Analysis of conditional MTTF of fault-tolerant systems

Mean time to failure (MTTF) is one of the most frequently used dependability measures in practice. By convention, MTTF is the expected time for a system to reach any one of the failure states. For some systems, however, the mean time to absorb to a subset of the failure states is of interest. Therefore, the concept of conditional MTTF may well be useful. In this paper, we formalize the definition of conditional MTTF and cumulative conditional MTTF with an efficient computation method in a finite state space Markov model. Analysis of a fault-tolerant disk array system and a fault-tolerant software structure are given to illustrate application of the conditional MTTF.     

A BDD-based algorithm for reliability analysis of phased-missionsystems

This paper presents a new algorithm (PMS-BDD) based on the binary decision diagram (BDD) for reliability analysis of phased-mission systems (PMS). PMS-BDD uses phase algebra to deal with the dependence across the phases, and a new BDD operation to incorporate the phase algebra. Due to the nature of the BDD, cancellation of common components among the phases can be combined with the BDD generation, without additional operations; and the sum of disjoint products (SDP) can be implicitly represented by the final BDD. Several examples and experiments show that PMS-BDD is more efficient than the algorithm based on SDP, in both computation time and storage space; this efficiency allows the study of some practical, large phased-mission systems     

Mathematical foundations of minimal cutsets

Since their introduction in the reliability field, binary decision diagrams have proved to be the most efficient tool to assess Boolean models such as fault trees. Their success increases the need of sound mathematical foundations for the notions that are involved in reliability and dependability studies. This paper clarifies the mathematical status of the notion of minimal cutsets which have a central role in fault-tree assessment. Algorithmic issues are discussed. Minimal cutsets are distinct from prime implicants and they have a great interest from both a computation complexity and practical viewpoint. Implementation of BDD algorithms is explained. All of these algorithms are implemented in the Aralia software, which is widely used. These algorithms and their mathematical foundations were designed to assess efficiently a very large noncoherent fault tree that models the emergency shutdown system of a nuclear reactor     

Methods for Probabilistic Analysis of Noncoherent Fault Trees

Four methods for the probabilistic analysis of s-coherent fault trees are investigated concerning their applicability to noncoherent fault trees. The inclusion-exclusion and min-max bounds can be extended to noncoherent fault trees, while the minimal cut (path) set bounds cannot. When a fault tree is modularized, the application of the min-max bounds or the inclusion-exclusion upper bound to both the modules and the organizing structure function yields the same bounds that are obtained without modular decomposition. If the organizing structure function or the modules are simple enough, exact calculations can be performed at either level to give an improved bound.     

Goal-seeking problem in discrete event systems simulation

For most complex stochastic systems such as microelectronic systems, the Mean Time To Failure (MTTF) is not available in analytical form. We resort to Monte-Carlo Simulation (MCS) to estimate MTTF function for some specific values of underlying density function parameter(s). MCS models, although simpler than a real-world system, are still a very complex way of relating input parameter(s) to MTTF. This study develops a polynomial model to be used as an auxiliary to a MCS model. The estimated metamodel is a Taylor expansion of the MTTF function in the neighborhood of the nominal value for the parameter(s). The Score Function methods estimate the needed sensitivities (i.e. gradient, Hessian, etc.) of the MTTF function with respect to the input parameter in a single simulation run. The explicit use of this metamodel is the target-setting problem in Taguchi's product design concept: given a desired target MTTF value, find the input parameter(s). A stochastic approximation algorithm of the Robbins-Monro type uses a linear metamodel to estimate the necessary controllable input parameter within a desired accuracy. The potential effectiveness is demonstrated by simulating a reliability system with a known analytical solution.     

