用频域感知核函数提升复杂系统预测精度
Frequency-aware Surrogate Modeling With SMT Kernels For Advanced Data Forecasting
- 设计可自定义的频域敏感核函数，支持多种核组合
- 在火山二氧化碳与航空客流数据上验证预测效果
- 开源工具箱支持工程与科研人员快速构建模型
本文提出一个完整的开源框架，用于开发相关核函数，重点在于用户自定义与核函数组合以实现代理建模。通过改进基于核的方法，引入频域感知机制，有效捕捉飞机系统中的复杂力学行为与时频动态。传统以指数类为主的核函数被扩展为包含指数平方正弦、有理二次等更多类型，并支持一阶与二阶导数。方法首先在正弦基数测试案例中验证，随后应用于毛纳洛阿火山二氧化碳浓度与航空公司乘客流量的预测。所有进展集成至开源代理建模工具箱（SMT 2.0），提供标准与可定制核配置的通用平台。该框架支持多种核函数组合，发挥各自优势，构建针对特定问题的复合模型。整体工具集为工程师与研究人员提供灵活解决方案，推动复杂频率敏感领域的元建模应用。
原文摘要 · Abstract (English)
This paper introduces a comprehensive open-source framework for developing correlation kernels, with a particular focus on user-defined and composition of kernels for surrogate modeling. By advancing kernel-based modeling techniques, we incorporate frequency-aware elements that effectively capture complex mechanical behaviors and timefrequency dynamics intrinsic to aircraft systems. Traditional kernel functions, often limited to exponential-based methods, are extended to include a wider range of kernels such as exponential squared sine and rational quadratic kernels, along with their respective firstand second-order derivatives. The proposed methodologies are first validated on a sinus cardinal test case and then applied to forecasting Mauna-Loa Carbon Dioxide (CO 2 ) concentrations and airline passenger traffic. All these advancements are integrated into the open-source Surrogate Modeling Toolbox (SMT 2.0), providing a versatile platform for both standard and customizable kernel configurations. Furthermore, the framework enables the combination of various kernels to leverage their unique strengths into composite models tailored to specific problems. The resulting framework offers a flexible toolset for engineers and researchers, paving the way for numerous future applications in metamodeling for complex, frequency-sensitive domains.
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