--- 207791 ' AIAA-98-2078 ACCELEROMETER PLACEMENT FOR THE c/7" J/,/ ,57/_' fG--- INTERNATIONAL SPACE STATION NODE MODAL TEST //v - 7-/)( Michael L. Tinker * Structural Dynamics and Loads Branch/ED23 Structures and Dynamics Laboratory t/ 4/-2 NASA/Marshall Space Flight Center Huntsville, AL 35812 Abstract Description of Approaches Used for Accelerometer location analysis for the modal survey test of the International Space Station Node is described. Three Sen_or Location Analysis different approaches were utilized: 1. Guyan reduction, 2. iterative Guyan reduction, and 3. the average driving point Sensor location analysis for modal testing begins with residue (ADPR) method. Both Guyan approaches worked engineering judgment supplemented by analysis to determine well, but poor results were observed for the ADPR method. an initial set of measurement locations. Of course, Although the iterative Guyan approach appears to locations that are not accessible, as well as rotational DOF, provide the best set of sensor locations, it is intensive can be immediately removed from consideration. This computationally, becoming impractical for large initial initial set is much smaller than the full finite element location sets. While this is computer dependent, it appears model, but considerably larger than a practical final set of that initial sets larger than about 1500 degrees of freedom are locations. The initial set of locations can partly be impractical for the interative technique. determined by visual inspection of the structure's geometry and mode shapes to determine critical regions of the structure for instrumentation. Critical regions will have well-defined Test Configuration and Fixtures motion in one or more of the target mode shapes, or provide paths by which loads are transmitted into the structure. The modal survey test of the International Space Station Kinetic energy and mass-to-stiffness ratio calculations can Node (Fig. 1) was one of the largest known tests in regard to also be used to help locate or verify critical locations. the volume of instrumentation required, utilizing over 400 Once the analyst has determined the character of the triaxial accelerometers and more than 1200 data channels. A mode shapes and identified several important areas to be primary reason for the large number of accelerometers was instrumented, the initial set of sensor locations includes the requirement of including numerous components interior these areas and also provides generally good coverage of the to the Node shell (Fig. 2). Great care was taken in all structure to define the mode shapes. A lot of conservatism can be utilized in the choice of the initial set to make sure phases of test planning, pre-test analysis, and conduct of the test due to the importance of the Node as the first U.S.-built that all possible regions of interest are covered. For component of the Space Station to be launched. example, initial sets of size greater than 2000 DOF may be Testing was done in a large fixed-base fixture developed reasonable for large complex structures. The next step in specifically for Space Station modules, but which can be the process is to use analytical techniques to reduce the large used for any trunnion- and keel-mounted Space Shuttle initial set to a realistic size, which can be on the order of payload (Ref. 1). Figure 1 shows the Node mounted in the 200-400 locations or more for very large modal tests. fixture. The test fixture utilizes flexure mechanisms to Several analytical techniques are commonly used for simulate the Shuttle Orbiter payload constraints. These determining measurement locations, including kinetic energy mechanisms constrain translational motion in two degrees of sorting, iterative Guyan reduction (Refs. 2-3), and effective freedom (DOF) at each primary trunnion, and one DOF at independence (Ref. 4). Reference 3 provides a good each secondary trunnion and the keel (Fig. 2). Reference 1 overview of these first three