Non-probabilistic fuzzy reliability analysis of pile foundation stability by interval theory

Randomness and fuzziness are among the attributes of the influential factors for stability assessment of pile foundation. According to these two characteristics, the triangular fuzzy number analysis approach was introduced to determine the probability-distributed function of mechanical parameters. Then the functional function of reliability analysis was constructed based on the study of bearing mechanism of pile foundation, and the way to calculate interval values of the functional function was developed by using improved interval-truncation approach and operation rules of interval numbers. Afterwards, the non-probabilistic fuzzy reliability analysis method was applied to assessing the pile foundation, from which a method was presented for non- probabilistic fuzzy reliability analysis of pile foundation stability by interval theory. Finally, the probability distribution curve of non- probabilistic fuzzy reliability indexes of practical pile foundation was concluded. Its failure possibility is 0.91%, which shows that the pile foundation is stable and reliable.

Efficient slope reliability and sensitivity analysis using quantile-based first-order second-moment method

This paper introduces a novel approach for parameter sensitivity evaluation and efficient slope reliability analysis based on quantile-based first-order second-moment method(QFOSM).The core principles of the QFOSM are elucidated geometrically from the perspective of expanding ellipsoids.Based on this geometric interpretation,the QFOSM is further extended to estimate sensitivity indices and assess the significance of various uncertain parameters involved in the slope system.The proposed method has the advantage of computational simplicity,akin to the conventional first-order second-moment method(FOSM),while providing estimation accuracy close to that of the first-order reliability method(FORM).Its performance is demonstrated with a numerical example and three slope examples.The results show that the proposed method can efficiently estimate the slope reliability and simultaneously evaluate the sensitivity of the uncertain parameters.The proposed method does not involve complex optimization or iteration required by the FORM.It can provide a valuable complement to the existing approximate reliability analysis methods,offering rapid sensitivity evaluation and slope reliability analysis.

Probabilistic back-analysis of rainfall-induced landslides for slope reliability prediction with multi-source information

Probabilistic back-analysis is an important means to infer the statistics of uncertain soil parameters,making the slope reliability assessment closer to the engineering reality.However,multi-source information(including test data,monitored data,field observation and slope survival records)is rarely used in current probabilistic back-analysis.Conducting the probabilistic back-analysis of spatially varying soil parameters and slope reliability prediction under rainfalls by integrating multi-source information is a challenging task since thousands of random variables and high-dimensional likelihood function are usually involved.In this paper,a framework by integrating a modified Bayesian Updating with Subset simulation(mBUS)method with adaptive Conditional Sampling(aCS)algorithm is established for the probabilistic back-analysis of spatially varying soil parameters and slope reliability prediction.Within this framework,the high-dimensional probabilistic back-analysis problem can be easily tackled,and the multi-source information(e.g.monitored pressure heads and slope survival records)can be fully used in the back-analysis.A real Taoyuan landslide case in Taiwan,China is investigated to illustrate the effectiveness and performance of the established framework.The findings show that the posterior knowledge of soil parameters obtained from the established framework is in good agreement with the field observations.Furthermore,the updated knowledge of soil parameters can be utilized to reliably predict the occurrence probability of a landslide caused by the heavy rainfall event on September 12,2004 or forecast the potential landslides under future rainfalls in the Fuhsing District of Taoyuan City,Taiwan,China.

A non-probabilistic reliability topology optimization method based on aggregation function and matrix multiplication considering buckling response constraints

A non-probabilistic reliability topology optimization method is proposed based on the aggregation function and matrix multiplication.The expression of the geometric stiffness matrix is derived,the finite element linear buckling analysis is conducted,and the sensitivity solution of the linear buckling factor is achieved.For a specific problem in linear buckling topology optimization,a Heaviside projection function based on the exponential smooth growth is developed to eliminate the gray cells.The aggregation function method is used to consider the high-order eigenvalues,so as to obtain continuous sensitivity information and refined structural design.With cyclic matrix programming,a fast topology optimization method that can be used to efficiently obtain the unit assembly and sensitivity solution is conducted.To maximize the buckling load,under the constraint of the given buckling load,two types of topological optimization columns are constructed.The variable density method is used to achieve the topology optimization solution along with the moving asymptote optimization algorithm.The vertex method and the matching point method are used to carry out an uncertainty propagation analysis,and the non-probability reliability topology optimization method considering buckling responses is developed based on the transformation of non-probability reliability indices based on the characteristic distance.Finally,the differences in the structural topology optimization under different reliability degrees are illustrated by examples.

