基于柯西-施瓦兹不等式的阻尼比计算方法

DAMPING RATIO ESTIMATION BASED ON THE CAUCHY-SCHWARTZ INEQUALITY

提出利用柯西-施瓦兹不等式计算阻尼的方法。该方法的原理是利用内积的相关诊断特性,首先构造一个函数,将该函数与响应信号作内积运算,求内积模的最大值;然后利用柯西-施瓦兹不等式定理诊断阻尼比。具体采用两个运算步骤,第一步,运用细化频谱方法(fast Fouriertransform+Fouriertransform,FFT+FT)求出固有频率;第二步,将求出的固有频率代入构造函数中,并将构造函数与信号作内积运算,通过优化搜索求内积模最大值,得到对应的衰减系数,即得阻尼比。最后通过仿真算例验证该方法的有效性。

A method for damping estimation based on the Cauchy-Schwartz inequality is presented. The correlated identification property of inner product is the principle of this method. A function is set and then is applied to do inner production with the response signal. Based on the theorem of Cauchy-Schwartz inequality the damping ratio can be estimated when the maximum of the inner product modules is found. There are two main calculation steps for this method. One step is using FFT＋FT （fast Fourier transform ＋ Fourier transform） to calculate resonance frequency. In the next step, the calculated resonance frequency is applied to the constructed function. Then, calculate the inner product of the constructed function with response signal. After searching the maximum value of the inner production modules by optimization, the decay factor and the damping ratio are estimated. Examples are calculated to prove this method.