Structure reliability analysis based on supercavity vehicle steady motion

Taking the steady motion status as a starting point,according to the modeling of actual state of theoretical analysis,a predigested model of supercavity vehicle was established,and relationship expressions of these angles were obtained when the movement of supercavity vehicle was stable.A theoretical analysis on the stability of underwater high-speed movement in the movement simulation program was conducted and the simulation results were given.Then the force status of the supercavity vehicle was elicited from the results.The finite element analysis was carried out based on the stability at all angles obtained from simulation results.Taking a pilot model as example,the Monte Carlo method was adopting to analyze the reliability with the given state of force and displacement.The result indicates that this method is feasible.

Assembly-oriented reliability analysis method for the top-connection structure of a nuclear fuel assembly

The nuclear fuel assembly is the core component of a nuclear reactor.In a pressurized water reactor fuel assembly,the top-connection structure connects the top nozzle to the guide thimble.Its performance reliability is essential for the stability of the nuclear fuel assembly.In this study,an assembly-oriented reliability analysis method for top-connection structures is presented by establishing an assembly-oriented top-connection structure parameter modeling method and a nonlinear contact gap and penetration correction method.A reliability model of the top-connection assembly structure,including multiple stochastic design variables,was constructed,and the overall reliability of the top-connection assembly structure was obtained via a Kriging model and Monte Carlo simulation.The acquired experimental data were consistent with real-world failure conditions,which verified the practicability and feasibility of the reliability analysis method proposed in this study.

Reliability analysis on bolt support structure of coal roadway under the influence of mining

Based on the features of the serious deformation of coal roadway,many random variables of the mechanics of the surrounding rocks and the influence of mining, the reliability analysis model of the support structure of coal roadway under the influence of mining is established,and the calculating formulas of reliability of the support structure is obtained with the engineering structure reliability theory. And the reliability is calculated based on the method of Monte Carlo to the coal roadway which is exampled on the influence of mining or not. The relationship between support parameters and reliability, the mining influence coefficients and reliability is established, which provides theory foundations for the design of the coal roadway bolt support.

Research for Non-probabilistic Structure Reliability

The paper discusses non-probabilistic approaches for uncertainty treatment in structure reliability analysis. Based on rough set theory, the uncertain parameters of structures are expressed by rough variables, the structure reliability index is computed by rough function and metric. This new methodology for structural reliability is proved to be valid and efficient using theory analysis and examples of practical application.

Non-probabilistic reliability method and reliability-based optimal LQR design for vibration control of structures with uncertain-but-bounded parameters

Uncertainty is inherent and unavoidable in almost all engineering systems. It is of essential significance to deal with uncertainties by means of reliability approach and to achieve a reasonable balance between reliability against uncertainties and system performance in the control design of uncertain systems. Nevertheless, reliability methods which can be used directly for analysis and synthesis of active control of structures in the presence of uncertainties remain to be developed, especially in non-probabilistic uncertainty situations. In the present paper, the issue of vibration con- trol of uncertain structures using linear quadratic regulator （LQR） approach is studied from the viewpoint of reliabil- ity. An efficient non-probabilistic robust reliability method for LQR-based static output feedback robust control of un- certain structures is presented by treating bounded uncertain parameters as interval variables. The optimal vibration con- troller design for uncertain structures is carried out by solv- ing a robust reliability-based optimization problem with the objective to minimize the quadratic performance index. The controller obtained may possess optimum performance un- der the condition that the controlled structure is robustly re- liable with respect to admissible uncertainties. The proposed method provides an essential basis for achieving a balance between robustness and performance in controller design ot uncertain structures. The presented formulations are in the framework of linear matrix inequality and can be carried out conveniently. Two numerical examples are provided to illustrate the effectiveness and feasibility of the present method.

