# US 2019/0171691 A1 · A method of mode order determination for engineering structural modal identification

> Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt

- Number: US 2019/0171691 A1
- Document ID: US20190171691A1
- Status: Published application
- Kind: A1
- Application number: 16/321,183
- Filed: 2018-03-06
- Published: 2019-06-06
- Earliest claimed: 2017-04-14
- Assignees: Dalian University of Technology
- Applicants: Dalian University of Technology
- Inventors: Chunxu QU; Tinghua YI; Hongnan LI
- Web page: https://patentgrep.com/patent/US20190171691A1

## CPC

- G06F 17/16: Matrix or vector computation {, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization (matrix transposition G06F7/78)}
- G01M 5/0066: {by exciting or detecting vibration or acceleration (vibration testing of structures G01M7/00)}
- G06F 17/14: Fourier, Walsh or analogous domain transformations {, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms (for correlation function computation G06F17/156; spectrum analysers G01R23/16)}
- G01N 29/12: by measuring frequency or resonance of acoustic waves {(measuring frequency or resonant frequency of mechanical vibrations or acoustic waves in general G01H1/06, G01H3/04, G01H13/00; acoustic resonators G10K11/04; vibration or shock testing of structures G01M7/00)}
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)
- G01M: TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01N: INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES (measuring or testing apparatus or processes other than immunoassay, involving enzymes or microorganisms C12M, C12Q)

## Abstract

The presented invention belongs to the technical field of data analysis for structural health monitoring, and relates to a method of the mode order determination for the modal identification of engineering structures. The presented invention first calculates the structural natural frequencies for every order by eigensystem realization algorithm. Then the modal responses for every natural frequency are extracted. After obtaining the square mean root of modal responses, the modal response contribution index (MRCI) is calculated by summation of square mean root for every degree-of-freedom. The relation map between mode order and MRCI is drawn. The mode order is determined by the obvious gap between two adjacent MRCI according to the relation map. This order is also the truncated order of singular matrix in the eigensystem realization algorithm, which is useful to identify other modal parameters accurately.

## Claims

### Claim 1

The procedures of the mode order determination method for the modal identification of engineering structures are as follows:
Step 1: Sample and process the impulse response;
The structural impulse responses yk are collected; The Hankel matrix and H(k−1) and H(k) are built by yk:
H

(
k
)
=
(
y
k
y
k
+
1
…
y
k
+
cH
-
1
y
k
+
1
y
k
+
2
…
y
k
+
cH
…
…
…
…
y
k
+
rH
-
1
y
k
+
rH
…
y
k
+
rH
+
cH
-
2
)
where k+i represents the k+i time point; the number from k to k+rH+cH−2 is the number of time points for the time history; H(k−1) can be obtained by replacing k with k−1; H(k−1) is then decomposed by singular matrix decomposition as follows:
H(k−1)=UΓ2VT
where Γ is singular value matrix; U and V are unitary matrix;
Step 2: obtain the modal shape matrix
The rank cH of singular matrix is assumed to be the structural mode order; Then the eigenvalue λj can be obtained by eigensystem realization algorithm; The relation equation between modal responses and structural responses is built using N eigenvalues, and the modal shape matrix Φj is obtained as follows:
(
Φ
1
Φ
1
…
Φ
N
)
=
(
y
1
y
2
…
y
p
)

(
λ
1
λ
1
2
…
λ
1
p
λ
2
λ
2
2
…
λ
2
p
⋮
⋮
⋱
⋮
λ
N
λ
N
2
…
λ
N
p
)
+
where “+” is the generalized inverse; p=rH+cH−1 is the pth time point;
Step 3: Obtain the modal response for the jth mode and the square mean root of the modal response for the jth mode;
The jth modal response Yp,j is expressed as follows:
Yp,j=(y1,jy2,j . . . yp,j)=Φj(λjλj2 . . . λjp)
The expression for the scalar, i.e. the square mean root of the jth modal response, is:
εj=sqrt(Yp,jYp,jH)
Step 4: Obtain the mode order;
The jth MRCI is obtained by the summation of the scalars for all degree-of-freedom as follow:
MRCI

(
j
)
=
∑
r
=
1
m

ɛ
j

(
r
)
where r denotes the number of degree-of-freedom;
The relation map between mode order and MRCI is drawn, where the horizontal axis denotes the mode order and the vertical axis represents the normalized MRCI by divided by the maximization of MRCI; The mode order is determined by the obvious gap between two adjacent MRCI.