• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

    A compositional method to model dependent failure behavior based on PoF models

    2017-11-17 08:31:56ZhiguoZENGYunxiCHENEnricoZIORuiKANG
    CHINESE JOURNAL OF AERONAUTICS 2017年5期

    Zhiguo ZENG,Yunxi CHEN,Enrico ZIO,c,Rui KANG

    aEDF Foundation Chair on Systems Science and Energetic Challenge,CentraleSupelec,Universite Paris-Saclay,Grande Voie des Vignes,92290 Chatenay-Malabry,France

    bSchool of Reliability and Systems Engineering,Beihang University,Beijing 100083,China

    cEnergy Department,Politecnico di Milano,Italy

    A compositional method to model dependent failure behavior based on PoF models

    Zhiguo ZENGa,Yunxia CHENb,*,Enrico ZIOa,c,Rui KANGb

    aEDF Foundation Chair on Systems Science and Energetic Challenge,CentraleSupelec,Universite Paris-Saclay,Grande Voie des Vignes,92290 Chatenay-Malabry,France

    bSchool of Reliability and Systems Engineering,Beihang University,Beijing 100083,China

    cEnergy Department,Politecnico di Milano,Italy

    In this paper,a new method is developed to model dependent failure behavior among failure mechanisms.Unlike the existing methods,the developed method models the root cause of the dependency explicitly,so that a deterministic model,rathe r than a probabilistic one,can be established.Three steps comprise the developed method.First,physics-of-failure(PoF)models are utilized to model each failure mechanism.Then,interactions among failure mechanisms are modeled as a combination of three basic relations,competition,superposition and coupling.This is the reason why the method is referred to as ‘compositional method”.Finally,the PoF models and the interaction model are combined to develop a deterministic model of the dependent failure behavior.As a demonstration,the method is applied on an actual spool and the developed failure behavior model is validated by a wear test.The result demonstrates that the compositional method is an effective way to model dependent failure behavior.

    1.Introduction

    Physics-of-failure(PoF)methods are widely applied to modeling components’failure behavior.In most PoF methods(e.g.,Ref.1),failure mechanisms are modeled first by deterministic PoF models,2–4and the n,by assuming that all the failure mechanisms are independent,the PoF model with the shortest time to failure(TTF)is used to describe the failure behavior of a component.1,5A fundamental assumption in PoF methods is that all the failure mechanisms are independent.This assumption,however,does not hold in many real cases,because in practice,failure mechanisms are often dependent.5For example,it is observed from experimental data that two failure mechanisms,like erosion and corrosion,can enhance each other,resulting in faster degradation.6Another example is that when test specimens are susceptible to high temperatures and heavy loads,fatigue can interacts with creep so that the specimens’TTFs are severely reduced.7

    In the literature,many effective methods have been developed to model such dependent failure behavior,e.g.,the multivariate distribution method(see,for example,Refs.8,9),the copula-based method(see,for example,Ref.10),and the shock-degradation interaction method (see,for example,Refs.11,12).In the multivariate distribution method,the dependency is modeled by identifying the joint probability distribution of the dependent variables and estimating the distribution parameters based on failure data.For example,if two components of a series system are dependent,the reliability of the system is

    where T1,T2denote the TTFs of the two components and PT1,T2(·)is the ir joint distributions.In Ref.13,PT1,T2(·)was assumed to be a Marshall-Olkin bivariate Weibull distribution and the parameters of the distribution were estimated from failure data.

    Refs.14,15reviewed the commonly used multivariate TTF distributions.Kotz et al.8investigated how the efficiency of parallel redundancy was affected when the two components were positively or negatively quadrant dependent.Navarro et al.16–18used the concept of Samaniego’s signature to obtain the mean time to failure and bounds for the reliability of dependent coherent systems.Cui and Li19developed an approach based on a Markov process to determine the joint TTF distribution of coherent systems with dependent components.Lai and Lin9extended the result in Ref.8by deriving new formulas to calculate the two-sided bounds of the MTTF of a parallel system with two dependent components.

    The multivariate distribution method is a simple and straightforward method to model dependent failure behavior.However,the method is based on probabilistic models and requires large amount offailure data to estimate the parameters of the models,which limits its applicability.

    A copula of the random vector [Z1,Z2]is defined as the joint cumulative distribution function of [U1,U2],

    where U1and U2are defined by (U1,U2)= (F1(Z1),F(xiàn)2(Z2)),in which Fi(·)is the cumulative distribution function of Zi.20According to Sklar’s Theorem,the joint distribution function of any random vector can be expressed as the marginal distribution of each element and a copula that describes the dependency.20Thus,the joint probability distribution can be determined by estimating the marginal distributions and the copula separately.

    Bunea and Bedford21developed a model where the dependency among competing risks is modeled by a copula.A similar model was developed in Refs.22,23,as well as a discussion on how the choice of copulas affected the estimated reliability.Yang et al.24used copulas to investigate the reliability of a partially perfect repairable system.Hong et al.25illustrated optimal condition-based maintenance in systems, whose dependency is described by copulas.In Ref.26,copulas were applied to modeling the failure behavior of a microgrid and a static network,respectively.Wang et al.10introduced a time-varying copula-based method to model the dependency between degradation processesand random shocks.In Ref.27,Jeddi et al.discussed the redundancy allocation problem when the components’lifetimes are dependent and described by copulas.Zhang et al.28used copulas to develop statistical inference methods for systems subject to dependent competing failures.Wu29established a new asymmetric copula and applied it to fitting two-dimensional warranty data.Ebrahimi and Lei30used copulas to account for the dependency among atoms and calculated the reliability of a nanocomponent.

    As the multivariate distribution method,the copula-based method is also based on probabilistic models and relies on failure data to estimate the model parameters.The only difference is that,in the multivariate distribution method,we identify the joint probability distribution directly,whereas in the copulabased method,we only have to identify the marginal probability distributions and the copula,and the joint probability distribution is calculated using Sklar’s Theorem.20Thus,the copula-based method shares the same limitation as the multivariate distribution method,that is,large amount offailure data need to be collected to estimate the model parameters.

    Another important dependency model is the shockdegradation interaction model developed by Feng and Coit.11In this model,two dependent failure processes,a degradation process and a shock process,are considered.Both processes can lead to failures and the degradation process is influenced by the shocks.Thefailure processes are referred to as multiple dependent competing failure processes(MDCFPs).Feng and Coit11assumed the arriving shock would bring an abrupt increase to the normal degradation process and developed a probabilistic model to calculate the system’s reliability.Wang and Pham31used a similar approach as Ref.11to model the DCFPs and determined the optimal imperfect preventive maintenance policy.Peng et al.12applied the model in Ref.11to calculate the reliability of a micro-engine and determined the optimal maintenance strategy.Keedy and Feng32applied the model in Ref.11on a stent,where the degradation process was modeled by a PoF model.Song et al.considered the reliability of a system whose components were subject to the MDCFPs33and distinct component shock sets.34Apart from the model in11,the MDCFPs can be modeled in many other ways.Jiang et al.35extended the work in11by assuming that the threshold of the degradation process was shifted by shocks.Rafiee et al.36developed a model in which the degradation rates were modified by different shock patterns.Fan et al.37developed a Stochastic Hybrid System(SHS)based framework for reliability modeling and analysis of MDCFPs.Zhang et al.38considered epistemic uncertainty in MDCFP modeling using a probability box(P-box)based approach.

    The shock-degradation interaction method provides new insights into dependency modeling by considering the actual way in which the dependency arises.However,this method only deals with a simplified scenario,where dependency arises from the superposition of two independently evolving failure mechanisms.By ‘independently evolving”,we mean that the failure behavior of each failure mechanism is not changed by the other failure mechanism.In practice,however,rathe r than evolving independently,the failure mechanisms might be actually coupled.Examples of coupling include the interaction between erosion and corrosion,6and between fatigue and creep.7The effect of coupling should thus be considered,when multiple dependent failure mechanisms are modeled.

