奇异值分解在设备振动激励力估算中的应用

Application of Singular Value Decomposition in the Estimation of Machinery Vibro-exciting Force

设备对船体基座的振动激励力是舰船结构振动、自噪声和辐射噪声的主要来源,而激励力间接估算时常会碰到病态问题,导致病态误差。讨论导纳矩阵求逆时病态问题的易发频率、奇异值分解方法、奇异阈值选取等,并讨论奇异值分解技术降低病态误差的实际算例。实验证明奇异值分解技术解决激励力间接估算时的病态问题有效率达到82%,可以满足工程应用需求。奇异阈值的选取技术还不够完善,在某些频率处取值过小而导致病态误差未能受到控制。从理论、实验两方面证实了应用间接方法估算设备对基座的激励力时,病态问题在基座模态频率处显然比其它频率严重。结论对激励力间接算法工程应用有明确的指导意义。

The primary source of structure-borne vibration, self-noise and radiation noise of warship is vibro-exciting force acting on the machine base in hull. In the estimation of exciting force, illposed problems often occur which will lead to ill-posed errors. In this paper, easily-occurred frequency of ill-posed problems when inversing mobility matrixes, the method of singular value decom- position （SVD） as well as the approach of selecting singular threshold, are stated. An application of SVD for validating the effect of reducing ill-posed errors is given. The experiment shows that SVD in the indirect forces estimation of solving ill-posed problems is effective. The efficiency factor is up to 82% ,which is high enough for engineering application. On the other hand, the approach of selecting singular threshold is not perfect, since the thresholds would be smaller at several frequencies. This means that ill-posed errors would not be controlled by SVD. It is validated in theoretical and experimental aspects, that ill-posed problems are remarkably more severe at modal frequencies of the base than other frequencies, when estimating exciting forces from the machine to its base by indirect method. The conclusions are valuable in the engineering application of indirect estimation of exciting force.