[1]张金芳,乔贝贝.基于Chi-square的非高斯控制系统性能评估[J].郑州大学学报(工学版),2027,48(XX):1-10.[doi:10.13705/j.issn.1671-6833.2026.06.012]
　ZHANG Jinfang,QIAO Beibei.Performance Assessment of Non-Gaussian Control Systems Based on Chi-square[J].Journal of Zhengzhou University (Engineering Science),2027,48(XX):1-10.[doi:10.13705/j.issn.1671-6833.2026.06.012]
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基于Chi-square的非高斯控制系统性能评估()
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《郑州大学学报(工学版)》[ISSN:1671-6833/CN:41-1339/T]

卷:
48
期数:
2027年XX
页码:
1-10
栏目:
出版日期:
2027-12-10

文章信息/Info

Title:
Performance Assessment of Non-Gaussian Control Systems Based on Chi-square
作者:
张金芳1，乔贝贝1,2
1.华北电力大学 控制与计算机工程学院,北京102206;2.国网冀北电力有限公司智能配电网中心,河北 秦皇岛 066100
Author(s):
ZHANG Jinfang1, QIAO Beibei1,2
1.School of Control and Computer Engineering, North China Electric Power University, Beijing 102206, China; 2.State Grid Jibei Electric Power Company Limited Smart Distribution Network Center, Qinhuangdao 066100, China
关键词:
非高斯系统; Chi-square指标; 性能评估; 参数辨识
Keywords:
non-gaussian systems;  chi-square index;  performance assessment;  parameter identification
分类号:
TP14
DOI:
10.13705/j.issn.1671-6833.2026.06.012
文献标志码:
A
摘要:
为了克服熵指标平移不变性的缺陷与卡方统计量无界的缺点，对非高斯控制系统的性能评估展开研究，提出一种基于Chi-square的性能评估指标，同时为了更快速、准确地估计基准输出，采用精英种群思想改进粒子群算法以获取系统未知参数和扰动噪声的概率密度函数，并根据反馈不变量其计算基准输出。该指标通过计算基准与实际输出概率分布间的Chi-square指标来反映给定系统的性能好坏，能有效避免熵指标数据量大、计算时间长、均值漂移等缺点。对不同噪声下的单变量与多变量系统进行仿真验证，结果表明辨识参数更接近真实值且迭代次数平均降低73.4%；在协方差矩阵具有相同迹的多变量场景下，最小方差指标无法判别，而Chi-square指标能显著区分分布状态（由0.89降至0.45），表明该指标具备较高的评估精度与敏感性，应用场景也更广。
Abstract:
A study was conducted to address the shift-invariance defect of entropy-based indices and the unboundedness problem of the chi-square statistic in evaluating the performance of non-Gaussian control systems. A Chi-square-based performance index was proposed, and the particle swarm optimization algorithm was enhanced with an elite-population strategy to enable faster and more accurate estimation of the benchmark output by identifying unknown system parameters and the probability density functions of disturbance noise; the benchmark output was subsequently computed using feedback invariants. The proposed index assessed system performance by calculating the Chi-square distance between the benchmark and actual output distributions, effectively mitigating the drawbacks of entropy indices, including large data requirements, long computation time, and sensitivity to mean shifts. Simulation studies conducted on univariate and multivariate systems under different noise conditions showed that the identified parameters were closer to the true values and that the required number of iterations decreased by an average of 73.4%. In multivariate scenarios where covariance matrices shared the same trace, the minimum-variance index was unable to differentiate among distributional states, whereas the Chi-square index provided significant discrimination (from 0.89 to 0.45), demonstrating its higher evaluation accuracy, greater sensitivity, and broader applicability

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更新日期/Last Update: 2026-06-29