    As reviewed before,most of the se existing methods are grounded on probabilistic models.Therefore,the y share a common limitation:the requirement on large amount of data for the accurate estimation of model parameters.To address this problem,we develop a mechanistic approach in this paper,which explicitly models the root cause of dependency to develop a deterministic model,rathe r than a probabilistic one,to describe the dependent failure behavior.The rest of this paper is organized as follows.In Section 2,we review the PoF-based failure behavior modeling method using the concept of performance parameters.The compositional method is developed in Section 3 and applied in Section 4 to model the dependent failure behavior of a spool.Experimental validation of the developed model is also conducted in Section 4.Finally,in Section 5,the paper is concluded with a discussion on potential future work.

    2.Performance parameters and PoF models

    In this paper,failure behavior is described by performance parameters and modeled based on PoF models.In this section,wefirst introduce the two concepts and the n discuss how to use the two concepts to describe failure behavior.

    2.1.Performance parameters and failure behavior

    Failure is defined as the event or statefor which a system or component no longer fulfills its intended function.2–4In most cases,failures can be described by performance parameters and failure thresholds.

    Definition 1(Performance parameters and failure thresholds).We suppose the required function of a system(or component)is not fulfilled if and only if the following inequality holds:

    Then,parameter p is defined as the performance parameter,while pthis defined as the failure threshold associated with performance parameter p.

    From Definition 1,a failure state is reached whenever a performance parameter exceeds its associated failure threshold.In other words,the smaller the value of the performance parameter is,the safer the system(or component)will be.This kind of performance parameters are referred to as smaller-the -better(STB)parameters.In reality,the re are also larger-the -better(LTB)and nominal-the -best(NTB)parameters,whose definitions can be generalized easily from Definition 1.For simplicity ofillustration,we assume that all the performance parameters discussed in this paper are STB.

    Example 1.The designed function of a beam is to withstand a given load.Thus,the performance parameter of the beam is its stress,σ,which results from the applied load.Thefailure threshold pthis the strength of the beam, [σ].Whenever σ ≥ [σ],the beam fails.

    Example 2.The designed function of a spool is to control hydraulic oil flows.When the oil leaks,the spool no longer fulfills its function.Thus,leakage is defined as the failure state of the spool.Increases of clearances due to wear will cause the leakage.Therefore,the clearance,denoted by x,is the performance parameter of the spool.The failure threshold,xth,is the clearance when the leakage takes place.Whenever x≥xth,the spool fails.Definition 2(Failure behavior).Failure behavior of a system(or component)is defined as the observable changes of the system’s(or component’s)states during its failure process.

    Since p and pthin Definition 1 can be used to characterize failures,the failure behavior can be described by modeling the variation of p over time,as shown in Fig.1.

    In Fig.1,fBE(x,t)represents the failure behavior model(FBM),in which x is a vector ofinput parameters.By substituting pthinto the FBM and solving for t,the TTF of the system(or the component)can be determined.

    2.2.Using PoF models to describe failure behavior

    The variation of p in Fig.1 is caused by failure mechanisms.Failure mechanisms are the physical or chemical processes which lead to failures.39In this section,we discuss how to model the failure mechanisms based on PoF models.These failure mechanism models are the n combined to model the failure behavior of the component,considering the interactions among the m,which will be discussed in detail in Section 3.

    Definition 3(PoF models).If the physics behind the failure mechanisms is well understood,physics-based models can be built to predict the behavior of the failure-inducing processes.These physics-based models are referred to as physics-offailure models(PoF models).

    Research on PoF models dates back to the late nineteenth century when A.Wohler investigated the effect of fatigue on railway axles.40Since the n,common failure mechanisms have been intensively investigated and many effective PoF models have been developed.For a review of PoF models commonly used in electronic and mechanical products,readers might refer to Refs.2–4PoF models can be used to determine the values of the performance parameters,which are used to describe the failure behavior of the system(or component),as shown in Fig.1.

    Example 3.According to Example 2,the performance parameter of the spool is its clearance,denoted by x.Since the spool is subject to adhesive wear,the Archard model in Eq.(2)is often used as its PoF model.41

    where xadhis the wear depth caused by adhesive wear,Kadha constant associated with surface conditions and lubrication,Wathe normal load on the wear surfaces,Hmthe hardness of the wear surface,and k1the wear rate.

    Fig.1 Describing failure behavior by modeling variation of p over time.

    The performance parameter x can be derived based on Eq.(2),since x=x0+xadh,where x0is the initial clearance.Substituting the previous expression into Eq.(2),we can describe the failure behavior of the valve.

    PoF models like Eq.(2)are used to describe the failureinducing process.However,a variety of PoF models only provide information about the TTF.For example,the Coffin-Manson model is a commonly applied model to describe low-cyclefatigue4:

    where Δ∈p/2 is the plastic strain amplitude,∈′fthe fatigue ductility coefficient and C the fatigue ductility exponent.

    In order to use PoF models like Eq.(3)to describe failure behavior,we need to define a dummy variable D,D ≥ 0,which represents the damage caused by the failure mechanism,and stipulate that a failure occurs whenever D≥1.We can easily verify from Definition 1 that D is a performance parameter and its associated failure threshold is Dth=1.Thus,the failure behavior can be described by D.

    To derive D from the PoF models,assumptions on how the damage accumulates need to be made.Often,Miner’s rule of linear accumulation is used,4so that

    where TTF is determined by the PoF models.Eq.(4)is used to describe the failure behavior of the system(or the component)based on PoF models like Eq.(3),which only predicts the TTF.It should be noted that the damage accumulation model in Eq.(4)is based on a strict assumption of linear accumulation.In practice,more complex situations might exist,which require more advanced damage accumulation models.

    Example 4.In this example,we use the damage,D,to describe the failure behavior resulted from low-cyclefatigue,based on the Coffin-Manson model in Eq.(5).The failure threshold associated with D is Dth=1.By using Miner’s rule in Eq.(4),the failure behavior can be described by

    3.Compositional method to model dependent failure behavior

    In this section,we investigate the interactions among failure mechanisms and develop a compositional method to model the dependent failure behavior.The method is called ‘compositional”because it assumes that the interactions among failure mechanisms can be modeled as a combination of three basic relations:competition,superposition and coupling.The interactions among failure mechanisms are modeled first in Section 3.1,and the n,in Section 3.2,the dependent failure behavior is modeled by combing the PoF models considering the interactions among the m.

    3.1.Modeling of interactions

    In this section,we develop a method to model the interactions as a combination of three basic relations.The three basic relations,competition,superposition and coupling,are introduced first in Sections 3.1.1–3.1.3.Then,in Section 3.1.4,a visualization tool,the interaction graph,is developed to model the interactions in terms of the three basic relations.

    3.1.1.Competition

    Competition refers to the situation where each failure mechanism contributes to a specific performance parameter and the presence of one failure mechanism has no influence on the others,as shown in Fig.2.

    In Fig.2,FMiand pirefer to the i th failure mechanism and its performance parameter,respectively.

    Example 5.An example of competition is the interaction among the three failure mechanisms of a composite ply.42There are three failure mechanisms for the composite ply,fiber tensile,matrix failure and fiber kinking/splitting.According to Ref.42,the composite ply may fail due to eithe r of the threefailure mechanisms.Moreover,the three failure mechanisms have no influence on one another.Thus,competition applies to the three failure mechanisms.

    3.1.2.Superposition

    Superposition refers to the situation where all the mechanisms contribute to a common performance parameter and the presence of one failure mechanism has no influence on the others,as shown in Fig.3.In Fig.3,FM1and FM2denote the failure mechanisms,p1denotes the common performance parameter,and pFM,1,1,pFM,1,2represent the contribution of the corresponding failure mechanism.

    Example 6.An example of superposition is the interaction between the pitting and corrosion-fatigue suffered by structures.43Let a denote the crack size.The structure fails whenever a exceeds the maximum allowable crack size,ath.Thus,a is the performance parameter of the structure.According to Ref.43,both pitting and corrosion-fatigue lead to the growth of the crack and thus contribute to the degradation of the common performance parameter a.Therefore,superposition applies to the two failure mechanisms.

    Fig.2 Illustration of competition.

    Fig.3 Illustration of superposition.

