RANDOM SINGULAR INTEGRAL OF RANDOM PROCESS WITH SECOND ORDER MOMENT

This paper discussses the random singular integral of random process with second order moment, establishes the concepts of the random singular integral and proves that it's a linear bounded operator of space Ha(L)(m, s). Then Plemelj formula and some other properties for random singular integral are proved.

An Efficient Method for Reliability-based Multidisciplinary Design Optimization

Design for modem engineering system is becoming multidisciplinary and incorporates practical uncertainties; therefore, it is necessary to synthesize reliability analysis and the multidisciplinary design optimization （MDO） techniques for the design of complex engineering system. An advanced first order second moment method-based concurrent subspace optimization approach is proposed based on the comparison and analysis of the existing multidisciplinary optimization techniques and the reliability analysis methods. It is seen through a canard configuration optimization for a three-surface transport that the proposed method is computationally efficient and practical with the least modification to the current deterministic optimization process.

AN IMPROVED FOSM METHOD FOR CALCULATING FAILURE PROBABILITY OF WELDED PIPES WITH FLAWS

The R F first order second moment method will produce more error for calculating the reliability of welded engineering pipe structures when the failure function is seriously nonlinear and the random variables don′t serve as normal distribution. In order to increase the computing accuracy of reliability, an improved FOSM method is used for calculating the failure probability of welded pipes with flaws in this paper. Because of solving the problems of the linear expansion of failure function at the failure point and constructing equivalent normal variables, the new algorithm can greatly improve the calculating accuracy of probability of the welded pipes with cracks. The examples show that this method is simple, efficient and accurate for reliability safety assessment of the welded pipes with cracks. It can save more time than the Monte Carlo method does, so that the improved FOSM method is recommended for engineering reliability safety assessment of the welded pipes with flaws.

A modified method to calculate reliability index using maximum entropy principle

Routine reliability index method, first order second moment (FOSM), may not ensure convergence of iteration when the performance function is strongly nonlinear. A modified method was proposed to calculate reliability index based on maximum entropy (MaxEnt) principle. To achieve this goal, the complicated iteration of first order second moment (FOSM) method was replaced by the calculation of entropy density function. Local convergence of Newton iteration method utilized to calculate entropy density function was proved, which ensured the convergence of iteration when calculating reliability index. To promote calculation efficiency, Newton down-hill algorithm was incorporated into calculating entropy density function and Monte Carlo simulations (MCS) were performed to assess the efficiency of the presented method. Two numerical examples were presented to verify the validation of the presented method. Moreover, the execution and advantages of the presented method were explained. From Example 1, after seven times iteration, the proposed method is capable of calculating the reliability index when the performance function is strongly nonlinear and at the same time the proposed method can preserve the calculation accuracy; From Example 2, the reliability indices calculated using the proposed method, FOSM and MCS are 3.823 9, 3.813 0 and 3.827 6, respectively, and the according iteration times are 5, 36 and 10 6 , which shows that the presented method can improve calculation accuracy without increasing computational cost for the performance function of which the reliability index can be calculated using first order second moment (FOSM) method.

A simplified fragility analysis of fan type cable stayed bridges

A simplified fragility analysis of fan type cable stayed bridges usingProbabilistic Risk Analysis (PRA) procedure is presented for determining their failure probabilityunder random ground motion. Seismic input to the bridge support is considered to be a riskconsistent response spectrum which is obtained from a separate analysis. For the response analysis,the bridge deck is modeled as a beam supported on springs at different points. The stiffnesses ofthe springs are determined by a separate 2D static analysis of cable-tower-deck system. The analysisprovides a coupled stiffness matrix for the spring system. A continuum method of analysis usingdynamic stiffness is Used to determine the dynamic properties of the bridges .The response of thebridge deck is obtained by the response spectrum method of analysis as applied to multi-degree offreedom system which duly takes into account the quasi - static component of bridge deck vibration.The fragility analysis includes uncertainties arising due to the variation in ground motion,material property, modeling, method of analysis, ductility factor and damage concentration effect.Probability of failure of the bridge deck is determined by the First Order Second Moment (FOSM)method of reliability. A three span double plane symmetrical fan type cable stayed bridge of totalspan 689 m, is used as an illustrative example. The fragility curves for the bridge deck failure areobtained under a number of parametric variations. Some of the important conclusions of the studyindicate that (ⅰ) not only vertical component but also the horizontal component of ground motionhas considerable effect on the probability of failure; (ⅱ) ground motion with no time lag betweensupport excitations provides a smaller probability of failure as compared to ground motion with verylarge time lag between support excitation; and (ⅲ) probability of failure may considerablyincrease for soft soil condition.

