A comparison of fuzzy clustering algorithms for bearing fault diagnosis

Fuzzy-Rough induced spectral ensemble clustering

Ensemble clustering helps achieve fast clustering under abundant computing resources by constructing multiple base clusterings. Compared with the standard single clustering algorithm, ensemble clustering integrates the advantages of multiple clustering algorithms and has stronger robustness and applicability. Nevertheless, most ensemble clustering algorithms treat each base clustering result equally and ignore the difference of clusters. If a cluster in a base clustering is reliable/unreliable, it should play a critical/uncritical role in the ensemble process. Fuzzy-rough sets offer a high degree of flexibility in enabling the vagueness and imprecision present in real-valued data. In this paper, a novel fuzzy-rough induced spectral ensemble approach is proposed to improve the performance of clustering. Specifically, the significance of clusters is differentiated, and the unacceptable degree and reliability of clusters formed in base clustering are induced based on fuzzy-rough lower approximation. Based on defined cluster reliability, a new co-association matrix is generated to enhance the effect of diverse base clusterings. Finally, a novel consensus spectral function is defined by the constructed adjacency matrix, which can lead to significantly better results. Experimental results confirm that the proposed approach works effectively and outperforms many state-of-the-art ensemble clustering algorithms and base clustering, which illustrates the superiority of the novel algorithm.

Improving Classification Performance of Fully Connected Layers by Fuzzy Clustering in Transformed Feature Space

Fully connected (FC) layers are used in almost all neural network architectures ranging from multilayer perceptrons to deep neural networks. FC layers allow any kind of symmetric/asymmetric interaction between features without making any assumption about the structure of the data. However, success of convolutional and recursive layers and findings of many studies have proven that the intrinsic structure of a dataset holds a great potential to improve the success of a classification problem. Leveraging clustering to explore and exploit this intrinsic structure in classification problems has been the subject of various studies. In this paper, we propose a new training pipeline for fully connected layers which enables them to make more accurate classification predictions. The proposed method aims to reflect the clustering patterns in the original feature space of the training dataset to the transformed feature space created by the FC layer. In this way, we intend to enhance the representation ability of the extracted features and accordingly increase the classification accuracy. The Fuzzy C-Means algorithm is employed in this study as the clustering tool. To evaluate the performance of the proposed method, 11 experiments were conducted on 9 benchmark UCI datasets. Empirical results show that the proposed method works well in practice and gives higher classification accuracies compared to a regular FC layer in most datasets.

A Water Consumption Forecasting Model by Using a Nonlinear Autoregressive Network with Exogenous Inputs Based on Rough Attributes

Scientific prediction of water consumption is beneficial for the management of water resources. In practice, many factors affect water consumption, and the various impact mechanisms are complex and uncertain. Meanwhile, the water consumption time series has a nonlinear dynamic feature. Therefore, this paper proposes a nonlinear autoregressive model with an exogenous input (NARX) neural network model based on rough set (RS) theory. First, the RS theory was used to analyze the importance of each attribute in water consumption. Then, the main influencing factor was selected as the input of the NARX neural network model, which was applied to predict water consumption. The proposed model is proved to give better results of a single NARX model and a back propagation neural network. The experimental results indicate that the proposed model has higher prediction accuracy in terms of the mean absolute error, mean absolute percentage error and root mean square error.

Current-Based Bearing Fault Diagnosis Using Deep Learning Algorithms

Artificial intelligence algorithms and vibration signature monitoring are recurrent approaches to perform early bearing damage identification in induction motors. This approach is unfeasible in most industrial applications because these machines are unable to perform their nominal functions under damaged conditions. In addition, many machines are installed at inaccessible sites or their housing prevents the setting of new sensors. Otherwise, current signature monitoring is available in most industrial machines because the devices that control, supply and protect these systems use the stator current. Another significant advantage is that the stator phases lose symmetry in bearing damaged conditions and, therefore, are multiple independent sources. Thus, this paper introduces a new approach based on fractional wavelet denoising and a deep learning algorithm to perform a bearing damage diagnosis from stator currents. Several convolutional neural networks extract features from multiple sources to perform supervised learning. An information fusion (IF) algorithm then creates a new feature set and performs the classification. Furthermore, this paper introduces a new method to achieve positive unlabeled learning. The flattened layer of several feature maps inputs the fuzzy c-means algorithm to perform a novelty detection instead of clusterization in a dynamic IF context. Experimental and on-site tests are reported with promising results.