    3.1.3.Coupling

    Coupling refers to the situation where the presence of one mechanism influences the other failure mechanisms.Coupling is caused by the synergistic effect among the coupled failure mechanisms,in which one failure mechanism changes the inputs of the other failure mechanisms,as described in Fig.4.

    In Fig.4,two failure mechanisms,FM1and FM2,are coupled.ThefFM,1(·)and fFM,2(·)are the PoF models for the coupled failure mechanisms,while p1and p2are corresponding performance parameters.Some of the inputs to the fFM,1(·)and fFM,2(·),denoted by xcouple,1and xcouple,2,are influenced by the other failure mechanism and thus result in coupling between the two failure mechanisms.These parameters are referred to as coupling factors.The influence from the other failure mechanism is represented by g1(·)and g2(·).

    Example 7.An example of coupling is the interaction between fatigue and creep.7According to Ref.7,when specimens are subject to the se two failure mechanisms,the resistance to fatigue is reduced due to the influence of creep.Thus,the two failure mechanisms are coupled.

    Example 8.Another example of coupling can be found in specimens subject to erosion and corrosion.6According to Ref.6,erosion removes the protection layer on the specimen,which makes the specimen more prone to corrosion and results in an increased corrosion rate.6

    Fig.4 Illustration of coupling.

    3.1.4.Interaction graph

    The first step of the compositional method is to model the interactions among failure mechanisms.In this paper,it is assumed that the interactions are composed of the three basic relations.A visualization tool,the interaction graph,is developed in this section to visualize how the interactions are composed in terms of the three basic relations.

    In an interaction graph,a box represents a failure mechanism while a circle denotes a performance parameter.An arrow from a box to a circle means that the performance parameter corresponding to the circle is influenced by the failure mechanism corresponding to the box.A diamond is a symbol for coupling.If coupling exists between two failure mechanisms,a diamond is placed between the corresponding boxes,with the coupling factors written inside the diamond.An illustration of the interaction graph is given in Fig.5.

    Once the interaction graph is constructed,we can easily determine how the interactions are composed.For example,for the interaction graph in Fig.5,it can be seen from the figure that superposition and coupling exist between failure mechanisms 2 and 3,while competition exists among failure mechanisms 1,2 and 3.With the help of the interaction graph,the interaction among failure mechanisms is modeled as a combination of the three basic relations(see Fig.6).

    Fig.5 Illustration of interaction graph.

    Fig.6 A general interaction graph.

    3.2.Modeling of dependent failure behavior

    In this section,we develop a method to model the dependent failure behavior.Thefailure behavior of a system(or a component)is influenced by the PoF models and the interactions among the m.The interactions,as discussed in Section 3.1,are composed of the three basic relations.Thus,in Sections 3.2.1–3.2.3,wefirst discuss how to model the influence of each basic relation.Then,in Section 3.2.4,a method is developed to model the failure behavior resulting from a combination of the basic relations.

    3.2.1.Case 1:Only competition exists

    Since the competing failure mechanisms contribute to different performance parameters and do not influence one another,the failure behavior can be modeled by the weakest-link model,whereby the failure mechanism with the shortest TTF determines the failure behavior of the component(or system):

    where TTFcompmeans the TTF of the component(or system),n the number of the failure mechanisms that the component(or system)is subject to,and TTFFM,ithe TTF predicted by the PoF model of the ith failure mechanism.

    In some PoF models,the performance parameters do not change over time.For the se models,Eq.(6)can be expressed in terms of the performance parameters.To do so,let us first define the performance margin of the ith failure mechanism,Mi,as

    where piand pth,iare the performance parameter and the failure threshold for the ith failure mechanism,respectively.It is obvious that a failure occurs whenever Mi<0.Then,the weakest-link model can be expressed using the concept of performance margin as

    where Mcompstands for the performance margin of the component(or system).The component(or system)fails whenever Mcomp<0.Eq.(8)states that the failure mechanism with the least performance margin determines the failure behavior of the component(or system).We suppose that the jth failure mechanism has the minimum performance margin,that is,Mcomp=Mj.Then,the performance parameter of the component is determined by the performance parameter of the jth failure mechanism,pcomp=pj.It is obvious that Eqs.(6)and(8)are equivalent expressions of the weakest-link model.

    Example 9.In this example,we use the proposed method to develop the failure behavior model for the composite ply in Example 5.According to Ref.42,the PoF models for the failure mechanisms in Example 5 are given in Eqs.(9)–(11).

    where σ1is the main stress andthe tensile strength in the longitudinal direction parallel to the fibers.

    where the meaning of each parameter is consistent with those in Eqs.(9)and(10).

    Since competition applies to the three failure mechanisms of the ply,the weakest-link model in Eq.(8)is used to model the interactions among failure mechanisms. Since pth,1=pth,2=pth,3=1,Eq.(8)can be simplified as

    where p and pthrefer to the performance parameter and failure threshold of the composite ply under the joint effect of the three failure mechanisms,respectively.The p1,p2,p3are determined from Eqs.(9)–(11),respectively.The results in Eq.(12)are the same as those obtained in Ref.42

    3.2.2.Case 2:Only superposition exists

    Superposition of failure mechanisms can be modeled by summing up the contribution from each failure mechanism.We suppose that superposition applies to nifailure mechanisms,where the jointly contributed performance parameter is denoted by pi,1 ≤ i≤ n.Then,the superposition can be modeled as

    where pFM,i,jis the contribution of the jth failure mechanism and is determined by the corresponding PoF model,fFM,i,j(xij,t).When all the fFM,i,j(xij,t)are derivable,Eq.(13)can be rewritten in the form of rate-summation as

    Example 10.In this example,we use Eq.(13)to model the superposition between two failure mechanisms in electronic devices.Both the two failure mechanisms contribute to the time-dependent dielectric breakdown(TDDB).3Here,we assume that the two failure mechanisms do not influence each other.Thus,superposition is applied to modeling the interaction among the m.The PoF models for the failure mechanisms are the E-model,given below in Eq.(15),and the 1/E model,given in Eq.(16):

    In Eq.(15),γ is the field-acceleration parameter,Eoxthe electric field in the oxide,Q the activation energy,A0a process/material-dependent coefficient,KBthe Boltzmann constant,and T the temperature in Kelvin.In Eq.(16), τ0(T)and G(T)are temperature-related constants.

    In order to use Eqs.(15)and(16)to describe the failure behavior of the component,wefirst define two dummy variables,DEand D1/E,to represent the damage caused by the corresponding failure mechanisms.Applying Miner’s rule of damage accumulation in Eq.(4),we have

    where TTFEand TTF1/Eare determined from Eqs.(15)and(16),respectively.

    Since superposition applies to the two failure mechanisms,from Eq.(14),we have

    In Eq.(18),D means damage of the component and is the performance parameter of the component.

    Since D>1 indicates a failure,by substituting Eq.(17)into Eq.(18),we have

    Eq.(19)describes the failure behavior resulting from the superposition of E-model and 1/E-model.The result in Eq.(19)is the same as that obtained in Ref.3

    3.2.3.Case 3:Only coupling exists

    Coupling can be modeled by introducing the concept of coupling factors.It can be seen from Fig.4 that coupling is caused when some input parameters(xcouple,1and xcouple,2in Fig.4)are changed by other failure mechanisms.These parameters are referred to as coupling factors.

