There are many population-based stochastic search algorithms for solving optimization problems. However, the universality and robustness of these algorithms are still unsatisfactory. This paper proposes an enhanced se...There are many population-based stochastic search algorithms for solving optimization problems. However, the universality and robustness of these algorithms are still unsatisfactory. This paper proposes an enhanced self-adaptiveevolutionary algorithm （ESEA） to overcome the demerits above. In the ESEA, four evolutionary operators are designed to enhance the evolutionary structure. Besides, the ESEA employs four effective search strategies under the framework of the self-adaptive learning. Four groups of the experiments are done to find out the most suitable parameter values for the ESEA. In order to verify the performance of the proposed algorithm, 26 state-of-the-art test functions are solved by the ESEA and its competitors. The experimental results demonstrate that the universality and robustness of the ESEA out-perform its competitors.展开更多
In this work, we consider different numerical methods for the approximation of definite integrals. The three basic methods used here are the Midpoint, the Trapezoidal, and Simpson’s rules. We trace the behavior of th...In this work, we consider different numerical methods for the approximation of definite integrals. The three basic methods used here are the Midpoint, the Trapezoidal, and Simpson’s rules. We trace the behavior of the error when we refine the mesh and show that Richardson’s extrapolation improves the rate of convergence of the basic methods when the integrands are sufficiently differentiable many times. However, Richardson’s extrapolation does not work when we approximate improper integrals or even proper integrals from functions without smooth derivatives. In order to save computational resources, we construct an adaptive recursive procedure. We also show that there is a lower limit to the error during computations with floating point arithmetic.展开更多
A new algorithm of structure random response numerical characteristics, namedas matrix algebra algorithm of structure analysis is presented. Using the algorithm, structurerandom response numerical characteristics can ...A new algorithm of structure random response numerical characteristics, namedas matrix algebra algorithm of structure analysis is presented. Using the algorithm, structurerandom response numerical characteristics can easily be got by directly solving linear matrixequations rather than structure motion differential equations. Moreover, in order to solve thecorresponding linear matrix equations, the numerical integration fast algorithm is presented. Thenaccording to the results, dynamic design and life-span estimation can be done. Besides, the newalgorithm can solve non-proportion damp structure response.展开更多
The background numerical noise#0 is determined by the maximum of truncation error and round-off error.For a chaotic system,the numerical error#(t)grows exponentially,say,#(t)=#0exp(kt),where k>0 is the so-called no...The background numerical noise#0 is determined by the maximum of truncation error and round-off error.For a chaotic system,the numerical error#(t)grows exponentially,say,#(t)=#0exp(kt),where k>0 is the so-called noise-growing exponent.This is the reason why one can not gain a convergent simulation of chaotic systems in a long enough interval of time by means of traditional algorithms in double precision,since the background numerical noise#0 might stop decreasing because of the use of double precision.This restriction can be overcome by means of the clean numerical simulation(CNS),which can decrease the background numerical noise#0 to any required tiny level.A lot of successful applications show the novelty and validity of the CNS.In this paper,we further propose some strategies to greatly increase the computational efficiency of the CNS algorithms for chaotic dynamical systems.It is highly suggested to keep a balance between truncation error and round-off error and besides to progressively enlarge the background numerical noise#0,since the exponentially increasing numerical noise#(t)is much larger than it.Some examples are given to illustrate the validity of our strategies for the CNS.展开更多
The aim of this paper is to achieve the radio frequency stealth(RFS) during the course of tracking by controlling the radiation energy and the interval of a radar. Firstly, we build the model of probability of interce...The aim of this paper is to achieve the radio frequency stealth(RFS) during the course of tracking by controlling the radiation energy and the interval of a radar. Firstly, we build the model of probability of interception with the once radiation during the course of tracking. Secondly, we establish the model of the cumulative probability of interception to describe the effect of RFS throughout the tracking process and obtain two solutions that are minimizing the probability of interception and the radiation times to reduce the cumulative probability of interception. Thirdly, we propose a self-adapting radiation energy control method(SARE)to minimize the probability of interception. Fourthly, we propose a self-adapting radiation interval control method(SARI) to minimize radiation times. Fifthly, combining SARE with SARI, we propose a SARE-SARI control method(SAEI) during the course of tracking.Finally, we compare SAEI with two others by simulation, and the results show the effect of RFS of SAEI is better than the other two,but we have to make a trade-off between the ability of RFS and the effect of tracking.展开更多
基金supported by the Aviation Science Funds of China(2010ZC13012)the Fund of Jiangsu Innovation Program for Graduate Education (CXLX11 0203)
文摘There are many population-based stochastic search algorithms for solving optimization problems. However, the universality and robustness of these algorithms are still unsatisfactory. This paper proposes an enhanced self-adaptiveevolutionary algorithm （ESEA） to overcome the demerits above. In the ESEA, four evolutionary operators are designed to enhance the evolutionary structure. Besides, the ESEA employs four effective search strategies under the framework of the self-adaptive learning. Four groups of the experiments are done to find out the most suitable parameter values for the ESEA. In order to verify the performance of the proposed algorithm, 26 state-of-the-art test functions are solved by the ESEA and its competitors. The experimental results demonstrate that the universality and robustness of the ESEA out-perform its competitors.