Reliability analysis of carbon fiber rod-reinforced umbilical cable under tension using an improved sampling method

The umbilical cable is a vital component of subsea production systems that provide power,chemical agents,control signals et al.,and its requirement for reliability is exceedingly high.However,as the umbilical cable is a composite structure comprising multiple functional units,the reliability analysis of such cables involves numerous parameters that can impact calculation efficiency.In this paper,the reliability analysis of a new kind of umbilical cable with carbon fiber rod under tension is analyzed.The global dynamic analytical model is first established to determine the maximum tension load,then the local analytical model of umbilical cable including each unit are constructed by finite element method(FEM).Based on the mechanical analytical model,the reliability of umbilical cable under tension load is studied using response surface method(RSM)and Monte Carlo method.During the calculation process,a new tangent plane sampling method to calculate the response surface function(RSF)is proposed in this paper,which could make sampling points faster come close to the RSF curve,and it is proved that the calculation efficiency increases about 33%comparing with traditional method.

On the Application of Mixed Models of Probability and Convex Set for Time-Variant Reliability Analysis

In time-variant reliability problems,there are a lot of uncertain variables from different sources.Therefore,it is important to consider these uncertainties in engineering.In addition,time-variant reliability problems typically involve a complexmultilevel nested optimization problem,which can result in an enormous amount of computation.To this end,this paper studies the time-variant reliability evaluation of structures with stochastic and bounded uncertainties using a mixed probability and convex set model.In this method,the stochastic process of a limit-state function with mixed uncertain parameters is first discretized and then converted into a timeindependent reliability problem.Further,to solve the double nested optimization problem in hybrid reliability calculation,an efficient iterative scheme is designed in standard uncertainty space to determine the most probable point(MPP).The limit state function is linearized at these points,and an innovative random variable is defined to solve the equivalent static reliability analysis model.The effectiveness of the proposed method is verified by two benchmark numerical examples and a practical engineering problem.

Saddlepoint Approximation Method in Reliability Analysis:A Review

The escalating need for reliability analysis(RA)and reliability-based design optimization(RBDO)within engineering challenges has prompted the advancement of saddlepoint approximationmethods(SAM)tailored for such problems.This article offers a detailed overview of the general SAM and summarizes the method characteristics first.Subsequently,recent enhancements in the SAM theoretical framework are assessed.Notably,the mean value first-order saddlepoint approximation(MVFOSA)bears resemblance to the conceptual framework of the mean value second-order saddlepoint approximation(MVSOSA);the latter serves as an auxiliary approach to the former.Their distinction is rooted in the varying expansion orders of the performance function as implemented through the Taylor method.Both the saddlepoint approximation and third-moment(SATM)and saddlepoint approximation and fourth-moment(SAFM)strategies model the cumulant generating function(CGF)by leveraging the initial random moments of the function.Although their optimal application domains diverge,each method consistently ensures superior relative precision,enhanced efficiency,and sustained stability.Every method elucidated is exemplified through pertinent RA or RBDO scenarios.By juxtaposing them against alternative strategies,the efficacy of these methods becomes evident.The outcomes proffered are subsequently employed as a foundation for contemplating prospective theoretical and practical research endeavors concerning SAMs.The main purpose and value of this article is to review the SAM and reliability-related issues,which can provide some reference and inspiration for future research scholars in this field.