AWK-TIS:An Improved AK-IS Based on Whale Optimization Algorithm and Truncated Importance Sampling for Reliability Analysis

In this work,an improved active kriging method based on the AK-IS and truncated importance sampling(TIS)method is proposed to efficiently evaluate structural reliability.The novel method called AWK-TIS is inspired by AK-IS and RBF-GA previously published in the literature.The innovation of the AWK-TIS is that TIS is adopted to lessen the sample pool size significantly,and the whale optimization algorithm(WOA)is employed to acquire the optimal Krigingmodel and themost probable point(MPP).To verify the performance of theAWK-TISmethod for structural reliability,four numerical cases which are utilized as benchmarks in literature and one real engineering problem about a jet van manipulate mechanism are tested.The results indicate the accuracy and efficiency of the proposed method.

Time-Dependent Reliability Analysis of Offshore Structures

During the life of an offshore structure, its structural strength declines due to various kinds of damages related to the time factor. In this paper, four major kinds of damages, including damages caused by fatigue, dent, corrosion and marine life, are discussed. Based on these analyses, formulas for the evaluation of the damaged structure reliability are derived. Furthermore the computer program ISM for the analysis of structural reliability is developed by the use of Advanced First Order Second Moment method and Monte-Carlo Importance Sampling method. The reliability of a turbular joint and a beam are studied as numerical examples. The results show that the theory and the analysis method given in this paper are reasonable and effective.

RELIABILITY OF ELASTO-PLASTIC STRUCTURE USING FINITE ELEMENT METHOD

A solution of probabilistic FEM for elastic-plastic materials is presented based on the incremental theory of plasticity and a modified initial stress method. The formulations are deduced through a direct differentiation scheme. Partial differentiation of displacement, stress and the performance function can be iteratively performed with the computation of the mean values of displacement and stress. The presented method enjoys the efficiency of both the perturbation method and the finite difference method, but avoids the approximation during the partial differentiation calculation. In order to improve the efficiency, the adjoint vector method is introduced to calculate the differentiation of stress and displacement with respect to random variables. In addition, a time-saving computational method for reliability index of elastic-plastic materials is suggested based upon the advanced First Order Second Moment (FOSM) and by the usage of Taylor expansion for displacement. The suggested method is also applicable to 3-D cases.

THE RELIABILITY ANALYSIS OF AIRCRAFT STRUCTURES

This paper presents a set of fundamental equations for reliability analysis of single-critical-point aircraft structures.The mathematical model is formulated by considering the following factors:the static strength of structure,initial crack,the initiation and propagation and unstability of fatigue crack,the residual strength of structure,the statistical distribution of load,the periods of overhaul,accident damage,the communication of damage among fleets etc.Based on this mathematical model,the influence of these factors on the reliability can be quantitatively analyzed,and various criteria for fatigue design of aircraft structures can be evaluated from the aspect of reliability.

Structural Interval Reliability Algorithm Based on Bernstein Polynomials and Evidence Theory

Structural reliability is an important method to measure the safety performance of structures under the influence of uncertain factors.Traditional structural reliability analysis methods often convert the limit state function to the polynomial form to measure whether the structure is invalid.The uncertain parameters mainly exist in the form of intervals.This method requires a lot of calculation and is often difficult to achieve efficiently.In order to solve this problem,this paper proposes an interval variable multivariate polynomial algorithm based on Bernstein polynomials and evidence theory to solve the structural reliability problem with cognitive uncertainty.Based on the non-probabilistic reliability index method,the extreme value of the limit state function is obtained using the properties of Bernstein polynomials,thus avoiding the need for a lot of sampling to solve the reliability analysis problem.The method is applied to numerical examples and engineering applications such as experiments,and the results show that the method has higher computational efficiency and accuracy than the traditional linear approximation method,especially for some reliability problems with higher nonlinearity.Moreover,this method can effectively improve the reliability of results and reduce the cost of calculation in practical engineering problems.

Assessment of Intangible Losses in Earthquake Engineering

In order to find optimum design parameters in earthquake engineering, an objective function is optimized. This function comprises the initial cost of a structure and the cost due to the damage of earthquakes. Intangible losses may be included in the latter, such as how much society is willing to invest to preserve a human life. In this paper, the expression of the objective function is developed in terms of the seismic design coefficient, and the aforementioned intangible loss is calculated from both the individual point of view and that of society. The calculation of the intangible is based on utility curves. Finally, optimum seismic design coefficients are calculated for a firm ground site.

