A Method for Determining the Reliability Index of a Materiel Subsystem

This paper presents a method for determining the reliability index of a subsystem in the materiel demonstration phase-AHP Failure Rate Method. It fully considers the various factors which influence a subsystem reliability index and solves a difficult problem that puzzles the demonstration personnel.

Derivation of Reliability Index Vector Formula for Series System and Its Application

In this study, a reliability index vector formula is proposed for series system with two failure modes in term of the concept of reliability index vector and equivalent failure modes. Firstly, the reliability index vector is introduced to determine the correlation coefficient between two failure modes, and then, the reliability index vector of a series system can be obtained. Several numerical cases and an analysis on offshore platform are performed, and the results show that this scheme provided here has better computational accuracy, and its calculation process is simpler for the series systems reliability calculations compared with the other methods. Also this scheme is more convenient for the engineering applications.

Instantaneous Reliability Index of a Typical Repairable System

A two-state system was taken as an example to show the method that we derived for analyzing the instantaneous reliability index,which was an important issue in the field of reliability.The paper first described the system as an abstract Cauchy problem by choosing suitable operators and state spaces.Then,with the TrotterKato theorem and strong continuous semi-group theorem,the method of solving the instantaneous reliability index of the repairable system was constructed.The convergence of the method was also proved in theory in this paper.To show the effectiveness of this method,some numerical examples were given at the end of the paper.

MODIFIED SCHEME BASED ON SEMI-ANALYTIC APPROACH FOR COMPUTING NON-PROBABILISTIC RELIABILITY INDEX

A new computation scheme proposed to tackle commensurate problems is devel- oped by modifying the semi-analytic approach for minimizing computational complexity. Using the proposed scheme, the limit state equations, usually referred to as the failure surface, are obtained from transformation of an interval variable to a normalized one. In order to minimize the computational cost, two algorithms for optimizing the calculation steps have been proposed. The monotonicity of the objective function can be determined from narrowing the scope of interval variables in normalized infinite space by incorporating the algorithms into the computational scheme. Two examples are used to illustrate the operation and computational efficiency of the approach. The results of these examples show that the proposed algorithms can greatly reduce the computation complexity without sacrificing the computational accuracy. The advantage of the proposed scheme can be even more efficient for analyzing sophistic structures.

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.

Reliability Comparison Between Parallel and Cold-standby Two-unit System Under Poisson Shock

This paper investigates the comparison problem of the reliability index between a parallel and a cold-standby system,both of which are consisting of two identical units.On the contrary to the general intuitive result,we proved that,under the condition that the system is shocked by a Poisson stream,the life time of the parallel system is longer than that of the cold-standby one in the sense of probability.

Reliability-Based Load and Resistance Factors Design for Offshore Jacket Platforms in the Bohai Bay:Calibration on Target Reliability Index

The target reliability index has been effectively used as the best solution to deal with the relationship between the structural safety and the optimal economy in any structural design. However, the target reliability index for offshore jacket platforms based on different sea areas in China has never been calibrated. This paper presents an approach for its calibration, and suggests many kinds of associated load cases. The uncertainties of loads and structural resistance are mainly in- vestigated. The target reliability index for structural components, tubular joints and piles of offshore jacket plaffortns are discussed respectively in detail. Finally, through the calibrated results from the offshore jacket platforms of QK18-1, JZ20-2, SZ36-1 and BZ28-1 in the Bohai Bay, it is proposed to adopt 2.8 as the target reliability index of offshore jacket platforms in the Bohai Bay for a 25-year design period. The results provide significant reference for the design of offshore jacket platforms.

Assessment on reliability of water quality in water distribution systems

Water leaving the treatment works is usually of a high quality but its properties change during the transportation stage. Increasing awareness of the quality of the service provided within the water industry today and assessing the reliability of the water quality in a distribution system has become a major significance for decision on system operation based on water quality in distribution networks. Using together a water age model, a chlorine decay model and a model of acceptable maximum water age can assess the reliability of the water quality in a distribution system. First, the nodal water age values in a certain complex distribution system can be calculated by the water age model. Then, the acceptable maximum water age value in the distribution system is obtained based on the chlorine decay model. The nodes at which the water age values are below the maximum value are regarded as reliable nodes. Finally, the reliability index on the percentile weighted by the nodal demands reflects the reliability of the water quality in the distribution system. The approach has been applied in a real water distribution network. The contour plot based on the water age values determines a surface of the reliability of the water quality. At any time, this surface is used to locate high water age but poor reliability areas, which identify parts of the network that may be of poor water quality. As a result, the contour water age provides a valuable aid for a straight insight into the water quality in the distribution system.