Efficient slope reliability analysis under soil spatial variability using maximum entropy distribution with fractional moments

Spatial variability of soil properties imposes a challenge for practical analysis and design in geotechnical engineering.The latter is particularly true for slope stability assessment,where the effects of uncertainty are synthesized in the so-called probability of failure.This probability quantifies the reliability of a slope and its numerical calculation is usually quite involved from a numerical viewpoint.In view of this issue,this paper proposes an approach for failure probability assessment based on Latinized partially stratified sampling and maximum entropy distribution with fractional moments.The spatial variability of geotechnical properties is represented by means of random fields and the Karhunen-Loève expansion.Then,failure probabilities are estimated employing maximum entropy distribution with fractional moments.The application of the proposed approach is examined with two examples:a case study of an undrained slope and a case study of a slope with cross-correlated random fields of strength parameters under a drained slope.The results show that the proposed approach has excellent accuracy and high efficiency,and it can be applied straightforwardly to similar geotechnical engineering problems.

Inverse reliability analysis and design for tunnel face stability considering soil spatial variability

The traditional deterministic analysis for tunnel face stability neglects the uncertainties of geotechnical parameters,while the simplified reliability analysis which models the potential uncertainties by means of random variables usually fails to account for soil spatial variability.To overcome these limitations,this study proposes an efficient framework for conducting reliability analysis and reliability-based design(RBD)of tunnel face stability in spatially variable soil strata.The three-dimensional(3D)rotational failure mechanism of the tunnel face is extended to account for the soil spatial variability,and a probabilistic framework is established by coupling the extended mechanism with the improved Hasofer-Lind-Rackwits-Fiessler recursive algorithm(iHLRF)as well as its inverse analysis formulation.The proposed framework allows for rapid and precise reliability analysis and RBD of tunnel face stability.To demonstrate the feasibility and efficacy of the proposed framework,an illustrative case of tunnelling in frictional soils is presented,where the soil's cohesion and friction angle are modelled as two anisotropic cross-correlated lognormal random fields.The results show that the proposed method can accurately estimate the failure probability(or reliability index)regarding the tunnel face stability and can efficiently determine the required supporting pressure for a target reliability index with soil spatial variability being taken into account.Furthermore,this study reveals the impact of various factors on the support pressure,including coefficient of variation,cross-correlation between cohesion and friction angle,as well as autocorrelation distance of spatially variable soil strata.The results also demonstrate the feasibility of using the forward and/or inverse first-order reliability method(FORM)in high-dimensional stochastic problems.It is hoped that this study may provide a practical and reliable framework for determining the stability of tunnels in complex soil strata.

Three-dimensional pseudo-dynamic reliability analysis of seismic shield tunnel faces combined with sparse polynomial chaos expansion

To address the seismic face stability challenges encountered in urban and subsea tunnel construction,an efficient probabilistic analysis framework for shield tunnel faces under seismic conditions is proposed.Based on the upper-bound theory of limit analysis,an improved three-dimensional discrete deterministic mechanism,accounting for the heterogeneous nature of soil media,is formulated to evaluate seismic face stability.The metamodel of failure probabilistic assessments for seismic tunnel faces is constructed by integrating the sparse polynomial chaos expansion method(SPCE)with the modified pseudo-dynamic approach(MPD).The improved deterministic model is validated by comparing with published literature and numerical simulations results,and the SPCE-MPD metamodel is examined with the traditional MCS method.Based on the SPCE-MPD metamodels,the seismic effects on face failure probability and reliability index are presented and the global sensitivity analysis(GSA)is involved to reflect the influence order of seismic action parameters.Finally,the proposed approach is tested to be effective by a engineering case of the Chengdu outer ring tunnel.The results show that higher uncertainty of seismic response on face stability should be noticed in areas with intense earthquakes and variation of seismic wave velocity has the most profound influence on tunnel face stability.

