The explicitly restarted Arnoldi method (ERAM) can be used to  nd some eigenvalues of large and sparse matri-ces. However, it has been shown that even this method may fail to converge. In this paper, we present two new methods to accelerate the convergence of ERAM algo-rithm. In these methods, we apply two strategies for the updated initial vector in each restart cycles. The implementation of the methods have been tested by nu-merical examples. The results show that we can obtain a good acceleration of the convergence compared to orig-inal ERAM.

We are interested in the numerical solution of the continuous-time Lyapunov equation. Generally, classical Krylov subspace methods for solving matrix equations use the Petrov-Galerkin condition to obtain projected equations from the original ones. The projected problems involves the restrictions of the coefficient matrices to a Krylov subspace. Alternatively, we propose a scheme based on the extended block Krylov subspace that leads to a smaller-scale equation, which also incorporates  the restriction of the inverse of the Lyapunov equation's square coefficient. The effectiveness of this approach is experimentally confirmed, particularly in terms of the required CPU time.

This study focuses on the investigation of intelligent form-finding and vibration analysis of a triangular polyhedral tensegrity that is enclosed within a sphere and subjected to external loads. The nonlinear dynamic equations of the system are derived using the Lagrangian approach and the finite element method. The proposed form-finding approach, which is based on a basic genetic Algorithm, can determine regular or irregular tensegrity shapes without dimensional constraints. Stable tensegrity structures are generated from random configurations and based on defined constraints (nodes located on the sphere, parallelism, and area of upper and lower surfaces), and shape finding is performed using the fitness function of the genetic Algorithm and multi-objective optimization goals. The genetic Algorithm's efficacy in determining the shape of structures with unpredictable configurations is evaluated in two distinct scenarios: one involving a known connection matrix and the other involving fixed or random member positions (struts and cables). The shapes obtained from the Algorithm suggested in this study are validated using the force density approach, and their vibration characteristics are examined. The findings of the comparative study demonstrate the efficacy of the proposed methodology in determining the vibrational behavior of tensegrity structures through the utilization of intelligent shape seeking techniques.

The cabin of a road vehicle contains multiple noise sources, which can be airborne or structure-borne. These sources include the transmission, engine, tire and road contact noise, aerodynamics noise, and more. The noise in the cabin can significantly affect passenger comfort. Therefore, it is crucial to have an accurate vibroacoustic model for analyzing and controlling vibrations. However, creating a simulation that closely reflects reality using a finite element model is highly complex. This complexity stems from the large number of degrees of freedom in the model, which requires significant computational resources for simulation. To overcome these challenges, various model order reduction (MOR) techniques for linear or nonlinear models have been developed. MOR has two approaches: projection data-based and equivalent model energy-based. In this paper, we utilize two MOR methods to simulate a reduced coupled model. The first method is based on the Krylov subspace method, which uses projection bases to reduce the large linear model. The second method is the modal coupling method, which uses the mode shape of the model to create a reduced model. Finally, we compare the pressure and displacement of the reduced model to the model at different frequency spectra.

Increasing population and food demand, disproportionate cultivation and annual production of various agricultural products with market needs and low productivity of the agricultural sector and the loss of water and soil resources have made it necessary to determine and implement the country's optimal cropping pattern. In this study, due to the limitations and problems of classical methods in order to reduce processing time and improve the quality of solutions, the Multi-Objective Chaotic Particle Swarm Optimization was used to determine the optimal cultivation pattern of Sistan plain in optimal conditions and deficit irrigation. The results of the Multi-Objective Chaotic Particle Swarm Optimization for the dominant cultures in the region showed that the current cropping pattern of the region is not optimal and with the implementation of the proposed model, the profit per unit area under cultivation will increase. The results of application of deficit irrigation during different growing periods of wheat, barley, alfalfa, sorghum, watermelon and grapes showed that applying deficit irrigation in this plain is not a good strategy and therefore only a full irrigation strategy is recommended. The results of sensitivity analysis of the model showed that at low prices, farmers reaction is less and at higher prices more reaction to price changes and with increasing prices, the program efficiency is lower.

One of the basic topics in hydrological and river engineering studies is flood routing.Flood flooding is common in multi-tributary rivers and rivers without intermediate basin statistics. Therefore, to achieve the determination of slopes and cross-sections in all sections of the river, the Muskingum hydrological model is a useful method that helps to save information on the depth and flow of the flood at any time by saving time and money. To specify. In this study, the nonlinear parameters of the new Muskingum model are optimized based on the fly Algorithm (MA). In this non-linear model of Muskingum, which has eight parameters, the recovery coefficient γ is used, which has more or less values ​​than the number of peaks discharged in the output hydrograph.To evaluate the performance of Muskingum's new nonlinear model with the new MA Algorithm, the Wilson and Weisman-Lewis case study has been used by many previous researchers for validation.The results of the MA Algorithm for Wilson and Weissman-Lewis rivers show the minimization of the residual squares (SSQ) as the objective function, which is 3.21 for the Wilson River and 68722 for the Weissman River. The results of this study showed that the proposed model has high accuracy in estimating the output discharge values.

The harmonic projection method can be used to compute some eigenpaires of large matrix, and it is more suitabele for finding interior eigenpairs. However, it has been shown that the harmonic projection method may converge erratically and even may fail to do so. In this paper, we present two new tecniques to improve convergence. The results show that the Algorithms converges fast and works with high accuracy.

This article investigates the problem of simultaneous attitude and vibration control of a flexible spacecraft to perform high precision attitude maneuvers and reduce vibrations caused by the flexible panel excitations in the presence of external disturbances, system uncertainties, and actuator faults. Adaptive integral sliding mode control is used in conjunction with an attitude actuator fault iterative learning observer (based on sliding mode) to develop an active fault tolerant Algorithm considering rigid-flexible body dynamic interactions. The discontinuous structure of fault-tolerant control led to discontinuous commands in the control signal, resulting in chattering. This issue was resolved by introducing an adaptive rule for the sliding surface. Furthermore, the utilization of the sign function in the iterative learning observer for estimating actuator faults has not only enhanced its robustness to external disturbances through a straightforward design, but has also led to a decrease in computing workload. The strain rate feedback control Algorithm has been employed with the use of piezoelectric sensor/actuator patches to minimize residual vibrations caused by rigid-flexible body dynamic interactions and the effect of attitude actuator faults. Lyapunov's law ensures finite-time overall system stability even with fully coupled rigid-flexible nonlinear dynamics. Numerical simulations demonstrate the performance and advantages of the proposed system compared to other conventional approaches.