A time domain method is presented for estimating the discrete input forces acting on a structure based upon its measured response. The structure is essentially transformed into its own loads transducer. A set of inverse system Markov parameters, in which the roles of input and output are reversed, is estimated from forward system Markov parameters using a linear predictive scheme. Inputs and acceleration outputs are assumed to be collocated to maintain minimum phase. Subsequently, any set of measured operational sensor data of any time duration can be convolved with the inverse Markov parameters to produce estimates of the input forces. This problem is ill-posed, so a regularization technique is employed to stabilize computations. A stability analysis is performed to illustrate the effects of the regularization. Predicted pseudo-forces qualitatively approximate the actual input forces and, when applied back to the structure, produce accelerations which accurately match the measured operational sensor data.

1.
Bartlett
F. D.
, and
Flannelly
W. G.
,
1979
, “
Model Verification of Force Determination for Measuring Vibratory Loads
,”
Journal of the American Helicopter Society
, Vol.
24
, pp.
10
18
.
2.
Bednar
J. B.
,
Yarlagadda
R.
, et al.,
1986
, “
L1 Deconvolution and its Application to Seismic Signal Processing
,”
IEEE Transactions on Acoustics, Speech, and Signal Processing
, Vol.
ASSP-34
, No.
6
, pp.
1655
1658
.
3.
Ben-Israel, A., and Greville, T. N. E., 1974, Generalized Inverses: Theory and Applications, New York, John Wiley & Sons.
4.
Carne, T. G., Mayes R. L., et al., 1994, “Force Reconstruction using Sum of Weighted Accelerations Technique—MAX-FLAT Procedure,” 12th International Modal Analysis Conference, Honolulu, HI, pp. 1054–1062.
5.
Demoment
G.
, and
Reynaud
R.
,
1985
, “
Fast Minimum Variance Deconvolution
,”
IEEE Transactions on Acoustics, Speech, and Signal Processing
, Vol.
ASSP-33
, No.
4
, pp.
1324
1327
.
6.
Drachman
B.
,
1984
, “
Two Methods to Deconvolve: L1-Method Using Simplex Algorithm and L2-Method Using Least-Squares and a Parameter
,”
IEEE Transactions on Antennas and Propagation
, Vol.
AP-32
, No.
3
, pp.
219
225
.
7.
Fabunmi
J. A.
,
1986
, “
Effects of Structural Modes on Vibratory Force Determination by the Pseudoinverse Technique
,”
AIAA Journal
, Vol.
24
, No.
3
, pp.
504
509
.
8.
Golub, G. H., Heath, M., et al., 1979, “Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter,” Technometrics, Vol. 21, No. 2, pp.
9.
Groetsch, C. W., 1993, Inverse Problems in the Mathematical Sciences, Vieweg.
10.
Hansen, M., and Starkey, J. M., 1990, “On Predicting and Improving the Condition of Modal-Model-Based Indirect Force Measurement Algorithms,” 8th International Modal Analysis Conference, Kissimmee, FL, pp. 115–120.
11.
Hillary, B., and Ewins, D. J., 1984, The Use of Strain Gauges in Force Determination and Frequency Response Function Measurements,” 2nd International Modal Analysis Conference, Orlando, CA, pp. 627–634.
12.
Horta, L. G., and Sandridge, C. A., 1992, “On-Line Identification of Forward/ Inverse Systems for Adaptive Control Applications,” AIAA Guidance, Navigation, and Control Conference, pp. 1639–1649.
13.
Hu
Y. H.
, and
Milenkovic
P. H.
,
1990
, “
A Fast Least-Square Deconvolution Algorithm for Vocal Tract Cross Section Estimation
,”
IEEE Transactions on Acoustics, Speech, and Signal Processing
, Vol.
38
, No.
6
, pp.
921
923
.
14.
Kammer, D. C., 1991, “Sensor Placement for On-Orbit Modal Identification and Correlation of Large Space Structures,” Vol. 14, No. 2, pp. 251–259.
15.
Mendel, J. M., 1990, Maximum-Likelihood Deconvolution, New York, Springer-Verlag.
16.
Nashed, M. Z., Ed. (1976), Generalized Inverses and Applications, New York, Academic Press, pp. 225–229.
17.
Sarkar
T. K.
,
Tseng
F. I.
, et al.,
1985
, “
Deconvolution of Impulse Response from Time-Limited Input and Output: Theory and Experiment
,”
IEEE Transactions Instrumentation and Measurement
, Vol.
IM-34
, No.
4
, pp.
541
546
.
18.
Starkey
J. M.
, and
Merrill
G. L.
,
1989
, “
On the Ill-Conditioned Nature of Indirect Force-Measurement Techniques
,”
International Journal of Analytical and Experimental Modal Analysis
, Vol.
4
, No.
3
, pp.
103
108
.
19.
Stevens, K. K., 1987, “Force Identification Problems—An Overview,” SEM Spring Conference on Experimental Mechanics, SEM, pp. 838–844.
20.
Stewart
G. W.
,
1972
, “
On the Sensitivity of the Eigenvalue Problem Ax = λBx
,”
SIAM Journal of Numerical Analysis
, Vol.
9
, No.
4
, pp.
669
686
.
21.
Tikhonov
A. N.
,
1963
, “
On the Solution of Ill-Posed Problems and the Method of Regularization
,”
Soviet Math.
, Vol.
4
, No. pp.
1035
1038
.
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