Advanced First-order Second-moment 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.

Reliability-based assessment of reasonable mid-tower lateral stiffness for a three-tower suspension bridge

A reasonable lateral stiffness of the bridge mid-tower should ensure that the deflection-to-span ratio and sliding resistance coefficient satisfy the design requirements. However, if this stiffness is determined by the deterministic parametric analysis, the above two verification indices may exceed the threshold due to the randomness of the high-dimensional structure and load parameters. To satisfy the structural safety requirements of a three-tower suspension bridge during its design life, this study proposes a method to quickly and accurately evaluate the reliability indices of the deflection-to-span ratio and sliding resistance coefficient of the three-tower suspension bridge. Based on advanced first-order second-moment, the proposed method transforms the reliability problem into an optimization problem with constraint functions, uses the single-cable theory to establish the limit state function, and combines the manta ray foraging optimization algorithm and penalty function to derive the reliability index. The effectiveness of the proposed method is verified by performing Latin hypercube sampling for an examplary three-tower suspension bridge. These results prove that the new technique avoids tedious finite element simulation and surrogate model fitting, ensuring the accuracy of the reliability index while improving the calculation efficiency. The study further identifies critical structural parameters by parametric analysis. Based on the inverse reliability, the dimensionless stiffness range for the mid-tower with the randomness of the parameters is derived, and the preliminary design method of the lateral stiffness of the mid-tower based on the reliability is established.

Reliability Analysis for Liquefaction Risk Assessment for the City of Patna, India using Hybrid Computational Modeling

ABSTRACT In the present study, the first-order reliability method (FORM) is applied to evaluate the failure of soil deposits during seismic excitation for the city of Patna, India. Patna is emerging as one of the metro cities and the rapid infrastructure development in the city with high pace construction of road and metro services along with several smart city projects have led to immense growth in civil engineering structures. Therefore, liquefaction assessment of Patna is an important subject due to the geographical and seismic location of the city. A detailed comparative study has been performed between first-order second moment (FOSM) and advanced first-order second-moment (AFOSM) reliability methods to determine the most suitable method to evaluate the potential risk of liquefaction for Patna city. Reliability index (β) values obtained from AFOSM analysis are in true accordance with the deterministic approach and therefore can be considered as an appropriate tool for reliability analysis for this city. The analysis establishes that the city of Patna exhibits high possibilities of liquefaction failure during high-intensity earthquakes i.e. Mw = 6.5. Also, a concept of a predictive computational model developed by the hybridization of ANN and GWO algorithms to determine β value using geotechnical and seismic parameters has been proposed. The high precision and error-free performance of the ANN-GWO model provides a powerful computational tool to assist the prediction of β. The results of the study could be used to comprehend the potential risk against liquefaction and provide a novel and insightful concept of risk assessment for safe and economic construction practices.

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.

Comparison of Reliability Based Design (RBD) With Eurocode 2 for A Singly Reinforced Concrete Beam

This research compares the Reliability-Based Design (RBD) method with the Eurocode 2 (EC2) for a singly reinforced concrete beam. Advanced First Order Second Moment (AFOSM) was used and the equation for the ultimate limit state design consideration for Moment of resistance and Applied moment was applied. The parameters which were all functions of the Ultimate load, G were replaced respectively with variables and their derivatives G(x) obtained with being the characteristic strengths of concrete and the yield stress of steel respectively. Given the original vector space and the transformed reduced vector space, the Taylor series was used to expand the reduced vector space and thus reliability index ßx expressed. The procedure was then coded using JAVA to produce the Reliability Index and Probability of failure for respective steel ratio. The required probability index of 3.9 corresponds to 0.048% of the steel ratio. Typical analysis of a singly reinforced beam according to EC2 for b=300mm, h=500mm, d=447mm, cover of 40 mm, gave a steel ratio of 1.31 %. Comparing this to the reliability-based design of 0.048%, the code provision exceeded the RBD output by 2000 times and 63 times the minimum reinforcement requirement by the code.

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.

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.

Deterministic and reliability-based design of necessary support pressures for tunnel faces

This paper provides methods for the deterministic and reliability-based design of the support pressures necessary to prevent tunnel face collapse. The deterministic method is developed by extending the use of the unique load multiplier, which is embedded within OptumG2/G3 with the intention of determining the maximum load that can be supported by a system. Both two-dimensional and three-dimensional examples are presented to illustrate the applications. The obtained solutions are validated according to those derived from the existing methods. The reliability-based method is developed by incorporating the Response Surface Method and the advanced first-order second-moment reliability method into the bisection algorithm, which continuously updates the support pressure within previously determined brackets until the difference between the computed reliability index and the user-defined value is less than a specified tolerance. Two-dimensional reliability-based support pressure is compared and validated via Monte Carlo simulations, whereas the three-dimensional solution is compared with the relationship between the support pressure and the resulting reliability index provided in the existing literature. Finally, a parametric study is carried out to investigate the influences of factors on the required support pressure.

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.

Simplified algorithm for reliability sensitivity analysis of structures: A spreadsheet implementation.