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.

Genetic Algorithms of Structural Fuzzy Reliability Index

In this paper the simple generation algorithms are improved. According to the geometric meaning of the structural reliability index, a method is proposed to deal with the variables in the standard normal space. With consideration of variable distribution, the correlation coefficient of the variables and its fuzzy reliability index, the feasibility and the reliability of the algorithms are proved with an example of structural reliability analysis and optimization.

The solution of minimum reliability index for modified weak point of arbitrary curved beam under pure bending

This paper is based on the fundamental loading model of pure bending and the analytical model of a circular beam element with arbitrary initial deflection. The L.W. Guo solution is modified and generalized according to the elastic theory, and the analytical solution for the stress of the beam element with arbitrary initial deflection under pure bending is derived. Using yield theory of edge strength, an expression for the safety margin of one point in the arbitrary curved beam under pure bending （ACPB） is built. This paper modifies the model for weak points of service structures and establishes a foundation for safe design and inspection of imperfect structures. Also, according to the theory of the method of advanced first-order second-moment（AFOSM） , this paper derives an expression for the reliability index of one point in ACPB. Lastly, it modifies the solution for weak points by solving the minimal reliability index.

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 analysis for seismic stability of tunnel faces in soft rock masses based on a 3D stochastic collapse model

A new horn failure mechanism was constructed for tunnel faces in the soft rock mass by means of the logarithmic spiral curve. The seismic action was incorporated into the horn failure mechanism using the pseudo-static method. Considering the randomness of rock mass parameters and loads, a three-dimensional (3D) stochastic collapse model was established. Reliability analysis of seismic stability of tunnel faces was presented via the kinematical approach and the response surface method. The results show that, the reliability of tunnel faces is significantly affected by the supporting pressure, geological strength index, uniaxial compressive strength, rock bulk density and seismic forces. It is worth noting that, if the effect of seismic force was not considered, the stability of tunnel faces would be obviously overestimated. However, the correlation between horizontal and vertical seismic forces can be ignored under the condition of low calculation accuracy.

Semi-Probabilistic Evaluation of System Redundancy for Existing Offshore Structures

In this paper, a new definition of structure system redundancy is proposed in view of the various measures for structure redundancy. By introducing the terms of structure system failure at the mechanism level and equivalent reliability index, the safety for existing offshore platforms can be evaluated by the semi-probabilistic method presented in this paper. Some numerical examples are given and satisfactory results have been obtained.

Study on slope reliability method Response Surface Method based on Morgenstern-Price Method

The combination of Morgenstern-Price Method （MPM） with Response Surface Method （RSM） improves the eonventional RSM by replacing Finite-Element Method （FEM） with MPM, which is a type of reliability analysis method-RSM based on MPM, and makes the computing process simpler. The stability of the slope was re-evaluated by use of Monte Carlo method （MCM） and the result contrasted with the fore is the conclusion. The reliability analysis of the artificial slope in Donggang Power Station was carried on, and obtained the reliable charaeteristics, which provided basis for the project.

STOCHASTIC BOUNDARY ELEMENT METHOD FOR RELIABILITY ANALYSIS OF PLATE AND BEAMS COMPOSITE STRUCTURES

In this paper, the reliability of orthotropic plate and beams composite structures, which is under the actions of the stochastic loading and stochastic boundary conditions, have been analyzed by stochastic boundary element method. First, the boundary integral equation of orthotropic plate and beams composite structures is given in this paper, and then based on the stochastic boundary element method, the method for reliability analysis of stochastic structures is establishes and formulas for computation of reliability index of orthotropic plate and beams composite structures are obtained. The computed examples show the efficient of the method used in this paper.