Reliability-Based Design for Jacket Platform Under Extreme Loads

In this paper, reliability analysis for the offshore jacket platform with the interaction of structure- pile- soil under extreme environmental loads is carried out. The inherent uncertainties of the environmental load, foundation soil, platform itself, and calculating models are evaluated. The action of extreme loads on the offshore platform is modeled as a function of extreme wave height. The system capacity of the whole platform is determined by nonlinear pushover analysis, and the relevant probability property is obtained by the simulation method. The reliability model for the whole jacket platform is described as the relationship between the load and resistance based on the offshore design codes. The reliability of whole platform is calculated by the analytical method and the importance sampling method on the basis of a case study for a tripod jacket platform.

RELIABILITY ANALYSIS OF FRP LAMINATED PLATES WITH CONSIDERATION OF BOTH INITIAL IMPERFECTION AND FAILURE SEQUENCE

A probabilistic progressive failure analyzing method is applied to estimating the reliability of a simply supported laminated composite plate with an initial imperfection under bi-axial compression load. The initial imperfection and the strength parameters are considered as random variables. Ply-level failure probability is evaluated by the first order reliability method (FORM) together with the Tsai-Wu strength criterion and Tan criterion. Current stresses in the laminated structure are calculated by the classical lamination theory with the stiffness modified based on the last step ply failure. Probabilistically dominant ply-level failure sequences leading to overall system failure are identified, based on which the system failure probability is estimated. A numerical example is presented to demonstrate the methodology proposed. Through parameter studies it is shown that the deviation of the initial imperfection and some of the strength parameters largely influence the system reliability.

An improved adaptive response surface method for structural reliability analysis

The response surface method(RSM) is one of the main approaches for analyzing reliability problems with implicit performance functions.An improved adaptive RSM based on uniform design(UD) and double weighted regression(DWR) was presented.In the proposed method,the basic principle of the iteratively adaptive response surface method is applied.Uniform design is used to sample the fitting points.And a double weighted regression system considering the distances from the fitting points to the limit state surface and to the estimated design points is set to determine the coefficients of the response surface model.Compared with the conventional approaches,the fitting points selected by UD are more representative,and a better approximation in the key region is also observed with DWR.Numerical examples show that the proposed method has good convergent capability and computational accuracy.

An Intelligent Method for Structural Reliability Analysis Based on Response Surface

As water depth increases, the structural safety and reliability of a system become more and more important and challenging. Therefore, the structural reliability method must be applied in ocean engineering design such as offshore platform design. If the performance function is known in structural reliability analysis, the first-order second-moment method is often used. If the performance function could not be definitely expressed, the response surface method is always used because it has a very clear train of thought and simple programming. However, the traditional response surface method fits the response surface of quadratic polynomials where the problem of accuracy could not be solved, because the true limit state surface can be fitted well only in the area near the checking point. In this paper, an intelligent computing method based on the whole response surface is proposed, which can be used for the situation where the performance function could not be definitely expressed in structural reliability analysis. In this method, a response surface of the fuzzy neural network for the whole area should be constructed first, and then the structural reliability can be calculated by the genetic algorithm. In the proposed method, all the sample points for the training network come from the whole area, so the true limit state surface in the whole area can be fitted. Through calculational examples and comparative analysis, it can be known that the proposed method is much better than the traditional response surface method of quadratic polynomials, because, the amount of calculation of finite element analysis is largely reduced, the accuracy of calculation is improved, and the true limit state surface can be fitted very well in the whole area. So, the method proposed in this paper is suitable for engineering application.

Structural reliability analysis using enhanced cuckoo search algorithm and artificial neural network

The present study proposed an enhanced cuckoo search(ECS) algorithm combined with artificial neural network(ANN) as the surrogate model to solve structural reliability problems. In order to enhance the accuracy and convergence rate of the original cuckoo search(CS) algorithm, the main parameters namely, abandon probability of worst nests paand search step sizeα0 are dynamically adjusted via nonlinear control equations. In addition, a global-best guided equation incorporating the information of global best nest is introduced to the ECS to enhance its exploitation. Then, the proposed ECS is linked to the well-trained ANN model for structural reliability analysis. The computational capability of the proposed algorithm is validated using five typical structural reliability problems and an engineering application. The comparison results show the efficiency and accuracy of the proposed algorithm.