Review: Recent Developments in the Non-Probabilistic Finite Element Analysis

Generally, the finite element analysis of a structure is completed under deterministic inputs.However,uncertainties corresponding to geometrical dimensions,material properties, boundary conditions cannot be neglected in engineering applications. The probabilistic methods are the most popular techniques to handle these uncertain parameters but subjective results could be obtained if insufficient information is unavailable. Non-probabilistic methods can be alternatively employed,which has led to the procedures for nonprobabilistic finite element analysis. Each non-probabilistic finite element analysis method consists of two individual parts,including the core algorithm and pre-processing procedure. In this context,three types of algorithms and two typical pre-processing procedures as well as their effectiveness are described in detail,based on which novel hybrid algorithms can be conceived for the specific problems and the future work in this research field can be fostered.

Reliability analysis of piles constructed on slopes under laterally loading

Response surface method is used to study the reliability analysis of laterally loaded piles in sloping ground. A development load-displacement （p-y） curve for laterally loaded pile response in sloping ground is used to model the pile-soil system, both the pile head displacement and the maximum bending moment of the piles are used as the performance criteria in this study. The reliability analysis method of the laterally loaded pile in sloping ground under the pile head displacement and the maximum bending moment failure modes is proposed, which is in good agreement with the Monte Carlo method. The influences on the probability index of failure by a number of parameters are discussed. It is shown that the variability of pile head displacement increases with the increase in the coefficients of variation of ultimate bearing capacity factor （Npu）, secant elastic modulus at 50%（E50） and level load （H）. A negative correlation between Npu and non-dimensional factor （λ） leads to less spread out probability density function （PDF） of the pile head displacement;in contrast, a positive correlation between Npu andλgives a great variation in the PDF of pile head displacement. As for bearing capacity factor on ground surface （Npo） and λ, both negative and positive correlations between them give a great variation in the PDF of pile head displacement, and a negative correlation will obviously increase the variability of the response.

Reliability Analysis of a Mixed Redundant Model in C 3I System

Aim To define a mixed redundant model(MRM), improving the reliability of C 3I system. Methods The model combined the technology characters of two? unit system with one warm stand by unit and function substitute system. The reliability and availability equations of MRM were deduced. Results and Conclusion Compared with several other reliability models, it has obvious effect upon improving the system reliability. The effect? cost rate is very high among these models. The model can be used in reliability design, evaluation and check of C 3I system. Only a little attached cost is needed to improve C 3I system reliability effectively.

GENERAL RELIABILITY ANALYSIS FOR TWO DIMENSIONAL SLOPES

The reliability analysis, based on the reliability index method, of two dimensional slopes is generalized by taking Sarma′s acceleration as the performance function. That is to say, a general expression of the performance function is given under various kinds of slice methods, even under various shapes of slice partition, beyond the traditional vertical slice method. A simple example shows explicitly the relationship of four commonly used slice methods in the slope reliability analysis. It is also found that the results of the reliability analysis are basically consistent with those of the stability analysis based on Sarma′s method.

Slope reliability and back analysis of failure with geotechnical parameters estimated using Bayesian inference

A Bayesian approach is proposed for the inference of the geotechnical parameters used in slope design.The methodology involves the construction of posterior probability distributions that combine prior information on the parameter values with typical data from laboratory tests and site investigations used in design.The posterior distributions are often complex,multidimensional functions whose analysis requires the use of Markov chain Monte Carlo(MCMC)methods.These procedures are used to draw representative samples of the parameters investigated,providing information on their best estimate values,variability and correlations.The paper describes the methodology to define the posterior distributions of the input parameters for slope design and the use of these results for evaluation of the reliability of a slope with the first order reliability method(FORM).The reliability analysis corresponds to a forward stability analysis of the slope where the factor of safety(FS)is calculated with a surrogate model from the more likely values of the input parameters.The Bayesian model is also used to update the estimation of the input parameters based on the back analysis of slope failure.In this case,the condition FS?1 is treated as a data point that is compared with the model prediction of FS.The analysis requires a sufficient number of observations of failure to outbalance the effect of the initial input parameters.The parameters are updated according to their uncertainty,which is determined by the amount of data supporting them.The methodology is illustrated with an example of a rock slope characterised with a Hoek-Brown rock mass strength.The example is used to highlight the advantages of using Bayesian methods for the slope reliability analysis and to show the effects of data support on the results of the updating process from back analysis of failure.

