Dynamic fault trees (DFTs) are powerful in modeling systems with sequence- and function dependent failure behaviors. The key point lies in how to quantify complex DFTs analytically and efficiently. Unfortunately, the existing methods for analyzing DFTs all have their own disadvantages. They either suffer from the problem of combinatorial explosion or need a long computation time to obtain an accurate solution. Sequential Binary Decision Diagrams (SBDDs) are regarded as novel and efficient approaches to deal with DFTs, but their two apparent shortcomings remain to be handled: That is, SBDDs probably generate invalid nodes when given an unpleasant variable index and the scale of the resultant cut sequences greatly relies on the chosen variable index. An improved SBDD method is proposed in this paper to deal with the two mentioned problems. It uses an improved ite (If-Then-Else) algorithm to avoid generating invalid nodes when building SBDDs, and a heuristic variable index to keep the scale of resultant cut sequences as small as possible. To confirm the applicability and merits of the proposed method, several benchmark examples are demonstrated, and the results indicate this approach is efficient as well as reasonable.

The permanental polynomial of IPR fullerene C-70(D-5h) is computed with quadruple precision arithmetic based on sparse graph on PC in acceptable time. The computing adopts 128 bits to store one float and works well for C-70, while the largest fullerene computed before is C-60, which can be easily obtained now. Some properties of the coefficients and zeroes of the permanental polynomials of IPR fullerenes C-60 and C-70 are also investigated. Computational results show the quadruple precision method can handle permanental polynomial of C-70 and even larger fullerenes, which are of interest in applications.

To solve long time-consuming problem in analysis of large-scale quantum transport systems based on first-principles calculations, we analyze hot spots of self-consistent iterations within the framework that combines non-equilibrium Green’ s function with density functional theory, namely DFT+NEGF method. Two parallel computing schemes based on MPI/OpenMP are proposed to deal with energy point integration and matrix inversion/multiplication. For energy point integral parallelism, sparse matrix as well as energy points should be assigned to each process over data initialization according to round-robin scheduling algorithm. Either MPI based ScaLAPACK subroutine or OpenMP based Intel MKL subroutine can be called to realize matrix inversion/multiplication parallelization. A sub-linear speedup ratio curve is obtained for energy point integral parallelism due to the fact that calculations related with different energy points are mutually independent. OpenMP parallelism adopts shared memory patterned data exchange mechanism and overhead of switching threads is rather small, and consequently it is better in computing efficiency but worse in code scalability than MPI implementation.

Dynamic fault tree as a powerful analyzing tool is used to model systems having sequence- and function-dependent failure behaviors. The problem is how to quantify a complex dynamic fault tree where different dynamic gates coexist and are highly coupled. Existing analytical methods for analyzing dynamic fault trees are mainly Markov-based, inclusion–exclusion-based and sequential binary decision diagram–based approaches. Unfortunately, all these methods have their own shortcomings. As to the Markov-based method, it is frequently subjected to the problem of state-space explosion and only applicable for systems having components with exponential time-to-failure distributions. For the inclusion–exclusion-based method, it is often vulnerable to the problem of combinatorial explosion. As to the sequential binary decision diagram method, it cannot be directly applied to a complex dynamic fault tree where dynamic gates are highly coupled together, and its computational efficiency greatly depends on the chosen variable index. In this article, we put forward using an adapted K.D. Heidtmann algorithm to analyze the reliability of a complex dynamic fault tree. To improve the computational efficiency of our proposed method, products are ordered according to their lengths and compositions. To illustrate the applicability and advantages of the proposed method, a case study is analyzed. The results show the proposed method is reasonable and efficient.

To analyze the reliability of safety system having multi‐failure behavior ,such as sequence‐,redundancy‐ and function‐dependent failure behaviors ,in nuclear power plant ,a dynamic fault tree model based on numerical simulation approach was proposed in this paper .It is implemented to analyze the reliability of safety system having multi‐failure behavior in nuclear power reactor through randomly simulating the multi‐failure behavior of component and judging the success rule of dynamic logic gate .T he results of the case study indicate the proposed method is applicable for evaluating the reliability of complicated system with multi‐failure behavior ,and offers great generality .

Many sequence- and function-dependent failure behaviors may exist in fault-tolerant systems, in which the failure of the systems depends not only on the combination of basic events but also on their failure sequences. Such systems can be modeled by dynamic fault tree with Priority AND gate, Spare gate, Sequence Enforcing gate and Functional Dependence gate. The existing analytical methods for analyzing these dynamic gates are mainly Markov-based or inclusion-exclusion-based approaches. Compared with Markov approaches, the inclusion-exclusion-based method presents notable advantages. However, to the author's knowledge, no references by far have presented general multi-integration formulas applicable for solving a generalized minimal cut sequence, which is an unavoidable problem in inclusion-exclusion-based method. In this article, new multi-integration formulas are proposed based on traditional probabilistic models, which are applicable for solving a generalized minimal cut sequence as well as any dynamic gate. The rigorous derivation processes are given. The application and advantages of our proposed approach are demonstrated through a case study and the results indicate our proposed approach is reasonable.

