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With the advancement of science and technology, industrial robots have become indispensable equipment in advanced manufacturing and a critical benchmark for assessing a nation’s manufacturing and technological capabilities. Enhancing the reliability of industrial robots is therefore a pressing priority. This paper investigates the drive system of industrial robots, modeling it as a series system comprising multiple components (n) with a repairman who operates under a single vacation policy. The system assumes that each component’s lifespan follows an exponential distribution, while the repairman’s repair and vacation times adhere to general distributions. Notably, the repairman initiates a vacation at the system’s outset. Using the supplementary variable method, a mathematical model of the system is constructed and formulated within an appropriate Banach space, leading to the derivation of the system’s abstract development equation. Leveraging functional analysis and the C[sub.0]-semigroup theory of bounded operators, the study examines the system’s adaptability, stability, and key reliability indices. Furthermore, numerical simulations are employed to analyze how system reliability indices vary with parameter values. This work contributes to the field of industrial robot reliability analysis by introducing a novel methodological framework that integrates vacation policies and general distribution assumptions, offering new insights into system behavior and reliability optimization. The findings have significant implications for improving the design and maintenance strategies of industrial robots in real-world applications.

In this paper, we study the component configuration issue of the line-shaped wave networks which is made of two viscoelastic components and an elastic component and the viscoelastic parts produce the infinite memory and damping and distributed delay. The structural memory of viscoelastic component results in energy dissipative and the damping memory arouses the instability, and the elastic component is energy conservation, such a hybrid effects lead to complex dynamic behaviour of network. Our purpose of the present paper is to find out stability condition of such a network, in particular, the configuration condition of the wave network under which the network is exponentially stable. At first, using a resolvent family approach, we prove the well-posed of the wave network systems under suitable assumptions on the memory kernel g(s), the damping coefficient μ1 and delay distributed kernel μ2(s). Next, using the Lyapunov function method, we seek for a structural condition of the wave networks under which the wave networks are exponentially stable. By constructing new functions we obtain the sufficient conditions for the exponential stability of the wave networks, the structural conditions are given as inequalities.

In the current research of debris flow geological disaster prediction, determining reasonable disaster-inducing factors and ensuring the accuracy and rapidity of the prediction model are considered vital issues, and also, essential foundations for disaster early warning and disaster prevention and mitigation. Aiming at the problems of low prediction accuracy and long prediction time in the current debris flow research, firstly, six debris flow impact factors were selected relying on the fast multiple principal component extraction (FMPCE) algorithm, including rainfall, slope gradient, gully bed gradient, relative height difference, soil moisture content and pore water pressure. Next, based on the broad learning (BL) algorithm, the debris flow prediction model based on FMPCE and the optimized BL is established with the input of debris flow-inducing factors and the output of debris flow probability. Then the model is optimized using matrix stochastic approximate singular value decomposition (SVD), and the debris flow disaster prediction model, based on SVDBL, is constructed. The prediction results of the optimized model are compared with those of the gradient descent optimized the BP neural network model(GD-BP), Support Vector Machines model(SVM) based on grid search and BL model. The results show that the accuracy of SVDBL is 7.5% higher than that of GD-BP, 3% higher than that of SVM and 0.5% higher than that of BL. The RMSE sum of SVDBL was 0.05870, 0.0478 and 0.0227 less than that of GD-BPSVM and BL, respectively; the MAPE sum of SVDBL was 1.95%, 1.66% and 0.49% less than that of GD-BPSVM and BL; the AUC values of SVDBL were 12.75%, 7.64% and 2.79% higher than those of the above three models, respectively. In addition, the input dataset is expanded to compare the training time of each model. The simulation results show that the prediction accuracy of this model is the highest and the training time is the shortest after the dataset is expanded. This study shows that the BL can be used for debris flow prediction, and can also provide references for disaster early warning and prevention.

A new conjugate gradient method is proposed by Applying Powell's symmetrical technique to conjugate gradient methods in this paper. Using Wolfe line searches, the global convergence of the method is analyzed by using the spectral analysis of the conjugate gradient iteration matrix and Zoutendijk's condition. Based on this, some concrete descent algorithms are developed. 200s numerical experiments are presented to verify their performance and the numerical results show that these algorithms are competitive compared with the PRP^sup +^ algorithm. Finally, a brief discussion of the new proposed method is given.[PUBLICATION ABSTRACT]