Trading off transient fault tolerance and power consumption in deep submicron (DSM) VLSI circuits

High fault tolerance for transient faults and low-power consumption are key objectives in the design of critical embedded systems. Systems like smart cards, PDAs, wearable computers, pacemakers, defibrillators, and other electronic gadgets must not only be designed for fault tolerance but also for ultra-low-power consumption due to limited battery life. In this paper, a highly accurate method of estimating fault tolerance in terms of mean time to failure (MTTF) is presented. The estimation is based on circuit-level simulations (HSPICE) and uses a double exponential current-source fault model. Using counters, it is shown that the transient fault tolerance and power dissipation of low-power circuits are at odds and allow for a power fault-tolerance tradeoff. Architecture and circuit level fault tolerance and low-power techniques are used to demonstrate and quantify this tradeoff. Estimates show that incorporation of these techniques results either in a design with an MTTF of 36 years and power consumption of 102 /spl mu/W or a design with an MTTF of 12 years and power consumption of 20 /spl mu/W. Depending on the criticality of the system and the power budget, certain techniques might be preferred over others, resulting in either a more fault tolerant or a lower power design, at the sacrifice of the alternative objective.     

Noncoherent iterative (turbo) decoding

Previously, noncoherent sequence detection schemes for coded linear and continuous phase modulations have been proposed, which deliver hard decisions by means of a Viterbi algorithm. The current trend in digital transmission systems toward iterative decoding algorithms motivates an extension of these schemes. In this paper, we propose two noncoherent soft-output decoding algorithms. The first solution has a structure similar to that of the well-known algorithm by Bahl et al. (1974), whereas the second is based on noncoherent sequence detection and a reduced-state soft-output Viterbi algorithm. Applications to the combined detection and decoding of differential or convolutional codes are considered. Further applications to noncoherent iterative decoding of turbo codes and serially concatenated interleaved codes are also considered. The proposed noncoherent detection schemes exhibit moderate performance loss with respect to corresponding coherent schemes and are very robust to phase and frequency instabilities     

A simple Markovian method for MTTF calculation

The MTTF of a system design with constant failure and repair rates and with some forms of stand-by redundancy and switching is an important characteristic of the system. Commonly, calculation of the MTTF requires knowledge of the reliability function R(t), which is integrated to yield the MTTF. In many cases obtaining the reliability function is a non-trivial task and its analytic integration may be quite tedious. In the following we describe a simple method of obtaining the MTTF of such systems which avoids the need of knowledge of R(t). The method is Markovian in nature and is based on summing the probabilities of all the possible routes (in the space of states) by which the system can get from its initial state at t = 0 to an absorbing state (failed state), where each such probability is multiplied by the average time required for the system to follow that route. This weighted sum yields the MTTF for any given initial conditions. The method is demonstrated on some useful systems and analytical formulas for the MTTF are derived. It is further demonstrated how the results of the method may be used in the calculation of the MTBF of the system in steady-state.     

基于深度强化学习的云边协同计算迁移研究

基于单一边缘节点计算、存储资源的有限性及大数据场景对高效计算服务的需求,本文提出了一种基于深度强化学习的云边协同计算迁移机制.具体地,基于计算资源、带宽和迁移决策的综合性考量,构建了一个最小化所有用户任务执行延迟与能耗权重和的优化问题.基于该优化问题提出了一个异步云边协同的深度强化学习算法,该算法充分利用了云边双方的计...     

Asymptotic Connectivity Properties of Cooperative Wireless Ad Hoc Networks

Extensive research has demonstrated the potential improvement in physical layer performance when multiple radios transmit concurrently in the same radio channel. We consider how such cooperation affects the requirements for full connectivity and percolation in large wireless ad hoc networks. Both noncoherent and coherent cooperative transmission are considered. For one-dimensional (1-D) extended networks, in contrast to noncooperative networks, for any path loss exponent less than or equal to one, full connectivity occurs under the noncoherent cooperation model with probability one for any node density. Conversely, there is no full connectivity with probability one when the path loss exponent exceeds one, and the network does not percolate for any node density if the path loss exponent exceeds two. In two-dimensional (2-D) extended networks with noncoherent cooperation, for any path loss exponent less than or equal to two, full connectivity is achieved for any node density. Conversely, there is no full connectivity when the path loss exponent exceeds two, but the cooperative network percolates for node densities above a threshold which is strictly less than that of the noncooperative network. A less conclusive set of results is presented for the coherent case. Hence, even relatively simple noncoherent cooperation improves the connectivity of large ad hoc networks.     