A Comprehensive Model for Structural Non-Probabilistic Reliability and the Key Algorithms

It is very difficult to know the exact boundaries of the variable domain for problems with small sample size,and the traditional convex set model is no longer applicable.In view of this,a novel reliability model was proposed on the basis of the fuzzy convex set(FCS)model.This new reliability model can account for different relations between the structural failure region and variable domain.Key computational algorithms were studied in detail.First,the optimization strategy for robust reliability is improved.Second,Monte Carlo algorithms(i.e.,uniform sampling method)for hyper-ellipsoidal convex sets were studied in detail,and errors in previous reports were corrected.Finally,the Gauss-Legendre integral algorithm was used for calculation of the integral reliability index.Three numerical examples are presented here to illustrate the rationality and feasibility of the proposed model and its corresponding algorithms.

Reliability Sensitivity-based Correlation Coefficient Calculation in Structural Reliability Analysis

The correlation coefficients of random variables of mechanical structures are generally chosen with experience or even ignored,which cannot actually reflect the effects of parameter uncertainties on reliability.To discuss the selection problem of the correlation coefficients from the reliability-based sensitivity point of view,the theory principle of the problem is established based on the results of the reliability sensitivity,and the criterion of correlation among random variables is shown.The values of the correlation coefficients are obtained according to the proposed principle and the reliability sensitivity problem is discussed.Numerical studies have shown the following results：（1） If the sensitivity value of correlation coefficient ρ is less than（at what magnitude 0.000 01）,then the correlation could be ignored,which could simplify the procedure without introducing additional error.（2） However,as the difference between ρs,that is the most sensitive to the reliability,and ρR,that is with the smallest reliability,is less than 0.001,ρs is suggested to model the dependency of random variables.This could ensure the robust quality of system without the loss of safety requirement.（3） In the case of ｜Eabs｜ρ0.001 and also ｜Erel｜ρ0.001,ρR should be employed to quantify the correlation among random variables in order to ensure the accuracy of reliability analysis.Application of the proposed approach could provide a practical routine for mechanical design and manufactory to study the reliability and reliability-based sensitivity of basic design variables in mechanical reliability analysis and design.

SUPPORT VECTOR MACHINE FOR STRUCTURAL RELIABILITY ANALYSIS

Support vector machine （SVM） was introduced to analyze the reliability of the implicit performance function, which is difficult to implement by the classical methods such as the first order reliability method （FORM） and the Monte Carlo simulation （MCS）. As a classification method where the underlying structural risk minimization inference rule is employed, SVM possesses excellent learning capacity with a small amount of information and good capability of generalization over the complete data. Hence, two approaches, i.e., SVM-based FORM and SVM-based MCS, were presented for the structural reliability analysis of the implicit limit state function. Compared to the conventional response surface method （RSM） and the artificial neural network （ANN）, which are widely used to replace the implicit state function for alleviating the computation cost, the more important advantages of SVM are that it can approximate the implicit function with higher precision and better generalization under the small amount of information and avoid the ＂curse of dimensionality＂. The SVM-based reliability approaches can approximate the actual performance function over the complete sampling data with the decreased number of the implicit performance function analysis （usually finite element analysis）, and the computational precision can satisfy the engineering requirement, which are demonstrated by illustrations.

A new look at the response surface method for reliability analysis using chaos theory

To overcome excessive computation errors and convergence failures encountered in an iterative calculation of the reliability index using the response surface method （RSM） for some nonlinear limit state functions, this study investigates an essential factor based on chaotic dynamics theory. The bifurcation diagrams of the reliability index are presented for some typical nonlinear limit state functions, and the computation results from the mapping functions due to the RSM iterations show the complicated dynamic phenomena such as the periodic oscillation, as well as bifurcation and chaos. From the numerical examples, it is concluded that the parameter of selection range fplays an important role in the convergence of the RSM iteration, and an improved RSM iterative algorithm is proposed with regard to the incorporation of the iterative sequential function of selection rangef The proposed method is shown to be efficient and to yield accurate results.