文摘In this work, we consider different numerical methods for the approximation of definite integrals. The three basic methods used here are the Midpoint, the Trapezoidal, and Simpson’s rules. We trace the behavior of the error when we refine the mesh and show that Richardson’s extrapolation improves the rate of convergence of the basic methods when the integrands are sufficiently differentiable many times. However, Richardson’s extrapolation does not work when we approximate improper integrals or even proper integrals from functions without smooth derivatives. In order to save computational resources, we construct an adaptive recursive procedure. We also show that there is a lower limit to the error during computations with floating point arithmetic.
基金This project is supported by National Natural Science Foundation of China (No.59805001)
文摘A new algorithm of structure random response numerical characteristics, namedas matrix algebra algorithm of structure analysis is presented. Using the algorithm, structurerandom response numerical characteristics can easily be got by directly solving linear matrixequations rather than structure motion differential equations. Moreover, in order to solve thecorresponding linear matrix equations, the numerical integration fast algorithm is presented. Thenaccording to the results, dynamic design and life-span estimation can be done. Besides, the newalgorithm can solve non-proportion damp structure response.
基金supported by National Natural Science Foundation of China(No.12272230)Shanghai Pilot Program for Basic Research-Shanghai Jiao Tong University(No.21TQ1400202).
文摘The background numerical noise#0 is determined by the maximum of truncation error and round-off error.For a chaotic system,the numerical error#(t)grows exponentially,say,#(t)=#0exp(kt),where k>0 is the so-called noise-growing exponent.This is the reason why one can not gain a convergent simulation of chaotic systems in a long enough interval of time by means of traditional algorithms in double precision,since the background numerical noise#0 might stop decreasing because of the use of double precision.This restriction can be overcome by means of the clean numerical simulation(CNS),which can decrease the background numerical noise#0 to any required tiny level.A lot of successful applications show the novelty and validity of the CNS.In this paper,we further propose some strategies to greatly increase the computational efficiency of the CNS algorithms for chaotic dynamical systems.It is highly suggested to keep a balance between truncation error and round-off error and besides to progressively enlarge the background numerical noise#0,since the exponentially increasing numerical noise#(t)is much larger than it.Some examples are given to illustrate the validity of our strategies for the CNS.
基金supported by the National Natural Science Foundation of China(61472441)
文摘The aim of this paper is to achieve the radio frequency stealth(RFS) during the course of tracking by controlling the radiation energy and the interval of a radar. Firstly, we build the model of probability of interception with the once radiation during the course of tracking. Secondly, we establish the model of the cumulative probability of interception to describe the effect of RFS throughout the tracking process and obtain two solutions that are minimizing the probability of interception and the radiation times to reduce the cumulative probability of interception. Thirdly, we propose a self-adapting radiation energy control method(SARE)to minimize the probability of interception. Fourthly, we propose a self-adapting radiation interval control method(SARI) to minimize radiation times. Fifthly, combining SARE with SARI, we propose a SARE-SARI control method(SAEI) during the course of tracking.Finally, we compare SAEI with two others by simulation, and the results show the effect of RFS of SAEI is better than the other two,but we have to make a trade-off between the ability of RFS and the effect of tracking.
