规范变换与误差修正结合的环境系统的前向网络和投影寻踪预测模型

Forward network and projection pursuit for environmental system prediction based on combination of standard transformation and error correction

为了建立适用于环境系统的结构简洁、形式统一、程序规范、应用普适的神经网络和投影寻踪回归预测模型,针对传统的神经网络和投影寻踪回归用于多因子、大样本预测建模,存在模型结构复杂、学习效率低的局限,提出设置环境系统预测量及其影响因子参照值和规范变换式的原则和方法,使规范变换后的影响因子皆“等效”于同一个规范影响因子,从而将多因子的的预测建模简化为等效规范因子的预测建模,使模型结构得到极大地简化,提高了学习效率;此外,为了提高预测模型的预测精度,还提出了对预测样本的模型输出值的误差修正公式.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,将m个规范影响因子的每个建模样本组成m个“等效”训练样本,应用免疫进化算法优化模型参数,分别建立适用于环境系统的2个或3个规范影响因子的前向神经网络和投影寻踪回归两类预测模型;并依据误差理论,对误差修正公式修正后的模型预测精度的提高进行了严格的数学论证.将基于规范变换与相似样本误差修正相结合的两类预测模型,用于某市5个点位的SO2浓度预测,并与6种传统预测模型和方法的预测结果进行了比较.结果表明:对同一个预测样本,同类模型的两种不同结构的的预测值及其相对误差都几乎完全相同或彼此相差甚小;此外,两种不同结构的两类预测模型用于5个样本预测,其相对误差绝对值的平均值分别为2.59%、2.67%;2.18%、2.62%,均远小于传统BP神经网络模型的25.72%、传统PPR模型的14.20%、传统SVR模型的22.13%、模糊识别模型的21.57%、组合算子模型的18.36%和多元回归模型的25.31%;而两类模型预测的最大的相对误差绝对值分别为4.11%和3.57%,更加远远小于传统的6种预测模型的37.18%、56.07%、27.40%、32.14%、38.38%和60.26%.实例分析结果证实了误差修正公式对提高模型预测精度具有切实可行性.基于规范变换与误差修正相结合的前向神经网络和投影寻踪回归两类预测模型不仅避免了“维数灾难”,提高了学习效率和模型的预测精确度,而且具有简洁、普适、规范、统一和稳定的特点,对其他预测建模也有借鉴作用.

The purpose of this study was to establish prediction models of neural network and projection pursuit regression for environmental system, which have the charactertctics of simple structure, unified form, standardized procedures and universal application. The predictive models of traditional neural network and projection pursuit regression, which are used in multi-factor and large sample numbers, have limits of complex model structure, low learning efficiency. Therefore,the design principles and methods of reference values and the standard transformation formula used predicting variable and its influencing factors were proposed. The normalized influence factors were equivalent to the same normative influence factor. Thus, the predictive modeling of multiple factors is simplified as the predictive modeling of the "equivalent" norm factor, which greatly simplifies the model structure and improves the learning efficiency. In addition, in order to improve the prediction accuracy of the prediction model, the error correction formula for the model output value of the prediction sample was also proposed. On the basis of standard transformations for the predictive variable and its influencing factors of environment system, each modeling sample with m canonical influence factors were formed m "equivalent" training samples. Then, the immune evolutionary algorithm was used to optimize the model parameters, two different structures of prediction models of forward neural network and projection pursuit regression for environment system prediction were built: the case of 2-2-1 structure, which was used to any 2 normative impact factors and the case of 3-2-1 structure was, which was used to any 3 normative impact factors. Furthermore, based on the error theory, a rigorous mathematical demonstration was made for the improvement of the prediction accuracy of the model by the error correction formula. Two kinds of prediction models based on standard transformation and similar sample error correction were applied to predict the SO2 concentration of 5 spots in a city. Results were compared with the prediction results of six traditional prediction models and methods. The results show that for the same forecast sample, the predicted values and relative errors of two different structures of the same model (forward neural networks or projection pursuit regression) were almost identical or very small. In addition, two kinds of prediction models with two different structures were used for the prediction of 5 samples, and the means of relative error absolute values were 2.59%, 2.67% and 2.18%, 2.62%, respectively. They were far less than the results of 22.13%, 25.72%,14.20%,21.57%, 18.36% and 25.31% of the prediction models of traditional BP neural network(BP), traditional projection pursuit regression(PPR), traditional support vector machine(SVM), fuzzy recognition, combination operator and multiple regression respectively. The maximum relative error absolute values of samples of the two prediction models were 4.11% and 3.57%,respectively. They were smaller than the results of 56.07%, 27.40%, 37.18%, 32.14%, 38.38% and 60.26% of six traditional forecasting models. The example analysis results confirm that the error correction formula is feasible for improving the prediction accuracy of the model. Two prediction models of forward neural network and projection pursuit regression based on the combination of standard transformation and error correction can avoid the "dimension disaster", improve the learning efficiency and model prediction accuracy. They have the characteristics of simplicity, universality, standardization, unity and stability. They can also be used for reference in other forecasting models.