expressed by the trained MKRVM in this paper. Finally, the AFOSM was adopted to calculate the reliability index of the slope, as the AFOSM was more reliable because the design point was located at the failure surface. With two samples, from a single-layer slope and a multilayer slope, the calculation results show that the MKRVM–AFOSM is easy to use, highly computationally efficient, and reliable.

A Parametric Model of Umbilical Cable with Siemens NX considering its Reliability

Abstract Umbilical cable is one of the key control equipment, for example, in the subsea oil and gas production system. That can be seen as a customized product related to specific parameters of use cases, e.g. installation site. In this paper, we first apply the calculation method for the reliability of the umbilical cable by advanced first-order second-moment method (AFOSM) and Monte Carlo method. Secondly, we demonstrate the use of Siemens NX and its framework for engineering knowledge representation called Knowledge Fusion (KF) to generate the parametric model of the umbilical cable design considering its reliability. Finally, we reveal the advantages of introducing a Knowledge-based Engineering (KBE) approach to integrate the CAD models extended with automated calculations for product reliability.

Dynamic characteristics and reliability analysis of ball screw feed system on a lathe

For ball screw feed system on a lathe, the randomness of geometric parameters deriving from the inevitable manufacturing and assembly errors significantly affected the system dynamic characteristics and turning accuracy. In this study, a novel lumped dynamic model accounting for the analytical piecewise restoring force function involving the overall axial deformation is proposed. The equivalent mechanical model of bearing joints including the change of nominal contact angle is made a reasonable simplification to facilitate acquisition of the system analytical equation of motion. Additionally, the approximate analytical solution of the proposed equation is obtained by the modified Lindstedt–Poincaré method (MLP). The advanced first order second moment method (AFOSM) is employed to evaluate the reliability of dynamic response error. Furthermore, the numerical simulation aims to demonstrate the capabilities of the MLP and AFOSM method in the practical applications. Eventually, the effects of external excitation, sliding platform position, and nominal contact angles on the dynamic response are discussed and the reliability and sensitivity analysis in accordance with actual turning accuracy level is presented.

A decoupled credibility-based design optimization method for fuzzy design variables by failure credibility surrogate modeling

In order to make a good compromise of cost and safety with small data in the early structural design stage, a practical decoupled credibility-based design optimization method is developed in the presence of fuzzy uncertainty. In the proposed approach, failure credibility is constructed as optimization constraints estimated by fuzzy advanced first-order second-moment method. By approximating the fuzzy credibility constraint by the adaptive Kriging surrogate model, a fuzzy credibility-based design is decoupled to a common deterministic optimization so that various existing optimization algorithms can be easily applied. Compared to the traditional double-loop approach, the newly proposed method is more efficient and strongly practical for complicated engineering problems. Design results of three structural engineering examples also show advantages in accuracy and computation speed of the proposed method over the traditional double-loop approach.

An Improved CPTu-based Method to Estimate Jacked Pile Bearing Capacity and Its Reliability Assessment

This paper presents an improved method for predicting the bearing capacity of single jacked pile based on piezocone penetration test (CPTu) data which contain tip resistance (qt), side friction (fs) and excess dynamic pore water pressure (u2). Firstly, the average value of qt was determined to calculate the pile unit base resistance according to the influence zone of the logarithmic spiral concerning the effect of soil types. Secondly, fs and u2 were used to calculate the pile unit shaft resistance considering the effect of friction fatigue. The pile jacking force was obtained in terms of unit base resistance and unit shaft resistance. The ultimate bearing capacity was finally determined using pile jacking force multiplied by a force ratio denoted as Rf. The ultimate bearing capacities calculated for two case projects show a good agreement with the measured results, which indicates that the proposed method is feasible and effective. Reliability assessment was carried out on the proposed method and other five estimation methods with respect to the reliability index obtained by advanced first-order second-moment (AFOSM) method. Comparison result showed that the method proposed in this study has a higher reliability index over other five existing methods. Therefore, the proposed method can be used as a reliable alternative to predict the bearing capacity in the engineering practice of jacked pile foundation.

Reliability-based design of truck escape ramps

The design method of truck escape ramps (TERs) presented by the Transportation Association of Canada and other organizations is deterministic and assumes fixed values of the design speed, rolling resistance, and ramp grade. This paper presents a reliability-based method for TER design based on the first-order second-moment (FOSM) method and the advanced FOSM (AFOSM) method. These methods rely on the distribution of the component random variables. Each method was used to analyze a TER with one grade and two grades. The FOSM is simple and can be easily used by practitioners, even with calculators. The AFOSM is more complicated but more accurate as it considers the design points in determining the probability of failure. The AFOSM method was used to establish design graphs for the required length of TERs. Application of the proposed method is illustrated using actual TERs in the United States and considering a hypothetical design scenario.