    In order to model the effect of coupling,the coupling factors need to be identified first.Then,the influence of the other failure mechanisms on the coupling factors,g1(·)and g2(·)in Fig.4,is determined based on an analysis of the nature of the influence.Finally,by substituting g1(·)and g2(·)into the corresponding PoF model,the effect of coupling can be modeled as follows:

    Example 11.In this example,we illustrate the method in Eq.(20)by modeling the coupling between fatigue and creep.For components subject only to low-cyclefatigue,a Coffin-Manson model is often used to approximate the failure behavior,as shown in Eqs.(3)and(4).Since coupling exists between fatigue and creep,k in Eq.(4)is assumed to be influenced by creep and is regarded as the coupling factor.In Ref.4,it is assumed that k is influenced by creep.

    where υ-(k-1)describes the influence from creep.According to Eq.(20),by substituting Eq.(21)into Eq.(4),the performance parameter and TTF under the effect of coupling between fatigue and creep can be obtained:

    It is easy to verify that the result in Eq.(22)is equivalent to the widely used frequency-modified Coffin-Manson model.4,44It should be noted that an important feature of coupling is that,when coupling exists,the PoF models for the failure mechanisms are usually changed due to the effect of the coupled mechanisms.For example,in Example 11,due to the coupling effect from creep,the PoF model for fatigue(Eq.(22))is different from the original Coffin-Manson model.This fact makes coupling distinct from superposition and competition,while in the latter two cases,the PoF models for each individual failure mechanism remain unchanged.Rathe r,the dependent failure behavior is caused by the joint effect of the PoF models.For example,in Example 10,although superposition exists between E-model and 1/E-model,the PoF model of each mechanism remains unchanged(Eqs.(15)and(16)).

    3.2.4.Case 4:Mixture of three basic relations

    In actual cases,the interaction among the failure mechanisms is a combination of the three basic relations.Thus,the modeling methods in Sections 3.2.1–3.2.3 should be combined to model the actual dependent failure behavior.We suppose that a general interaction graph in Fig.6 contains n performance parameters,which are denoted by pi,i=1,2,···n.Furthe r,let us assume that the i th performance parameter is influenced by nifailure mechanisms under superposition.We suppose that the corresponding PoF models are

    where pFM,i,jis the performance parameter associated with the j th failure mechanism and fFM,i,j(·)the PoF model.Note that if the k th performance parameter pkis subject to only onefailure mechanism,the n nk=1.

    The dependent failure behavior can be modeled in two steps:

    First,determine the performance parameters according to Eq.(24):

    where pi,jis the contribution of the j th failure mechanism on piand is determined by

    Next,since competition applies to all pi,the failure behavior of the system(or the component)can be predicted using Eqs.(6)and(8).

    Example 12.In this example,we use the compositional method to model the dependent failure behavior of the multiple dependent competing failure processes(MDCFPs)presented in Ref.12In the MDCFP,a component is subject to the joint effect of three failure mechanisms.12

    Fig.7 Interaction graph of MDCFP.

    The first failure mechanism,denoted by FM1,is the over stress failure,which is caused by shocks.When a shock arrives,a damage of W will be incurred.If W≥D,where D stands for the resistance to shocks,an over stress failure will happen.According to Definition 1,W is a performance parameter,and we denote it by p1.The second failure mechanism,denoted by FM2,results in gradual degradations of the performance parameter,p2.When p2>H,a soft failure will be caused.Meanwhile,p2is also subject to the influence from the third failure mechanism,denoted by FM3,which is caused by shocks:when the i th shock arrives,an additional degradation to p2will be caused.

    In order to apply the compositional method,we first construct the interaction graph to visualize the interactions among the three failure mechanisms.The interaction graph is given in Fig.7.

    It can be seen from Fig.7 that p2is subject to the joint effect of FM2and FM3,and the two failure mechanisms do not influence each other.Thus,superposition applies to FM2and FM3.Also,since no interactions exist among FM1,FM2and FM3,competition applies to p1and p2.According to Eqs.(24)and(25),p1and p2are determined by

    wherefFMi(xi;t) is the PoF model for the i th failure mechanism.

    Then,according to Eq.(6),the TTF is predicted by

    Eqs.(26)–(28)describe the failure behavior of the MDCFP.Furthe r,we can use Eqs.(26)–(28)to predict the reliability:

    When the arrival of shocks follows a Poisson process with rate λ,it is easy to verify that the result in Eq.(29)is equivalent to the one from Ref.12Thus,this example demonstrates that the compositional method is effective in modeling a mixture of competition and superposition.In Section 4,we will demonstrate,through an actual case study,that the method is also effective in modeling coupling.

    It should be noted that a premise of applying the compositional method is that the interactions among the failure mechanisms can be identified explicitly using the three basic relations defined in the paper.However,we admit that in some practical applications,especially when the interactions among the failures are complex,the interaction cannot be easily identified explicitly and,the refore,the compositional method cannot be applied.In this case,since the root cause of the dependency cannot be understood,we have to resort to probabilistic methods or design experiments and fit the failure behavior model from the collected data.

    4.A case study

    In this section,we use the compositional method to model the dependent failure behavior of an actual spool.We also design and implement a wear test,which validates the failure behavior model originated from the compositional method.

    4.1.Failure mechanisms and PoF models

    As discussed in Example 1,the performance parameter of the spool is its clearance,x.According to the result of a failure mode,mechanism,effect analysis(FMMEA),45since the spool and its sleeve are made from the same material,the spool is subject to adhesive wear.Besides,due to the possible existence of hard pollutants,the spool is also subject to three-body abrasive wear(hereafter referred to as abrasive wear).46Adhesive wear can be modeled by Archard model,41as shown in Eq.(2).Abrasive wear can be modeled by the following differential equation46:

    where Kabris a constant associated with the properties of the wear surfaces,while the other parameters in Eq.(30)share the same meanings as those in Eq.(2).In actual cases,the values of k1and k2are often estimated from wear tests.

    4.2.Modeling of interactions

    The interaction graph of the two failure mechanisms are given in Fig.8.

    From Fig.8,we can see that superposition exists between adhesive wear and abrasive wear,since both the two failure mechanisms contribute to a common performance parameter,the total wear depth,xtotal.Besides,coupling between the adhesive wear and abrasive wear also exists.

    From Eq.(24),the rate of xtotalcan be determined as

    where k1,k2are rateconstants in Eqs.(2)and (30),respectively.

    k1and k2in Eq.(31)are influenced by the coupling of adhesive wear and abrasive wear.From Eq.(2),k1is dependent on Kadh.According to Ref.45,Kadhis influenced by the surface roughness σS:

    where a1,a2,a3,a4are constants associated with the surface conditions.

    The surface roughness is influenced by both the two failure mechanisms,according to Eq.(33)below.45In Eq.(33),xtotalis the total wear depth and b1,b2are two constants associated with the surface conditions.

    Fig.8 Interaction graph of spool.

    Fig.9 Test setup.

    Fig.10 Experimental results and model fitting.

    Eqs.(32)and(33)describe the root cause of the coupling.In order to develop a failure behavior model to describe the coupling,we make some simplifications to Eqs.(32)and(33).From Eqs.(32)and(33),we can see that Kadhis a function of σSand σSis a function of xtotal.Thus,Kadhis a function of

    Table 1 Parametric uncertainties in Eq.(36).

    Fig.11 Reliability of spool(i.e.predicted joint distribution of TTFs).

    By using first-order Taylor expansion as an approximation,and assuming that g(0)=0,equation Eq.(34)becomes

    Substituting Eq.(35)into Eq.(31)and solving for xtotal,we have

    In Eq.(36),x(t)is the time-variant total wear depth and,k2should be determined by conducting wear tests.Eq.(36)describes the dependent failure behavior of the spool under the joint contribution of the adhesive and abrasive wear.

    4.3.Experimental validation and discussion

    In order to validate the developed model,a wear test is designed and implemented.Wear depths are monitored at fixed intervals by measuring the loss of weight due to the wear.The test setup is shown in Fig.9.

    The result of the wear test is shown in Fig.10(the x and y axes are scaled,for confidential reasons).It should be noted that in the test,the quantity directly measured at each inspection is the mass-loss of the test specimen,denoted by Δm.The wear depth d in Fig.10 is calculated from Δm using the density of the valve material ρ and the nominal surface area A:

    The model in Eq.(36)is fitted to the test data using the least square method.The result is shown as the solid line in Fig.10.

    As a comparison,we also develop a failure behavior model using the PoF method.In the PoF method,the two failure mechanisms are assumed to be independent.Since both PoF models suggest that the wear depth is a linear function of time(see Eqs.(2)and(30)),the resulting failure behavior model is also a linear function of time,

    where a and b are constants associated with the wear process and need to be estimated from test data.We also use the least square method to estimate the values of the parameters a and b.The result is represented by the dashed line in Fig.10.

