In this paper, a new islanding detection technique is proposed for a three-phase grid connected photovoltaic inverter system using the multi-signal analysis method. The proposed strategy is divided into two steps: first step, all possible grid faults, switching transients and islanding events are simulated and the essential detection parameters are measured. By means of the Slantlet Transform theory, the energy, mean value, minimum, maximum, range, standard deviation and log energy entropy at any decomposition level of Slantlet Transform for parameter detection is computed and the best of them are selected as input data of second step. Second step, an advanced machine learning based on Ridgelet Probabilistic Neural Network is utilized to predict islanding and none islanding states. In order to train Ridgelet Probabilistic Neural Network, a modified differential evolution algorithm with new mutation phase, crossover process, and selection mechanism is proposed. The results depicting the effectiveness of the proposed method are explained and outcomes are drawn.