系统工程与电子技术 ›› 2025, Vol. 47 ›› Issue (1): 153-163.doi: 10.12305/j.issn.1001-506X.2025.01.16

• 系统工程 • 上一篇    下一篇

定量和定性因子混合的罚盲克里金模型

陈大豪1,2, 程志君1,*, 钟健1, 潘正强1   

  1. 1. 国防科技大学系统工程学院, 湖南 长沙 410073
    2. 中国人民解放军92957部队, 浙江 舟山 316000
  • 收稿日期:2022-12-13 出版日期:2025-01-21 发布日期:2025-01-25
  • 通讯作者: 程志君
  • 作者简介:陈大豪(1996—), 男, 硕士研究生, 主要研究方向为试验数据分析与建模
    程志君(1978—), 女, 教授, 博士, 主要研究方向为试验设计与评估、试验数据分析与建模
    钟健(1998—), 女, 硕士研究生, 主要研究方向为试验设计与评估
    潘正强(1981—), 男, 副教授, 博士, 主要研究方向为武器装备试验鉴定、可靠性建模与分析
  • 基金资助:
    国家自然科学基金(72171231)

Penalized blind Kriging model with mix quantitative and qualitative factors

Dahao CHEN1,2, Zhijun CHENG1,*, Jian ZHONG1, Zhengqiang PAN1   

  1. 1. College of Systems Engineering, National University of Defense Technology, Changsha 410073, China
    2. Unit 92957 of the PLA, Zhoushan 316000, China
  • Received:2022-12-13 Online:2025-01-21 Published:2025-01-25
  • Contact: Zhijun CHENG

摘要:

克里金模型是一种十分有效的空间插值方法, 被广泛研究并应用于地质学、环境科学及大气科学等工程领域观测的代理模型。针对含有定量和定性因子混合输入的高维观测样本, 提出定量和定性因子混合的罚盲克里金模型。在罚盲克里金模型的基础上, 对输入数据中含有定量和定性因子混合的情况, 利用定量和定性因子混合的高斯相关模型, 建立混合因子的罚盲克里金模型, 并通过惩罚函数对均值函数进行因子选择。通过线性和非线性分段函数的数值实验验证定量和定性因子混合的罚盲克里金模型具有较高精度。结果表明, 有限样本下一阶罚盲克里金模型和二阶罚盲克里金模型均具有较小的相对均方根误差、标准均方根误差和根均方百分比误差。

关键词: 惩罚盲克里金, 定量定性因子, Lasso惩罚, 最小角回归

Abstract:

Kriging model is a very effective spatial interpolation method, which is widely studied and applied to surrogate models for observation in engineering fields such as geographical science, environmental science and atmospheric science. For high-dimensional observation samples with both quantitative and qualitative factors as input, a penalized blind Kriging (PBK) model with a mix of quantitative and qualitative factors is proposed. On the basis of the PBK model, for the case that the input data contains a mixture of quantitative and qualitative factors, the Gaussian correlation model with a mixture of quantitative and qualitative factors is used to establish the PBK model with mixed factors, and the penalty function is used to select factors for the mean function. The numerical experiments of linear and nonlinear piecewise functions verify that the PBK model with quantitative and qualitative factors has a high accuracy. The results show that the first-order PBK model and the second-order PBK model with limited samples both have less relative root mean square error, normalized root mean squared error, and root mean square percentage error.

Key words: penalized blind Kriging (PBK), quantitative and qualitative factor, Lasso penalty, least angle regression

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