Research on anomaly detection method of rock mechanics time series data based on KPCA and GMM

In view of the problems of data calibration difficulties, data redundancy, and low algorithm efficiency caused by the excessive amount of data generated by current rock mechanics experiments and the high dimension of data features, this paper combines the Kernel Principal Component Analysis (KPCA) feature selection algorithm with the Gaussian mixture model (GMM) to propose an unsupervised abnormal data detection method KPCA-GMM for rock mechanics multidimensional time series data. This method first applies the kernel technique to nonlinear high-dimensional time series data using KPCA, mapping the original data to a higher-dimensional space. This transformation makes the originally linearly inseparable data linearly separable in the new space, allowing for the extraction of the main components in the high-dimensional feature space while retaining the key features of the data. Then, a local Gaussian mixture model is constructed on the reduced-dimensional data through GMM, and the expectation maximization (EM) algorithm is used to estimate the parameters of GMM to accurately capture the local structure of the data. The abnormality of the data point is measured by the probability density function of GMM. The experimental results demonstrate that the KPCA-GMM method excels in detecting anomalies in multi-dimensional time series data generated by rock mechanics equipment, achieving an accuracy of 80.1% and a recall of 79.5%. These results are significantly superior to those of the traditional sliding window method and the LSTM-GAN method. This study provides an efficient and reliable unsupervised detection method for anomaly detection of rock mechanics experimental data, which has high practical application value.