Modified fictitious play

We describe a modification of Brown's fictitious play method for solving matrix (zero-sum two-person) games and apply it to both symmetric and general games. If the original game is not symmetric, the basic idea is to transform the given matrix game into an equivalent symmetric game (a game with a skew-symmetric matrix) and use the solution properties of symmetric games (the game value is zero and both players have the same optimal strategies). The fictitious play method is then applied to the enlarged skew-symmetric matrix with a modification that calls for the periodic restarting of the process. At restart, both players' strategies are made equal based on the following considerations: Select the maximizing or minimizing player's strategy that has a game value closest to zero. We show for both symmetric and general games, and for problems of varying sizes, that the modified fictitious play (MFP) procedure approximates the value of the game and optimal strategies in a greatly reduced number of iterations and in less computational time when compared to Brown's regular fictitious play (RFP) method. For example, for a randomly generated 50% dense skew-symmetric 100 × 100 matrix (symmetric game), with coefficients |a_ij| ≤ 100, it took RFP 2,652,227 iterations to reach a gap of 0.03118 between the lower and upper bounds for the game value in 70.71 s, whereas it took MFP 50,000 iterations to reach a gap of 0.03116 in 1.70 s. Improved results were also obtained for general games in which the MFP solves a much larger equivalent symmetric game. © 1996 John Wiley & Sons, Inc.     

Two-agent scheduling with linear resource-dependent processing times

This paper considers a two-agent scheduling problem with linear resource-dependent processing times, in which each agent has a set of jobs that compete with that of the other agent for the use of a common processing machine, and each agent aims to minimize the weighted number of its tardy jobs. To meet the due date requirements of the jobs of the two agents, additional amounts of a common resource, which may be in discrete or continuous quantities, can be allocated to the processing of the jobs to compress their processing durations. The actual processing time of a job is a linear function of the amount of the resource allocated to it. The objective is to determine the optimal job sequence and resource allocation strategy so as to minimize the weighted number of tardy jobs of one agent, while keeping the weighted number of tardy jobs of the other agent, and the total resource consumption cost within their respective predetermined limits. It is shown that the problem is -hard in the ordinary sense, and there does not exist a polynomial-time approximation algorithm with performance ratio unless ; however it admits a relaxed fully polynomial time approximation scheme. A proximal bundle algorithm based on Lagrangian relaxation is also presented to solve the problem approximately. To speed up convergence and produce sharp bounds, enhancement strategies including the design of a Tabu search algorithm and integration of a Lagrangian recovery heuristic into the algorithm are devised. Extensive numerical studies are conducted to assess the effectiveness and efficiency of the proposed algorithms.     

泛函在射表逼近中的应用

运用泛函理论,对方差最小原则下射表逼近进行分析,给出了在给定基函数形式条件下的统一计算公式,并对最小二乘方法作了改进,消除系数矩阵的原理误差,给出了提高精度的方法。最后,提出了一个选择基函数的有效方法。     

监视器的可变行频电路设计

文中讨论了几种可变行频电路方案及其计算方法,通过实例计算和实验归纳了连续可变行频的设计要点。     

面向柔性加工环境的过程状态振动监测

本文运用提出的通用状态监测模型及策略,以振动信号监测为例,提取设备运行状态的振动信号方差和振动信号建立AR模型的参数估计的变化率参数作为两类通用特征参数,对柔性加工系统进行归一化监测,取得了良好的效果。建立的监测系统简洁、快速、可靠,满足柔性制造环境下设备运行状态监测的要求。     

紧固件用钢复验的动态抽验方案

本文针对现行紧固件原材料进厂抽样复验方法的不足,套改《ISO2859计数抽查程序和图表》,提出动态抽样方案,并对新旧方案实际应用进行了比较。以比较科学的决策,取得提高效益、降低消耗的结果.     

用填充函数法解决舰炮武器系统性能参数最佳化问题

本文研究的是舰炮武器系统的性能参数在满足一定的约束条件下,以什么样的匹配,可使舰炮武器系统的射击效力最佳,我们以多发射弹对目标的毁伤概率R_s(X)为目标函数,建立了数学模型。为了求解这样一个总体最优化问题,我们应用了填充函数的理论和方法,建立了算法,并扩充了一类填充函数的理论。通过在VA×11/780机上实际计算,获得了满意的结果,较好地解决了舰炮武器系统性能、参数的最佳化问题。     

Blast resistance evaluation of urban utility tunnel reinforced with BFRP bars

To improve corrosion-resistance of shallow-buried concrete urban utility tunnels(UUTs),basalt fiber reinforced polymer(BFRP)bars are applied to reinforce UUTs.As the UUT must have excellent survival capability under accidental explosions,a shallow-buried BFRP bars reinforced UUT(BBRU)was designed and constructed.Repetitive blast experiments were carried out on this BBRU.Dynamic responses,damage evolutions and failure styles of the BBRU under repetitive explosions were revealed.The tunnel roof is the most vulnerable component and longitudinal cracks develop along the tunnel.When the scaled distance is larger than 1.10 m/kg1/3,no cracks are observed in the experiments.When the BBRU is severely damaged,there are five cracks forming and developing along the roof.The roof is simplified as a clamped-supported one-way slab,proved by the observation that the maximum strain of the transverse bar is much larger than that of the longitudinal bar.Dynamic responses of the roof slab are predicted by dynamic Euler beam theory,which can consistently predict the roof displacement under large-scaled-distance explosion.Compared with the UUT reinforced with steel bars,the BBRU has advantages in blast resistance with smaller deflections and more evenly-distributed cracks when the scaled distance is smaller than 1.260 m/kg1/3 and the steel bars enter plastic state.Longer elastic defamation of the BFRP bars endows the UUT more excellent blast resistance under small-scaled-distance explosions.     

柔性加工单元故障诊断的模糊Petri网模型

针对故障诊断专家系统中专家知识的模糊性和不确定性,给出用模糊Ｐｅｔｒｉ网（ＦＰＮ）模型表示模糊产生式规则（ＦＰＲ）知识的方法、知识的存储、模糊推理机制及算法的实现。同时,以ＪＣＳ—０２０（ＦＡＮＵＣ）加工中心主轴伺服故障诊断为例,说明该方法在故障诊断专家系统（ＦＤＥＳ）中应用的可行性与有效性。     

Two novel critical shock models based on Markov renewal processes

In this paper, we investigate systems subject to random shocks that are classified into critical and noncritical categories, and develop two novel critical shock models. Classical extreme shock models and run shock models are special cases of our developed models. The system fails when the total number of critical shocks reaches a predetermined threshold, or when the system stays in an environment that induces critical shocks for a preset threshold time, corresponding to failure mechanisms of the developed two critical shock models respectively. Markov renewal processes are employed to capture the magnitude and interarrival time dependency of environment-induced shocks. Explicit formulas for systems under the two critical shock models are derived, including the reliability function, the mean time to failure and so on. Furthermore, the two critical shock models are extended to the random threshold case and the integrated case where formulas of the reliability indexes of the systems are provided. Finally, a case study of a lithium-ion battery system is conducted to illustrate the proposed models and the obtained results.