Atmospheric temperature and humidity prediction of Gaussian process mixed model

Abstract: Temperature and humidity prediction plays an important role in various fields of the national economy. In view of the poor predictions of temperature and humidity and the failure to achieve multimodal prediction, this paper uses the Gaussian mixture process (GPM) model to predict the multimodal temperature and humidity. GPM model was developed from the Gaussian process (GP) model. It was proposed by Tresp in 2000. The main idea of GPM is to fit the samples in various input regions with different GP models in order to fit different patterns in these regions. However, the existing GPM models are rather complicated and thus the learning algorithms involve various approximation schemes, which can lead to much computation or rough prediction. So, in order to improve the model learning efficiency, a variable-hidden posterior hard-cut iterative training algorithm is proposed for the GPM model. This algorithm improves the EM (expectation maximization) learning with a new approximation strategy, which achieves the optimal grouping of samples through iterative learning and using the maximum a posteriori estimation. Prior to the experiment, the autocorrelation function and partial autocorrelation function were used to verify the nonlinear and non-stationary property of humidity and temperature sequences. Largest Lyapunov, saturation correlation dimension and recursive graph were used to verify the chaotic characteristic of humidity and temperature sequences. Finally, the GPM proposed in this paper is compared with the kernel regression (K-R), the minimax probability machine regression (MPMR), the linear regression (L-R), and GP models. K-R is a kind of prediction model based on kernel function. By adjusting the optimal window width, K-R gradually gets the corresponding prediction result. K-R has been the basis of predictive model because it can predict the linear and non-linear time series simultaneously. MPMR does not need to make specific assumptions about the model distribution. It only needs to know the mean and covariance matrix of the data distribution. This model improves the neural network easy to fall into the minimum and over-fitting. L-R is a very traditional model, using the quantitative relationship between variables to obtain a linear expression and then predict the test sample. The results show that not only GPM can perform multimodal prediction, but also the accuracy of the model is significantly better than other traditional models. In the humidity sequence prediction, the minimum of RMSE can reach 0.0620 and the maximum of R2 can reach 0.9362. In the temperature sequence prediction, the minimum of RMSE can reach 0.0426 and the maximum of R2 can reach 0.9666. In the prediction time consumed, GPM is a little more than the other 4 traditional models. The main reason is that GPM requires iterative learning to achieve the optimal grouping of samples. Finally, humidity prediction needs 113.4175 s and temperature prediction needs 90.0049 s. The research in this paper not only can promote atmospheric temperature and humidity forecasting, but also has some reference value for indoor and solid surface temperature and humidity forecasting because GPM is the prediction model without environment factors input.