Approximating probability distribution of circuit performance function for parametric yield estimation using transferable belief model
Approximating probability distribution of circuit performance function for parametric yield estimation using transferable belief model
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DOI：
10.1007/s11432-012-4709-1
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发表时间：
2012-10
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影响因子：
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通讯作者：
Xiaobin Xu;Donghua Zhou;Yindong Ji;Chenglin Wen
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文献类型：
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作者：
Xiaobin Xu;Donghua Zhou;Yindong Ji;Chenglin Wen
本文将Dempster-Shafer证据理论的可转移信念模型(TBM)解释应用于电路性能函数的近似分布，用于参数成品率估计。该方法将性能函数的输入参数视为定义在实数连续框架上的可信变量，构造了这些参数的随机集型证据。利用随机集的延拓原理，得到函数输出对应的随机集。在TBM框架内，在信用状态下的函数输出的随机集合可以被变换成比格状态，在该状态中它由比格累积分布表示。作为对实际累积分布的近似，它可用于根据电路响应规范来估计成品率。与蒙特卡罗(MC)方法相比，该方法的优点在于只需执行一次模拟过程即可获得具有确定性估计误差的可用成品率近似值。在误差相同的情况下，新方法所需的计算量比MC方法少。以高速铁路轨道电路和数值八维二次函数为例，验证了该方法的有效性。
This paper applies the transferable belief model (TBM) interpretation of the Dempster-Shafer theory of evidence to approximate distribution of circuit performance function for parametric yield estimation. Treating input parameters of performance function as credal variables defined on a continuous frame of real numbers, the suggested approach constructs a random set-type evidence for these parameters. The corresponding random set of the function output is obtained by extension principle of random set. Within the TBM framework, the random set of the function output in the credal state can be transformed to a pignistic state where it is represented by the pignistic cumulative distribution. As an approximation to the actual cumulative distribution, it can be used to estimate yield according to circuit response specifications. The advantage of the proposed method over Monte Carlo (MC) methods lies in its ability to implement just once simulation process to obtain an available approximate value of yield which has a deterministic estimation error. Given the same error, the new method needs less number of calculations than MC methods. A track circuit of high-speed railway and a numerical eight-dimensional quadratic function examples are included to demonstrate the efficiency of this technique.