methods. Other techniques that provides a description of the flexure mechanisms and their have been investigated include use of flexibility shapes and development. genetic algorithms, as discussed in Refs. 5-7. Listed below _u'eseveral techniques that were determined to be of interest for selection of measurement locations for the Node modal *Aerospace Technologist, Structural Dynamics; Senior Member AIAA test. Copyright O 1998 by the American Institute of Aeronautics Kinetic Energy SortinQ_ and Astronautics, Inc. No copyright is asserted in the United As described in Ref. 8, kinetic energy sorting involves an States under Title 17, U.S. Code. The U.S. government has a examination of each DOF's contribution of kinetic energy to royalty-free license to exercise all rights under the copyright each mode shape. By summing the energy over all the claimed herein for Governmental purposes. All other rights are modes for each DOF, those coordinates having the greatest reserved by the copyright owner. contribution or most energy can be indentified and retained in a candidate set. American Institute of Aeronautics and Astronautics Referenc8eindicates that a problem with this approach selected. For that particular application, kinetic energy lies in its inability to recognize when many DOF have sorting, mass weighted effective independence, and iterative approximately equal kinetic energies, and that it cannot Guyan reduction performed best. retain one such coordinate without retaining them all. A second comparative study is described in Ref. 8, where kinetic energy sorting, iterative Guyan reduction, effective Guyan Reduction independence, and genetic algorithm methods were evaluated Standard or noniterative Guyan reduction (Ref. 2) involves for four structural models. The test structures evaluated examining each DOF in the full model to determine which were a general-purpose spacecraft model, 10-bay space truss, DOF have the largest diagonal mass to diagonal stiffness avionics box, and satellite model. Size of the full models ratio. That is, the locations on the structure where inertia ranged from 360 DOF for the 10-bay truss to about 22,000 forces are large compared to elastic forces are to be retained. DOF for the satellite model. The initial set size varied from A sorting procedure can be used for finding the N degrees of 168 to 576 DOF, and the final accelerometer set size was freedom with the largest diagonal M/K ratio in descending typically on the order of 30-75 DOF. Results consistently order. showed good performance of all four methods, but the The result of this process is that a reduced model is genetic algorithm seeded with results of the other algorithms generated that accurately preserves the dynamic did best followed by iterative Guyan reduction. characteristics of the structure at the lower frequencies (Refs. Reference 3 compares the iterative Guyan reduction and 3-4). If some higher-order modes are of interest for model ADPR methods for a cantilever beam, free-free H-frame, 2-D correlation, then a larger set should be retained, a different truss pinned at one end, and a free-free plate. Generally, the technique should be used, or the results should be modified iterative Guyan procedure gave the best results, particularly using engineering judgment. for constrained structures with no rigid body modes. For free-free structures or those with one or more rigid body Iterative Guyan Reduction modes, the ADPR approach seemed to work better, but In this approach (Refs. 3-4), the ratio of diagonal mass iterative Guyan also did an adequate job. Both methods are to diagonal stiffness is again examined, but the DOF with easily implemented. the smallest ratio is removed. The mass and stiffness In conclusion of comparative studies, iterative Guyan matrices are reduced, and the process is repeated. This reduction fares very well generally for different boundary procedure is continued until the desired model size and conditions, though kinetic