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An algorithm based on the Paterson-Stockmeyer (PS) scheme and filtering technology is developed to compute the large matrix functions in dynamic problems accurately and efficiently. With the assistance of analysis on truncation error and error caused by filtering, the error growth law during the computation is studied, based on which an adaptive filtering threshold is proposed to help the proposed algorithm more efficiently achieve similar accuracy as the original PS scheme. Numerical examples, including 30 random matrices with different bandwidths, 10 adjacency matrices in the complex network dynamic problems, and a trampoline vibration problem, are given to verify the efficiency and accuracy of the proposed algorithm. Numerical results suggest that the proposed algorithm can achieve good accuracy and efficiency in computing the matrix function in the considered dynamic problems. [ABSTRACT FROM AUTHOR]

• A time-averaged method is proposed for efficient analysis of slender rods moving in tubes. • Two time-averaged contact models are developed based on the time-averaged sample set between the time-averaged gaps and time-averaged forces. • The inclined and rolling experiments are conducted to validate the accuracy of the time-averaged method. • The high computational efficiency of the time-averaged method is confirmed compared with six continuous contact models. The motion of slender rods in narrow tubes involves the coupling of axial movements and transverse vibrations, in which the transverse vibration exhibits high frequency and chaotic characteristics. These characteristics render the computational cost of the time integration to the motions of rods and tubes expensive. To solve this problem, this paper proposes a novel time-averaged method, which contains two innovations: 1) By time averaging the traditional dynamic equations, the time-averaged dynamic equations describing the rod-tube system are established based on the time-averaged concept used in turbulence problems; 2) Two time-averaged contact models are developed, by fitting the time-averaged sample set using the polishing function and the machine learning, respectively, to construct the relationship between the time-averaged contact gaps and the time-averaged contact forces. The time-averaged method can use a large time step, which is far larger than that required for the time integration of traditional methods, thus reducing the computational cost. Inclined and rolling experiments of the rod-tube system, as well as numerical experiments of the control rod drop in a nuclear reactor, are conducted to validate the accuracy of the time-averaged method. Comparative analyses are carried out between the time-averaged method and six continuous contact models, demonstrating the high computational efficiency of the proposed method. Moreover, the experimental results can provide benchmark data for algorithm verification for scholars studying dynamic contact algorithms. [Display omitted] [ABSTRACT FROM AUTHOR]

Generating uniform design tables (UDTs) is the first step to experimenting efficiently and effectively, and is also one of the most critical steps. Thus, the construction of uniform design tables has received much attention over the past decades. This paper presents a new algorithm for constructing uniform design tables: restart discrete dynamical evolutionary algorithm (RDDE). This algorithm is based on a well-designed dynamical evolutionary algorithm and utilizes discrete rounding technology to convert continuous variables into discrete variables. Considering the optimization of UDT is a multi-objective optimization problem, RDDE uses Friedman rank to select the optimal solution with better comprehensive comparison ranking. RDDE also utilizes a simulated annealing-based restart technology to select control parameters, thereby increasing the algorithm's ability to jump out of local optima. Comparisons with state-of-the-art UDTs and two practical engineering examples are presented to verify the uniformity of the design table constructed by RDDE. Numerical results indicate that RDDE can indeed construct UDTs with excellent uniformity at different levels, factors, and runs. Especially, RDDE can flexibly construct UDTs with unequal intervals of factors that cannot be directly processed by other designs of experiment. [ABSTRACT FROM AUTHOR]

The numerical oscillation problem is a difficulty for the simulation of rapidly varying shallow water surfaces which are often caused by the unsmooth uneven bottom, the moving wet-dry interface, and so on. In this paper, an adaptive artificial viscosity (AAV) is proposed and combined with the displacement shallow water wave equation (DSWWE) to establish an effective model which can accurately predict the evolution of multiple shocks effected by the uneven bottom and the wet-dry interface. The effectiveness of the proposed AAV is first illustrated by using the steady-state solution and the small perturbation analysis. Then, the action mechanism of the AAV on the shallow water waves with the uneven bottom is explained by using the Fourier theory. It is shown that the AVV can suppress the wave with the large wave number, and can also suppress the numerical oscillations for the rapidly varying bottom. Finally, four numerical examples are given, and the numerical results show that the DSWWE combined with the AAV can effectively simulate the shock waves, accurately capture the movements of wet-dry interfaces, and precisely preserve the mass. [ABSTRACT FROM AUTHOR]

