With the rapid development of industrial Internet of Things (IIoT), the edge-cloud collaboration architecture combining the powerful computing ability of cloud computing with the low latency of edge computing plays an increasingly important role in providing the computing resources and reducing the latency for IIoT. However, under this architecture, existing methods in scheduling the resources for IIoT often focus on latency and energy consumption but ignore some other important factors especially the reliable factor, thereby making it difficult for them to adapt to real-world IIoT scenarios. To this end, we propose a reliable resource scheduling method with knowledge transfer for edge-cloud collaboration-enabled IIoT. Specifically, we first model the resource scheduling as a many-objective optimization problem, considering these optimized objectives: latency, energy consumption, load balance, resource utilization, and trust measure between tasks and servers. Then, we develop a knowledge transfer accelerated clustering evolutionary algorithm (KTCEA) for many-objective optimization to solve the model, where the knowledge transfer aims at accelerating the evolution and the clustering makes the population converge from various directions. Under the collaboration of knowledge transfer and clustering, KTCEA can utilize the small population size to effectively search the objective space, and thus have the high real-time performance. Extensive experiment results on a benchmark test suite and the constructed model demonstrate that KTCEA is highly competitive compared with some advanced methods and our method can efficiently achieve the resource scheduling for edge-cloud collaboration-enabled IIoT, respectively.

With the rapid development of 5G, numerous data is generated in the blockchain-enabled industrial Internet of Things (IIoT). Although these peers in the blockchain system have the storage ability, they are far from meeting the storage requirements of the generated data. In addition, all data is stored in the blockchain network, which is unfriendly to applications that require real-time information. To address the above storage problems, this article proposes a block storage optimization method for blockchain-enabled IIoT, whose core idea is to conditionally select some blocks to store in the cloud. This method firstly models the selection conditions of blocks as a many-objective optimization problem, where the selection conditions include using probability, storage cost, space occupation, and transmission cost. Then, a cascading selection-based evolutionary algorithm (CSEA) for many-objective optimization is developed to solve the model and thereby obtain the optimal blocks stored in the cloud, where CSEA adopts the diversity-first principle. Finally, CSEA is first compared with seven state-of-the-art methods on two benchmark test suites for validating its ability to obtain reliable experimental results, and then is used to solve the proposed model. The corresponding results demonstrate that CSEA has high competitiveness, and our method can effectively address the storage problems above. In summary, this article provides a novel method for addressing the storage problem in the blockchain-enabled IIoT.

The incipient fault detection of a complex industrial process is a challenging problem for traditional dynamic detection methods. Traditional dynamic detection methods usually decouple the correlations among the variables and dynamic correlations simultaneously, which makes the two types of correlations mixed and may lead to performance deterioration in long-sequence dynamic detection. Some incipient faults may not change the amplitudes of process variables but change the long-sequence dynamic features. Based on the$T^{2}$statistic and matrix multiplication transformation ($T^{2}$S-MMT), traditional dynamic detection methods can detect many faults effectively. However, the$T^{2}$S-MMT can not effectively detect some incipient faults due to the above two types of correlations mixed. In order to overcome the shortcomings of$T^{2}$S-MMT and improve the detection ability of some incipient faults, this paper proposes a fault detection method based on the dynamic k-nearest neighbor model and Dual Control Chart (DKNN-DCC), which can improve the incipient fault detection performance by using long-sequence dynamic detection. The proposed method is verified by the Tennessee Eastman (TE) process and the continuously stirred tank reactor (CSTR) process. The experimental results show the effectiveness of the proposed method in incipient fault detection compared with traditional dynamic detection methods.Note to Practitioners—This paper presents a novel incipient fault detection method, which directly mines the long-sequence dynamic abnormal information from the process variable and overcomes the problem of some abnormal information being submerged in the$T^{2}$statistic calculated based on the matrix multiplication transformation. The proposed method can detect incipient faults that are not easily detected by some traditional methods and can help operators find the abnormal and avoid more serious losses. The structure of the proposed method jumps out of the frameworks of traditional dynamic detection methods, which is feasible to apply to different stable industrial processes.

