# Air Conditioning Load Forecasting and Optimal Operation of Water Systems
## 3 Results  
### Analysis of Load-Forecasting Results  
In the load-forecasting results, without the dimensionality reduction in input parameters, the optimization results of core parameters c and G are 8 and 0.25, T = 435.59 s. RMSE = 118.14, and R\({}^{2}\) = 0.9468 for the prediction result of the training set, and RMSE = 130.89, R\({}^{2}\) = 0.9289 for the prediction result of the test set. The prediction results of the test set and training set are similar, and the generalization performance of the model is good. The load-forecasting results of the training set and test set are shown in Figure 1.  
In the training set forecasting results, when the air conditioning system load is within 1200 and 2400 kW, the error between the load-forecasting results and the real value is basically within \(\pm\)10%, and the load-forecasting accuracy is high; when the load of the air conditioning system is within 280 and 1200 kW, the predicted value of some data is far greater than the real value. In the test set's forecasting results, it can be found that the error between most load-forecasting results and the real value is within \(\pm\)10%. The absolute errors of the prediction results of the training set and the test set are counted. The data with an absolute error of less than 10% account for 92.22% and 88.27%, respectively, and the data with an absolute error of less than 20% account for 94.06% and 92.92%, respectively. The load-forecasting results have high accuracy.  
In the load-forecasting results after dimensionality reduction in input parameters, the optimization results of core parameters c and G are 4 and 1.414, T = 256.74 s. RMSE = 169.72, R\({}^{2}\) = 0.8843 for the prediction results of the training set, RMSE = 180.33, R\({}^{2}\) = 0.8630 for the prediction results of the test set. The prediction results of the test set and the training set are similar, and the generalization performance of the model is good. The load-forecasting results of the training set and test set are shown in Figure 2.  
Figure 1: Load-forecasting results without PCA dimensionality reduction. (**a**) Training set prediction results; (**b**) test set prediction results.  
Figure 2: Load-forecasting results after dimension reduction by PCA. (**a**) Training set prediction results; (**b**) test set prediction results.  
Compared with the load-forecasting results without dimensionality reduction in input parameters, the accuracy of load forecasting after dimensionality reduction is significantly reduced. Among them, the RMSE of the training set is increased by 43.66%, R\({}^{2}\) is reduced by 6.6%, the RMSE of the test set is increased by 37.77%, and R\({}^{2}\) is reduced by 7.1%, but the modeling process time is reduced by 41.06%. In conclusion, using PCA to reduce the dimension of input parameters can avoid the increase in the model calculation cost caused by too many input parameters, but it will reduce the accuracy of load forecasting, which may be due to the loss of information when extracting principal components from high-dimensionality data.  
The actual load-forecasting results show that when PCA is not used for data dimensionality reduction, T = 435.59 s, RMSE = 118.14, R\({}^{2}\) = 0.9468, RMSE = 130.89, and R\({}^{2}\) = 0.9289; after data dimensionality reduction with PCA, T = 256.74 s, RMSE = 169.72, and R\({}^{2}\) = 0.8843 for the prediction results of training set, and RMSE = 180.33 and R\({}^{2}\) = 0.8630 for the prediction results of the test set. Therefore, whether PCA is used for dimensionality reduction or not, the prediction results of the test set and training set are similar, which shows that the model has good generalization performance; that is, the operation-load-forecasting method of an air conditioning system based on data mining proposed in this paper is feasible.