基于数据驱动技术的非高斯过程模拟

From a new vision, the proposed project aims to form the data-driven technology based simulation algorithms for non-Gaussian processes with proprietary intellectual property rights. The following research directions are included in this project. . In order to overcome the limitations of the nonlinear static transformations, with resorting to the data-driven technologies, namely, support vector machines (SVM) and least squares support vector machines (LSSVM), the direct simulation algorithms are proposed for the first kind of non-Gaussian processes with spiky fluctuation features through constructing the underlying relationships from input to output. . In order to solve the problem that the inverse functions of non-Gaussian cumulative distribution functions (CDF) do not exist, with resorting to SVM and LSSVM, a methodology is developed for numerically searching the inverse functions of CDF and then, the SVM and LSSVM based simulation algorithms are proposed for the second kind of non-Gaussian processes. . In order to fulfill the high-speed computational demands for large scale problems, the LSSVM based conditional simulation algorithms of non-Gaussian processes are proposed, respectively, in accordance with the interpolation and extrapolation machine learning patterns. . The full scale experiments are made to verify both the high efficiency and practicality of the SVM and LSSVM based simulation algorithms and the progressiveness (i.e., high-precision and high-speed computational capability) of the LSSVM based conditional simulation algorithms in the digital generation of non-Gaussian fluctuating wind pressure time series. Likewise, the key technologies for wind engineering are exacted from the experimental verification.

本项目从一个新的视角，研究形成具有自主知识产权的基于数据驱动技术非高斯过程模拟算法，具体为以下四个方面。. 为了解决非线性静态转换的局限性，基于数据驱动技术：支持向量机(SVM)和最小二乘支持向量机(LSSVM)，通过建立输入和输出之间的潜在关系，建立第一类具有尖刺特征非高斯过程的直接模拟算法。. 为了解决非高斯累积分布函数(CDF)的反函数不存在问题，提出使用SVM和LSSVM，建立数值寻找CDF反函数的方法，从而建立基于SVM和LSSVM的第二类非高斯过程模拟算法。. 为了满足大尺度问题的高速计算需求，建立基于LSSVM的非高斯过程内插和外插条件模拟算法。. 实测试验验证：基于SVM和LSSVM的第一、二类模拟算法对非高斯风压的高效性和实用性以及基于LSSVM的内插和外插条件模拟算法对非高斯风压的先进性(高精度和高速计算能力)；并在验证中综合出适用于风工程的关键技术。

项目在第一类和第二类多变量非高斯过程建模与模拟和非高斯过程与非平稳非高斯过程高性能预测（条件模拟）方向展开了研究，具体为：. 建立了第一类和第二类多变量非高斯过程的AR和ARMA模型直接模拟和非迭代模拟算法，数值结果证明AR和ARMA模型和非迭代算法均能有效地模拟低、中和高斜度的多变量非高斯过程。基于最小二乘支持向量机（LSSVM），探索了非高斯过程的非参数建模与模拟；使用数控理论的方法，并经实测刚性和柔性结构非高斯风压数据的验证，发现LSSVM不具备非高斯过程模拟中的转换条件。. 建立了混合蚁群和粒子群优化LSSVM、混合遗传算法和粒子群优化LSSVM和混合人工蜂群和鱼群优化LSSVM、多种小波核LSSVM和多种组合（混合）核LSSVM，并使用模拟高斯和非高斯风速与非高斯风压数据验证了这些集群智能优化LSSVM和高性能核LSSVM的亮点与优势。. 运用混合蚁群（ACO）和粒子群（PSO）优化LSSVM正则化和核参数，形成多变量非高斯风压的ACO+PSO-LSSVM内插预测算法；基于实测多变量非高斯风压数据的验证，发现ACO+PSO-LSSVM对小样本风压预测具有应用前景。提出了集群智能优化小波核LSSVM的多变量非高斯风压内插和外插预测算法；基于实测多变量风压（呈水平空间分布）数据的验证，发现其拥有高有效性和强稳定性。. 联合运用经验模态分解和小波变换技术，建立了Hermite+径向基函数（RBF）的组合核LSSVM非平稳非高斯风压预测算法；基于实测超高层建筑、刚性和柔性结构多变量非高斯和非平稳非高斯风压数据的验证，发现Hermite+RBF-LSSVM是一种强鲁棒性的空间点（单点）预测算法。. 提出了改进经验小波变换（IEWT）的非平稳非高斯风压数据处理与分析方法，建立了IEWT-LSSVM多变量非平稳非高斯风压预测算法；基于实测多变量非平稳非高斯风压数据的验证，发现IEWT和IEWT–LSSVM是先进的信号处理和空间点（单点）预测算法。建立了小波核极限学习机（WKELM）非平稳非高斯风压的单点多步预测算法；基于实测柔性结构非平稳非高斯风压数据的验证，发现WKELM的多步预测具有先进性。