A novel doublet extreme learning machines for Delta 3D printer fault diagnosis using attitude sensor

Extreme learning machine (ELM) has better operation efficiency in fault diagnosis. However, the recognition accuracy of ELM algorithm is actually affected by the activation function. Moreover, most of the testing dataset are coming from high precision and expensive sensors. In this paper, raw data are collected by a low-cost attitude sensor, which is installed on the mobile platform of a delta 3D printer. A doublet activation function is proposed to improve the performance of ELM, named doublet ELM (DELM). The proposed method is evaluated using experimental data collected from the 3D printer, and its advantages are demonstrated by comparing with other activation functions. The experimental results indicate that the proposed method leads to the highest accuracy in different hidden nodes and the testing classification rate achieves 93% and 96% using only 8.33% of the dataset for model training, for R75 and R90 sub-datasets, respectively. Moreover, compared with peer methods, such as random forest, echo state network, and so on, the results show that the present DELM exhibits the best performance in small-sample and improves the accuracy of the 3D printer fault diagnosis.

Fuzzy Measures: A solution to deal with community detection problems for networks with additional information

In this work we introduce the notion of the weighted graph associated with a fuzzy measure. Having a finite set of elements between which there exists an affinity fuzzy relation, we propose the definition of a group based on that affinity fuzzy relation between the individuals. Then, we propose an algorithm based on the Louvain’s method to deal with community detection problems with additional information independent of the graph. We also provide a particular method to solve community detection problems over extended fuzzy graphs. Finally, we test the performance of our proposal by means of some detailed computational tests calculated in several benchmark models.

Rolling Bearings Fault Diagnosis Based on Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise, Nonlinear Entropy, and Ensemble SVM

Rolling bearings are fundamental elements that play a crucial role in the functioning of rotating machines; thus, fault diagnosis of rolling bearings is of great significance to reduce catastrophic failures and heavy economic loss. However, the vibration signals of rolling bearings are often nonlinear and nonstationary, resulting in difficulty for feature extraction and fault recognition. In this paper, a hybrid method for multiple fault diagnosis of rolling bearings is presented. The bearing vibration signals are decomposed with the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) to denoise and extract nonlinear entropy features. The nonlinear entropy features are further processed to select the more discriminative fault features and to reduce feature dimension. Then a multi-class intelligent recognition model based on ensemble support vector machine (ESVM) is constructed to diagnose different bearing fault modes as well as fault severities. The effectiveness of the proposed method is assessed via experimental case studies of rolling bearings under multiple operational conditions (i.e., speeds and loads). The results show that our method gives better diagnosis results as compared to some existing approaches.

A Deep Regression Model with Low-Dimensional Feature Extraction for Multi-Parameter Manufacturing Quality Prediction

Manufacturing quality prediction can be used to design better parameters at an earlier production stage. However, in complex manufacturing processes, prediction performance is affected by multi-parameter inputs. To address this issue, a deep regression framework based on manifold learning (MDRN) is proposed in this paper. The multi-parameter inputs (i.e., high-dimensional information) were firstly analyzed using manifold learning (ML), which is an effective nonlinear technique for low-dimensional feature extraction that can enhance the representation of multi-parameter inputs and reduce calculation burdens. The features obtained through the ML were then learned by a deep learning architecture (DL). It can learn sufficient features of the pattern between manufacturing quality and the low-dimensional information in an unsupervised framework, which has been proven to be effective in many fields. Finally, the learned features were inputted into the regression network, and manufacturing quality predictions were made. One type (two cases) of machinery parts manufacturing system was investigated in order to estimate the performance of the proposed MDRN with three comparisons. The experiments showed that the MDRN overwhelmed all the peer methods in terms of mean absolute percentage error, root-mean-square error, and threshold statistics. Based on these results, we conclude that integrating the ML technique for dimension reduction and the DL technique for feature extraction can improve multi-parameter manufacturing quality predictions.

Generative Transfer Learning for Intelligent Fault Diagnosis of the Wind Turbine Gearbox

Intelligent fault diagnosis algorithms based on machine learning and deep learning techniques have been widely used in industrial applications and have obtained much attention as well as achievements. In real industrial applications, working loads of machines are always changing. Hence, directly applying the traditional algorithms will cause significant degradation of performance with changing conditions. In this paper, a novel domain adaptation method, named generative transfer learning (GTL), is proposed to tackle this problem. First, raw datasets were transformed to time–frequency domain based on short-time Fourier transformation. A domain discriminator was then built to distinguish whether the data came from the source or the target domain. A target domain classification model was finally acquired by the feature extractor and the classifier. Experiments were carried out for the fault diagnosis of a wind turbine gearbox. The t-distributed stochastic neighbor embedding technique was used to visualize the output features for checking the effectiveness of the proposed algorithm in feature extraction. The results showed that the proposed GTL could improve classification rates under various working loads. Compared with other domain adaptation algorithms, the proposed method exhibited not only higher accuracy but faster convergence speed as well.

