Study Of Closely Spaced Modes Damping Identification Using Inner Product Operation Combined With Genetic Algorithm

Damping shows the level of energy dissipation when the structure in process of vibration, and it is one of the most important parameters for the structural vibration response analysis. Accurate identification of damping is important for improving structural stability. Damping identification accuracy and efficiency are greatly influenced by the method we used. At present, there are many methods of damping recognition. Traditional methods have many restrictions, and they can not identify damping of closely spaced modes accurately. These methods can not be effectively used in engineering. Therefore, improving damping identification methods and increasing damping identification accuracy are always important subjects in the area of structural dynamic analysis.Some commonly used damping identification methods are concluded, advantages and disadvantages of these methods are analyzed. This paper introduced basic principle of the method based on inner product. This method ignored the interference of the negative frequency item, so its precision is limited by the sampling length and damping value size. A new method using inner product operation combined with genetic algorithm is presented. This method dose not need to ignore the negative frequency item, and it obtains the complete objective function according to inner product operation. Natural frequency and attenuation coefficient of signal are optimized by genetic algorithm, damping is obtained. Global optimization strategy can improve diagnosis efficiency of damping. Identification process of this method is simple. Diagnostic results are not restricted by sampling time and damping size. The method has high damping identification precision.In multi degree of freedom system, intensity of modes is the main factor affecting damping identification accuracy. At present, damping ratio of closely spaced modes can not be identified by the traditional methods effectively. The method using inner product operation combined with genetic algorithm can diagnose single degree of freedom system damping accurately. On this basis, use this method to identify damping ratios of closely spaced modes. Construct relevant function series according to the orders of response. Process the discrete function series with Schmidt orthogonalization. Inner product operations are conducted between the responsesignal and every orthonormal vector, the objective function is obtained. According to Parseval theorem, damping identification of closely spaced modes is converted to the problem of searching the optimized solution of the objective function maximum value.After optimizing, natural frequencies and attenuation coefficients of every mode are found, and damping ratios are obtained. The method presented in this paper can eliminate interference between modes. Damping ratios of closely spaced modes can be identified accurately.The method using inner product operation combined with genetic algorithm has been verified by digital simulations, and compared with the inner product method and the traditional half-power bandwidth method. Identification results of the digital simulations show that the method using inner product operation combined with genetic algorithm are not restricted by sampling time and damping size, and it has high recognition precision. To identification of closely spaced modes, the method presented in this paper can identify damping ratios of high-intensity modes accurately.Digital simulations show that the method using inner product operation combined with genetic algorithm is effective and accurate. Although there is noise interference in the signal, this method is still accurate.The method using inner product operation combined with genetic algorithm is applied in the oil pan experiment. By analyzing and processing the response signal of the oil pan, damping ratios of the oil pan are identified accurately. The method presented in this paper is practical in engineering.