Resistance Partial Factor and Reliability of Cast Ball-and-Socket Support Joint

Considering the uncertainty of material performance, geometric characteristic and analysis method, the analysis of statistical parameters of the resistance of cast ball-and-socket support joints and the reliability analysis are carried out by JC method （improved first-order second-moment method） based on the relevant experimental data. Results show that the resistance partial factor of the joint increases with the increase of the reliability index. The resis- tance partial factors are suggested corresponding to the reliability index under different load combinations. Moreover, the suggested resistance partial factor is adopted in reliability design, and it is found that the reliability index of the joint is larger than the target reliability index. The optimal load combination is the one in which live load plays an im- portant control role. Finally, based on the suggested resistance partial factors, the reliability analysis of cast bail-and- socket support ioints of a proiect is conducted.

Comparison of Structural Probabilistic and Non-Probabilistic Reliability Computational Methods under Big Data Condition

In this article,structural probabilistic and non-probabilistic reliability have been evaluated and compared under big data condition.Firstly,the big data is collected via structural monitoring and analysis.Big data is classified into different types according to the regularities of the distribution of data.The different stresses which have been subjected by the structure are used in this paper.Secondly,the structural interval reliability and probabilistic pre-diction models are established by using the stress-strength interference theory under big data of random loads after the stresses and structural strength are comprehensively considered.Structural reliability is computed by using various stress types,and the minimum reliability is determined as structural reliability.Finally,the advan-tage and disadvantage of the interval reliability method and probability reliability method are shown by using three examples.It has been shown that the proposed methods are feasible and effective.

Inspection-replacement policy of system under predictive maintenance

In general, every system is in one of the three states： normal, abnormal, or failure state. When the system is diagnosed as abnormal state, it needs predictive maintenance, lfthe system fails, an identical new one will replace it. The predictive maintenance cannot make the system ＂as good as new＂. Under these assumptions, the reliability index and the inspection-replacement policy of a system were studied. The explicit expression of the reliability index and the average income rate （i.e., the long-run average income per unit time） are derived by using probability analysis and vector Markov process method. The criterion of feasibility for the optimal inspection-replacement policy under the maximum average income rate is obtained. The numerical example shows the optimal inspection-replacement policy can raise the average income rate when the optimal inspection-replacement policy is feasible.

The Effect of Anthropogenic Increase on the Earth as a Life-Support System for Mankind

Exponential increase of anthropogenic impact （human population number, some technological parameters） becomes menacing for biosphere functioning. Anyway, we should be able to estimate quantitatively limits of our impact on functional parameters of the biosphere. Considering biosphere as a natural life-support system （LSS）, we can receive the helpful information for working out and creation of artificial LSS of various types. Big biotic cycle induced with flows of a solar energy, is a basis of functioning of the biosphere and its basic cells-ecosystems. It＇s possible to summarize briefly the main functional and structural properties of the biosphere： integrity, closure, substance cycling, steady state, energy dependence and biodiversity. These properties of the biosphere, as a LSS, ensure potentially everlasting life under the conditions of a limited quantity of substrate suitable for the life on the planet. Ecological Footprint （EF） as a quantitative measure of anthropogenic impact on biosphere functioning is discussed in the paper. The index of the ecological reliability （IER） is introduced as a quantitative ecological indicator of different territories. The comparative dynamics of the United Nations＇ Human Development Index （HDI） and EF is discussed. The vital goal of sustainable human development： all humans can have opportunity to fulfill their lives without degrading the biosphere. To support sustainability, we should try to develop each nation and the mankind as a whole with a high HDI and a low ecological footprint. It means to have high level of HDI at low level of EF. But current tendency of economical and social development shows that the higher HDI is, the bigger EF is. EF of mankind is growing menacingly. Now actual pressure of the human civilization of our planet （2010） upon 50% exceeds its potential possibilities biological capacity （BC）, measured on the area ＂global＂ green hectares）. It means that we need 1.5 planets of the Earth＇s type. It leads to ecological incident in the scale of biosphere. Our biosphere is the large, multilevel, hierarchically organized system, and our civilization is only a part of it. This part is not central; it can disappear for ever, if we do not cope to be included in the biosphere as a great system.