Intelligent Selection of Simulation Experiment Design Methods Based on Hybrid Reasoning
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摘要: 针对仿真实验设计方法众多而在实际应用中难以准确选择的问题，提出一种用于仿真实验设计方法智能选择的混合推理方法.首先，给出了基于混合推理的仿真实验智能化设计流程；然后，针对案例检索策略，将仿真实验设计案例的属性分为三种类型，分别给出其属性差异度量模型及特征值归一化方法，并采用训练后的神经网络模型分配属性权重；进一步，当推荐的案例未能满足给定的相似度阈值时，引入属性优先级的概念，提出了一种基于规则的柔性逐层推理方法；在此基础上，设计了案例库和规则库；最后，通过实验验证了所提出方法的有效性.Abstract: Due to the variety of simulation experiment design methods, it is difficult to choose an appropriate method in the practical application. In order to solve this problem, a hybrid reasoning method for selecting simulation experiment design methods intelligently is proposed in this paper. Firstly, a workflow of intelligent design of simulation experiment based on hybrid reasoning is given. Then, the attributes of cases are divided into three types towards the case retrieval strategy. The difference measurement models and methods are given for each type. Meanwhile, the weight assignment method of attributes based on neural network is given. Furthermore, when the recommended case fails to meet the given similarity threshold, a rule-based flexible layer-by-layer reasoning (RBFLR) method is proposed by introducing the concept of attribute priority. Based on above, the case base and the rule base are designed. Finally, the effectiveness of the proposed method is verified by experiments.1) 本文责任编委 刘艳军
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图 3 基于NN的属性权重分配网络结构
Fig. 3 Network structure of attribute weight assignment based on neural network
图 5 不同分配比例下各推理方法的平均分配准确率
Fig. 5 Averaging classification accuracy of different assignment proportions
表 1 案例属性
Table 1 Attributes of the cases
ID 属性 属性取值 属性类型 1 实验目的 $\text{EP}\in\textbf{ N}$ 语义型离散 2 实验点分布 $\text{ED}\in\textbf{ N}$ 语义型离散 3 系统复杂度假设 $\text{SC}\in\textbf{ N}$ 语义型离散 4 二因子交互效应估计 $\text{FI}\in\textbf{ N}$ 语义型离散 5 模型独立性 $\text{MI}\in\textbf{ N}$ 语义型离散 6 处理群组因子 $\text{CG}\in\textbf{ N}$ 语义型离散 7 实验点可扩展性 $\text{EE}\in\textbf{ N}$ 语义型离散 8 水平数 $\text{FL}\in\textbf{ N}$ 语义型离散 9 实验次数 $\text{EN}\in\textbf{ N}$ $^{+}$ 实数型离散 10 因子数 $\text{FN}\in\textbf{ N}$ $^{+}$ 实数型离散 11 仿真实验设计方法 $\text{EM}\in\textbf{ N}$ $^{+}$ 语义型离散 
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表 2 规则属性
Table 2 Attributes of the rules
