Research into fault diagnosis in machines with a wide range of variable loads and speeds, such as wind turbines, is of great industrial interest. Analysis of the power signals emitted by wind turbines for the diagnosis of mechanical faults in their mechanical transmission chain is insufficient. A successful diagnosis requires the inclusion of accelerometers to evaluate vibrations. This work presents a multi-sensory system for fault diagnosis in wind turbines, combined with a data-mining solution for the classification of the operational state of the turbine. The selected sensors are accelerometers, in which vibration signals are processed using angular resampling techniques and electrical, torque and speed measurements. Support vector machines (SVMs) are selected for the classification task, including two traditional and two promising new kernels. This multi-sensory system has been validated on a test-bed that simulates the real conditions of wind turbines with two fault typologies: misalignment and imbalance. Comparison of SVM performance with the results of artificial neural networks (ANNs) shows that linear kernel SVM outperforms other kernels and ANNs in terms of accuracy, training and tuning times. The suitability and superior performance of linear SVM is also experimentally analyzed, to conclude that this data acquisition technique generates linearly separable datasets.