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Nonlinearity may cause a model deviation problem, and hence, it is a challenging problem for process monitoring. To handle this issue, local kernel principal component analysis was proposed, and it achieved a satisfactory performance in static process monitoring. For a dynamic process, the expectation value of each variable changes over time, and hence, it cannot be replaced with a constant value. As such, the local data structure in the local kernel principal component analysis is wrong, which causes the model deviation problem. In this paper, we propose a new two-step dynamic local kernel principal component analysis, which extracts the static components in the process data and then analyzes them by local kernel principal component analysis. As such, the two-step dynamic local kernel principal component analysis can handle the nonlinearity and the dynamic features simultaneously.

Exponential kernels have been used considerably in statistics, machine learning, and artificial intelligence for tasks such as kernel principal component analysis (Kernel PCA), support vector machines(SVM), visualization, clustering, and pattern recognition. Selecting different bandwidth parameters for the exponential kernel can lead to varying insights about the data. Hence, understanding the theoretical impact of the bandwidth parameter is crucial. This paper investigates the influence of the exponential kernel’s bandwidth parameter on the approximation of continuous operators by their empirical counterparts, supported by some experimental algorithms.

Tool wear is one of the consequences of a machining process. Excessive tool wear can lead to poor surface finish, and result in a defective product. It can also lead to premature tool failure, and may result in process downtime and damaged components. With this in mind, it has long been desired to monitor tool wear/tool condition. Kernel principal component analysis (KPCA) is proposed as an effective and efficient method for monitoring the tool condition in a machining process. The KPCA-based method may be used to identify faults (abnormalities) in a process through the fusion of multi-sensor signals. The method employs a control chart monitoring approach that uses Hotelling’s T2-statistic and Q-statistic to identify the faults in conjunction with control limits, which are computed by kernel density estimation (KDE). KDE is a non-parametric technique to approximate a probability density function. Four performance metrics, abnormality detection rate, false detection rate, detection delay, and prediction accuracy, are employed to test the reliability of the monitoring system and are used to compare the KPCA-based method with PCA-based method. Application of the proposed monitoring system to experimental data shows that the KPCA based method can effectively monitor the tool wear.

Diagnosis and prognosis of gear systems play an important role in modern manufacturing. While first-principle-based inverse analysis is subject to various limitations, data-driven approaches such as many machine learning techniques have shown great promise in recent years. Nevertheless, major challenges remain. Machine learning generally requires large amount of high-quality training data which may not be available for many industrial systems. In particular, while gear faults are continuous in nature and exhibit many different scenarios, in practical situations owing to the high cost in data acquisition especially for fault scenarios, only a small number of discrete classes of faults, i.e., fault types and severities, can be recorded and employed in training. As such, the neural networks trained will need to deal with unseen faults when they are actually implemented. To tackle this challenge, in this research, we develop a fuzzy classification approach capable of handling fault scenarios that are not included in the training dataset. Through the integration of a fuzzification procedure, this fuzzy neural network (FNN) can produce classification outcome with probability and confidence level. An unseen fault scenario will be classified into the nearest fault class with probability, effectively yielding the diagnosis result under limited data. While fault features in gear vibration signals are hidden and have complex nonlinear relations with respect to fault scenarios, it is found that the kernel principal component analysis (KPCA) can enable the FNN to facilitate the correlation of fault features. Systematic case studies using experimental data acquired from a lab-scale gear system are carried out to validate the new approach.

Several methods utilizing common spatial pattern (CSP) algorithm have been presented for improving the identification of imagery movement patterns for brain computer interface applications. The present study focuses on improving a CSP-based algorithm for detecting the motor imagery movement patterns. A discriminative filter bank of CSP method using a discriminative sensitive learning vector quantization (DFBCSP-DSLVQ) system is implemented. Four algorithms are then combined to form three methods for improving the efficiency of the DFBCSP-DSLVQ method, namely the kernel linear discriminant analysis (KLDA), the kernel principal component analysis (KPCA), the soft margin support vector machine (SSVM) classifier and the generalized radial bases functions (GRBF) kernel. The GRBF is used as a kernel for the KLDA, the KPCA feature selection algorithms and the SSVM classifier. In addition, three types of classifiers, namely K-nearest neighbor (K-NN), neural network (NN) and traditional support vector machine (SVM), are employed to evaluate the efficiency of the classifiers. Results show that the best algorithm is the combination of the DFBCSP-DSLVQ method using the SSVM classifier with GRBF kernel (SSVM-GRBF), in which the best average accuracy, attained are 92.70% and 83.21%, respectively. Results of the Repeated Measures ANOVA shows the statistically significant dominance of this method at p < 0.05. The presented algorithms are then compared with the base algorithm of this study i.e. the DFBCSP-DSLVQ with the SVM-RBF classifier. It is concluded that the algorithms, which are based on the SSVM-GRBF classifier and the KLDA with the SSVM-GRBF classifiers give sufficient accuracy and reliable results.

