弹性势能最大结构模型演示
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此处输入要素的个数:
弹性势能最大——层级结构模型计算过程演示
弹性势能最大能量结构图,就是两边扩张性,或者是上下扩张型:即在满足层次数最少的情况下使得骨架阵中的边跨越的层级数目最多:
显示的是一个随机 20 * 20 的方阵
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子 | 丑 | 寅 | 卯 | 辰 | 巳 | 午 | 未 | 申 | 酉 | 戌 | 亥 | 乾 | 坤 | 震 | 巽 | 坎 | 离 | 艮 | 兑 |
子 |
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1 |
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1 |
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卯 |
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午 |
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戌 |
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亥 |
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乾 |
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震 |
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巽 |
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坎 |
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离 |
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1 |
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艮 |
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兑 |
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对上述矩阵进行两次缩减获得骨架矩阵
首先:根据有序环排序
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卯 | 午 | 辰 | 离 | 坤 | 子 | 坎 | 申 | 丑 | 未 | 寅 | 巳 | 戌+乾+震+巽 | 艮 | 兑 | 酉 | 亥 |
卯 |
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午 |
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辰 |
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离 |
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坤 |
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巳 |
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戌+乾+震+巽 |
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接着:根据得到的DAG图去向前边
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卯 | 午 | 辰 | 离 | 坤 | 子 | 坎 | 申 | 丑 | 未 | 寅 | 巳 | 戌+乾+震+巽 | 艮 | 兑 | 酉 | 亥 |
卯 |
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巳 |
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戌+乾+震+巽 |
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艮 |
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可达矩阵如下
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卯 | 午 | 辰 | 离 | 坤 | 子 | 坎 | 申 | 丑 | 未 | 寅 | 巳 | 戌+乾+震+巽 | 艮 | 兑 | 酉 | 亥 |
卯 |
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午 |
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辰 |
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离 |
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坤 |
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坎 |
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申 |
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丑 |
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未 |
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寅 |
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巳 |
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戌+乾+震+巽 |
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艮 |
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兑 |
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酉 |
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基于原因优先的层级划分方法
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辰 |
卯 |
午 |
离 |
坤 |
坎 |
子 |
申 |
未 |
丑 |
寅 |
巳 |
戌+乾+震+巽 |
艮 |
兑 |
酉 |
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辰 | |
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离 | 1 |
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戌+乾+震+巽 | |
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基于结果优先的层级划分方法
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卯 |
午 |
辰 |
坎 |
未 |
离 |
坤 |
申 |
子 |
寅 |
巳 |
丑 |
艮 |
戌+乾+震+巽 |
亥 |
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坤 | 1 |
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戌+乾+震+巽 | |
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通过观察,对原来的矩阵进行层级分解后有如下几个特点
第一:箭头方向一致,非环路的箭头一致向一个方向,本处显示的是一致向上!
第二:同一个环路的要素必定处于同一层级!所以环路要素可以用缩点表示
第三:原因优先抽取的方式与结果优先抽取的方式,得到的层级数目是相同的!
上述可以计算出其层级的要素分别为:
层级的序号 | 原因优先的方法-得到的各层级的要素 | 结果优先的方法-得到的各层级要素 | 共同有的要素 | 活动的要素 |
1 | 辰 | 卯,午,辰,坎,未 | 辰 | 卯,午,坎,未 |
2 | 卯,午,离 | 离 | 离 | 卯,午 |
3 | 坤,坎 | 坤,申 | 坤 | 坎,申 |
4 | 子,申,未 | 子,寅,巳 | 子 | 申,未,寅,巳 |
5 | 丑,寅,巳 | 丑,艮 | 丑 | 寅,巳,艮 |
6 | 戌+乾+震+巽,艮 | 戌+乾+震+巽,亥 | 戌+乾+震+巽 | 艮,亥 |
7 | 兑 | 兑 | 兑 | |
8 | 酉,亥 | 酉 | 酉 | 亥 |
由上表计算得出活动的要素以及它们活动的层级:
要素的序号 | 要素的名称 | 要素的标题 | 开始层级 | 终止层级 |
0 | 卯 | 卯兔 | 1 | 2 |
1 | 午 | 午马 | 1 | 2 |
6 | 坎 | 坎水 | 1 | 3 |
9 | 未 | 未羊 | 1 | 4 |
7 | 申 | 申猴 | 3 | 4 |
10 | 寅 | 寅虎 | 4 | 5 |
11 | 巳 | 巳蛇 | 4 | 5 |
13 | 艮 | 艮山 | 5 | 6 |
16 | 亥 | 亥猪 | 6 | 8 |
该系统非刚性拓扑结构,现在根据活动要素手动调整层级顺序
第一步,看原因优先的分层结果
第一层可以活动到的要素有,(0,1,6.9),直接提升上去
观察要素7其处于上半部分,把其往上拉
先移动7一层
本案例中最大的要素是考虑7要素移动的位置,在最小缩边的情况下,根据其出度与入度来计算!
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