# US 12,181,490 B2 · Mode decomposition method applicable to flow field analysis and reconstruction of internal solitary wave test

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- Number: US 12,181,490 B2
- Document ID: US12181490B2
- Status: Granted
- Kind: B2
- Application number: 17/596,241
- Filed: 2019-12-31
- Published: 2022-12-08
- Granted: 2024-12-31
- Earliest claimed: 2019-06-06
- Assignees: Dalian University of Technology
- Applicants: Dalian University of Technology
- Inventors: Li Zou; Tiezhi Sun; Jiuming Zhang; Yuguo Pei; Zhenhao Li; Xinyu Ma; Zhe Sun; Zongbing Yu
- Web page: https://patentgrep.com/patent/US12181490B2

## CPC

- G01P 5/20: using particles entrained by a fluid stream (G01P5/22 takes precedence)
- G06F 17/16: Matrix or vector computation {, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization (matrix transposition G06F7/78)}
- G06F 18/2135: based on approximation criteria, e.g. principal component analysis
- G06F 18/22: Matching criteria, e.g. proximity measures
- G06V 20/52: Surveillance or monitoring of activities, e.g. for recognising suspicious objects (recognising microscopic objects G06V20/69)
- Y02A 90/10: Information and communication technologies [ICT] supporting adaptation to climate change, e.g. for weather forecasting or climate simulation
- G01P: MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT (measuring or recording blood flow A61B5/02, A61B8/06; monitoring speed or deceleration of electrically-propelled vehicles B60L3/00; vehicle lighting systems adapted to indicate speed B60Q1/54; determining position or course in navigation, measuring ground distance in geodesy or surveying G01C; combined measuring devices for measuring two or more variables of movement G01C23/00; measuring velocity of sound G01H; measuring velocity of light G01J7/00; measuring direction or velocity of solid objects by reception or emission of radiowaves or other waves and based on propagation effects, e.g. Doppler effect, propagation time, direction of propagation, G01S; measuring speed of nuclear radiation G01T; measuring acceleration of gravity G01V; {measuring or recording the speed of trains B61L23/00; speed indicators incorporated in motor vehicles B60K35/00; measuring frequency or phase G01R; traffic control G08G})
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)
- G06V: IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
- Y02A: TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE

## Abstract

An improved modal decomposition method applicable to the analysis and reconstruction of the measured flow fields of internal solitary waves includes the following steps: S1. generating internal solitary waves and measuring a two-dimensional flow field sequence during the interaction of the internal solitary waves with the terrain; S2. extracting a target information from the two-dimensional flow field sequence and obtaining a flow field snapshot; S3. stitching the snapshots into a snapshot matrix in time order; S4. plotting the information density curve; S5. normalizing the information density curve and determining split points; S6. setting the snapshot matrix between two adjacent split points as a linear evolutionary characteristic stage; and S7. performing dynamic mode decomposition on the linear evolutionary characteristic stages.

## Claims

### Claim 1

An improved modal decomposition method applicable to the analysis and reconstruction of measured flow fields of internal solitary waves, comprising the following steps,
S1. generating internal solitary waves in a stratified experimental wave tank by using the gravity collapse method, and measuring a two-dimensional flow field sequence at a same time interval during an interaction of the internal solitary wave with the terrain by using particle image velocimetry method;
S2. extracting target information from the two-dimensional flow field sequence for each time interval and organizing it end to end in column vector form, wherein the column vector for each moment is named as flow field snapshot;
S3. stitching the flow field snapshots into a snapshot matrix in time order;
S4. projecting the snapshot matrix on a orthogonal basis by performing principal component analysis method, then calculating a projection value of each flow field snapshot onto a major basis vector, wherein the projection value is named as information density; plotting an information density curve according to the information density;
S5. normalizing the information density curve and determining a upper envelope and maximum points of the upper envelope; according to a distance between adjacent maximum points and a value of minimal point between them, choosing effective maximum points; setting the effective maximum points as split point;
S6. setting the snapshot matrix between two adjacent split points as a linear evolutionary characteristic stage; and
S7. performing dynamic modal decomposition on the linear evolutionary characteristic stages and extracting multi-order modes based on energy ranking, completing noise reduction and reconstruction of the two-dimensional flow field sequence.

### Claim 2 (depends on 1)

The improved modal decomposition method applicable to the analysis and reconstruction of measured flow fields of internal solitary waves according to claim 1, wherein the target information is one of vorticity, horizontal velocity, and vertical velocity.

### Claim 3 (depends on 1)

The improved modal decomposition method applicable to the analysis and reconstruction of measured flow fields of internal solitary waves according to claim 1, wherein in step S4, the principal component analysis method comprises the following steps:
S41. subtracting an average value of matrix elements from each element in the snapshot matrix to obtain a matrix X;
S42. computing a covariance matrix of the matrix X,
C
=
1
m
⁢
X
⁢
X
T
,
wherein, m represents the column number of the snapshot matrix and XT represents the transposed matrix of the matrix X;
S43. computing eigenvalues and eigenvectors of the covariance matrix C, setting the eigenvector corresponding to the maximum eigenvalue as the main base vector V;
S44. computing the projection value of each time snapshot on the main base vector, Y=VX, wherein Y is the projection value.

### Claim 4 (depends on 1)

The improved modal decomposition method applicable to the analysis and reconstruction of measured flow fields of internal solitary waves according to claim 1, wherein a number of extracted modes in step S7 is 6.