As a computational fluid dynamics (CFD) method on mesoscopic level, lattice Boltzmann method (LBM) is supposed to be very suitable for using the graphics processing unit (GPU) on a large scale parallel computing due to its simple models, local data as well as clear physical image. On CPU-GPU heterogeneous platform, the conventional LBM algorithm is redesigned based on the compute unified device architecture (CUDA) programming model to implement that the GPU takes over compute-intensive tasks while the CPU is responsible for memory management, launching GPU kernel functions, data distribution and collection during every time step of particle relaxation. In program tuning phase, an optimization scheme is proposed to improve the efficiency of GPU's global memory access. Taking the two-dimensional plan Poiseuille flow and the lid-driven flow for example, calculation results show that the GPU based acceleration applied to LBM is not only feasible but also efficient, achieving a maximum increase in speed of 110x tested with NVIDIA GTS 450 GPU.

Dynamic fault tree (DFT) is a commonly used method to model systems having sequence-dependent and function-dependent failure behaviors. The failure structure function of a DFT can be expressed by logic OR of all minimal cut sequences, that is, minimal cut sequence set (MCSS). The occurrence probability to the top event of a DFT can be calculated using inclusion-exclusion (IE) principle based on enumerating the MCSS. However, the IE-based approach would have exponential evaluation complexity. Then, a sequential binary decision diagram (SBDD)-based method is proposed and successfully applied to analyze simple dynamic systems. This method is more efficient than IE-based method in asymptotic analysis. But this method cannot handle complex systems modeled by different highly coupled dynamic gates. In this paper, we put forward using Independent Random Variable Probabilistic Model-based plus SBDD-based methods to quantify an MCSS to obtain the failure probability of a complex DFT. The results obtained by the proposed method are exactly matched with those obtained by the existing methods. In addition, this method enhances the analyzing ability of the original SBDD and retains the advantage of high computational efficiency. The application and advantage of our proposed method is demonstrated by a case study. Copyright (c) 2014 John Wiley & Sons, Ltd.

Many fault-tolerant systems in real life are involved in sequence- and function-dependent failure behaviors, in which the failure of these systems depends not only on the combination of basic events, but also on their failure orders. Dynamic fault tree (DFT) as an extension of the conventional static fault tree is widely used to model such systems. The existing analytical approaches for reliability evaluation of DFT are mainly Markov-based, Inclusion-exclusion-based and sequential-BDD - based methods. Those approaches either suffer from the problem of state-space explosion or are subjected to combinatorial explosion knot or have small flaws. To overcome the shortcomings of the existing methods, a pivotal decomposition scheme upon the structure function of a given DFT is proposed in this paper. The proposed approach rewrites the structure function into equivalent sum-of-disjoint products based on Shannon decomposition theorem and exactly calculates the unreliability of non-repairable dynamic systems modeled by DFT. In addition, the proposed method is efficient compared with existing approaches. The application and advantages of the proposed method are demonstrated by analysis of a case study.

Existing analytical methods for analyzing warm standby systems are mainly Markov-based and inclusion-exclusion-based approaches. However, both approaches have their own shortcomings. As to Markov-based methods, they often confront the problem of state space explosion and require exponential components time-to-failure distributions. For the inclusion-exclusion-based approaches, the multi-integration formulas developed for quantifying minimal cut sequences generated from warm spare gate system base on exponential components time-to-failure distribution as well. In this paper, new sequential multi-integration formulas are proposed for quantifying warm spare systems, which are applicable for system having components with arbitrary time-to-failure distributions. The rigorous mathematical derivations are presented thoroughly. For a validation purpose, an illustrative example is analyzed. The results indicate that our proposed method is reasonable.

The quantitative analyses of Nuclear Power Plant (NPP)'s repairable systems are conventionally Markov-based methods. The thing is, systems' state space grows exponentially with the increase of basic events, which makes the problem hard or even impossible to solve. In addition, the maintenance /test activities are frequently imposed on some safety-critical components, which make the Markov based approach unavailable. In this paper, a new numerical simulation approach based on MCSS (Minimal Cut Sequence Set) is proposed, which can get over the shortcomings of the conventional Markov method. Two typical cases are analyzed and results indicate that the new approach is correct as well as feasible.

Testing and maintenance activities of safety equipment have drawn much attention in Nuclear Power Plant (NPP) to risk and cost control. The testing and maintenance activities are often implemented in compliance with the technical specification and maintenance requirements. Technical specification and maintenance-related parameters, that is, allowed outage time (AOT), maintenance period and duration, and so forth, in NPP are associated with controlling risk level and operating cost which need to be minimized. The above problems can be formulated by a constrained multiobjective optimization model, which is widely used in many other engineering problems. Particle swarm optimizations (PSOs) have proved their capability to solve these kinds of problems. In this paper, we adopt PSO as an optimizer to optimize the multiobjective optimization problem by iteratively trying to improve a candidate solution with regard to a given measure of quality. Numerical results have demonstrated the efficiency of our proposed algorithm.

Several relations between the coefficients of the permanental and characteristic polynomials were given by Gutman and Cash [MATCH Commun. Math. Comput. Chem. 45 (2002) 55-70]. In this paper, some more and general connections between those coefficients are presented.