Fault Trees, Prime Implicants, and Noncoherence

The K&H algorithm for finding the p.i.'s of a noncoherent fault tree is too long and complicated for the purpose. The example that was used by K&H to illustrate the algorithm is reworked with known methods to show that alternatives are available that require less work. This correspondence is a series of four letters published as a sequel to a paper by Kumamoto & Henley (K&H) that presented an ``algorithm based on top-down analysis particularly designed for noncoherent fault trees'. The first of these letters is by Locks, claiming that the article is too complicated and that a shorter procedure is available. This is followed by Reply #1 by Ogunbiyi and Reply #2 by K&H. The note is concluded with a rebuttal by Locks to both replies.     

译码转发中继系统的广义最大似然非相干分组检测（英文）

This paper considers noncoherent cooperative decode-and-forward(DF) halfduplex multi-branch relay systems.Each relay branch is modeled as a probabilistic transition system at the last hop,and thus it can be considered as a relaying chain comprising multi-hop relays.An approximation to the generalized maximum likelihood(ML) noncoherent block detection is derived for uncoded M-ary modulation in a faded noisy environment.In particular,the derived noncoherent block detection in a noiseless case is equivalent to a multichannel reception with full diversity.Furthermore,the generalized detection is extended specifically to block coded M-ary phase shift keying(MPSK) modulation.For a DF three node relay system using block coded quadrature phase shift keying(QPSK),simulation results are provided to examine the end-to-end error performance of the noncoherent detection with considering the effects of network geometry and power allocation,respectively.It is shown that under a fixed power allocation,a proper relay placement can yield near full diversity for large signal-to-noise ratio.     

A sectoring algorithm for exact computation of the frequency response of linear interval systems

An algorithm for the exact computation of the frequency responses of linear interval systems is obtained. For the computation a sectoring stage is added to an elimination algorithm to eliminate interior curves. It is shown that the intersection of a ray and the frequency response set is an empty set or a line segment whose endpoints are extrema of the functions defined. Required mathematical analysis tools for the development of the sectoring algorithm and an illustrative example are provided.     

容错计算机系统中潜在故障的分析和处理途径

潜在故障是容错系统的潜在危害，因为大多数容错系统是基于单故障假设。以汽车导航系统为例来研究这一潜在危害，并用马尔可夫模型说明潜在故障恶化系统平均故障前时间。本文深入研究了一些可能的补救措施，其中透明的在线测试是最有效的方法之一，而用暂时离线的热贮备系统进行测试则是更可靠的方法。     

多元LDPC译码器设计

在多元低密度奇偶校验码(NB-LDPC)的扩展最小和译码算法（EMS）中,由于消息向量的递归计算和校验/变量节点信息之间的迭代交换,导致译码器存在较大延迟。针对此问题本文提出了一种新型译码器结构,它优化了校验节点更新单步运算单元,根据前向后向算法规则,以3路单步运算单元完成校验节点更新,硬件资源消耗略有增加,但所需时钟周期约降为一般结构的1/3;并采用全并行运算的变量节点信息更新单元,无需利用前向后向算法将更新过程分解为多个单步运算,消除了变量节点更新的递归计算,且具有低复杂度低延时等优点,并在现场可编程门阵列(FPGA)Xilinx Virtex-4 (XC4VLX200)平台上对一个GF(16)域上(480,360)的准循环多元LDPC码进行了综合仿真。仿真结果证明,设计的译码器在较小资源消耗条件下能成倍提高吞吐量。      

Further results on noncoherent block-coded MPSK [transactions papers]