    It can be seen from Fig.10 that the compositional method provides a better fit to the test data than the linear model suggested by the PoF method.This conclusion is also justified by calculating the mean square error(MSE)for both models.The MSE of the model from the compositional method is 0.5298,which is far less than 5.7981,the MSE of the model from the traditional method.

    The differences can be explained by analyzing the trend of the test data.From the test data in Fig.10,we can see that the wear rates decrease over time,which suggests that the spool is in the running-wear period.45,46In this period,the interaction between the two wear mechanisms tends to slow down the wear process.45,46The PoF method ignores the interaction by assuming that the two failure mechanisms are independent.Therefore,inaccurate results are obtained.In the compositional method,on the contrary,the interaction is considered.Thus,it fits the experimental data better.

    In the existing dependency modeling methods,such as the multivariate distribution methods9and the copula-based methods,21the dependent failure behavior is described by the joint distribution of the TTFs.The compositional method provides a PoF-based approach to determine the joint distribution.For example,by propagating the parametric uncertainties in Eq.(36)(see Table 1)using Monte-Carlo sampling,the joint TTF distribution of the spool is obtained.The result is given in Fig.11,where T1and T2represent the TTF predicted based on the abrasive wear model and adhesive wear model,respectively.The joint distribution P(T1>t,T2>t)in Fig.11 represents the reliability of the spool at t,under the joint effect of the two failure mechanisms.Note that we assume that the failure threshold of Eq.(36)is pth=20.

    In Fig.11,we also compare P(T1>t,T2>t)to the predicted reliability under the independence assumption,which is simply given by the product P(T1>t)× P(T2>t).It can be seen from Fig. 11 that P(T1>t,T2>t)≥P(T1>t)× P(T2>t),?t≥ 0.According to the definition given by Lai and Lin9,P(T1>t,T2>t)is more diagonal dependent than P(T1>t)× P(T2>t),which indicates that the dependency among the two failure mechanisms increases the reliability of the spool.This is because,as discussed earlier,the spool is in the running-wear period,in which the wear processes are slowed down by the interactions among wear mechanisms.45,46

    5.Conclusions

    In this paper,a compositional method is developed to model dependent failure behavior.The interactions among failure mechanisms are modeled as a combination of the three basic relations, competition, superposition and coupling.The method has the merit that it physically models the root cause of the dependency,so that a deterministic model can be derived to describe the dependent failure behavior.The developed method is applied to modeling the failure behavior of a spool subject to two dependent failure mechanisms.A wear test has been implemented to validate the failure behavior model.The results demonstrate that the developed method is capable of modeling dependent failure behavior.

    In the work,we have considered dependency among failure mechanisms using a physics-based method.In the future,dependency among components can also be investigated in a similar way.For example,physics-based models can be developed to model the dependency due to shared loads,where the common loads shared by a group of components result in the dependency among the m.Also,the dependency among components resulting from cascading failures can be considered,where the failure of some components increases the failure probability of other components.

    Acknowledgements

    This work has been performed within the initiative of the Center for Resilience and Safety of Critical Infrastructures(CRESCI,http://cresci.cn).The participation of Dr.Zhiguo Zeng to this research is partially supported by the National Natural Science Foundation of China(No.71671009).The research of Prof.Rui Kang is supported by the National Natural Science Foundation of China(No.61573043).The research of Prof.Yunxia Chen is supported by the National Natural Science Foundation of China(No.51675025).The authors would like to thank Mr.Xun Liao from Beihang University for his generous help in designing and conducting the wear test.

    1.Pecht M,Dasgupta A.Physics-of-failure:An approach to reliable product development.Proceedings ofintegrated reliability workshop;1995 Jul 1-10;Lake Tahoe,Piscataway(NJ):IEEE Press;1995.p.532–7.

    2.Tinga T.Principles of loads and failure:Applications in maintenance,reliability and design.London:Springer;2013.p.1–33.

    3.Mcpherson JW.Reliability physics and engineering:Time-to-failure modeling.New York:Springer;2013.p.1–18.

    4.Collins JA,Busby HR,Staab GH.Mechanical design of machine elements and machines.London:Wiley;2009.p.1–15.

    5.Zeng Z,Kang R,Chen Y.Using PoF models to predict system reliability considering failure collaboration.Chin J Aeronaut 2016;29(5):1294–301.

    6.Malka R,Nesˇic′S,Gulino DA.Erosion-corrosion and synergistic effects in disturbed liquid-particle flow.Wear 2007;262(7):791–9.

    7.Zhu S,Huang H,He L,Liu Y,Wang Z.A generalized energybased fatigue-creep damage parameter for life prediction of turbine disk alloys.Eng Fracture Mech 2012;90:89–100.

    8.Kotz S,Lai CD,Xie M.On the effect of redundancy for systems with dependent components.IIE Trans 2003;35(12):1103–10.

    9.Lai C,Lin GD.Mean time to failure of systems with dependent components.Appl Math Comput 2014;246:103–11.

    10.Wang Y,Pham H.Modeling the dependent competing risks with nultiple degradation processes and random shock using timevarying copulas.IEEE Trans Reliability 2012;61(1):13–22.

    11.Feng Q,Coit DW.Reliability analysis for multiple dependent failure processes:An MEMS application.Int J Per formability Eng 2010;6(1):100–10.

    12.Peng H,Feng Q,Coit DW.Reliability and maintenance modeling for systems subject to multiple dependent competing failure processes.IIE Trans 2011;43(1):12–22.

    13.Feizjavadian SH,Hashemi R.Analysis of dependent competing risks in the presence of progressive hybrid censoring using Marshall-Olkin bivariate Weibull distribution.Comput Stat Data Anal 2015;82:19–34.

    14.Xie M,Lai CD.Stochastic ageing and dependence for reliability.London:Springer;2006.p.1–18.

    15.Murthy DP,Xie M,Jiang R.Weibull models.New York:John Wiley&Sons;2006.p.1–12.

    16.Navarro J,Rychlik T.Comparisons and bounds for expected lifetimes of reliability systems.Eur J Operational Res 2010;207(1):309–17.

    17.Navarro J,Lai C.Ordering properties of systems with two dependent components.Commun Statistics-Theory Methods 2007;36(3):645–55.

    18.Navarro J,Ruiz JM,Sandoval CJ.Properties of coherent systems with dependent components.Commun Statistics-Theory Methods 2007;36(1):175–91.

    19.Cui L,Li H.Analytical method for reliability and MTTF assessment of coherent systems with dependent components.Reliability Eng Syst Saf 2007;92(3):300–7.

    20.Nelsen RB.An introduction to copulas.New York:Springer;2007.p.32–40.

    21.Bunea C,Bedford T.The effect of model uncertainty on maintenance optimization.IEEE TransReliability 2002;51(4):486–93.

    22.Tang X,Li D,Zhou C,Zhang L.Bivariate distribution models using copulas for reliability analysis.Proceedings Inst Mech Eng,Part O:J Risk Reliability 2013;227(5):499–512.

    23.Tang X,Li D,Zhou C,Phoon K,Zhang L.Impact of copulas for modeling bivariate distributions on system reliability.Structural Saf 2013;44:80–90.

    24.Yang Q,Zhang N,Hong Y.Reliability analysis of repairable systems with dependent component failures under partially perfect repair.IEEE Trans Reliability 2013;62(2):490–8.

    25.Hong HP,Zhou W,Zhang S,Ye W.Optimal condition-based maintenance decisions for systems with dependent stochastic degradation of components. Reliability Eng Syst Saf 2014;121:276–88.

    26.Wang S,Zhang X,Liu L.Multiple stochastic correlations modeling for microgrid reliability and economic evaluation using pair-copula function.IntJ Electrical Power Energy Syst 2016;76:44–52.

    27.Jeddi H,Doostparast M.Optimal redundancy allocation problems in engineering systems with dependent component lifetimes.Appl Stochastic Models Business Industry 2015;4(1):850–66.

    28.Zhang XP,Shang JZ,Chen X,Zhang CH,Wang YS.Statistical inference of accelerated life testing with dependent competing failures based on copula the ory.IEEE Trans Reliability 2014;63(3):764–80.

