基于内积运算与迭代算法的密集模态阻尼识别

摘要

Damping estimation is difficult as a result of modal interference existing in closely spaced modes, a combinational method of inner product calculation and iterative algorithm was presented. Firstly, resonant frequency of the topmost spectral peak was counted by the application of FFT-FT. Secondly, inner product was conducted between response signal and the constructed exponential function. According to the theorem of Cauchy-Schwarz inequality, the attenuation coefficient was achieved by calculating the maximum of the inner product module, meanwhile, the amplitude and phase of the corresponding modal signal were obtained. One modal signal could be estimated from the above calculations. Thirdly, the estimated signal was subtracted from the overall response signal, and then estimated the next modal signal. In this way, an iteration process was formed by repeating the above diagnosing procedures, which could solve the modal interference. Both simulation calculation and experiment were conducted to validate the method.%密集模态存在模态干涉,导致阻尼识别困难,提出内积运算与迭代算法相结合诊断阻尼比.首先,运用频谱细化的傅里叶变换(FFT-FT),得频谱峰值最大对应的共振频率;然后,构造指数函数,与响应信号作内积运算,根据柯西-施瓦茨不等式定理,当内积模取得极大值时,可优化搜索到衰减系数,得出幅值及相位.由此获得某一模态信号的估计,从总响应信号中减去估计信号.重复上述诊断步骤,形成迭代,消除模态干涉.通过算例和试验验证了该方法的有效性,识别结果准确.