均值对奇异特征值分解算法的影响机制

Abstract

Abstract:

The proper orthogonal decomposition (POD) has been known as an efficient reduction technique in simulating physical process which governed by partial differential equations. In this paper, the basic properties of time coefficients in POD method are studied. Based on the theories and matrix analysis, by introducing the cross-correlation matrix (CROM) of the whole signals and the covariance matrix of the fluctuating parts of signals (in which the mean values have been cancelled, COVM), we derive the influence mechanism of mean values on the POD method in theory. There are fewer relevant studies in previous works. Finally, numerical examples are provided for verification and demonstration the influence mechanism in POD process.

Key words: POD method, Mean values, Whole signals

CLC Number:

O324

Yanhua Cao,Nan Li,Mengcheng Chen. Influence Mechanism of the Mean Values on POD Method[J].Acta mathematica scientia,Series A, 2019, 39(5): 1205-1212.

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Figures/Tables 6

References 17

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模态数	$u^w$	$u_1^w$	$u_2^w$	$u^f$	$u_1^f$	$u_2^f$
1	410(96.2)	229(97.2)	189(99.1)	13.4(82.4)	8.8(89)	4.7(74.9)
2	13.4(3.14)	6.2(2.61)	1.6(0.83)	2.8(17)	1.0(10.4)	1.6(24.78)
3	2.8(0.65)	0.45(0.19)	0.02(0.01)	0.08(0.5)	0.06(0.57)	0.02(0.31)
4	0.068(0.02)	0.038(0.02)	7e-4(3.8e-4)	1.1e-2(0.07)	2e-4(0.02)	7e-4(0.01)

模态数	$u^w$	$u_1^w$	$u_2^w$	$u^f$	$u_1^f$	$u_2^f$
1	0.77	0.49	0.04	0.09	0.01	0.04
2	9.7e-2	1.7e-2	6.6e-3	1.3e-2	7.1e-3	2.3e-3
3	1.2e-2	1.3e-2	2.6e-3	1.3e-2	4.7e-3	1.3e-3
4	8.9e-3	4.7e-3	5.5e-4	6.5e-3	2.6e-3	5.5e-4

模态数	$u^w$	$u_1^w$	$u_2^w$	$u^f$	$u_1^f$	$u_2^f$
1	21.1	14.0	0.42	0.95	0.36	0.41
2	0.97	0.49	0.10	0.14	0.37	0.10
3	0.19	0.16	0.02	0.11	0.08	0.02
4	2.3e-2	8.0e-2	1.1e-2	2.1e-2	3.8e-2	1.1e-2

模态数	$u^w$	$u_1^w$	$u_2^w$	$u^f$	$u_1^f$	$u_2^f$
1	2.7	1.3	0.09	0.33	0.03	0.09
2	3.2e-1	3.9e-2	1.6e-2	4.8e-2	3.1e-2	1.6e-2
3	3.0e-2	2.5e-2	6.0e-3	2.7e-2	7.7e-3	6.0e-3
4	1.4e-2	7.7e-3	1.4e-3	4.8e-3	3.0e-3	1.4e-3

Influence Mechanism of the Mean Values on POD Method

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