An important segment of the reliability-based optimization problems is to get access to the sensitivity derivatives. However, since the failure probability is not a closed-form function of the input variables, the derivatives are not explicitly computable and rather require a full reliability analysis which is computationally expensive. In this paper, a step-by-step algorithm has been presented to calculate the derivatives of the probability of failure and safety index with respect to the input parameters based on the advanced first-order second-moment (AFOSM) reliability method. The proposed algorithm is then implemented in a spreadsheet using Visual Basic for Application (VBA) programming language. Two geotechnical and structural examples are then presented to examine the program and describe the modeling procedure. The robustness of the proposed method is examined using a Gaussian random perturbation. The capability of the proposed method in the calculation of the sensitivity derivatives of the model uncertainty is explained in a separate section. Finally, the proposed model has been compared to the forward finite difference (FFD) method and the results are validated.

Reliability assessment of reinforced concrete rectangular columns subjected to biaxial bending using the load contour method

This paper presents the reliability assessment of reinforced concrete (RC) columns subjected to biaxial bending using the advanced first-order second-moment reliability method. The strength of an RC column under the biaxial bending condition is estimated by the load contour, which is utilized as the limit state function in the reliability analysis. The random variables include the strength parameters of the RC columns, the load parameters and the eccentricities of axial force. The Hasofer-Lind-Rackwitz-Fiessler algorithm with the gradient projection method is employed to calculate the most probable failure point and the reliability index. The surface exponents of the load contours are determined by the values presented by Bresler. The cubic spline interpolation is adopted to construct P-M interaction diagrams for uniaxial bending about the principal axes that are required in the load contour method. The sensitivities of the limit state function are calculated through the direct differentiation method. The reliability indices are calculated for a rectangular section and a square section. The effect of the surface exponent on the results of the reliability analysis is investigated for the rectangular section, and the uncertainty of the eccentricity of axial force is considered in the example for the square section.

Probabilistic analysis of chatter stability in turning

In practical engineering, randomness of the parameters (mass, stiffness, and cutting coefficients) significantly impacts the stability of turning processes. In this study, the method involving the probabilistic analysis of the regenerative chatter stability in turning is comprehensively investigated. Considering the influences of random factors, the probability characteristic of the regenerative chatter stability in turning is studied using the Monte Carlo simulation (MCS) method and advanced first order second moment (FOSM) method. Dynamic model of regenerative chatter in turning is obtained, and the relationship between the limiting width of cut for stable machining and the rotation speed of the spindle is acquired based on the Laplace transform. The MCS and advanced FOSM methods for predicting the reliability of the stability in turning are proposed by identifying whether the actual cutting width is less than the limiting width of cut. Finally, practical applications and a detailed analysis to evaluate the accuracy of the proposed methods are discussed.

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.

Predictive assessment of heat exchange performance of geothermal piles

Heat exchange performance of geothermal piles with single U-shaped circulation tube is quantified as a function of design, operational and site-specific variables. A finite difference model is developed to simulate heat transport by circulation fluid and heat conduction in pile and surrounding soil. Finite difference analyses (FDAs) are performed to quantify the effects of several input parameters on heat transfer performance of a geothermal pile. Based on FDA results, closed-form equations are proposed that can be used in calculation of power output from a single geothermal pile with U-shaped circulation tube embedded in it. Parameter sensitivity study and advanced first order second moment (AFOSM) reliability analysis are performed to determine the hierarchy of different input variables in order of their relative impacts on heat transfer performance. Thermal conductivity of soil, initial temperature difference between circulation fluid and ground, and radius of the circulation tube are identified as the three most important parameters that control heat transfer through geothermal piles.

An intelligent method for contact fatigue reliability analysis of spur gear under EHL

To complete the contact fatigue reliability analysis of spur gear under elastohydrodynamic lubrication (EHL) efficiently and accurately, an intelligent method is proposed. Oil film pressure is approximated using quadratic polynomial with intercrossing term and then mapped into the Hertz contact zone. Considering the randomness of the EHL, material properties and fatigue strength correction factors, the probabilistic reliability analysis model is established using artificial neural network (ANN). Genetic algorithm (GA) is employed to search the minimum reliability index and the design point by introducing an adjusting factor in penalty function. Reliability sensitivity analysis is completed based on the advanced first order second moment (AFOSM). Numerical example shows that the established probabilistic reliability analysis model could correctly reflect the effect of EHL on contact fatigue of spur gear, and the proposed intelligent method has an excellent global search capability as well as a highly efficient computing performance compared with the traditional Monte Carlo method (MCM).

Reliability assessment of reinforced concrete columns based on the P–M interaction diagram using AFOSM

This paper presents a new approach for evaluating the reliability index and most probable failure point (MPFP) of a reinforced concrete (RC) column using the advanced first-order second-moment reliability method without Monte-Carlo simulations. The P–M interaction diagram (PMID) is selected as the limit state function of an RC column. The strength parameters of an RC column include the material properties and geometric properties of the cross section of an RC column. The strength and load parameters are considered as random variables. An iterative solution scheme with double iteration loops is adopted for obtaining the MPFP and reliability index. The continuous and differentiable PMID is constructed with discretely defined sampling points of the PMID using the cubic spline interpolation. The sensitivities of the PMID are calculated through the direct differentiation of the cubic spline and sampling points of the PMID. Detailed expressions of the sensitivities of the PMID with respect to the random variables are presented. The validity of the proposed method is demonstrated through a simple rectangular column and the pylon of a real cable-stayed bridge. It is shown that the proposed method yields physically meaningful solutions efficiently for the examples presented.

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.