energy sorting and mass-weighted accuracy are achieved. The advantage of this iterative effective independence also did quite well. The ADPR process is that the effects of each removed DOF are method appears to work well for free-free structures, or those distributed to the remaining DOF, providing greater accuracy with rigid body modes. Newer approaches such as genetic than the standard or non-iterative approach (Ref. 3). algorithms show great potential, but do not appear to be as easily implemented as the the more commonly used Avera_oe Drivin_o Point Residue {ADPR) Method methods, and apparendy must be seeded with results of the This approach is utilized in commercial software for other algorithms. Based on these findings, Guyan reduction modal testing and model correlation (Ref. 9). As described was given considerable attention in the accelerometer in Ref. 3, it uses an average magnitude or amplitude of location analysis for the Space Station Node, as described in mode shapes. Degrees of freedom with the highest average the remainder of the paper. driving point residue, or highest weighted average modal magnitude, could make up a measurement set. A sorting procedure can be used to list these DOF in descending order. ADDlication Of Methods to the International Space Station Node Previo'us Comparative Studies As stated in Ref. 6, "...no one method stands out as the The general approach taken for accelerometer placement clear choice. Methods which perform well in one instance for the Node external shell included the following steps: 1. may give completely unacceptable results in another." Begin with a fairly large set based mainly on visual However, the authors of Ref. 6 go on to point out that the inspection of the structure geometry and analytical mode commonly used methods such as iterative Guyan reduction, shapes, but also based on kinetic energy sorting, 2. Add kinetic energy sorting, and effective independence typically locations known to be paths by which loads are transmitted give reasonable results. Results of some comparative to the structure, and other locations that appear to be of studies of several techniques are described in this section. interest, such as trunnion and keel support structures, shell The comparative study in Ref. 6 describes selection of reinforcing rings, and end cones, 3. Run iterative Guyan sensor locations for the Pegasus launch vehicle constrained reduction, beginning with the set described in 2., to reduce at attach locations to the carrier aircraft. The full model had the number of locations for the Node external shell to about approximately 30,000 DOF, and the initial candidate 190, 4. Use standard non-iterative Guyan reduction and measurement set consisted of 150 locations and 450 DOF. ADPR reduction to also obtain candidate sets of Several commonly-used methods (kinetic energy sorting, measurement coordinates, 5. Run eigenvalue analyses for the iterative Guyan reduction, and effective independence) were reduced models and a reference Craig-Bampton model (Ref. evaluated for the problem and compared to results using 6) or full model, and form cross-orthogonality of the flexibility shapes. The methods were compared for a resulting modes normalized with respect to the reduced mass reduction of the measurement set to 150 DOF (300 matrix. coordinates eliminated), and 24 target modes to 50 Hz were American Institute of Aeronautics and Astronautics Resultsof frequencycomparisonsand cross- References orthogonalictyalculationwsereusedasthefigures-of-merit or standardbsy whicheachcandidasteetandreduction 1.Tinker, M. L., "Modal Vibration Test Facilities and techniquweasevaluatedIn. Tables1 and2, thecross- Methods for Space Station Modules," AIAA Paper 95- orthogonalivtyaluesareshownfortwoinitialsetso,newith 1295, 1995. nearly500externaslhelllocationasnd1500DOFandthe 2. Guyan, R.J., "Reduction of Stiffness and Mass seconwdithapproximate8l0y0locationasnd2400DOF.It Matrices", AIAA Journal. Vol. 