Annex B · MIL-STD-810H

4 tables appear under this heading.

1. PDF page 923

1.	TRANSFER-FUNCTION ESTIMATIONS	B-1
2.	SIGNAL TRANSFORMATION	B-1
3.	CONTROL IMPLEMENTATION	B-1
3.1	SISO AUTO AND CROSS-SPECTRAL DEFINITIONS REVIEW	B-1
3.2	SISO TRANSFER FUNCTION AND COHERENCE FUNCTION DEFINITIONS REVIEW	B-2
3.3	MIMO AUTO-SPECTRA, CROSS-SPECTRA, AND INITIAL FUNCTION ESTIMATES	B-3
3.3.1	FREQUENCY DOMAIN TRANSFER FUNCTION RELATIONSHIP	B-3
3.3.2	KEY TRANSFER FUNCTION DERIVATIONS	B-4
3.3.3	KEY TRANSFER FUNCTION DERIVATIONS ALTERNATIVE	B-5
3.4	MIMO COHERENCE FUNCTIONS	B-6
3.4.1	ORDINARY COHERENCE	B-6
3.4.2	PARTIAL COHERENCE	B-7
3.4.3	MULTIPLE COHERENCE	B-7
3.5	DRIVE SIGNAL COMPENSATION	B-7

METHOD 527.2 ANNEX C PROCEDURE I MET (TIME WAVEFORM REPLICATION (TWR) SPECIFIC)
1.	PROCEDURE I MET (TIME DOMAIN REFERENCE CRITERIA)	.C-1
1.1	PREPROCESSING.	C-1
2.	ANALYSIS CONSIDERATIONS FOR A PROCEDURE I MET	C-1
2.1	ADDRESSING TRANSLATIONAL MOTION.	C-1
2.2	ADDRESSING ANGULAR MOTION.	C-1
3.	TEST TOLERANCES FOR A PROCEDURE I MET	C-2
3.1	COMPOSITE (GLOBAL) ERROR DISCUSSION FOR PROCEDURE I	C-2
3.2	GLOBAL RMS ERROR	C-2
3.3	GLOBAL ASD ERROR..	C-4
3.4	GLOBAL SRS ERROR	C-6
METHOD 527.2 ANNEX D PROCEDURE II MET (SPECTRAL DENSITY MATRIX (SDM) SPECIFIC)
1.	PROCEDURE II MET (FREQUENCY DOMAIN REFERENCE CRITERIA)	.D-1
1.1	PREPROCESSING.	.D-1
2.	ANALYSIS CONSIDERATIONS FOR A PROCEDURE II MET.	.D-1
2.1	MESA AND MEMA SPECIFICATION PARAMETERS.	D-1
2.1.1	CROSS SPECTRAL DENSITY STRUCTURE	.D-2
2.2	CONTROL HIERARCHY	.D-2
2.2.1	MEASURED DATA AVAILABLE.	D-2
2.2.2	MEASURED DATA NOT AVAILABLE.	.D-2
2.2.3	USE OF 1-DOF REFERENCES.	D-3
3.	TEST TOLERANCES FOR A PROCEDURE II MET.	.D-3
3.1	COMPOSITE (GLOBAL) ERROR DISCUSSION FOR PROCEDURE II..	.D-3
ANNEX D TABLES
TABLE	527.2D-I. REFERENCE CRITERIA FOR A 2-DOF LINEAR MOTION RANDOM MET.	.D-1
TABLE	527.2D-II. REFERENCE CRITERIA FOR A 3-DOF LINEAR MOTION RANDOM MET.	D-1
METHOD 527.2 ANNEX E LABORATORY VIBRATION TEST SCHEDULE DEVELOPMENT FOR MULTI-EXCITER APPLICATIONS
1.	SCOPE	E-1
2.	FACILITIES AND INSTRUMENTATION.	E-1
2.1	FACILITIES	E-1

