状态空间模型在海洋波能转换系统中的应用 Ⅰ.数值模拟方法改进
Application of the state-space model to the system of wave energy conversion I. Improvement on numerical methods
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摘要: 状态空间模型是研究海洋波能转换系统相互作用的一种有效数学模型.应用该模型的关键之一是如何根据实验或计算的脉冲响应函数来高效地确定状态空间模型中的矩阵参数.结合最优化理论中的单纯形法、最小二乘法以及矩阵指数的简化算法,提出了一种确定状态空间模型矩阵参数的有效数值方法.数值试验表明,由于该方法克服了高斯-牛顿方法的局部收敛性及其需求解矩阵指数关于参数的导数的缺点,因此大大扩展了初值的可选范围,有效地提高了数值模拟效率,并且使数值模拟结果具有较高精度.Abstract: The state-space model is one of the effective mathematical models to study the interaction between ocean waves and the wave energy conversion system.One of the key aspects of the application of the model is how to efficiently obtain the matrix parameters of the model according to the experimental data or the computed values of the impulse response function.In combination with the simplex method, the least square method and a simplified method for the matrix exponential, an effectively numerical method is proposed to determine the parameters in the state space model.The numer ical tests show that the range for the initial values of matrix parameters is enlarged very much, the numerical simulation efficiency is increased effectively and the numerical results are high accuracy.The reason lies in that the present method over comes the shortcomings of local convergence and the requirement for solving the derivatives of matrix exponential relative to parameters of Gauss-Newton method.
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Key words:
- state-space model /
- numerical method /
- wave energy conversion system
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