3, No. 2, p. 380. wasfoundthatthe iterativeGuyanapproacphrovided 3. Penny, J.E.T, Friswell, M.I., and Garvey, S.D., measuremesenttsthatcomparevderywellwiththereference"The Automatic Choice of Measurement Locations for model.Table3showsthecross-orthogonavlaitlyuesfora Dynamic Testing", AIAA Journal. Vol. 32, No. 2, 1994, setreducetod 195locationsand577DOF. Comparison pp. 407-414. withTables1and2 verifiesthegoodperformanocfethe 4. Kammer, D.C., "Sensor Placement for On-Orbit iterativeGuyanapproach.Poorresultsin all casesfor Modal Identification and Correlation of Large Space modes19-22werefoundtobedueto impropecronstraints Structures", Journal of Guidance. Control. and Dynamics. forsomeinternaclonnectioninstheNodefiniteelement Vol. 14, No. 2, pp. 251-259. model. Whenthe constraintwserecorrectedg,ood 5. Flanigan, C.C., and Botts, C.D., "Automated orthogonaliatyndfrequenccyomparisonwsereobtainefdor Selection of Accelerometer Locations for Modal Survey mode1s9-22. Tests", Proceedings of the 10th International Modal TheADPRmethoddidnotperformwellfortheNode #nalysis Conference, San Diego, CA, Feb. 3-7, 1992, structurea,sseeninTable4. Possibltehisisbecausthee Nodetestwasafixed-boundacroynfigurationR.esultsin pp. 1205-1208. 6. Stabb, M., and Blelloch, P., "Application of Ref.3 suggestthattheADPRapproacwhorksbetterfor Flexibility Shapes to Sensor Selection", 13th free-freteesctonfigurations. International Modal Analysis Conference, Detroit, MI, It wasalsofoundinthisstudythatthekineticenergy Feb. 12-15, 1995, pp. 1255-1262. sortingmethoadsastand-alosneensolorcatiopnrocedudreid 7. Stabb, M.C., and Bleiloch, P.A., "A Genetic notworkwell. It wasdiscovertehdatthemethopdrovided locationosnthestructurtehatareheavyandstiff,andnota Algorithm for Optimally Selecting Accelerometer Locations", Proceedings of _he 13th International Modal gooddistributioonfdesirabmleeasurempeonitnts. Analysis Conference, Detroit, MI, Feb. 12-15, 1995, pp. 1530-1534. 8. Flanigan, C.C., and Stabb, M.C., Jr., Summary and Conclusions "Comparison of Automated Methods for Optimum Accelerometer Selection", 13th International Modal This paper describes results of accelerometer placement Analysis Conference, Detroit, MI, Feb. 12-15, 1995. analysis for the International Space Station Node fixed-base 9. LMS International, "Large-Scale Modal Testing of modal survey test. It was found that the iterative Guyan a Space Frame Structure--From Pretest Analysis fo FEA reduction method performed very well, yielding a Model Validation," Sound and Vibration, March 1991, pp. measurement set with good frequency and cross- 6-16. orthogonality comparisons to the reference model. 10. Craig, R. R., Jr., and Bampton, M. C. C., However, the iterative method was computationally "Coupling of Substructures for Dynamic Analysis", intensive, requiring long run times (about 4 hours wallclock AIAA Journal, Vol. 6, No. 7, July 1968, pp. 1313-1319. time for the initial 1500 DOF set, and 2 weeks for the initial 2400 DOF set). Although the run times are dependent on computer platform and workload, it is clear that the iterative approach becomes impractical for initial candidate sets larger than about 1500 DOF. Standard non-iterative Guyan reduction also provided a good measurement set, but the ADPR technique gave poor results for the Node structure in aconstrained configuration. Acknowledgments Steven Woletz of Boeing Company in Huntsville, Alabama determined initial candidate accelerometer locations for the Node exterior, as well as the final set used in the modal test. Bobby Evars, also of the Boeing Company in Huntsville, determined sensor locations for the Node interior components. 3 American Institute of Aeronautics and Astronautics Figure 1. International Space Station Node in Modal Test Configuration .