• 关键词：环境系统  规范变换  预测模型  回归支持向量机  核函数

• 基金项目：国家自然科学基金（No.51679155）

• 李祚泳
• 成都信息工程大学, 资源环境学院, 成都 610225

• 汪嘉杨
• 成都信息工程大学, 资源环境学院, 成都 610225

• 徐源蔚
• 成都信息工程大学, 资源环境学院, 成都 610225

• 摘要：为了建立不同环境系统皆能规范、统一、简洁、实用的回归支持向量机预测模型，针对传统的回归支持向量机预测模型存在结构不能普适、规范和统一及用于大样本、多因子预测会出现学习效率低、求解精度差的局限，提出适用于环境系统预测量及其影响因子参照值和规范变换式的设计原则和方法，使规范变换后的影响因子皆"等效"于同一个规范影响因子；为提高样本的预测精度，还提出预测样本的模型输出的误差修正法.在对环境系统的预测量及其影响因子进行规范变换的基础上，由有m个规范影响因子的每个建模样本生成m个"等效"训练样本，从建模样本中，选择各影响因子的最大规范值组成训练样本集的"参考样本"，计算核函数中每个训练样本相对于"参考样本"的范数；并应用优化算法优化模型参数，建立适用于预测量及其影响因子规范值的仅有2个或3个支持向量的两种简单结构的回归支持向量机预测模型.将基于规范变换的两种简单结构的回归支持向量机模型与相似样本误差修正法相结合，用于河津大桥监测断面6个样本的COD月平均值预测，并与多种传统预测模型和方法进行了比较.结果表明：对同一个预测样本，两种模型的预测值十分接近；此外，两种预测模型用于6个样本预测，其相对误差绝对值的平均值分别为2.09%、2.79%，均远小于传统的投影寻踪回归预测的41.63%、支持向量机预测的40.99%、灰色神经网络预测的25.94%和马尔可夫预测的10.16%；而两种预测模型对异常样本预测的最大的相对误差绝对值分别为5.85%、5.13%，更加远远小于传统的4种预测模型的169.07%、180.45%、68.44%、41.96%.两种基于规范变换的回归支持向量机预测模型简洁、普适、规范和统一，避免了"大样本数困难"，提高了学习效率和模型的预测精确度，对其他预测建模法也有借鉴作用.

• Abstract：The purpose of this study was to build a universal, normative, simple and unified model of regression support vector machines,which can meet environment system predictions. The predictive model of traditional regression support vector machines has limits, which of the structure can not be universal, standardized and unified, the learning efficiency is low and the solution accuracy is poor for large sample and multi factor prediction. Therefore,the design principles and methods of reference values and the gauge transformation formula were proposed for predicting variable and its influencing factors of environment system,it makes all of the normalized influencing factors equivalent to the same normative influence factor. Furthermore, in order to improve the prediction accuracy of samples, an error correction method was also proposed for the model output of the predicted samples. On the basis of gauge transformations for the predictive variable and its influencing factors of environment system, each modeling sample with m canonical influence factors formed m training samples. Furthermore, from the modeling samples, the maximum values of the normative values of each influence factor was selected as the "reference sample" of the training sample set, and the norms of each training sample in a kernel function relative to the "reference sample" were calculated. Then, the optimization algorithm was used to optimize the model parameters, two types of NV-SVR models for environment system prediction were built:the NV-SVR(2), which was suitable for the case involved any 2 support vectors and the NV-SVR (3), which was suitable for the case involved 3 support vectors. The regression support vector machine models of two simple structures based on normative canonical transformation,which were combined with the error correction method of similar samples,were used to predict the average monthly COD of 6 samples in Hejin bridge monitoring section, and were compared with a variety of traditional forecasting models and methods. The results show that for the same forecast sample, the predicted values of the two models are very close. In addition, two prediction models were used for the prediction of 6 samples, and the average values of relative error absolute values were 2.09% and 2.79% respectively, were far less than 41.63%,40.99%, 25.94% and 10.16% of the prediction models of traditional projection pursuit regression, support vector machine,grey neural network and Markov respectively. The maximum relative error absolute values of the two prediction models for abnormal samples were 5.85% and 5.13% respectively, much smaller than 169.07%, 180.45%, 68.44% and 41.96% of the traditional 4 prediction models, respectively. Two types of NV-SVR, which avoid the difficulties of large sample size, improve learning efficiency and forecasting accuracy of models,are simple, universal, standard and unified. The two models are also useful for other prediction modeling and methods.

• Key words：environment system  normative transformation  prediction model  regression support vector machines  kernel function

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