Prediction of soil moisture based on multilayer neural network with multi-valued neurons

Abstract: In order to improve the multi-step ahead predication accuracy of soil moisture, we established a multi-step soil moisture prediction model using multilayer neural network with multi-valued neurons (MLMVN). It is a complex-valued neural network with derivative-free back-propagation learning algorithm and error-correction learning rule. Different to the traditional network, the inputs/outputs and weights of MLMVN are complex numbers located on the unit circle, and its learning does not require a derivative of the activation function; all these make it possible to increase the functionality of the network. In order to learn the characteristics of soil moisture better, we employed continuous multi-valued neurons (MVN) as the basic neurons of MLMVN. MVN is based on the principle of multiple-valued threshold function, and the function maps the complex plane into a whole unit circle. The experiment was carried out in an experimental filed of China Agricultural University located in Zuozhou City, Hebei Province during the spring growing season of maize (from March 15 to September 30 in 2015) to measure soil moisture hourly, and the performance of the MLMVN network was tested. At first, in the pre-process, the outlier values and missing values in the sample were replaced by the average values of the data points in the interval of 100 preceding and 100 succeeding data points to smooth the data. Moreover, timing analysis and autocorrelation analysis of preprocessed soil moisture showed that soil moisture was nonlinear non-stationary time series. Secondly, taking rainfall as the key environmental factor according to correlation analysis between soil moisture and atmospheric environmental factors (rainfall, temperature and wind speed), the correlation value of the rainfall was 0.875, which was the maximum among the 3 correlation values. Finally, real-valued soil moisture, rainfall and target values were transformed to complex numbers by a linear transformation, which could be used as MLMVN inputs and outputs. It is important to specify the value ranges below the maximum value and above the minimum value to avoid closeness between the maximal value and the minimal values. On the basis of the experiments, taking into account the network stability and prediction accuracy, two-hidden-layer MLMVN 240- 15-1200-1 was set up as the predictive neural network structure (240 neurons in the input layer, 15 neurons in the 1st hidden layer, 1 200 neurons in the 2nd layer and 1 neuron in the output layer). In addition, two-hidden-layer MLMVN with large number in the 2nd hidden layer worked closely to a high-pass filter. In detail, training dataset contained 3 312 samples, testing dataset contained 1 200 samples and input length was set as 240 steps (which corresponded to soil moisture and rainfall of 5 days). In order to study soil moisture sequence characteristics comprehensively, the training dataset was distributed throughout the maize growing period evenly. Experimental results showed that, when specifying the tolerance threshold for RMSE (root mean square error) was 0.1 radian, and one step ahead prediction accuracy of MLMVN neural network was 0.883, and using iterative method to make 72 steps ahead prediction, the prediction accuracy reached 0.853, showing small accumulating errors. The results also showed that MLMVN outperformed the real-valued BP (back propagation) neural network, which enhanced prediction precision by 9.1%. The study has validated that the soil moisture prediction model based on MLMVN neural network can predict the soil moisture precisely and is significant for the management of water-saving irrigation. Additionally, MLMVN is able to generalize the development of the soil moisture and show a good generalization ability.