Optimization of System Reliability Allocation via Improved Cost Function
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摘要: 为了得到系统在一定的可靠性水平下成本最低的可靠性分配方案,根据系统成本与可靠性的关系以及成本函数的一般特点,提出了一种改进的成本函数。结合可靠性工程应用的实际情况,构建了以系统成本为目标函数,以系统可靠性达到设计要求为约束条件的可靠性分配非线性规划模型。模型具有构造简单,参数容易获取等优点,便于可靠性工程人员实际使用。采用障碍函数法对模型进行求解,结果表明,在满足系统预设可靠性要求的条件下,能够得出总成本较低的系统可靠性设计方案。Abstract: In order to obtain the lowest cost reliability allocation scheme of the system under certain reliability level, an improved cost function is proposed based on the relationship between the system cost and the reliability and the general characteristics of the cost function. Combined with the actual situation of the reliability application in practice, a nonlinear programming model for reliability allocation via system cost as the objective function and system reliability as the design requirement is constructed. The model has the advantages of simple structure, easy access to parameters, etc., which is convenient for the reliability engineering personnel in practice. The obstacle function method is used to solve the model. The results show that the system reliability design scheme via lower total cost can be obtained under the condition that the system reliability requirements are met.
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Key words:
- mathematical programming /
- cost function /
- cost optimization /
- reliability allocation
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表 1 曲柄连杆结构可靠性数据及参数
Ri fi Ri, min Ri, max R1 0.6 0.96 0.999 9 R2 0.65 0.96 0.999 9 R3 0.7 0.95 0.999 9 R4 0.75 0.97 0.999 9 R5 0.65 0.9 0.999 9 R6 0.65 0.92 0.999 9 R7 0.6 0.92 0.999 9 R8 0.7 0.92 0.999 9 R9 0.65 0.95 0.999 9 R10 0.62 0.94 0.999 9 R11 0.65 0.95 0.999 9 表 2 曲柄连杆系统可靠性分配结果
Ri 单缸工作时 双缸工作时 本文分配结果 文献[19]分配结果 本文分配结果 文献[19]分配结果 R1 0.974 0 0.984 0 0.988 1 0.990 0 R2 0.974 8 0.985 0 0.988 7 0.990 0 R3 0.971 1 0.981 0 0.987 0 0.988 0 R4 0.981 0 0.991 0 0.991 9 0.994 0 R5 0.939 1 0.903 0 0.977 0 0.973 0 R6 0.948 7 0.934 0 0.981 1 0.980 0 R7 0.947 0 0.923 0 0.980 0 0.979 0 R8 0.950 3 0.939 0 0.982 0 0.981 0 R9 0.964 1 0.969 0 0.987 4 0.989 0 R10 0.958 0 0.955 0 0.984 8 0.986 0 R11 0.964 1 0.969 0 0.987 4 0.989 0 RS1=0.830 5 RS1C=0.830 4 RS2=0.750 3 RS2C=0.750 8 表 3 分配结果的成本比较
Ri 单缸工作时 双缸工作时 本文方法成本 文献[19]方法成本 本文方法成本 文献[19]方法成本 R1 1.497 9 1.955 9 2.881 7 3.845 1 R2 1.532 1 2.083 5 3.068 2 3.765 0 R3 1.193 5 1.727 6 2.601 5 2.899 2 R4 1.336 9 2.090 4 2.352 5 3.565 1 R5 1.231 3 1.013 6 4.353 9 3.278 1 R6 1.112 0 1.097 4 4.144 9 3.740 0 R7 1.200 6 1.021 0 4.993 0 4.506 8 R8 1.086 3 1.132 9 3.996 7 3.636 4 R9 1.530 4 1.332 4 4.040 1 5.310 7 R10 1.741 1 1.184 4 4.496 2 5.348 1 R11 1.174 7 1.332 4 4.040 1 5.310 7 总成本 13.975 0 15.970 0 40.968 7 45.200 0 -
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