Around the world, soft soils can be found in many areas close to seas and rivers. These areas play an indispensable and crucial role in the development of government plans, especially in the population growth sector. Due to maintaining a weak shear power and vast settlement under the buildings, soft soils are considered problematic soil. The significant risks associated with building structures and infrastructures in soft soil are high, requiring engineers' extreme attention. It depends on undrained shear strength (USS) that the foundation of structures can bear in soft soil, and this factor vigorously controls the selection of soil improvement techniques. In recent years, there have been enhancements and extensions in the methodologies employed for estimating soil characteristics, including USS. These methods are divided into three main sections: Laboratory Testing, Field Testing, and Correlation with Other Soil Parameters. In recent research, data science techniques have created more reliable and accurate models for predicting USS. This study aims to apply the K-Nearest Neighbors (KNN) classifying method for predicting USS. Mountain Gazelle Optimizer (MGO) and Coronavirus Herd Immunity Optimizer (CHIO) appeal for developing hybrid models with KNN and facilitating accuracy enhancement. The dataset which utilized in this study contains four input variables including liquid limit (LL), plastic limit (PL), and sleeve friction (SF), overburden weight (OBW). Comparative analysis across all data phases reveals that the KNCH model, optimized using the CHIO, achieved superior predictive performance with the highest coefficient of determination (R² = 0.993), and the lowest values in root mean square error (RMSE = 85.19), mean squared error (MSE = 7256.15), normalized RMSE (NRMSE = 0.470), and scatter index (SI = 0.065). In contrast, the KNN model without optimization reported R² = 0.971, RMSE = 168.17, and SI = 0.132, while the KNMG model—optimized using the MGO—resulted in R² = 0.983, RMSE = 128.15, and SI = 0.101.

This article studies a parallel repairable degradation system with two similar components and a repairman who can take a single vacation. Suppose that the system consists of two components that cannot be repaired \"as good as new\" after failures; when the repairman has a single vacation, the fault component of system may not be repaired immediately, namely, if a component fails and the repairman is on vacation, the repair of the component will be delayed, if a component fails and the repairman is on duty, the fault component can be repaired immediately. Under these assumptions, a replacement policy N based on the failed times of component 1 is studied. The explicit expression of the system average cost rate C(N) and the optimal replacement policy N∗ by minimizing the C(N) are obtained, which means the two components of the system will be replaced at the same time if the failures of component 1 reach N∗ . To show the advantage of a parallel system, a replacement policy N of the cold standby system consisting of the two similar components is also considered. The numerical results of both systems are given by the numerical analysis. The optimal replacement policy N∗ for both systems are obtained. Finally, the comparison of numerical results shows the advantages of the parallel system.

A family of new conjugate gradient methods is proposed based on Perry’s idea, which satisfies the descent property or the sufficient descent property for any line search. In addition, based on the scaling technology and the restarting strategy, a family of scaling symmetric Perry conjugate gradient methods with restarting procedures is presented. The memoryless BFGS method and the SCALCG method are the special forms of the two families of new methods, respectively. Moreover, several concrete new algorithms are suggested. Under Wolfe line searches, the global convergence of the two families of the new methods is proven by the spectral analysis for uniformly convex functions and nonconvex functions. The preliminary numerical comparisons with CG_DESCENT and SCALCG algorithms show that these new algorithms are very effective algorithms for the large-scale unconstrained optimization problems. Finally, a remark for further research is suggested.

In this paper, we investigate the spectral distribution and stability of a star-shaped wave network with N edges, of which the feedback gain constants fail to satisfy the assumptions for Riesz basis generation. By a detailed spectral analysis, we present the explicit expressions of the spectra, which consist of simple eigenvalues located on a vertical line in the complex left half-plane. In addition we show that the eigenvectors are not complete in the state space. Further, we decompose the state space into the spectral-subspace and another invariant subspace of infinite dimension, which form a topological direct sum. We prove that, in the spectral-subspace, the solution can be expanded according to the eigenvectors, and hence the solution is exponentially stable; in the other subspace, the associated semigroup is super-stable, i.e., the solution is identical to zero after finite time. In particular, we give the explicit decay rate and the maximum existence time of the nonzero part of the solution.

Distributed energy is an energy supply mode based on load demand side. It aims at maximizing energy utilization and environmental benefits, integrates and optimizes various energy demands and resource allocation of users, and adopts a new energy system with demand response design and modular allocation. Because most of the energy it consumes is renewable and clean, it is environmentally friendly. Energy community is an important part of active distribution system. The method of power grid planning is studied and analyzed, and the energy management model of energy community is established. On this basis, the active distribution system is studied comprehensively and solidly. The research results can effectively improve the economy and reliability of active distribution system, and promote the large-scale grid connection of renewable energy. By using the heat storage system to periodically transfer heat load, the contradiction between the ratio of electric load to heat load in microgrid and the electric heat ratio of cogeneration system can be alleviated, thus realizing efficient and economical electric heat dispatching.