Force Estimation Using Operational Data
John C. O'Callahan, F. Piergentili · 1996
The technique of estimating forcing conditions that are applied to a tshwhce and locating their input positions is im inverse process that requires the acquiring operational data in the form of fiequency spectra, developing system tier matrices fkmn measured FRFs and performing a generalized inverse of the transfer matrices relative to the output speztm. An advantage of this technique is that it can approximate the power of the input at locations that are inaccessible while only collecting data at a limited number of locations. The major disadvantages am that tbe input locations may not be known and since it is an inverse pmcess, the results may be suspect depending cm the conditions of the generalized inverse. Various cases are studied to de&mine the e%cts of the number of included force locations relative to the output responses and cases that actual force locations were excluded t?om the input set of DOFs. It is folmd that wfien all possible inputs were included in the set, then muits are excellent. When actual input locations were not included, then results were distributed depending on the relative position of the included or assumed input locations. The data cases studied here did not include noise since the study was to investigate tends of distributions of forces. Jf noise is included, input reduction must be pafcnmed especially in the areas of resonant fxquencies of the structme. NOMENCLATtJlW MatriceS: [G] : input/output cross-power matrix [H] : transfer matrix [I] : identity matrix [K] : stifkss matrix [M] : mass matrix [Q],[v],[w] :ortbonormalmatricesforSVDandQR [R] : upper triangular matrix [E] : singular value matrix