116 6. SYSTEMATIC TEST ANALYSIS CORRELATION
ISPE Test Modal Orthogonality
(SFD-2018 Complex Modes)
ISPE TAM Mode Orthogonality
(State-Space Format)
ISPE TAM to Test Modal Cross-Orthogonality
(Complex Least Squares)
ISPE TAM to Test Modal Coherence
(Complex Least Squares)
100
90
80
70
60
50
40
30
20
10
100
90
80
70
60
50
40
30
20
10
0
90
80
70
60
50
40
30
20
10
90
80
70
60
50
40
30
20
10
10
20
30
40
50
60
Test Mode
10
20
30
40
50
60
70
TAM Mode
10
20
30
40
50
60
70
10
20
30
40
50
60
TAM Mode
Test Mode
10 20 30 40 50 60
Test Mode
10 20 30 40 50 7060
TAM Mode
10 20 30 40 50 60
Test Mode
10 20 30 40 50 60
Test Mode
Figure 6.2: Orthogonality, cross-orthogonality coherence of TAM and test complex eigenvec-
tors.
6.2.6 ROADMAP FOR A HIGHLY IMPROVED INTEGRATED TEST
ANALYSIS PROCESS
Introduction of the complex state-space viewpoint for experimental modal analysis (SFD-2018)
and the TAM mass matrix independent metrics described in the present chapter, suggests a po-
tential paradigm shift for the integrated test-analysis process. A roadmap for this envisioned
highly improved test analysis process, encompassing experimental modal analysis and system-
atic test analysis correlation, employing ISPE modal test data and mathematical model data, is
outlined in Figures 6.3–6.6.
6.2. PART 2: CORRELATION OF TEST AND FEM MODES 117
Orthogonality of Normalized SFD Modes Orthogonality of Normalized SFD Modes
100
90
80
70
60
50
40
30
20
10
100
90
80
70
60
50
40
30
20
10
10
20
30
40
50
60
10
20
30
40
50
60
Test
Test
10 20 30 40 50 60
Test
10 20 30 40 50 60
Test
Magnitude
Magnitude
Magnitude
Imaginary
Imaginary Real
Phase (Deg)
Phase (Deg)
Hz
Hz
Real
Frequency (Hz) Frequency (Hz)
Frequency (Hz)
FRF Display: File: ISPETESTDFRFs, Mode 1, Input 1, Coh=99%, 06-Mar-2019 11:35 AM
h(f)
h
modal
(f)
Current Practice
• Mode V&V via “Curve Fitting”
• Mode V&V: Self-orthogonality
[OR
t
] = [Φ
t
T
M
aa
Φ]
• Perfect Self-orthogonality
[OR]
TEST
= [Φ
L
]
TEST
[Φ]
TEST
≡ [I]
Emerging Option
• V&V via Isolated Mode FRF
Note: Emerging option is independent of the math model’s TAM mass matrix
Figure 6.3: ISPE experimental modal analysis and modal orthogonality.
118 6. SYSTEMATIC TEST ANALYSIS CORRELATION
Coherence, |COH| of normalized (Real) TAM vs. Test Modes Coherence, |COH| of normalized Shade-Space TAM vs. Test Modes
90
80
70
60
50
40
30
20
10
90
80
70
60
50
40
30
20
10
10
20
30
40
50
60
10
20
30
40
50
60
Test
Test
10 20 30 40 50 60
Test
10 20 30 40 50 60
Test
Cross-Orthogonality, |COH| of normalized Shade-Space TAM vs. Test Modes
90
80
70
60
50
40
30
20
10
10
20
30
40
50
60
70
Test
10 20 30 40 50 60
Tam
Current Practice
• Test-Analysis Cross-Orthogonality
[COR] = [OR
a
]
-1
[Φ
a
T
M
aa
Φ
t
]
• Test-Analysis Modal Coherence
[COH ] = ![I ]–[OR
t
]
-1/2
"R
T
MR#[OR
t
]
-1/2
$=
[OR
t
]
-1/2
"COR
t
OR
a
COR#[OR
t
]
-1/2
• Test-Analysis Modal Coherence
[COH] = [OR
TEST
]–[R
*
R] = [C]
*
[OR
TAM
][C]
Emerging Option
• Test-Analysis Cross-Orthogonality
[COR] = [Φ
TAM
]
n
*
[Φ
TEST
]
n
Cross-Orthogonality, |COH| of normalized (Real) TAM vs. Test Modes
90
80
70
60
50
40
30
20
10
10
20
30
40
50
60
70
Test
10 20 30 40 50 60
Tam
Note: Emerging option is independent of the math model’s TAM mass matrix
Figure 6.4: ISPE test-analysis cross-orthogonality and modal coherence.
6.2. PART 2: CORRELATION OF TEST AND FEM MODES 119
Current Practice
• Modal Kinetic Energy
[KE
Φ
] = [MΦ]⊗
[Φ]
• Mode Shape 1 (real)
• Kinetic Energy 1 (real) • Kinetic Energy 1 (complex)
Emerging Option
• Modal Kinetic Energy
[KE
Φ
] = conj[Φ* ]⊗
[Φ]
• Mode Shape 1 (complex)
Note: Emerging option is independent of the math model’s TAM mass matrix
L
Figure 6.5: ISPE test mode 1 mode shape and modal kinetic energy.
120 6. SYSTEMATIC TEST ANALYSIS CORRELATION
Current Practice
• Modal Kinetic Energy
[KE
Φ
] = [MΦ]⊗
[Φ]
• Mode Shape 3 (real)
• Kinetic Energy 3 (real) • Kinetic Energy 3 (complex)
Emerging Option
• Modal Kinetic Energy
[KE
Φ
] = conj[Φ* ]⊗
[Φ]
• Mode Shape 3 (complex)
Note: Emerging option is independent of the math model’s TAM mass matrix
L
Figure 6.6: ISPE test mode 3 mode shape and modal kinetic energy.
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