A novel noncoherent block coding scheme, called noncoherent block-coded MPSK (NBC-MPSK), was proposed recently. In this paper, we present further research results on NBC-MPSK. We first focus on the rotational invariance (RI) of NBC-MPSK. Based on the RI property of NBC-MPSK with multistage decoding, a noncoherent near-optimal linear complexity multistage decoder for NBC-MPSK is proposed. Then we investigate a tree-search ML decoding algorithm for NBCMPSK. The derived algorithm is shown to have low complexity and excellent error performance. In this paper, we also utilize the idea of the NBC-MPSK to design noncoherent space-time block codes, called noncoherent space-time block-coded MPSK (NSTBC-MPSK). For two transmit antennas, we propose a signal set with set partitioning and derive the minimum noncohent distance of NSTBC-MPSK with this signal set. For the decoding of NSTBC-MPSK, we modify the ML decoding algorithm of NBC-MPSK and propose an iterative hard-decision decoding algorithm. Compared with training codes and unitary space-time modulation, NBC-MPSK and NSTBC-MPSK have larger minimum noncoherent distance and thus better error performance for the noncoherent ML decoder.     

Optimal structure of sensor systems composed of nonidentical sensors

The sensor system has two types of contradictory failures; a fail-dangerous failure and a fail-safe failure. A method of obtaining the optimal structure is developed for the sensor system which is composed of general components. The optimal structure minimizes an expected damage, considering all possible boolean structures including noncoherent systems. A simple optimality criterion is obtained and several properties of the optimal structures are derived; a noncoherent structure can be optimal in some cases. A simple systematic search algorithm can be used effectively to determine the optimal system. Analytic solutions are obtained for systems composed of identical components. Illustrative examples are given.     

Short-length rate-compatible code design for noncoherent detection

In this paper, we propose a simple method for generating short-length rate-compatible codes that are robust to noncoherent detection forM-PSK constellations. For any given constellation set, first we use a greedy algorithm to construct a family of rotationally invariant codes. Then, by properly modifying such codes, we obtain a new family of codes that are robust to noncoherent detection. We briefly discuss the optimality of the constructed codes for special cases of BPSK and QPSK constellations. Our method provides an upper bound for the length of optimal codes with a given desired noncoherent distance. We also derive a simple asymptotic upper bound on the frame error rate (FER) of such codes and provide some simulations. Finally, the problem of designing binary codes that are robust to noncoherent detection for QPSK constellation is briefly discussed.     

Joint Failure Importance for Noncoherent Fault Trees

There exist several risk importance measures in the literature to rank the relative importance among basic events within a fault tree. Most of the importance measures indicate how important a basic event is with respect to the top event of the fault tree. However, the mutual influence among the basic events should also be considered. This is particularly true in practice when making maintenance decisions with a limited resource. This paper investigates the Joint Failure Importance (JFI), which reflects the interaction among basic events, namely, the change in the Birnbaum Importance of one basic event when the probability of another basic event changes. Even though the JFI for coherent fault trees and its properties have been examined in the literature, the results cannot be easily extended to noncoherent fault trees. The current work has shown that, for both coherent, and noncoherent fault trees, the sign of the JFI can provide useful information. However, the properties of the JFI for noncoherent fault trees are more complex, and do not always share with those for coherent fault trees. The Shutdown System Number One (SDS1) in a Canadian Deuterium-Uranium (CANDU) Nuclear Power Plant (NPP) is utilized to illustrate the theoretical results developed in this paper.     

An efficient numerical technique for the solution of the monodomain and bidomain equations

Most numerical schemes for solving the monodomain or bidomain equations use a forward approximation to some or all of the time derivatives. This approach, however, constrains the maximum timestep that may be used by stability considerations as well as accuracy considerations. Stability may be ensured by using a backward approximation to all time derivatives, although this approach requires the solution of a very large system of nonlinear equations at each timestep which is computationally prohibitive. In this paper we propose a semi-implicit algorithm that ensures stability. A linear system is solved on each timestep to update the transmembrane potential and, if the bidomain equations are being used, the extracellular potential. The remainder of the equations to be solved uncouple into small systems of ordinary differential equations. The backward Euler method may be used to solve these systems and guarantee numerical stability: as these systems are small, only the solution of small nonlinear systems are required. Simulations are carried out to show that the use of this algorithm allows much larger timesteps to be used with only a minimal loss of accuracy. As a result of using these longer timesteps the computation time may be reduced substantially.