Abstract This paper proposes a new monotonicity extraction method which is used to constrain the modeling process of a neural network. The main contributions of this paper are the sensitivity analysis on monotonicity based on Spearman coefficient, and the application of monotonicity on neural network modeling. This study uses scatter plots of bivariate variables and the Spearman coefficient to extract the monotonic information. To weaken the influence of noise, binary 0–1 integer linear program is applied to filter the scatter diagram. Based on the monotonicity information, a constraint optimization problem is proposed to obtain the BP neural network model and an Alopex-based evolutionary algorithm (AEA) is used to search for the optimal weights and thresholds. The results of a numeral example and an ethylene cracking furnace show that the proposed approach can achieve a good predicting performance in the two cases.

中文翻译：

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基于Spearman系数单调性敏感性分析的BP神经网络建模

摘要 本文提出了一种新的单调性提取方法，用于约束神经网络的建模过程。本文的主要贡献是基于Spearman系数对单调性的敏感性分析，以及单调性在神经网络建模中的应用。本研究使用双变量变量的散点图和 Spearman 系数来提取单调信息。为了减弱噪声的影响，采用二进制0-1整数线性规划对散点图进行滤波。基于单调性信息，提出约束优化问题以获得BP神经网络模型，并使用基于Alopex的进化算法(AEA)搜索最优权重和阈值。