基于Lotka-Volterra模型的复杂产品设计指标分解关联定量分析

doi:10.3969/j.issn.1004-132X.2025.07.010

摘要/Abstract

摘要： 针对复杂产品设计指标演化过程中关联关系往往会使分解的子功能结构设计指标被高估或低估的问题，且鉴于设计指标分解与群落生态学类似，提出了一种基于Lotka-Volterra模型的设计指标分解关联定量分析方法。分析了复杂产品演化过程，定义了设计指标分解过程中的生态主体和关联关系；基于Lotka-Volterra模型构建了系统与子功能结构设计指标之间的分解关联模型，利用龙格库塔法结合最小二乘法求解了模型系数，定量分析了设计指标之间的关联关系；最后，以高速列车系统指标能耗与子功能结构设计指标关联求解为例，验证了方法的有效性。研究结果表明，该方法能够量化识别复杂产品设计指标演化过程中的相互作用关系，可为正向创新设计优先突破的方向提供定量依据。

关键词: 设计指标, 正向设计, Lotka-Volterra模型, 关联建模, 定量分析

Abstract: Aiming at the problems of the correlations in the evolution processes of product design indicators made the decomposed sub-functional structure design indicators overestimated or underestimated, and the decomposition of design indicators was similar to community ecology, a method of quantitative analysis of the correlations in the decomposition of design indicators was proposed based on the Lotka-Volterra model. Firstly, the complex product evolution processes were analysed, then the ecological subjects and correlations in design indicators decomposition was defined. Secondly, the decomposition correlation model between system and sub-functional structure design indicators was constructed based on the Lotka-Volterra model, and the coefficients were solved by using the Runge-Kutta combined with the least-squares method to quantitatively analyze the correlation among design indicators. Finally, the effectiveness of the method was verified by taking the example of solving the correlation between the energy consumption of high-speed train system and the design indicators of sub-functional structure. The findings show that the methodology may quantify the interaction between identifying complex product design indicators in the evolution processes and may provide a quantitative basis for positive directions towards innovative design priority breakthroughs.

Key words: design indicator, forward design, Lotka-Volterra model, correlation modeling, quantitative analysis

中图分类号:

TP391

谷孙权, 张海柱, 黎荣, 饶坝, 汪豪. 基于Lotka-Volterra模型的复杂产品设计指标分解关联定量分析[J]. 中国机械工程, 2025, 36(07): 1479-1486.

GU Sunquan, ZHANG Haizhu, LI Rong, RAO BaWANG Hao. Quantitative Analysis of Correlation for Complex Product Design Indicator Decomposition Based on Lotka-Volterra Model[J]. China Mechanical Engineering, 2025, 36(07): 1479-1486.

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链接本文: https://www.cmemo.org.cn/CN/10.3969/j.issn.1004-132X.2025.07.010

https://www.cmemo.org.cn/CN/Y2025/V36/I07/1479

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