We applied our previously developed wireless sensor node (WSN), which is powered by a piezoelectric vibration energy harvester (VEH), to structural health monitoring and verified its classification performance. The self-powered WSN can measure structural vibrations and transmit the three-axis acceleration waveform data wirelessly. A normal intact beam and four beams that had a single notch cut at four different locations were prepared for classification testing. The WSN, which was connected to the piezoelectric VEH, was mounted on the tip of an aluminum alloy beam, and a random vibration was then applied to the clamped end of the beam. First, the power of the piezoelectric VEH under the random vibration condition was investigated by introducing the probability of harvesting. The beam's vibrational modes were identified within the 0-1,600 Hz frequency range using the transmitted waveform data. Second, based on an analogy to 2D image classification, we created an input image by arranging the x, y, z-axis acceleration spectrum data vertically and then classifying the arranged data using 2D convolutional neural network (2D-CNN) layers. The Bayesian optimization technique was used to maximize classification accuracy by optimizing the hyperparameters. We confirmed that the selfpowered WSN can provide high classification accuracy of 99.9%. We also revealed the basis of this high classification accuracy using gradient-weighted class activation mapping (Grad-CAM) and the continuous wavelet transform (CWT). Our self-powered WSN, which can provide additional features by transmitting the three-axis acceleration waveforms, represents a useful tool for structural health monitoring or predictive maintenance applications.