Improved Reliability Analysis Method Based on the Failure Assessment Diagram

With the uncertainties related to operating conditions,in-service non-destructive testing（NDT） measurements and material properties considered in the structural integrity assessment,probabilistic analysis based on the failure assessment diagram（FAD） approach has recently become an important concern.However,the point density revealing the probabilistic distribution characteristics of the assessment points is usually ignored.To obtain more detailed and direct knowledge from the reliability analysis,an improved probabilistic fracture mechanics（PFM） assessment method is proposed.By integrating 2D kernel density estimation（KDE） technology into the traditional probabilistic assessment,the probabilistic density of the randomly distributed assessment points is visualized in the assessment diagram.Moreover,a modified interval sensitivity analysis is implemented and compared with probabilistic sensitivity analysis.The improved reliability analysis method is applied to the assessment of a high pressure pipe containing an axial internal semi-elliptical surface crack.The results indicate that these two methods can give consistent sensitivities of input parameters,but the interval sensitivity analysis is computationally more efficient.Meanwhile,the point density distribution and its contour are plotted in the FAD,thereby better revealing the characteristics of PFM assessment.This study provides a powerful tool for the reliability analysis of critical structures.

Combination of structural reliability and interval analysis

In engineering applications, probabilistic reliability theory appears to be presently the most important method, however, in many cases precise probabilistic reliability theory cannot be considered as adequate and credible model of the real state of actual affairs. In this paper, we developed a hybrid of probabilistic and non-probabilistic reliability theory, which describes the structural uncertain parameters as interval variables when statistical data are found insufficient. By using the interval analysis, a new method for calculating the interval of the structural reliability as well as the reliability index is introduced in this paper, and the traditional probabilistic theory is incorporated with the interval analysis. Moreover, the new method preserves the useful part of the traditional probabilistic reliability theory, but removes the restriction of its strict requirement on data acquisition. Example is presented to demonstrate the feasibility and validity of the proposed theory.

Performance Degradation and Reliability Analysis for Redundant Actuation System

Redundant actuator is the key component of Fly-By-Wire （FBW） system in which exists the inherent force fighting among different redundant channels at colligation point, This paper establishes the mathematical model of quad redundant actuator （QRA）, investigates the force equalization algorithm and carries out the performance degradation simulation and reliability analysis under the first failure and the second failure. The results indicate that the optimal equalization algorithm can solve the force fighting effectively, and the QRA can operate at degradation performance continuously under the first failure and the second failure. With the dynamic fault tree analysis, this paper calculates the reliability based on the performance of QRA and proves that the redundant actuator has very high reliability and safety.

Research on the Reliability Tolerance Analysis Method of Electromagnetic Relay in Aerospace

Electromagnetic relay in aerospace is one of the main electronic components in aerospace electronic systems for information transfer, control and power distribution, and its reliability will influence the reliability of the whole aerospace electronic systems. Reliability design is the key technique of electromagnetic relay reliability engineering. This paper synthetically analyzes the present reliability design methods, and presents the reliability tolerance analyzing mathematic models of electromagnetic force basing on orthogonal design, mechanical spring force basing on probability statistics theory, and matching characteristics of electromagnetic force and mechanical spring force basing on method of stressstrength interference. Some instructive conclusions are draw by researching on the reliability tolerance of some type electromagnetic relay in aerospace.

RELIABILITY ANALYSIS OF THE PRIMARY CYLINDER OF THE 10MN HYDRAULIC PRESS

According to the demand of high reliability of the primary cylinder of the hydraulic press, the reliability model of the primary cylinder is built after its reliability analysis. The stress of the primary cylinder is analyzed by finite element software—MARC, and the structure reliability of the cylinder based on stress strength model is predicted, which would provide the reference to the design.