• The mechanical friction force during the control rod drop is treated as a time-variant uncertainty for uncertainty analysis; • The interval process model is used to describe the time-variant uncertain mechanical friction during the CR drop; • The uncertainty analysis of CR drop considering various uncertain parameters is conducted; • A novel and general computational framework for uncertainty analysis of CR drop, UA-CRD, is proposed. Due to the influence of multiple factors, the control rod drop involves some uncertain parameters. The mechanical friction on the control rod is a time-variant uncertain parameter and is related to the position of the control rod. For the first time, this paper adopts the interval process model, which accurately describes the uncertainty parameters by using small-scale samples, to describe the uncertain mechanical friction on the control rod. The numerical experimental results demonstrate that the interval process model can describe the mechanical friction with high accuracy, even when employing small-scale samples. Furthermore, it is found that the uncertainty analysis can be considered as solving the extremal problem of a black-box model. Based on it, we propose a novel and general calculation framework for uncertainty analysis of control rod drop, UA-CRD. Through the analysis of numerical examples, it is verified that UA-CRD can accurately and efficiently conduct the uncertainty analysis of control rod drop. [ABSTRACT FROM AUTHOR]

• A deterministic simplified model of the control rod drop and fluid flow is established. • A fifth-order adaptive collocation stochastic perturbation (ACSP) method is established to approximate the random responses. • The uncertainty analysis of the CR drop based on the ACSP method is carried out in both large and small reactor. • The research results can provide guidance for the analysis and design optimization of the control rod scram process. There are many uncertain factors to affect the control rod drop from its design and manufacture to the chain reaction in the reactor. They have to be considered in the simulation to realistically predict the dynamic behavior of control rod drop. Different from the previous method by using the nominal and extreme values of the uncertain factors, a statistical method is applied in this paper to analyze them in the process of the control rod drop. The uncertain factors obey uniform distribution, based on which a fifth-order adaptive collocation stochastic perturbation (ACSP) method is established in this paper, which is featured with simple format, high precision, and high calculation efficiency. The mean and standard deviation of the responses (such as the final time of the control rod drop) in two different types of reactors are calculated by using the ACSP method. On this basis, the response intervals and corresponding probabilities of the control rod drop are obtained. Besides, influences of each random variable on the responses are analyzed by the sensitivity analysis. In addition, the linear correlation degree and correlation between the two are discussed through the correlation coefficient of random variables and the responses. The uncertainty analysis of control rod drop in this paper not only provides a relatively strong theoretical support for scientifically dealing with uncertain factors, but also offers specific help for the optimal design of control rod assembly. [ABSTRACT FROM AUTHOR]

Control rod drop is the key part of ensuring the safety of nuclear reactor shutdown. Aiming at the control rod drop problem, we established a physical model of the control rod drive line. The proposed model considers the influence of the absorbing rod's position and hence evaluates the resultant force accurately on the control rod during the whole dropping process. Based on the physical model, a unified coupling state equation on the control rod drop and fluid flow is developed by integrating the motion variables of the control rod and the fluid into a state vector. A time step adaptive symplectic (TSAS) algorithm is proposed to solve the proposed state equation. The TSAS algorithm efficiently and stably predicts the motion states of the control rod and the fluid synchronously and accurately captures the sudden change of flow state. Numerical examples confirm the correctness of the proposed model and the TSAS algorithm. Sensitivity analysis is also conducted to discuss the effects of different parameters on the control rod drop, which provides reference and help for the design and manufacturing of the control rod drive line. [ABSTRACT FROM AUTHOR]