With the development of communication technology, the demand for location-based services is growing rapidly. This paper presents an algorithm for indoor localization based on Received Signal Strength (RSS), which is collected from Access Points (APs). The proposed localization algorithm contains the offline information acquisition phase and online positioning phase. Firstly, the AP selection algorithm is reviewed and improved based on the stability of signals to remove useless AP; secondly, Kernel Principal Component Analysis (KPCA) is analyzed and used to remove the data redundancy and maintain useful characteristics for nonlinear feature extraction; thirdly, the Affinity Propagation Clustering (APC) algorithm utilizes RSS values to classify data samples and narrow the positioning range. In the online positioning phase, the classified data will be matched with the testing data to determine the position area, and the Maximum Likelihood (ML) estimate will be employed for precise positioning. Eventually, the proposed algorithm is implemented in a real-world environment for performance evaluation. Experimental results demonstrate that the proposed algorithm improves the accuracy and computational complexity.

To address the challenges of difficult feature extraction and suboptimal parameter configuration for cyclotron ion source fault diagnosis in complex environments, this study proposes an intelligent diagnostic framework integrating Kernel Principal Component Analysis (KPCA), an Improved Sparrow Search Algorithm (ISSA), and a Support Vector Machine (SVM). The KPCA algorithm is employed for dimensionality reduction to handle the highly nonlinear nature of fault data. Regarding algorithmic evolution, the basic SSA is enhanced by integrating dynamic weights, opposition-based learning, and Cauchy mutation strategies, which effectively overcome the diagnostic bottlenecks inherent in cyclotron scenarios. Furthermore, the ISSA facilitates the global adaptive optimization of key SVM parameters, eliminating the stochasticity of empirical tuning and fundamentally enhancing the model’s robustness. Experimental results across 30 independent tests demonstrate that the KPCA-ISSA-SVM model achieves an average accuracy of 97.6% in multi-class fault detection. Compared with other classic diagnostic models, the proposed framework exhibits superior precision and stability, providing an effective technical approach with significant engineering value for the precise monitoring of ion source statuses.

To predict the risk of water inrush from coal seam floor more effectively, a prediction model of water inrush risk level of coal seam floor based on KPCA-DBO-SVM is proposed. Firstly, the risk level of water inrush of coal seam floor is graded based on the influencing factors of water inrush from coal seam floor which are determined by data of water inrush accident and related literature, and probability of water inrush in working face. Secondly, Kernel Principal Component Analysis (KPCA) is used to reduce the dimension of high-dimensional features of the influencing factors, Then, results of feature extraction are input into the DBO-SVM model. Penalty parameters and kernel parameters of Support Vector Machine (SVM) are optimized by Dung Beetle Optimization algorithm (DBO). Next, these data is mapped to high-dimensional space by SVM to separate. In this way, water inrush risk level of coal seam floor is predicted. Finally, 94 groups of sample data are selected and divided into training set and test set. Prediction results of KPCA-DBO-SVM model are compared with these that DBO-SVM, PSO-SVM and PSO-BPNN models. The results show that the accuracy of KPCA-DBO-SVM model prediction is increased by 0.18, 0.12, 0.29 respectively; the macro precision is increased by 0.16, 0.11, 0.27 respectively; the macro recall rate is increased by 0.14, 0.10, 0.28 respectively; and the Macro-F 1 is increased by 0.15, 0.10, 0.28 respectively. The KPCA-DBO-SVM model is applied to three coal mine working face to verify the stability and universality of the model whose prediction results are consistent with the actual engineering situation. Therefore, KPCA-DBO-SVM model is suitable for the risk prediction of water inburst of coal seam floor.

As a typical machine olfactory system index, the accuracy of hybrid gas identification and concentration detection is low. This paper proposes a novel hybrid gas identification and concentration detection method. In this method, Kernel Principal Component Analysis (KPCA) is employed to extract the nonlinear mixed gas characteristics of different components, and then K-nearest neighbour algorithm (KNN) classification modelling is utilized to realize the recognition of the target gas. In addition, this method adopts a multivariable relevance vector machine (MVRVM) to regress the multi-input nonlinear signal to realize the detection of the concentration of the hybrid gas. The proposed method is validated by using CO and CH4 as the experimental system samples. The experimental results illustrate that the accuracy of the proposed method reaches 98.33%, which is 5.83% and 14.16% higher than that of principal component analysis (PCA) and independent component analysis (ICA), respectively. For the hybrid gas concentration detection method, the CO and CH4 concentration detection average relative errors are reduced to 5.58% and 5.38%, respectively.

Aiming at the typical faults in the coal mills operation process, the kernel extreme learning machine diagnosis model based on variational model feature extraction and kernel principal component analysis is offered. Firstly, the collected signals of vibration and loading force, corresponding to typical faults of coal mill, are decomposed by variational model decomposition, and the intrinsic model functions at different scales are obtained. Then, the eigenvectors consisting of feature energy and sample entropy in these functions are respectively calculated, and the kernel principal component analysis is used for noise removal and dimensionality reduction. Finally, the kernel extreme learning machine model is trained and tested with the dimension reduced feature vector as input and the corresponding coal mill state as output. The results show that the variational model decomposition extraction can improve the input features of the model compared with the single eigenvector model, and the kernel principal component analysis method can significantly reduce the information redundancy and the correlation of eigenvectors, which can effectively save time and cost, and improve the prediction performance of the model to some extent. The establishment of this model provides a new idea for the study of coal mill fault diagnosis.