特定湍动激励-响应类型二次非线性系统双谱分析仿真建模

Bispectral analysis and simulation modeling of quadratic nonlinear system with specific turbulent-fluctuationexcitationresponse types

自然界存在一类特定湍动激励类型二次非线性系统,属于一种特殊的非高斯信号系统,其特征是输入信号谱由湍流波动产生,而且这种湍流波动信号功率谱分布接近高斯分布.本文从拓展Choi等(1985 J.Sound Vib.99309]和Kim等(1987 IEEE J.Ocean.Eng.OE-12568)的工作入手,对以海浪激励-系泊船舶响应和充分发展湍流为代表的特定湍动激励-响应类二次非线性系统,基于双谱分析技术进行系统仿真,并对仿真系统进行了扩展的、系统的建模分析,并首次应用完备迭代法(2020 Phys.Scr.95055202)进行模型求解,计算了线性传递函数与二次非线性传递函数.所得结果均符合预期.相干分析表明,随机海浪-船舶摇动系统二次相干性远大于线性相干性,但近高斯输入型充分发展湍流的线性相干性更大.反算验证或与真实系统的对比表明,本文的湍流仿真手段与系统建模方法准确性好,求解算法效率高,可以有效应用于与湍动激励相关的二次非线性系统的模型描述与系统分析.

There exists a kind of quadratic nonlinear system with specific type of turbulent fluctuation excitation in nature,which belongs to a special non-Gaussian input signal system.Its characteristic is that the input signal spectrum is generated by turbulent fluctuations,and the power spectrum distribution of this turbulence fluctuation signal is close to Gaussian distribution.Starting with the work of Choi et al.(1985 J.Sound Vib.99309)and Kim et al.[1987 IEEE J.Ocean.Eng.OE-12568),we extend the simulation of a specific turbulent fluctuation excited response-type quadratic nonlinear system represented by the wave excited mooring ship response,and fully develop the internal development of turbulence based on bispectral analysis technology.We also extend the simulation system and conduct systematic modeling analysis.The complete iterative method[2020 Phys.Scr.95055202]is used to solve the model,and calculate the linear transfer function and quadratic nonlinear transfer function.The comparison of simulation and modeling results with the real systems and their models confirms the correctness of the results from system simulation,system modeling,and model solving.The results obtained are all in line with expectations.The coherence analysis shows that the quadratic coherence of the random wave-ship swaying system is much greater than the linear coherence,but the linear coherence of the fully developed turbulence is greater for the near Gaussian input type.The reverse computation verification or comparison with real systems indicates that the turbulence simulation and system modeling method in this work have good accuracy and high efficiency in solving algorithms,and the research results can be effectively applied to the model description and system analysis of the quadratic nonlinear systems related to specific turbulent fluctuation excitation response.