Paragraph		Page
2.2	INSTRUMENTATION.	E-1
3.	REQUIRED TEST CONDITIONS.	E-1
3.1	TEST CONFIGURATIONS	E-1
3.1.1	BASIC REPRESENTATION OF A MIMO SYSTEM	E-2
3.1.2	GENERALIZED REPRESENTATION OF A MIMO SYSTEM	E-2
3.2	GENERALIZED MDOF VIBRATION CONTROL DISCUSSION..	E-3
4.	TEST PROCEDURES	E-4
4.1	DEVELOPMENT OF MISSION OR LIFETIME SCENARIO	E-4
4.2	LIMITATIONS..	E-4
4.3	FIELD DATA ACQUISITION	E-5
4.3.1	INSTRUMENTATION.	E-5
4.4	USE OF RIGID BODY MODES	E-5
4.4.1	ACCELERATION (INPUT) TRANSFORMATION	E-5
4.4.1.1	ACCELERATION (INPUT) TRANSFORMATION DERIVATION	E-6
4.4.1.2	EQUATION 4.1	E-6
4.4.2	DRIVE (OUTPUT) TRANSFORMATION	E-7
4.4.2.1	DRIVE (OUTPUT) TRANSFORMATION DERIVATION.	E-8
4.5	DATA ANALYSIS	E-9
4.5.1	PHASE AND COHERENCE BASED REPRESENTATIONS OF CSD TERMS	E-10
4.5.2	POSITIVE DEFINITE SDM CONSIDERATIONS	E-10
4.5.3	DATA COMPRESSION..	E-11
4.5.4	LIMITING STRATEGIES	E-12
4.5.5	MINIMUM DRIVE CONSIDERATIONS	E-12
4.5.5.1	INDEPENDENT DRIVES.	E-12
4.6	INDEPENDENT REFERENCES.	E-13
4.7	RECOMMENDED PRACTICES SUMMARY	E-14
5.	DATA REQUIRED.	E-15
5.1	REFERENCE SDM DEVELOPMENT.	E-15
5.1.1	SDM ENSEMBLE CSD CHARACTERISTICS	E-15
5.2	TEST TOLERANCE RECOMMENDATIONS	E-16
5.3	LABORATORY DATA	E-16
6.	MDOF VSD METHODS	E-16
6.1	OPTIONS CONSIDERED	E-16
6.1.1	METHOD I	E-16
6.1.2	METHOD II	E-18
6.2	EXAMPLE	E-19
6.3	CONCLUDING REMARKS	E-25
APPENDIX A	GLOSSARY	E-27
APPENDIX B	ABBREVIATIONS	E-29
APPENDIX C	NOMENCLATURE.	E-31
APPENDIX D	MATRIX ALGEBRA REVIEW	E-33
APPENDIX E	REFERENCES	E-37

G_{xx_mm} (f) = auto-spectrum of the input m

G_{yy_nn} (f) = auto-spectrum of the output n

G_{xy_nn} (f)=cross-spectrum between input m and output n

1. PDF page 923

1.	TRANSFER-FUNCTION ESTIMATIONS	B-1
2.	SIGNAL TRANSFORMATION	B-1
3.	CONTROL IMPLEMENTATION	B-1
3.1	SISO AUTO AND CROSS-SPECTRAL DEFINITIONS REVIEW	B-1
3.2	SISO TRANSFER FUNCTION AND COHERENCE FUNCTION DEFINITIONS REVIEW	B-2
3.3	MIMO AUTO-SPECTRA, CROSS-SPECTRA, AND INITIAL FUNCTION ESTIMATES	B-3
3.3.1	FREQUENCY DOMAIN TRANSFER FUNCTION RELATIONSHIP	B-3
3.3.2	KEY TRANSFER FUNCTION DERIVATIONS	B-4
3.3.3	KEY TRANSFER FUNCTION DERIVATIONS ALTERNATIVE	B-5
3.4	MIMO COHERENCE FUNCTIONS	B-6
3.4.1	ORDINARY COHERENCE	B-6
3.4.2	PARTIAL COHERENCE	B-7
3.4.3	MULTIPLE COHERENCE	B-7
3.5	DRIVE SIGNAL COMPENSATION	B-7

