  Reliable fault detection is an essential requirement for safe and efficient
operation of complex mechanical systems in various industrial applications.
Despite the abundance of existing approaches and the maturity of the fault
detection research field, the interdependencies between condition monitoring
data have often been overlooked. Recently, graph neural networks have been
proposed as a solution for learning the interdependencies among data, and the
graph autoencoder (GAE) architecture, similar to standard autoencoders, has
gained widespread use in fault detection. However, both the GAE and the graph
variational autoencoder (GVAE) have fixed receptive fields, limiting their
ability to extract multiscale features and model performance. To overcome these
limitations, we propose two graph neural network models: the graph wavelet
autoencoder (GWAE), and the graph wavelet variational autoencoder (GWVAE). GWAE
consists mainly of the spectral graph wavelet convolutional (SGWConv) encoder
and a feature decoder, while GWVAE is the variational form of GWAE. The
developed SGWConv is built upon the spectral graph wavelet transform which can
realize multiscale feature extraction by decomposing the graph signal into one
scaling function coefficient and several spectral graph wavelet coefficients.
To achieve unsupervised mechanical system fault detection, we transform the
collected system signals into PathGraph by considering the neighboring
relationships of each data sample. Fault detection is then achieved by
evaluating the reconstruction errors of normal and abnormal samples. We carried
out experiments on two condition monitoring datasets collected from fuel
control systems and one acoustic monitoring dataset from a valve. The results
show that the proposed methods improve the performance by around 3%~4% compared
to the comparison methods.