Target reliability index for serviceability limit state of single piles

The objective is to develop an approach for the determination of the target reliability index for serviceability limit state(SLS) of single piles. This contributes to conducting the SLS reliability-based design(RBD) of piles. Based on a two-parameter,hyperbolic curve-fitting equation describing the load-settlement relation of piles, the SLS model factor is defined. Then, taking into account the uncertainties of load-settlement model, load and bearing capacity of piles, the formula for computing the SLS reliability index(βsls) is obtained using the mean value first order second moment(MVFOSM) method. Meanwhile, the limit state function for conducting the SLS reliability analysis by the Monte Carlo simulation(MCS) method is established. These two methods are finally applied to determine the SLS target reliability index. Herein, the limiting tolerable settlement(slt) is treated as a random variable. For illustration, four load test databases from South Africa are compiled again to conduct reliability analysis and present the recommended target reliability indices. The results indicate that the MVFOSM method overestimates βsls compared to that computed by the MCS method. Besides, both factor of safety(FS) and slt are key factors influencing βsls, so the combination of FS and βsls is welcome to be used for the SLS reliability analysis of piles when slt is determined. For smaller slt, pile types and soils conditions have significant influence on the SLS target reliability indices; for larger slt, slt is the major factor having influence on the SLS target reliability indices. This proves that slt is the most key parameter for the determination of the SLS target reliability index.

An Explicit Iteration Algorithm for Structural Reliability and its Realization by MATLAB

Based on the improved first order second moment method of the structural reliability, an explicit iteration algorithm is proposed, which can avoid solving structural performance function to obtain reliability index β and have simple calculation forms. Finally, the validity of the explicit iteration algorithm is illustrated through two examples by MATLAB programming.

ASYMPTOTICS OF THE SOLUTIONS TO STOCHASTIC WAVE EQUATIONS DRIVEN BY A NON-GAUSSIAN LéVY PROCESS

In this article, we consider the long time behavior of the solutions to stochastic wave equations driven by a non-Gaussian Lévy process. We shall prove that under some appropriate conditions, the exponential stability of the solutions holds. Finally, we give two examples to illustrate our results.

Reliability-based concurrent subspace optimization method

To avoid the high computational cost and much modification in the process of applying traditional reliability-based design optimization method, a new reliability-based concurrent subspace optimization approach is proposed based on the comparison and analysis of the existing multidisciplinary optimization techniques and reliability assessment methods. It is shown through a canard configuration optimization for a three-surface transport that the proposed method is computationally efficient and practical with the least modification to the current deterministic optimization process.

A multi-index coupling system of ice slope stability and its application

Based on the Simplified Bishop Method, the minimum safety factor of ice slope both with and without tension cracks is calculated in combination with triaxial compression tests. It is found that there exists a critical depth for each crack. Then, factors influencing ice slope stability such as slope ratio, slope height, ice cohesion, internal friction angle, unit weight and temperature were analyzed. Meanwhile, a regression equation between the aforementioned factors and safety factor is obtained, with which sensitivity analysis is carried out. The performance function is built in combination with random distribution of physical and mechanical parameters to analyze the reliability index. The Advanced First Order Second Moment Method is employed on the solution to the perfor- mance function. The one-way coupling system of ice slope stability is therefore formed based on safety factor and reliability index. Finally, an illustrated example of ice slope is provided, which shows that failure probability is relatively high, up to 6.18%, alt- hough safety factor is 2.77. Thus, it is objective and reasonable to apply the coupled system method to the slope stability rating.

Reliability Sensitivity Analysis for Drum Brake on Modal Stress

A reliability sensitivity analysis based on modal stress is presented and applied to predict the influence factors of parameters on drum brake.Firstly,the first 10 modes of prestress of the brake drum are performed in the software ANSYS Workbench.According to the results of brake noise research,it can be detected whether the drum brake meets the results that the noise frequency range of 500-1000 Hz.The reliability sensitivity design of mechanical parts based on the normal distribution parameters for complex mechanical system is discussed.Secondly,according to the first order second moment(FOSM)theory on reliability,the reliability sensitivity of drum brake is analyzed and calculated,and compared with the Monte Carlo(MC)numerical simulation results,The variation rules of reliability sensitivity is given,which provides a theoretical basis for the design of drum brake.

