Genetic Programming for Evolving a Front of Interpretable Models for Data Visualization

Multivariate Fusion Covariance Matrix Network and Its Application in Multichannel Fault Diagnosis With Fewer Training Samples

Due to the large number of monitoring variables in engineering, it is extremely to reflect fault information in machinery and equipment with a single channel signal, which poses a significant challenge for fault diagnosis. Furthermore, most existing intelligent recognition methods rely on label samples, yet ignore the high cost of label interpretation in practical engineering. In this work, a novel multivariate fusion covariance matrix network (MFCMN) is developed for multichannel fault diagnosis with fewer training samples. First, the collected multichannel signals are separated into mode functions by using cyclic autocorrelation analysis. Thereafter, the acquired mode functions are utilized to construct the multivariate fusion covariance matrix (MFCM), which retains the linkage of signals from different channels. Finally, MFCM is fed into the standard autoencoder to form the MFCMN network, which is applied to implement multichannel fault diagnosis. To assess effectiveness, the MFCMN is compared with the deep residual network (ResNet), convolutional neural network (CNN), long short-term memory (LSTM), and K-nearest neighbor (KNN) in two experimental cases with fewer training samples. The results clarify that the MFCMN offers excellent performance and high accuracy in multichannel fault diagnosis.

Interpretable Rule Discovery Through Bilevel Optimization of Split-Rules of Nonlinear Decision Trees for Classification Problems

For supervised classification problems involving design, control, and other practical purposes, users are not only interested in finding a highly accurate classifier but they also demand that the obtained classifier be easily interpretable. While the definition of interpretability of a classifier can vary from case to case, here, by a humanly interpretable classifier, we restrict it to be expressed in simplistic mathematical terms. As a novel approach, we represent a classifier as an assembly of simple mathematical rules using a nonlinear decision tree (NLDT). Each conditional (nonterminal) node of the tree represents a nonlinear mathematical rule (split-rule) involving features in order to partition the dataset in the given conditional node into two nonoverlapping subsets. This partitioning is intended to minimize the impurity of the resulting child nodes. By restricting the structure of the split-rule at each conditional node and depth of the decision tree, the interpretability of the classifier is ensured. The nonlinear split-rule at a given conditional node is obtained using an evolutionary bilevel optimization algorithm, in which while the upper level focuses on arriving at an interpretable structure of the split-rule, the lower level achieves the most appropriate weights (coefficients) of individual constituents of the rule to minimize the net impurity of two resulting child nodes. The performance of the proposed algorithm is demonstrated on a number of controlled test problems, existing benchmark problems, and industrial problems. Results on 2-500 feature problems are encouraging and open up further scopes of applying the proposed approach to more challenging and complex classification tasks.

Automatic Feature Extraction and Construction Using Genetic Programming for Rotating Machinery Fault Diagnosis

Feature extraction is an essential process in the intelligent fault diagnosis of rotating machinery. Although existing feature extraction methods can obtain representative features from the original signal, domain knowledge and expert experience are often required. In this article, a novel diagnosis approach based on evolutionary learning, namely, automatic feature extraction and construction using genetic programming (AFECGP), is proposed to automatically generate informative and discriminative features from original vibration signals for identifying different fault types of rotating machinery. To achieve this, a new program structure, a new function set, and a new terminal set are developed in AFECGP to allow it to detect important subband signals and extract and construct informative features, automatically and simultaneously. More important, AFECGP can produce a flexible number of features for classification. Having the generated features, k -Nearest Neighbors is employed to perform fault diagnosis. The performance of the AFECGP-based fault diagnosis approach is evaluated on four fault diagnosis datasets of varying difficulty and compared with 14 baseline methods. The results show that the proposed approach achieves better fault diagnosis accuracy on all the datasets than the competitive methods and can effectively identify different fault conditions of rolling bearing, gear, and rotor.