Modern industrial processes are characterized by numerous measurement points and wide operating ranges, resulting in extremely complex correlations among variables. Therefore, an effective monitoring system should balance diverse process characteristics such as nonlinearity, non-Gaussianity, and multiscale simultaneously. Moreover, it should have the ability to detect and diagnose faults in the incipient stage, thus avoiding accident escalation. With these goals in mind, this paper proposes an integrated monitoring solution based on multiscale kernel entropy component analysis (MSKECA). Specifically, process variables are first decomposed into approximations and details at different scales in real-time using the moving window-based wavelet, and contributions from each scale are collected in separate matrices. Then, KECA-based local-scale models are built to sift out important detail scales for reconstruction along with the approximate scale. Lastly, a KECA-based global-scale model is developed to monitor the reconstructed data. To improve the fault detection performance, a novel monitoring index based on the angle metric called angle variance index (AVI) is designed. In addition, to achieve effective diagnosis, MSKECA-based contribution plots are constructed, which depict the contributions of variables to faults at each scale, thus comprehensively revealing the root causes. Finally, the effectiveness and superiority of the proposed solution are validated by comparisons with other advanced counterparts in two industrial scenarios.Note to Practitioners—This paper proposes an integrated monitoring solution for complex industrial processes, i.e., MSKECA-based fault detection and diagnosis. The solution takes into account the diversity of process characteristics, the effectiveness of incipient fault detection, and the richness of diagnostic information. Specifically, 1) MSKECA can simultaneously handle the nonlinear, non-Gaussian, and multiscale characteristics that are prevalent in real process data. It enables on-line detection of significant events occurring at different scales and extraction of fault-sensitive features for monitoring; 2) based on the angular structure of KECA, the AVI statistic is designed, which exhibits low autocorrelation and is sensitive to faults. Leveraging the statistic, MSKECA allows reliable and prompt responses to faults; 3) MSKECA-based contribution plots not only convey diverse diagnostic information including fault variable, type, and grade but also are not susceptible to the smearing effect, which is helpful for practitioners to achieve fault repair. The solution has proven useful for a real hot rolling process. It can also be extended to other industrial processes.

The evolution of multi-constellation Global Navigation Satellite Systems (GNSS) has presented an opportunity to enhance user positioning accuracy. However, practical constraints, such as limited receiver channels and power consumption, necessitate judicious satellite selection. Geometric Dilution of Precision (GDOP) serves as a critical indicator for optimizing positioning performance, but determining the subset with the optimal GDOP value involves solving an impractical combinatorial optimization problem. A compromise solution seeks to balance computational complexity while sacrificing some optimality. Consequently, finding an optimal combination of satellites with a low computational burden yet quasi-optimal GDOP value remains a challenge. In response to this challenge, we introduce a pioneering approach in this paper: a super-fast satellite selection algorithm based on power series expansion (SF-PSE). This paper derives a “Xiao-Liang formula” based on power series expansion and the Sherman-Morrison formula. Using this formula, we propose two low-computational-cost rapid iterative algorithms (F-PSE and SF-PSE). Among these algorithms, SF-PSE notably reduces the computational burden through an approximate iterative inverse matrix-guided search method. Experimental results demonstrate that satellite combinations identified by F-PSE and SF-PSE yield nearly the same accuracy while reducing computation time by 70% and 87%, respectively, compared to the SMALLER method.

Traditional projection dynamic monitoring methods focus on simultaneously decoupling the correlations among the process variables and the autocorrelations of the variables, which leads to a mixing problem of the two correlations. The mixing problem decreases the ability to model the dynamic correlations, thus decreasing the detection rates (DRs) of some faults. Considering that the projection matrix may cause the mixing of the two correlations, this article proposes a dynamic monitoring method based on directly monitoring original variables. This article first adopts the kernel least-mean-squares (KLMS) method to establish a univariate dynamic model, then adopts the univariate dynamic model and the dual control chart (DCC) to build the multivariate direct monitoring method, which is named the KL2C method (KL represents KLMS and 2 C represents DCC). Then, the dynamic nearest neighbor kernel space (DNNKS) is proposed to overcome the redundant dimensions problem of the KL2C method, which is named the DKL2C method (D represents DNNKS). Furthermore, based on the joint control chart, this article puts forward a dynamic monitoring method of two sequences, which both considers the advantages of the projection dynamic monitoring method and the direct dynamic monitoring method together. Finally, this article utilizes the Tennessee Eastman process and the continuously stirred tank reactor process to verify the effectiveness of the proposed methods.

With the continuous development of the economy and society, decision-making problems and decision-making scenarios have become more complex. The q-rung orthopair fuzzy set is getting more and more attention from researchers, which is more general and flexible than Pythagorean fuzzy set and intuitionistic fuzzy set under complex vague environment. In this study, the concept of q-rung orthopair fuzzy linguistic set (q-ROFLS) is proposed and a new q-rung orthopair fuzzy linguistic method is developed to handle MAGDM problem. Firstly, the conception, operation laws, comparison methods, and distance measure methods of the q-ROFLS are proposed. Secondly, the q-ROFL weighted average operator, q-ROFL ordered weighted average operator, q-ROFL hybrid weighted average operator, q-ROFL weighted geometric operator, q-ROFL ordered weighted geometric operator, and q-ROFL hybrid weighted geometric operator are proposed, and some interesting properties, special cases of these operators are investigated. Furthermore, a new method to cope with MAGDM problem based on q-ROFL weighted average operator (q-ROFL weighted geometric operator) is developed. Finally, a practical example for suppliers selection is provided to verify the practicality of the presented method, and the effectiveness and flexibility of the presented method are illustrated by sensitive analysis and comparative analysis.