    29.Wu S.Construction of asymmetric copulas and its application in two-dimensional reliability modelling.Eur J Operational Res 2014;238(2):476–85.

    30.Ebrahimi N,Lei H.Assessing the reliability of a nanocomponent by using copulas.IIE Trans 2014;46(11):1196–208.

    31.Wang Y,Pham H.A multi-objective optimization of imperfect preventive maintenance policy for dependent competing risk systems with hidden failure.IEEE Trans Reliability 2011;60(4):770–81.

    32.Keedy E,Feng Q.Reliability analysis and customized preventive maintenance policies for stents with stochastic dependent competing risk processes.IEEE Trans Reliability 2013;62(4):887–97.

    33.Song S,Coit DW,Feng Q,Peng H.Reliability analysis for multicomponent systems subject to multiple dependent competing failure processes.IEEE Trans Reliability 2014;63(1):331–45.

    34.Song S,Coit DW,Feng Q.Reliability for systems of degrading components with distinct component shock sets.Reliability Eng Syst Saf 2014;132:115–24.

    35.Jiang L,Feng Q,Coit DW.Reliability and maintenance modeling for dependent competing failure processes with shifting failure thresholds.IEEE Trans Reliability 2012;61(4):320–36.

    36.Rafiee K,Feng Q,Coit DW.Reliability modeling for dependent competing failure processes with changing degradation rate.IIE Trans 2014;46(5):483–96.

    37.Fan M,Zeng Z,Zio E,Kang R,Chen Y.A stochastic hybrid systems based framework for modeling dependent failure processes.PloS One 2017;12(2):e0172680.

    38.Zhang Q,Zeng Z,Zio E,Kang R.Probability box as a tool to model and control the effect of epistemic uncertainty in multiple dependent competing failure processes.Appl Soft Comput 2016;56:570–9.

    39.ASSOCIATION JSST.Failure mechanisms and models for semiconductor devices.Arlington,VA:JEDEC Publication JEP122C;2006.p.320.

    40.Chatterjee K,Modarres M,Bernstein J.Fifty years of physics of failure.J Reliability Information Anal Center 2012;20(1):1–5.

    41.Archard JF.Contact and rubbing of flat surfaces.J Appl Phys 1953;24(8):981–8.

    42.Whiteside MB,Pinho ST,Robinson P.Stochastic failure modelling of unidirectional composite ply failure.Reliability Eng Syst Saf 2012;108:1–9.

    43.Chookah M,Nuhi M,Modarres M.A probabilistic physics-offailure model for prognostic health management of structures subject to pitting and corrosion-fatigue.Reliability Eng Syst Saf 2011;96(12):1601–10.

    44.Plumbridge WJ,Matela RJ.Structural integrity and reliability in electronics.London:Springer;2004.p.34–5.

    45.Chen Y,Gong W,Kang R.Coupling behavior between adhesive and abrasive wear mechanism of aero-hydraulic spool valves.Chin J Aeronaut 2016;29(4):1119–31.

    46.Engel PA.Failure models for mechanical wear modes and mechanisms.IEEE Trans Reliability 1993;42(2):262–7.

    23 September 2016;revised 22 January 2017;accepted 13 April 2017

    Available online 7 June 2017

    Degradation;

    Dependent failures;

    Multiple dependent competing failure processes;

    Reliability modeling;

    Shock

    *Corresponding author.

    E-mail address:chenyunxia@buaa.edu.cn(Y.CHEN).

    Peer review under responsibility of Editorial Committee of CJA.

    Production and hosting by Elsevier

    http://dx.doi.org/10.1016/j.cja.2017.05.009

    1000-9361?2017 Chinese Society of Aeronautics and Astronautics.Production and hosting by Elsevier Ltd.

    This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

    ?2017 Chinese Society of Aeronautics and Astronautics.Production and hosting by Elsevier Ltd.This is an open access article under the CCBY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.0/).

