• 关键词：规范变换  预测模型  误差修正  兼容性  等效性  对易性

• 基金项目：国家自然科学基金（No.51679155）；四川省科技厅项目（No.19JDJQ0006）；四川省社科规划项目（No.SC18B027）

• 李祚泳
• 成都信息工程大学, 资源环境学院, 成都 610225

• 魏小梅
• 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

• 摘要：传统的不同预测变量的预测模型之间不具有兼容性和等效性，而同型规范变换和误差修正相结合的不同变量的预测模型的预测相对误差与预测对象的维数、样本数及预测模型类型皆无关，仅与预测变量的数据特性、相似样本的模型输出值及其相对误差和相似度有关，因而同型规范变换的不同预测变量的预测模型之间具有兼容性和等效性.其重要意义在于：只要对任意一个预测变量建立了基于规范变换的某种预测模型，就可以将此预测模型直接用于具有同型规范变换的其他预测变量的预测；若再将其与误差修正法相结合，还可以极大地提高模型的预测精度，获得与实际值很接近的预测结果.依据受3个因子影响的灞河口COD_Mn指数数据、受4个因子影响的伊犁河雅马渡站年径流量数据和牡丹江市TSP年均值的时序数据，分别建立具有同型规范变换（n_j=2）的3个不同预测变量的3种智能预测模型和一元线性回归预测模型，并验证了3个不同预测变量的预测模型之间的兼容性和等效性.对同一个预测样本，用同型规范变换和误差修正相结合的不同预测变量的预测模型的实际预测值及其预测相对误差绝对值不仅差异甚微，而且预测值与实际值非常接近，其预测的相对误差绝对值平均值几乎全都小于3%，最大相对误差绝对值均小于5%，小于或远小于20种传统预测模型和方法预测的相应误差.

• Abstract：Traditional prediction models with different prediction variables are not compatible and equivalent, while the relative prediction errors of different prediction models with different variables combined with the same type of gauge transformation and error correction are not related to the dimension, sample size and type of prediction model, which is only related to the data characteristics of the predicted variables, the output value of the model of similar samples and their relative errors and similarities. Therefore, the predicted models of different predicted variables with the same type of canonical transformation have compatibility and equivalence. Its significance lies in that as long as a prediction model based on canonical transformation is established for any prediction variable, it can be directly applied to the prediction of other prediction variables with the same canonical transformation. If it is combined with the error correction method, the prediction accuracy of the model can be greatly improved, and the prediction results are very close to the actual values. Based on COD_Mn annual mean data affected by three factors in Bahe estuary, annual runoff data affected by four factors in Yamadu Station of Yili River and time series data of TSP annual mean value in Mudanjiang City, three intelligent prediction models and one-variable linear regression prediction models with three different prediction variables with the same type of normative transformation (n_j=2)were established respectively. The compatibility and equivalence of three prediction models with different prediction variables were verified. For the same forecasting sample, the actual forecasting value and the absolute value of the relative error of the forecasting model with different forecasting variables combined with the same type gauge transformation and error correction are not only slightly different, but also very close to the actual value. The average absolute value of relative error is almost all less than 3%, and the maximum absolute value of relative error is less than 5%,which is less than or far less than the corresponding error of 20 traditional prediction models and methods.

• Key words：canonical transformation  prediction model  error correction  compatibility  equivalence  commutativity

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