2. PDF page 924

METHOD 527.2 ANNEX C PROCEDURE I MET (TIME WAVEFORM REPLICATION (TWR) SPECIFIC)
1.	PROCEDURE I MET (TIME DOMAIN REFERENCE CRITERIA)	.C-1
1.1	PREPROCESSING.	C-1
2.	ANALYSIS CONSIDERATIONS FOR A PROCEDURE I MET	C-1
2.1	ADDRESSING TRANSLATIONAL MOTION.	C-1
2.2	ADDRESSING ANGULAR MOTION.	C-1
3.	TEST TOLERANCES FOR A PROCEDURE I MET	C-2
3.1	COMPOSITE (GLOBAL) ERROR DISCUSSION FOR PROCEDURE I	C-2
3.2	GLOBAL RMS ERROR	C-2
3.3	GLOBAL ASD ERROR..	C-4
3.4	GLOBAL SRS ERROR	C-6
METHOD 527.2 ANNEX D PROCEDURE II MET (SPECTRAL DENSITY MATRIX (SDM) SPECIFIC)
1.	PROCEDURE II MET (FREQUENCY DOMAIN REFERENCE CRITERIA)	.D-1
1.1	PREPROCESSING.	.D-1
2.	ANALYSIS CONSIDERATIONS FOR A PROCEDURE II MET.	.D-1
2.1	MESA AND MEMA SPECIFICATION PARAMETERS.	D-1
2.1.1	CROSS SPECTRAL DENSITY STRUCTURE	.D-2
2.2	CONTROL HIERARCHY	.D-2
2.2.1	MEASURED DATA AVAILABLE.	D-2
2.2.2	MEASURED DATA NOT AVAILABLE.	.D-2
2.2.3	USE OF 1-DOF REFERENCES.	D-3
3.	TEST TOLERANCES FOR A PROCEDURE II MET.	.D-3
3.1	COMPOSITE (GLOBAL) ERROR DISCUSSION FOR PROCEDURE II..	.D-3
ANNEX D TABLES
TABLE	527.2D-I. REFERENCE CRITERIA FOR A 2-DOF LINEAR MOTION RANDOM MET.	.D-1
TABLE	527.2D-II. REFERENCE CRITERIA FOR A 3-DOF LINEAR MOTION RANDOM MET.	D-1
METHOD 527.2 ANNEX E LABORATORY VIBRATION TEST SCHEDULE DEVELOPMENT FOR MULTI-EXCITER APPLICATIONS
1.	SCOPE	E-1
2.	FACILITIES AND INSTRUMENTATION.	E-1
2.1	FACILITIES	E-1

3. PDF page 925

Paragraph		Page
2.2	INSTRUMENTATION.	E-1
3.	REQUIRED TEST CONDITIONS.	E-1
3.1	TEST CONFIGURATIONS	E-1
3.1.1	BASIC REPRESENTATION OF A MIMO SYSTEM	E-2
3.1.2	GENERALIZED REPRESENTATION OF A MIMO SYSTEM	E-2
3.2	GENERALIZED MDOF VIBRATION CONTROL DISCUSSION..	E-3
4.	TEST PROCEDURES	E-4
4.1	DEVELOPMENT OF MISSION OR LIFETIME SCENARIO	E-4
4.2	LIMITATIONS..	E-4
4.3	FIELD DATA ACQUISITION	E-5
4.3.1	INSTRUMENTATION.	E-5
4.4	USE OF RIGID BODY MODES	E-5
4.4.1	ACCELERATION (INPUT) TRANSFORMATION	E-5
4.4.1.1	ACCELERATION (INPUT) TRANSFORMATION DERIVATION	E-6
4.4.1.2	EQUATION 4.1	E-6
4.4.2	DRIVE (OUTPUT) TRANSFORMATION	E-7
4.4.2.1	DRIVE (OUTPUT) TRANSFORMATION DERIVATION.	E-8
4.5	DATA ANALYSIS	E-9
4.5.1	PHASE AND COHERENCE BASED REPRESENTATIONS OF CSD TERMS	E-10
4.5.2	POSITIVE DEFINITE SDM CONSIDERATIONS	E-10
4.5.3	DATA COMPRESSION..	E-11
4.5.4	LIMITING STRATEGIES	E-12
4.5.5	MINIMUM DRIVE CONSIDERATIONS	E-12
4.5.5.1	INDEPENDENT DRIVES.	E-12
4.6	INDEPENDENT REFERENCES.	E-13
4.7	RECOMMENDED PRACTICES SUMMARY	E-14
5.	DATA REQUIRED.	E-15
5.1	REFERENCE SDM DEVELOPMENT.	E-15
5.1.1	SDM ENSEMBLE CSD CHARACTERISTICS	E-15
5.2	TEST TOLERANCE RECOMMENDATIONS	E-16
5.3	LABORATORY DATA	E-16
6.	MDOF VSD METHODS	E-16
6.1	OPTIONS CONSIDERED	E-16
6.1.1	METHOD I	E-16
6.1.2	METHOD II	E-18
6.2	EXAMPLE	E-19
6.3	CONCLUDING REMARKS	E-25
APPENDIX A	GLOSSARY	E-27
APPENDIX B	ABBREVIATIONS	E-29
APPENDIX C	NOMENCLATURE.	E-31
APPENDIX D	MATRIX ALGEBRA REVIEW	E-33
APPENDIX E	REFERENCES	E-37