A new approach for model validation in solar radiation using wavelet, phase and frequency coherence analysis

The performance of solar radiation models is evaluated based on time domain statistical metrics. These metrics include root mean square error (RMSE), mean absolute percentage error (MAPE) and coefficient of determination (R2). However, this study adopts a new approach to model validation in phase and frequency domains. The study proposes frequency coherence and phase synchronization methods quantified into frequency coherence index (FCI) and phase lock value (PLV), respectively. To get more in-depth insight of the model's performance, important visual indicators based on wavelet cross-spectrum (WCS) and wavelet coherence analysis (WCA) are presented. Two different widely used solar radiation models based on artificial neural network (ANN) namely, the multi-layer perceptron (MLP) and the adaptive neuro-fuzzy inference system (ANFIS), are analysed. The proposed techniques are used to exploit weaknesses and strengths of the models. Anomalies in phase and frequency components are identified and the information is used to increase their performance. The MLP is modified into a non-linear autoregressive recurrent exogenous neural networks (NARX-NN) using recursive filtering. Results show that NARX-NN corrects the phase differences, filters out the faulty frequency components and increases the time domain validation metric, i.e. R2.