A Novel Intelligent Method for Bearing Fault Diagnosis Based on EEMD Permutation Entropy and GG Clustering

For a rolling bearing fault that has nonlinearity and nonstationary characteristics, it is difficult to identify the fault category. A rolling bearing clustering fault diagnosis method based on ensemble empirical mode decomposition (EEMD), permutation entropy (PE), linear discriminant analysis (LDA), and the Gath–Geva (GG) clustering algorithm is proposed. Firstly, we decompose the vibration signal using EEMD, and several inherent modal components are obtained. Then, the permutation entropy values of each modal component are calculated to get the entropy feature vector, and the entropy feature vector is reduced by the LDA method to be used as the input of the clustering algorithm. The data experiments show that the proposed fault diagnosis method can obtain satisfactory clustering indicators. It implies that compared with other mode combination methods, the fault identification method proposed in this study has the advantage of better intra-class compactness of clustering results.

Transmission Condition Monitoring of 3D Printers Based on the Echo State Network

Three-dimensional printing quality is critically affected by the transmission condition of 3D printers. A low-cost technique based on the echo state network (ESN) is proposed for transmission condition monitoring of 3D printers. A low-cost attitude sensor installed on a 3D printer was first employed to collect transmission condition monitoring data. To solve the high-dimensional problem of attitude data, feature extraction approaches were subsequently performed. Based on the extracted features, the ESN was finally employed to monitor transmission faults of the 3D printer. Experimental results showed that the fault recognition accuracy of the 3D printer was obtained at 97.17% using the proposed approach. In addition, support vector machine (SVM), locality preserving projection support vector machine (LPPSVM), and principal component analysis support vector machine (PCASVM) were also used for comparison. The contrast results showed that the recognition accuracies of our method were higher and more stable than that of SVM, LPPSVM, and PCASVM when collecting raw data via the low-cost attitude sensor.

3D SSY Estimate of EPFM Constraint Parameter under Biaxial Loading for Sensor Structure Design

Conventional sensor structure design and related fracture mechanics analysis are based on the single J-integral parameter approach of elastic-plastic fracture mechanics (EPFM). Under low crack constraint cases, the EPFM one-parameter approach generally gives a stress overestimate, which results in a great cost waste of labor and sensor components. The J-A two-parameter approach overcomes this limitation. To enable the extensive application of the J-A approach on theoretical research and sensor engineering problem, under small scale yielding (SSY) conditions, the authors developed an estimate method to conveniently and quickly obtain the constraint (second) parameter A values directly from T-stress. Practical engineering application of sensor structure analysis and design focuses on three-dimensional (3D) structures with biaxial external loading, while the estimate method was developed based on two-dimensional (2D) plain strain condition with uniaxial loading. In the current work, the estimate method was successfully extended to a 3D structure with biaxial loading cases, which is appropriate for practical sensor design. The estimate method extension and validation process was implemented through a thin 3D single edge cracked plate (SECP) specimen. The process implementation was completed in two specified planes of 3D SECP along model thickness. A wide range of material and geometrical properties were applied for the extension and validation process, with material hardening exponent value 3, 5 and 10, and crack length ratio 0.1, 0.3 and 0.7.

A Simplified SSY Estimate Method to Determine EPFM Constraint Parameter for Sensor Design

To implement a sensor structure analysis and design (as well as other engineering applications), a two-parameter approach using elastic–plastic fracture mechanics (EPFM) could be applied to analyze a structure more accurately than a one-parameter approach, especially for structures with low crack constraint. The application of the J-A two-parameter approach on sensors and other structures depends on the obtainment of a constraint parameter A. To conveniently and effectively obtain the A parameter values, the authors have developed a T-stress-based estimate method under a small-scale yielding (SSY) condition. Under a uniaxial external loading condition, a simplified format of the T-stress-based estimate has been proposed by the authors to obtain the parameter A much more conveniently and effectively. Generally, sensors and other practical engineering structures endure biaxial external loading instead of the uniaxial one. In the current work, the simplified formation of the estimate method is extended to a biaxial loading condition. By comparing the estimated A parameter values with their numerical solutions from a finite element analysis (FEA) results, the extension of the simplified formation of T-stress-based estimate method to biaxial loading was discussed and validated. The comparison procedure was completed using a wide variety of materials and geometrical properties on three types of specimens: single edge cracked plate (SECP), center cracked plate (CCP), and double edge cracked plate (DECP).