ID 属性 属性取值 属性类型 优先级 1 实验目的 $\text{EP}\in\textbf{ N}$ 语义型离散 ${{k}_{1}}$ 2 实验点分布 $\text{ED}\in\textbf{ N}$ 语义型离散 ${{k}_{2}}$ 3 系统复杂度假设 $\text{SC}\in\textbf{ N}$ 语义型离散 ${{k}_{3}}$ 4 二因子交互效应估计 $\text{FI}\in\textbf{ N}$ 语义型离散 ${{k}_{4}}$ 5 模型独立性 $\text{MI}\in\textbf{ N}$ 语义型离散 ${{k}_{5}}$ 6 处理群组因子 $\text{CG}\in\textbf{ N}$ 语义型离散 ${{k}_{6}}$ 7 实验点可扩展性 $\text{EE}\in\textbf{ N}$ 语义型离散 ${{k}_{7}}$ 8 水平数 $\text{FL}\in\textbf{ N}$ 语义型离散 ${{k}_{8}}$ 9 实验次数 $\text{EN}\in [{s}_{1}, {s}_{2}]$ 实数型区间 ${{k}_{9}}$ 10 因子数 $\text{FN}\in [{n}_{1}, {n}_{2}]$ 实数型区间 ${{k}_{10}}$ 11 仿真实验设计方法 $\text{EM}\in\textbf{ N}$ $^{+}$ 语义型离散 $/$ 备注: EP $\in $ {1)寻找重要因子, 2)寻找稳健参数, 3)优化, 4)不确定性分析, 5)灵敏度分析, 6)方差分析, 7)综合评估}; ED $\in $ {1)均匀性, 2)正交性, 3)空间填充性, 4)随机性, 5)鲁棒性, 6)序贯性}; SC $\in $ {1)一阶多项式(主效应模型), 2)一阶多项式+二因子交互效应, 3)二阶多项式(含完全平方项), 4)高阶交互效应}; FI $\in $ {1)能, 2)否}; MI $\in $ {1)是, 2)否}; CG $\in $ {1)能, 2)否}; EE $\in $ {1)能, 2)否}; FL $\in $ {1) 2$ \sim $3水平为主, 2) 4$ \sim $10水平为主, 3)大于10水平为主, 4)水平较为分散}; EN $\in $ {1) $[1, n)$, 2) $[n, +\infty)$, 3) $[{{2}^{n}}, +\infty)$}, 其中$n$为因子数; FN $\in $ {1) $[2, 13]$, 2) $[14, 50]$, 3) $[51, 100]$, 4) $[101, 500]$, 5) $[501, +\infty)$}; EM $\in $ {1)全面析因设计, 2)分式析因设计, 3)正交设计, 4)均匀设计, 5)拉丁超立方抽样, 6)蒙特卡罗抽样, 7)拟蒙特卡罗抽样, 8)重要性抽样, 9)中心复合设计, 10)稳健设计, 11)顺序分支法, 12)迭代分式析因设计, 13)二阶段组筛选法, 14) Trocine筛选流程}.
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表 3 规则库
Table 3 Rule base
ID $Pc$ $Cq$ 1 $\text{EP}=2$ $\text{EM}=\left\{ 10 \right\}$ 2 $\text{ED}=3$ $\text{EM}=\left\{ 3, 4, 5 \right\}$ 3 $\text{CG}=1$ $\text{EM}=\left\{ 11, 12, 13, 14 \right\}$ $\vdots $ $\vdots $ $\vdots $ 60 $\text{FL}=4$, $\text{EN}=2$, $\text{FN}=3$ $\text{EM}=\left\{ 11, 14 \right\}$
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表 4 规则的条件属性优先级
Table 4 Priority of condition attribute for the rules
EP ED SC FI MI CG EE FL EN FN 5 2 3 3 4 4 3 1 1 1
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表 5 案例库
Table 5 Case base
ID EP ED SC FI MI CG EE FL EN FN EM 1 6 2 2 1 1 2 2 1 32 5 1 2 5 3 1 1 1 2 2 1 8 7 3 3 5 3 2 1 1 2 1 3 500 7 5 $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ 142 3 1 1 1 1 2 2 2 10 8 4
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表 6 不同推理方法的平均分类准确率($\%$)
Table 6 Averaging classification accuracy of different reasoning methods ($\%$)
推理方法 分配比例 1 : 1 3 : 2 2 : 1 2 : 3 MA-CBR 67.61 66.67 72.34 68.24 NN$\_$Rel-CBR 74.51 72.46 79.57 71.41 NN$\_$Sal-CBR 73.10 72.63 79.15 71.18 MA-CBR&RBFLR 80.28 80.70 85.11 ${\bf 80.00}$ NN$\_$Rel-CBR & RBFLR ${\bf 81.13}$ ${\bf 82.11}$ 85.74 ${\bf 80.00}$ NN$\_$Sal-CBR & RBFLR 79.58 80.00 ${\bf 86.60}$ 78.59
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