    精品人妻一区二区三区麻豆| 午夜日本视频在线| 日产精品乱码卡一卡2卡三| 亚洲伊人久久精品综合| 少妇裸体淫交视频免费看高清| av女优亚洲男人天堂| 亚洲天堂国产精品一区在线| 亚洲国产日韩一区二区| 蜜臀久久99精品久久宅男| 日产精品乱码卡一卡2卡三| 啦啦啦在线观看免费高清www| 午夜福利视频精品| 韩国高清视频一区二区三区| 少妇的逼水好多| 国产成人精品久久久久久| 精品国产三级普通话版| 精品少妇久久久久久888优播| 日韩 亚洲 欧美在线| 亚洲av成人精品一区久久| 黄色日韩在线| 欧美bdsm另类| 久久99热这里只频精品6学生| 久久精品国产亚洲网站| 秋霞伦理黄片| 我的老师免费观看完整版| 亚洲一级一片aⅴ在线观看| 午夜福利视频精品| 国产91av在线免费观看| 十八禁网站网址无遮挡 | 可以在线观看毛片的网站| av.在线天堂| 亚洲国产精品专区欧美| 在线观看免费高清a一片| 免费看日本二区| 国产伦理片在线播放av一区| 婷婷色麻豆天堂久久| 国产成人福利小说| 在线 av 中文字幕| 国产成人a区在线观看| 高清午夜精品一区二区三区| 少妇人妻久久综合中文| 一个人观看的视频www高清免费观看| 人妻系列 视频| 80岁老熟妇乱子伦牲交| 成年女人看的毛片在线观看| 99久久中文字幕三级久久日本| 亚洲高清免费不卡视频| 内地一区二区视频在线| 欧美激情久久久久久爽电影| 亚洲成人中文字幕在线播放| 久久久久久久精品精品| 超碰97精品在线观看| 欧美老熟妇乱子伦牲交| freevideosex欧美| 亚洲精品国产色婷婷电影| 乱系列少妇在线播放| 欧美潮喷喷水| 22中文网久久字幕| 国产亚洲午夜精品一区二区久久 | 一区二区三区精品91| 亚洲最大成人av| 99热6这里只有精品| a级一级毛片免费在线观看| 日韩欧美 国产精品| 欧美精品国产亚洲| 亚洲欧美清纯卡通| 日本一本二区三区精品| 亚洲国产高清在线一区二区三| av免费在线看不卡| 18禁裸乳无遮挡免费网站照片| av黄色大香蕉| 亚洲国产高清在线一区二区三| 亚洲精品色激情综合| 亚洲精品国产av成人精品| 真实男女啪啪啪动态图| 免费观看av网站的网址| 亚洲综合色惰| 一本久久精品| 丝袜喷水一区| 制服丝袜香蕉在线| 大片电影免费在线观看免费| 国产老妇伦熟女老妇高清| 联通29元200g的流量卡| 午夜福利高清视频| 久久久精品94久久精品| 麻豆精品久久久久久蜜桃| 欧美+日韩+精品| 日本午夜av视频| 久久6这里有精品| 国产91av在线免费观看| 亚洲成人av在线免费| 亚洲av男天堂| 嫩草影院新地址| 一本一本综合久久| 日本一本二区三区精品| 中文天堂在线官网| 97在线视频观看| 在线免费观看不下载黄p国产| 免费av观看视频| 亚洲自拍偷在线| 日本av手机在线免费观看| 国产v大片淫在线免费观看| 岛国毛片在线播放| 国产伦精品一区二区三区视频9| 精品久久久久久久末码| 亚洲图色成人| 国产精品久久久久久久电影| 2018国产大陆天天弄谢| 狂野欧美激情性bbbbbb| 熟女av电影| 深夜a级毛片| 久久6这里有精品| 国产乱人偷精品视频| 在线天堂最新版资源| xxx大片免费视频| 简卡轻食公司| 成人午夜精彩视频在线观看| 亚洲精品久久久久久婷婷小说| 欧美性感艳星| 欧美成人精品欧美一级黄| 三级经典国产精品| 免费av毛片视频| 99久国产av精品国产电影| 成人一区二区视频在线观看| 午夜日本视频在线| 免费观看性生交大片5| 99热这里只有精品一区| 国产精品久久久久久久电影| 一级a做视频免费观看| 国产视频内射| 五月开心婷婷网| 久久久久久久久大av| 男人和女人高潮做爰伦理| 秋霞伦理黄片| 亚洲成人精品中文字幕电影| 国产黄片视频在线免费观看| 直男gayav资源| 免费观看在线日韩| 亚洲国产欧美人成| 干丝袜人妻中文字幕| 十八禁网站网址无遮挡 | 男的添女的下面高潮视频| a级毛片免费高清观看在线播放| 日本黄色片子视频| 国产成人精品福利久久| 99热网站在线观看| 国产人妻一区二区三区在| 91精品一卡2卡3卡4卡| 婷婷色综合大香蕉| 91精品伊人久久大香线蕉| 亚洲天堂国产精品一区在线| 97在线视频观看| 51国产日韩欧美| 精品少妇黑人巨大在线播放| 免费av毛片视频| 丝袜脚勾引网站| 亚洲无线观看免费| 亚洲美女视频黄频| 国产老妇伦熟女老妇高清| 日韩在线高清观看一区二区三区| 欧美日韩精品成人综合77777| 欧美成人一区二区免费高清观看| 日韩视频在线欧美| av播播在线观看一区| 国产精品不卡视频一区二区| 国产午夜精品久久久久久一区二区三区| 日日摸夜夜添夜夜爱| 老女人水多毛片| 国内少妇人妻偷人精品xxx网站| 美女xxoo啪啪120秒动态图| 久久精品国产a三级三级三级| 永久网站在线| 在线观看国产h片| 在线亚洲精品国产二区图片欧美 | 97精品久久久久久久久久精品| 国产毛片在线视频| 精品一区二区免费观看| 欧美xxxx性猛交bbbb| 日韩,欧美,国产一区二区三区| 一本—道久久a久久精品蜜桃钙片 精品乱码久久久久久99久播 | 亚洲欧美日韩东京热| 99久久精品热视频| 女人十人毛片免费观看3o分钟| 丰满少妇做爰视频| 亚洲精品国产成人久久av| 亚洲综合精品二区| 丝瓜视频免费看黄片| 欧美激情久久久久久爽电影| 亚洲天堂av无毛| 久久ye,这里只有精品| 日韩 亚洲 欧美在线| 日本熟妇午夜| 中文精品一卡2卡3卡4更新| 99热这里只有是精品在线观看| 三级男女做爰猛烈吃奶摸视频| 有码 亚洲区| 18禁动态无遮挡网站| 成年女人看的毛片在线观看| 色视频在线一区二区三区| 国产日韩欧美亚洲二区| 亚洲av中文av极速乱| 国产成人免费无遮挡视频| 成人美女网站在线观看视频| 成人黄色视频免费在线看| 国产亚洲av嫩草精品影院| 熟女av电影| 色吧在线观看| 女人被狂操c到高潮| 精品熟女少妇av免费看| 偷拍熟女少妇极品色| av在线app专区| 国产极品天堂在线| 一区二区三区免费毛片| 久久亚洲国产成人精品v| 精品一区二区免费观看| 三级国产精品片| 国产精品久久久久久久电影| 天美传媒精品一区二区| 国产色婷婷99| 日本色播在线视频| 男人爽女人下面视频在线观看| 久久久久国产网址| 国产成人福利小说| 99久久人妻综合| 蜜臀久久99精品久久宅男| 一区二区三区乱码不卡18| 日韩成人伦理影院| 中国三级夫妇交换| 日本黄色片子视频| 大话2 男鬼变身卡| 欧美激情在线99| 国产伦精品一区二区三区四那| 一区二区av电影网| 亚洲精品第二区| 插逼视频在线观看| 日韩成人av中文字幕在线观看| 国产免费又黄又爽又色| 日韩精品有码人妻一区| 亚洲精品成人av观看孕妇| .国产精品久久| 国产精品精品国产色婷婷| 老师上课跳d突然被开到最大视频| 只有这里有精品99| 色婷婷久久久亚洲欧美| 少妇高潮的动态图| 久久ye,这里只有精品| 免费黄频网站在线观看国产| 少妇人妻一区二区三区视频| 在线 av 中文字幕| 黄色日韩在线| 青青草视频在线视频观看| 亚洲三级黄色毛片| 最新中文字幕久久久久| 午夜激情福利司机影院| 一级毛片黄色毛片免费观看视频| 啦啦啦中文免费视频观看日本| 男女无遮挡免费网站观看| 少妇人妻 视频| 麻豆乱淫一区二区| 日本-黄色视频高清免费观看| 久久97久久精品| av专区在线播放| 国产精品一及| 女的被弄到高潮叫床怎么办| 男女边摸边吃奶| 亚洲综合精品二区| 精品酒店卫生间| 亚洲av福利一区| 欧美xxxx性猛交bbbb| 伊人久久精品亚洲午夜| 国产av不卡久久| 久久精品国产亚洲av天美| 亚洲欧美精品专区久久| 久久久久网色| 欧美日韩综合久久久久久| 超碰av人人做人人爽久久| 成人欧美大片| 亚洲一级一片aⅴ在线观看| 中文字幕亚洲精品专区| 汤姆久久久久久久影院中文字幕| 国产片特级美女逼逼视频| 成人亚洲欧美一区二区av| 视频中文字幕在线观看| 另类亚洲欧美激情| 精品午夜福利在线看| 内地一区二区视频在线| 成人黄色视频免费在线看| 最近的中文字幕免费完整| 亚洲国产高清在线一区二区三| 91久久精品国产一区二区成人| 久久亚洲国产成人精品v| 一级爰片在线观看| 精品久久久久久久久亚洲| 51国产日韩欧美| 国产成人精品久久久久久| 精品久久久久久久末码| 九草在线视频观看| 综合色丁香网| 91精品一卡2卡3卡4卡| 九色成人免费人妻av| 国产乱人偷精品视频| eeuss影院久久| 色视频www国产| 中文字幕av成人在线电影| 日本欧美国产在线视频| 久久久久久久久久人人人人人人| 亚洲精品久久午夜乱码| 