Probability analysis of submarine landslides based on the Response Surface Method: A case study from the South China Sea

As deep-sea engineering develops, it becomes essential to analyze the stability of submarine slopes when considering the stability of submarine foundations or evaluating the safety of offshore structures. However, the traditional method for analyzing slope stability does not give adequate consideration to the uncertainty of soil properties, and so the reliability method has been proposed and used to settle the variation of soil parameters. Regarding the northern slope of the South China Sea, the present paper summarizes its geomorphic features, seismic characteristics, and the soil strength at certain boreholes. A typical slope section is chosen with which to conduct probability analysis using the polynomial-based Response Surface Method (RSM) and the Advanced First Order Second Moment method(AFOSM). A novel form of the RSM based on Gaussian Process Regression (GPR) is also proposed and applied in this case to approximate the limit state function, and its efficiency is confirmed. The simulation results of Latin-hypercube analysis are set as the benchmark for the other methods. The influences of slope gradient and seismic action on the stability of submarine slopes are also investigated.

사용중 PSC-I 거더 철도 교량의 휨모멘트에 대한 신뢰도 분석

철도교량의 신뢰도 기반 한계상태설계법 도입 시 목표신뢰도지수 산정을 위하여 기존 철도교량의 신뢰도지수 산정이 선행되어야 한다. 대표적인 복선 철도교량 중 하나인 6주형 PSC-I형 거더교량에 대해 신뢰도지수를 산정하였다. 최외측 거더의 휨모멘트에 대한 신뢰도 해석을 수행하였다. 휨저항강도 및 고정하중효과는 도로교 한계상태설계법 도입 시 적용된 선행연구자들의 평균과 변동계수를 활용하였고, 열차의 활하중 효과는 여객/화물 혼용선 중 중량화차 통행이 빈번한 중앙선에서 현장계측 데이터를 활용하였다. 한계상태방정식에 대하여 개선된 일계이차 모멘트법(AFOSM)으로 신뢰도 분석을 수행하였으며, 하중효과와 저항효과의 각 요소가 신뢰도지수에 미치는 민감도를 분석하여 중요도를 검토하였다. It is necessary to determine reliability indexes of existing railway bridges prior to setting up a proper target reliability index that can be used to introduce a reliability based limit state design method to design practice. Reliability is evaluated for a six PSC-I girder railway bridge, which is one of many representative types of double-track railway bridges. The reliability assessment is carried out for an edge girder subjected to bending moment. In the assessment, the flexural resistance and the fixed-load effect were obtained using existing statistical values from previous research on the introduction of limit state design to road bridge design. On the other hand, the live-load effect was determined using statistical values obtained from field measurement for the Joong-ang corridor, on which heavy freight trains are frequently passing. The reliability assessment is performed by AFOSM(Advanced First Order Second Moment method) for the limit state equation, and a sensitivity analysis for the reliability is performed for each factor of the load and resistance effects.

Evaluation of load and resistance factors for the reliability-based design of the main cables of earth-anchored suspension bridges

This paper presents load and resistance factors for the reliability-based design of the main cables of earth-anchored suspension bridges for the Strength I Limit State defined in the AASHTO LRFD Bridge Design Specifications. Reliability analyses are performed for three suspension bridges in Korea with main span lengths ranging from 650 m to 1545 m, and the reliability indices and the Most Probable Failure Points (MPFP) of random variables are evaluated. The strength, load and stiffness parameters are taken into account as random variables. The advanced first-order second-moment method is employed to evaluate the reliability indices and the MPFP of the random variables. The elastic catenary cable element is utilized to discretize the main cables. Load factors are proposed based on the normalized MPFP of each load component considered in the Strength I Limit State. The resistance factor that yields the reference target reliability index for the main cable is found as 0.53. Two alternative resistance factors, which give lower and higher reliability indices than the reference value, are also proposed. The proposed load and resistance factors lead to a uniform reliability level for a main cable regardless of the length of the main span of a suspension bridge.

Reliability-Based Design Optimization for Crane Metallic Structure Using ACO and AFOSM Based on China Standards

The design optimization of crane metallic structures is of great significance in reducing their weight and cost. Although it is known that uncertainties in the loads, geometry, dimensions, and materials of crane metallic structures are inherent and inevitable and that deterministic structural optimization can lead to an unreliable structure in practical applications, little amount of research on these factors has been reported. This paper considers a sensitivity analysis of uncertain variables and constructs a reliability-based design optimization model of an overhead traveling crane metallic structure. An advanced first-order second-moment method is used to calculate the reliability indices of probabilistic constraints at each design point. An effective ant colony optimization with a mutation local search is developed to achieve the global optimal solution. By applying our reliability-based design optimization to a realistic crane structure, we demonstrate that, compared with the practical design and the deterministic design optimization, the proposed method could find the lighter structure weight while satisfying the deterministic and probabilistic stress, deflection, and stiffness constraints and is therefore both feasible and effective.