-\111¢ I'iC_lll 111_,[lI LtIC _lJ",-\c" li ilILIU[ i( _, _I11_l ,\_,II_ HILItll IC_ AIF CYLINOER LONGERON t Structure Figure 2, Space Station Node External Shell and Internal 5 American Institute of Aeronautics and Astronautics Table2. Frequency Table1. ConstrainedFrequencyandMode and Mode Shape Comparisons Comparisonsfor 1500DOFInitialSetandFull for 2400 DOF Initial Set and Full Model Model Full Reduced Correl, F011 Reduced Correl, 1 7.3152 1 7.3161 -1.00000 1 7.2171 1 7.2180 1.00000 2 10.7081 2 10.7113 1.00000 2 10.6779 2 10.6811 -1.00000 3 11.4486 3 11.4549 -1.00000 3 11.4250 3 11.4314 1.00000 4 14.6754 4 14.6805 1.00000 4 14.6389 4 14.6438 -1.00000 5 17.8832 5 17.8851 -1.00000 5 17.7590 5 17.7607 1.00000 6 18.1015 6 18.1042 0.99999 6 17.9636 6 17.9662 -1.00000 7 18.7835 7 18.7913 -0.99999 7 18.7371 7 18.7451 -0.99999 8 21.0240 8 21.1234 -0.99908 8 21.0096 8 21.1164 0.99965 9 21.1056 9 21.2139 -0.99919 9 21.1045 9 21.2092 0.99993 10 21.3428 10 21.4625 -0.99983 10 21.3496 10 21.4598 0.99993 11 22.3180 11 22.3595 -0.99666 11 22.0088 11 22.0379 -0.99962 12 22.5698 12 22.6420 0.98907 12 22.3737 12 22.4292 0.99339 13 22.6876 13 22.7260 -0.99202 13 22.5631 13 22.6261 0.99183 14 23.2005 14 23.2457 -0.99932 14 22.9024 14 22.9506 -0.99825 15 24.0261 15 24.0306 -0.99970 15 23.6325 15 23.6373 -0.99981 16 24.2233 16 24.2530 0.99909 16 23.8722 16 23.9002 0.99933 ! 17 24.9343 17 24.9727 0.99507 17 26.6069 17 24.6218 -0.99864 18 25.5143 18 25.7124 -0.98312 18 25.3699 18 25.5671 0.99471 19 25.7490 19 26.5827 -0.63343 19 25.7425 19 26.5074 0.63960 20 25.8087 21 27.4732 -0.43050 20 25.8066 21 27.4022 0.43515 21 25.8489 22 28.1236 0.24650 21 25.8478 22 28.0672 0.25581 22 25.9833 18 25.7124 0.75599 22 25.9583 18 25.5671 -0.66351 23 26.5815 19 26.5827 -0.99812 23 26.5134 19 26.5074 0.99578 24 26.7932 20 26.8195 -0.99944 24 26.7016 20 26.7220 -0.99949 25 27.3517 21 27.4732 -0.99831 25 27.2882 21 27.4022 0.99865 26 28.0258 22 28.1235 -0.98411 26 27.9624 22 28.0672 -0.97481 27 28.1892 23 28.2791 -0.81537 27 28.1374 24 28.2892 0.95073 28 28.2009 24 28.3412 0.78309 28 28.1636 23 28.2482 0.99463 29 28.3107 25 28.3923 -0.99533 29 28.3037 25 28.3845 -0.99634 30 28.3453 26 28.4274 0.99176 30 28.3365 26 28.4180 0.99306 Table 3. Comparison of Model Reduced Using Iterative Table 4. Results for Model Reduced Using Guyan Reduction to 577 DOF and Full Model ADPR Method in Comparison to Full Model Full Reduced Correl. Full Reduced Correl. 1 7.2196 1 7.2205 1.00000 1 7.2185 1 7.2957 -i.00000 2 10.6819 2 10.6850 1.00000 2 10.6796 2 11.2582 0.92248 3 11.4300 3 11.4363 1.00000 3 11.4261 3 11.7480 0.89365 4 14.6456 4 14.6507 1.00000 4 14.6400 4 16.8584 0.94562 5 17.7610 5 17.7628 1.00000 5 17.7593 5 17.8977 0.77481 6 17.9643 6 17.9670 1.00000 6 17.9637 6 18.2141 0.74335 7 18.7479 7 18.7561 -0.99999 7 18.7400 7 21.3759 0.41561 8 21.0198 8 21.1186 0.99916 8 21.0186 8 21.4238 0.64090 9 21.1021 9 21.2103 -0.99929 9 21.1018 7 21.3759 0.62388 10 21.3405 10 21.4601 0.99984 10 21.3409 8 21.4238 -0.60177 11 22.0126 11 22.0415 0.99969 11 22.0095 10 22.0903 -0.61034 12 22.3859 12 22.4425 0.99368 12 22.3766 12 22.8021 0.72083 13 22.5785 13 22.6385 0.99201 13 22.5662 12 22.8021 0.54391 14 22.9062 14 22.9541 -0.99816 14 22.9037 13 23.3842 -0.70360 15 23.6384 15 23.6431 0.99982 15 23.6353 14 23.6921 0.72775 16 23.8784 16 23.9065 0.99935 16 23.8746 15 24.0488 -0.68995 17 24.6093 17 24.6257 0.99872 17 24.6069 16 24.8842 0.83705 18 25.3_5 _8 2.%_88/) -0_99470 18 25.3765 16 24.8842 0.56847 19 25.7470 19 26.5738 0.64030 19 25.7443 17 26.4460 -0.62584 20 25.8082 21 27.4616 0.43106 20 25.8077 19 27.2857 0.41153 21 25.8482 22 28.1058 0.25143 21 25.8481 29 29.9961 -0.21809 _Z 25,9_2 I_ :lS. SlUL0 O. G?SZ3 22 25.9603 16 24.8842 -0.30521 23 26.5742 19 26.5738 0.998>2 23 26.5249 17 26.4460 -0.95181 24 26.7992 20 26.8268 0.99937 24 26.7178 18 26.7485 0.99338 25 27.3403 21 27.4616 -0.99836 25 27.3099 19 27.2857 0.91490 26 27.9739 20 28.1439 -0.63554 27 28.1436 22 28.2872 0.79567 23 28.3781 -0.9t85_ 28 28.1739 24 28.4429 -0.57695 29 28.3062 25 28.3876 0.99487 29 28.3052 23 28.4286 0.59759 30 28.3393 26 28.4217 0.99090 30 28.3383 23 28.4286 -0.72719 6 American Institute of Aeronautics and Astronautics