Discrete Time Mean-variance Analysis with Singular Second Moment Matrixes and an Exogenous Liability

We apply the dynamic programming methods to compute the analytical solution of the dynamic mean-variance optimization problem affected by an exogenous liability in a multi-periods market model with singular second moment matrixes of the return vector of assets. We use orthogonai transformations to overcome the difficulty produced by those singular matrixes, and the analytical form of the efficient frontier is obtained. As an application, the explicit form of the optimal mean-variance hedging strategy is also obtained for our model.

A new many-body potential with the second-moment approximation of tight-binding scheme for Hafnium

In this work,we develop a new many-body potential for alpha-hafnium(α-Hf)based on the second moment approximation of tight-binding(TB-SMA)theory by introducing an additional Heaviside step function into the potential model and a new analytical scheme of density function.All the parameters of the new potential have been systematically evaluated by fitting to ground-state properties including cohesive energy,lattice constants,elastic constants,vacancy formation energy,structure stability and equation of state.By using the present model,the melting point,melt heat,thermal expansion coefficient,point defects,and low-index surface energies ofα-Hf were calculated through molecular dynamics simulations.Comparing with experiment observations from others,it is shown that these properties can be reproduced reasonably by the present model,some results being more consistent to the experimental data than those by previous suggested models.This indicates that this work is sutiable in TB-SMA potential for hexagonal close packed metals.

The relationship between morphology and flight in Drosophila:a study of two pairs of sibling species from a natural population

Insect flight is a complex trait involved in different behaviors,from the search for sexual partners,food,or breeding sites.Many studies have postulated the adaptive advantages of certain morphological traits in relation to increased flight capacity,such as low values of wing loading or high values of wing:thorax ratio and wing-aspect ratio.However,few studies have evaluated the relationship between variables related to flight and morphological traits in Drosophila.This work aimed to study morphological traits in males and females of two pairs of sibling species:Drosophila buzzati Patterson and Wheeler-Drosophila koeferae Fontdevila and Wasserman,and Drosophila melanogaster Meigen-Drosophila simulans Sturtevant,and to analyze its relationship with flight.We detected the highest proportion of flight time in D.koepferae and D.simulans compared to D.buzzati and D.melanogaster,respectively.Our results also revealed sexual dimorphism,with males exhibiting a higher proportion of flight time than females.Surprisingly,we did not find a general pattern to explain the relationship between morphology and the proportion of flight time because associations varied depending upon the analyses(considering all groups together or each sex-species combination separately).Moreover,these associations explained a low percentage of variation,suggesting that other nonmorphological components related to flight,such as physiological variables,should be taken into account.This work allowed us to show the variability and complexity of an aspect of flight,suggesting that the adaptive role of the morphological traits studied might have been overestimated.

Modelling of pressure-strain correlations for Taylor-Proudman turbulence

The theoretical foundation for the modelling of the turbulent pressure\|strain correlations in rotating reference frame is presented. Based on the recently developed materially\|frame indifference principle it is observed that most of the existing second\|moment closures violate the Taylor\|Proudman theorem in the limit of rapid rotation. It is shown that the application of the materially\|frame indifference principle gives rise to the formation of a new pressure\|strain correlation model which satisfies the Taylor\|Proudman theorem.

On the Phase Transitions of (k,q)-SAT

Call a sequence of k Boolean variables or their negations a k-tuple. For a set V of n Boolean variables, let Tk（V） denote the set of all 2^kn^k possible k-tuples on V. Randomly generate a set C of k-tuples by including every k-tuple in Tk（V） independently with probability p, and let Q be a given set of q ＂bad＂ tuple assignments. An instance I = （C, Q） is called satisfiable if there exists an assignment that does not set any of the k-tuples in C to a bad tupie assignment in Q. Suppose that θ, q 〉 0 are fixed and ε=ε（n） 〉 0 be such in 2 that ε Inn/ In Inn → ∞. Let k ≥ （1 ＋ θ） log2 n and let p0 = ln2/qn^k-1. We prove thatlim∞ P[I issatisfiable] ={1,p≤（1-ε）p0, 0,p≥（1＋ε）p0.

EXPONENTIALLY FITTED TRAPEZOIDAL SCHEME FOR A STOCHASTIC OSCILLATOR

This paper applies exponentially fitted trapezoidal scheme to a stochastic oscillator. The scheme is convergent with mean-square order 1 and symplectic. Its numerical solution oscillates and the second moment increases linearly with time. The numerical example verifies the analysis of the scheme.