Incorporating serviceability limit state requirements into reliability-based analysis and design of piles

This study develops a novel reliability-based approach for the analysis and design of piles by incorporating Serviceability Limit State (SLS) requirements into Load and Resistance Factor Design (LRFD) for Ultimate Limit States (ULS). Three methods for reliability-based analysis and design, namely the Mean Value First Order Second Moment (MVFOSM) method, the Advanced First Order Second Moment (AFOSM) method, and the Monte Carlo Simulation (MCS) method, are employed for comparison. In order to expediently quantify model uncertainties for SLS and incorporate them into the process of reliability-based analysis and design of piles, the SLS model factor (or bias factor) is established based on a two-parameter, hyperbolic curve-fitting equation describing the load-settlement relation. Herein, the limiting tolerable foundation settlement (slt) is treated as a random variable. Four load test databases from South Africa presented by Dithinde et al. (2011) are compiled again to conduct reliability analysis and calculate resistance factors. The case studies illustrate that the AFOSM method has the higher accuracy than the MVFOSM method as verified using the MCS method. This study recommends the AFOSM method to perform reliability analysis and determine resistance factors for Reliability-Based Design (RBD).

Gradient-based design robustness measure for robust geotechnical design

This paper presents a gradient-based robustness measure for robust geotechnical design (RGD) that considers safety, design robustness, and cost efficiency simultaneously. In the context of robust design, a design is deemed robust if the system response of concern is insensitive, to a certain degree, to the variation of noise factors (i.e., uncertain geotechnical parameters, loading parameters, construction variation, and model biases or errors). The key to a robust design is a quantifiable robustness measure with which the robust design optimization can be effectively and efficiently implemented. Based on the developed gradient-based robustness measure, a robust design optimization framework is proposed. In this framework, the design (safety) constraint is analyzed using advanced first-order second-moment (AFOSM) method, considering the variation in the noise factors. The design robustness, in terms of sensitivity index (SI), is evaluated using the normalized gradient of the system response to the noise factors, which can be efficiently computed from the by-product of AFOSM analysis. Within the proposed framework, robust design optimization is performed with two objectives, design robustness and cost efficiency, while the design (safety) constraint is satisfied by meeting a target reliability index. Generally, cost efficiency and design robustness are conflicting objectives and the robust design optimization yields a Pareto front, which reveals a tradeoff between the two objectives. Through an illustrative example of a shallow foundation design, the effectiveness and significance of this new robust design approach is demonstrated.

The SVC Based AFOSM Method for the Structure Reliability Sensitivity Analysis

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.

Mechanical Component Reliability Calculation through Multi-Plane Combination Method

For the performance function with high nonlinearity around the most probable failure region, stress-strength interference model and advanced first-order second-moment method (AFOSM) can cause huge errors in the computation results. The multi-plane combination method is presented to calculate reliability of the mechanical component, in which the component reliability calculation is first transformed into a relatively simple system reliability problem, and then the equivalent calculation method is applied to estimate system reliability. The example application shows the accuracy and efficiency of the multi-plane combination method.

Buckling Reliability Analysis for the Cylindrical Shell with Initial Defects

in this paper, the asymptotic expression of the buckling critical load coefficient of the thin cylindrical shell with local axial symmetry initial defects under the axial loads is deduced by used the Karman-Donnel Equation. The buckling safety margin equation of the cylindrical shell with initial defects is constructed. Furthermore, the buckling reliability index is solved by used AFOSM (Advanced First-Order Second Moment) method. In the end, a numerical example is given to analyze the influence of the band width and amplitude of local axial symmetry initial defects on the structural buckling reliability index.

Maximum-Entropy Method for Evaluating the Slope Stability of Earth Dams

The slope stability is a very important problem in geotechnical engineering. This paper presents an approach for slope reliability analysis based on the maximum-entropy method. The key idea is to implement the maximum entropy principle in estimating the probability density function. The performance function is formulated by the Simplified Bishop’s method to estimate the slope failure probability. The maximum-entropy method is used to estimate the probability density function (PDF) of the performance function subject to the moment constraints. A numerical example is calculated and compared to the Monte Carlo simulation (MCS) and the Advanced First Order Second Moment Method (AFOSM). The results show the accuracy and efficiency of the proposed method. The proposed method should be valuable for performing probabilistic analyses.

A modified gravitational search algorithm for slope stability analysis

This paper first proposes an effective modification for the gravitational search algorithm. The new strategy used an adaptive maximum velocity constraint, which aims to control the global exploration ability of the original algorithm, increase its convergence rate and thereby to obtain an acceptable solution with a lower number of iterations. We testify the performance of the modified gravitational search algorithm (MGSA) on a suite of five well-known benchmark functions and provide comparisons with standard gravitational search algorithm (SGSA). The simulated results illustrate that the modified GSA has the potential to converge faster, while improving the quality of solution. Thereafter, the proposed MGSA is employed to search for the minimum factor of safety and minimum reliability index in both deterministic and probabilistic slope stability analysis. The factor of safety is formulated using a concise approach of the Morgenstern and Price method and the advanced first-order second-moment (AFOSM) method is adopted as the reliability assessment model. The numerical experiments demonstrate that the modified algorithm significantly outperforms the original algorithm and some other methods in the literature.