亚洲精华国产精华液的使用体验| 九色成人免费人妻av| 国产高清三级在线| 99热网站在线观看| 欧美成人午夜免费资源| 少妇被粗大猛烈的视频| 欧美丝袜亚洲另类| 中文字幕av成人在线电影| 亚洲av免费高清在线观看| 亚洲成人av在线免费| 国产免费视频播放在线视频| 欧美+日韩+精品| 国产高清国产精品国产三级 | 岛国毛片在线播放| 午夜免费鲁丝| 国产午夜精品一二区理论片| 久久人人爽人人爽人人片va| 真实男女啪啪啪动态图| 一级毛片 在线播放| 别揉我奶头 嗯啊视频| eeuss影院久久| 成人二区视频| 国产午夜精品久久久久久一区二区三区| 国产美女午夜福利| 午夜福利网站1000一区二区三区| 性色avwww在线观看| 亚洲经典国产精华液单| 在线观看免费高清a一片| 日本熟妇午夜| 久久99热这里只频精品6学生| 亚洲性久久影院| 我要看日韩黄色一级片| 80岁老熟妇乱子伦牲交| 欧美国产精品一级二级三级 | 丝袜喷水一区| 国产精品一及| 中文在线观看免费www的网站| 少妇人妻 视频| 国产欧美日韩一区二区三区在线 | 国产免费又黄又爽又色| 国产成年人精品一区二区| 亚洲精品一区蜜桃| 菩萨蛮人人尽说江南好唐韦庄| 亚洲久久久久久中文字幕| 亚洲精品日韩av片在线观看| 一级av片app| 国产精品偷伦视频观看了| 免费在线观看成人毛片| 男人舔奶头视频| 国产成人aa在线观看| 国产爱豆传媒在线观看| 简卡轻食公司| 久久久亚洲精品成人影院| 乱系列少妇在线播放| 国产爱豆传媒在线观看| 亚洲人与动物交配视频| 91午夜精品亚洲一区二区三区| 国产美女午夜福利| 男人舔奶头视频| 亚洲精品成人av观看孕妇| 亚洲精品自拍成人| 少妇 在线观看| 亚洲精品视频女| 熟女人妻精品中文字幕| 亚洲激情五月婷婷啪啪| 一级黄片播放器| 亚洲精品视频女| 秋霞在线观看毛片| 2021天堂中文幕一二区在线观| 韩国高清视频一区二区三区| 亚洲欧美日韩无卡精品| 国产精品伦人一区二区| 97人妻精品一区二区三区麻豆| 久热久热在线精品观看| 久久精品国产自在天天线| 欧美极品一区二区三区四区| 国产精品秋霞免费鲁丝片| 伊人久久国产一区二区| 日日撸夜夜添| 又黄又爽又刺激的免费视频.| 一级毛片 在线播放| 国产色爽女视频免费观看| 国产精品人妻久久久影院| 精品一区二区三卡| 久久精品综合一区二区三区| 中文资源天堂在线| 青青草视频在线视频观看| 亚洲在久久综合| 亚洲欧美日韩卡通动漫| av天堂中文字幕网| 国语对白做爰xxxⅹ性视频网站| 日本免费在线观看一区| 国产精品嫩草影院av在线观看| 欧美xxⅹ黑人| 熟女人妻精品中文字幕| 蜜臀久久99精品久久宅男| 啦啦啦啦在线视频资源| av国产免费在线观看| 18禁动态无遮挡网站| 亚洲av成人精品一二三区| 又爽又黄a免费视频| 日韩大片免费观看网站| 免费少妇av软件| 国产精品三级大全| 亚洲精华国产精华液的使用体验| 综合色丁香网| 久久久久久久久久久免费av| 一区二区三区乱码不卡18| 欧美xxⅹ黑人| 久久精品夜色国产| 久久国产乱子免费精品| av线在线观看网站| 国产一区亚洲一区在线观看| 日韩一区二区视频免费看| 久久久精品欧美日韩精品| 久久久久久久久久成人| 午夜福利视频精品| av.在线天堂| 国产人妻一区二区三区在| 男人舔奶头视频| 啦啦啦啦在线视频资源| 少妇人妻 视频| 免费黄频网站在线观看国产| 精品久久国产蜜桃| 亚洲,欧美,日韩| 69av精品久久久久久| av福利片在线观看| 中文乱码字字幕精品一区二区三区| 日韩一本色道免费dvd| 久久99热6这里只有精品| av国产免费在线观看| 直男gayav资源| 国产一区亚洲一区在线观看| 赤兔流量卡办理| 黄色怎么调成土黄色| 三级经典国产精品| 男人和女人高潮做爰伦理| 亚洲激情五月婷婷啪啪| 极品教师在线视频| 我的女老师完整版在线观看| 成人一区二区视频在线观看| 免费大片18禁| 黄色日韩在线| av女优亚洲男人天堂| 亚洲真实伦在线观看| 国产精品蜜桃在线观看| 免费av毛片视频| 青春草视频在线免费观看| 噜噜噜噜噜久久久久久91| 免费看光身美女| 欧美成人一区二区免费高清观看| 91久久精品电影网| 日本黄色片子视频| 久久久成人免费电影| 亚洲三级黄色毛片| 青青草视频在线视频观看| 久久久久久久久久久免费av| 国产老妇伦熟女老妇高清| 国产亚洲5aaaaa淫片| 久久久久久久大尺度免费视频| 七月丁香在线播放| 亚洲av中文字字幕乱码综合| av国产精品久久久久影院| 亚洲成人av在线免费| 亚洲欧美一区二区三区国产| 中文天堂在线官网| 如何舔出高潮| 各种免费的搞黄视频| 国产精品国产av在线观看| 精品少妇久久久久久888优播| 欧美日韩综合久久久久久| 黄色视频在线播放观看不卡| 精品久久久久久久久亚洲| av在线老鸭窝| 欧美性感艳星| 久久精品夜色国产| 亚洲精品,欧美精品| 高清毛片免费看| 国产av不卡久久| 伦精品一区二区三区| videossex国产| 日韩人妻高清精品专区| 欧美极品一区二区三区四区| 国产成人精品婷婷| 亚洲,欧美,日韩| 欧美xxxx黑人xx丫x性爽| av天堂中文字幕网| 久久久久精品久久久久真实原创| 国精品久久久久久国模美| 欧美人与善性xxx| 国产精品女同一区二区软件| 免费av观看视频| a级毛片免费高清观看在线播放| 一级毛片aaaaaa免费看小| 亚洲综合色惰| 亚洲天堂国产精品一区在线| 亚洲最大成人av| 波野结衣二区三区在线| 少妇人妻精品综合一区二区| 亚洲美女视频黄频| 赤兔流量卡办理| 一个人观看的视频www高清免费观看| 1000部很黄的大片| 女的被弄到高潮叫床怎么办| 高清av免费在线| 内射极品少妇av片p| 国产在视频线精品| 国产精品福利在线免费观看| 亚洲天堂国产精品一区在线| av在线天堂中文字幕| 亚洲av二区三区四区| 国产精品99久久99久久久不卡 | 成人亚洲精品av一区二区| 啦啦啦在线观看免费高清www| 搞女人的毛片| 国产精品熟女久久久久浪| 日韩欧美精品v在线| 国产色爽女视频免费观看| 久久人人爽av亚洲精品天堂 | 美女国产视频在线观看| 丝袜喷水一区| 日韩av免费高清视频| 国产精品人妻久久久久久| av国产久精品久网站免费入址| 亚洲精品视频女| 久久精品国产鲁丝片午夜精品| 国产亚洲最大av| 成人亚洲欧美一区二区av| 少妇熟女欧美另类| 免费av毛片视频| 久久亚洲国产成人精品v| 一级毛片我不卡| 只有这里有精品99| 国产高清三级在线| 日本爱情动作片www.在线观看| 国内精品美女久久久久久| 香蕉精品网在线| 一边亲一边摸免费视频| 久久久久国产网址| 亚洲成人久久爱视频| 最新中文字幕久久久久| 少妇的逼水好多| 欧美日韩国产mv在线观看视频 | 午夜免费鲁丝| 在线看a的网站| 在线亚洲精品国产二区图片欧美 | 成年版毛片免费区| 亚洲精品第二区| 七月丁香在线播放| 国产精品99久久久久久久久| 热99国产精品久久久久久7| 五月伊人婷婷丁香| 成人午夜精彩视频在线观看| 欧美日韩国产mv在线观看视频 | 国产av国产精品国产| 22中文网久久字幕| 久久精品国产亚洲av天美| 在线观看国产h片| 精品熟女少妇av免费看| 欧美 日韩 精品 国产| 亚洲内射少妇av| 看十八女毛片水多多多| 免费黄色在线免费观看| 最近最新中文字幕免费大全7| 亚洲在久久综合| 在线免费十八禁| 久久久久精品久久久久真实原创| 国产又色又爽无遮挡免| 99久久精品国产国产毛片| 精品久久久久久久久亚洲| 成人午夜精彩视频在线观看| 插阴视频在线观看视频| 深夜a级毛片| 秋霞伦理黄片| 一级毛片我不卡| 亚洲天堂av无毛| 久久久精品免费免费高清| 亚洲婷婷狠狠爱综合网| 免费高清在线观看视频在线观看| 亚洲av成人精品一区久久| 丝袜美腿在线中文| 国产极品天堂在线| 亚洲在线观看片| av卡一久久| av播播在线观看一区| 免费人成在线观看视频色| av卡一久久| 街头女战士在线观看网站| 成年女人在线观看亚洲视频 | 亚洲激情五月婷婷啪啪| 丝袜喷水一区| 一二三四中文在线观看免费高清| 亚洲一区二区三区欧美精品 | 在线观看美女被高潮喷水网站| 肉色欧美久久久久久久蜜桃 | 日韩av免费高清视频| 三级男女做爰猛烈吃奶摸视频| 超碰97精品在线观看| 夫妻午夜视频| 九九在线视频观看精品| 亚洲国产成人一精品久久久| 搡老乐熟女国产| 成人毛片60女人毛片免费| 成人亚洲精品av一区二区| 我要看日韩黄色一级片| 三级国产精品欧美在线观看| 直男gayav资源| 久久99热这里只频精品6学生|