CN100468422C - Method for modifying structural model by cross modal of cross model - Google Patents

Abstract

It is a structure module amendment method using a cross-modal cross-model, by adjusting the stiffness matrix and the quality matrix of finite element model to make the modal frequencies and mode through calculation match with the actual structure. Therefore for each unit of the finite element model, the stiffness matrix and the quality matrix coefficients have two amendments. Through the comparison of the structural finite element numerical model and experimental actual model, get the correction coefficient of each module, and thus amend the stiffness matrix and quality matrix to achieve the model amendment purpose. The invention has both advantages of adjustment direct and indirect physical matrix without iteration, improving work efficiency. It also can maintain the physical contact between structural models. In addition, the measurement mode required in the method does not require a return of the quality. Combined with the modal parameter identification technologies based on the output response, it can amend the offshore structure model in environment incentives. So the method has more practical value.

Description

Utilize the structural model modification method of cross over model intersection mode

Technical field

The present invention relates to a kind of cross over model that utilizes and intersect the structural model modification method of mode, particularly at the correction method for finite element model of ocean engineering structure.

Background technology

Finite Element Method also is Finite Element, is that object is separated into limited unit, by concrete analysis to each unit, and a kind of numerical method of analysis-by-synthesis on this basis then.Its basic thought is to find the solution the assembly that discrete region is a group limited and the unit that is connected with each other by certain way with continuous.Finite Element Method is to set up various structural system numerical models method the most commonly used.

The model correction is the numerical value that data that employing obtains by relevant empirical model are revised some parameter in the numerical model, makes revised model can react the process of the kinematic behavior of practical structures more accurately.With the closely-related damage diagnosis method that is based on model of model correction---with revised matrix compare with the matrix that originally was associated as the damage index can judge the position of damage and the degree of damage.

The model correction is divided into many methods according to the type of the parameter that will revise and the measurement data of use.Usually, model modification method can be divided into two big classes: direct matrix type method and indirect physical characteristics method of adjustment.First method is non-alternative manner, directly quality and stiffness matrix is revised.When the characteristic close of correction model and empirical model, this method is effectively, but the model that obtains does not often have physical significance.Second method is then revised by the adjustment to parameter, more is close to physical significance, for each finite element or set correction factor for each design parameter of each finite element independently.This method is regarded as the developing direction of correction technique, but when using because iterative computation can spend more machine the time, causes inefficiency.

Ocean structures such as engineering structure, particularly ocean platform, complex structure, bulky, involve great expense.Because residing marine environment is very complicated, on the one hand, marine environment kinetic factor, environmental corrosion, member defective, mechanical damage can cause the variation of the rigidity of structure; On the other hand, marine growth adheres to, the change of platform device or oil storage (water) must cause the variation of architecture quality.Therefore, variation how to consider practical structures has the model correction of physical significance, and the modeling of offshore engineering structures such as ocean platform is even more important.

Summary of the invention

It is too much when the present invention does not have actual physics meaning or iterative computation cost machine for solving the structural model modification method that exists in the prior art, problems such as inefficiency, new model modification method-cross over model intersection modal method is proposed, this method is revised rigidity and mass matrix simultaneously, have direct matrix and indirect physical characteristics concurrently and adjust the advantage of method, do not need iteration, when saving machine, and can keep the physics contiguity of structural model.

Structure finite element numerical model and experiment realistic model mainly are embodied in the difference of the model frequency and the vibration shape, revise these modal parameters, will adjust by stiffness matrix and mass matrix to finite element model.Make its kinematic behavior and practical structures coupling.Therefore for each unit of finite element model, its stiffness matrix and mass matrix have two correction factors respectively.Relatively calculating by to structure finite element numerical model and experiment realistic model obtains the correction factor of each unit, thereby stiffness matrix and mass matrix is revised, and reaches the purpose of model correction.

For solving the problems of the technologies described above, the present invention is achieved by the following technical solutions:

A kind of structural model modification method that utilizes cross over model intersection mode may further comprise the steps:

A) set up structural finite element model with computer software;

B) modal parameter of said structure finite element model is calculated and data storage is gone in the private memory;

C) utilize the structural dynamic response data of sensor test empirical model and obtain modal parameter information, be stored in the described private memory by the mode recognition technology;

D) utilize the modal parameter of structural finite element model and empirical model, carry out the structural model correction, that is: from described private memory, read above-mentioned steps b), c) in stored parameters information, and from structural finite element model, extract N _iRank mode extracts N from empirical model _jRank mode, by the intersection of structural finite element model and empirical model, and the mode of same order does not intersect to form cross over model intersection modal equations, is written as

Matrix form has: C α+E β=f

C and E are respectively N in the formula _m* N _kRank matrix and N _m* N _MThe rank matrix; α and β are N _KAnd N _MThe rank column vector; F is N _mThe rank column vector, formula can be written as thus: G γ=f

G＝[C E]

In the formula:

$\mathrm{\γ}=\left\{\begin{array}{c}\mathrm{\α}\\ \mathrm{\β}\end{array}\right\}$

Have one to be that γ solves by least square method under the known prerequisite in quality or rigidity correction term: $\widehat{\mathrm{\γ}}={\left(G^{T}G\right)}^{-1}{G}^{T}f,$ Subscript T represents transposition, $C_{n,m}={\left({\mathrm{\Φ}}_i\right)}^T{K}_n{\mathrm{\Φ}}_j^{*}{C}_M,$ E _{N, m}=-b _mD _{N, m}, f _m=b _m-1, wherein $D_{n,m}={\left({\mathrm{\Φ}}_i\right)}^T{M}_n{\mathrm{\Φ}}_j^{*}{C}_K,$ $b_m=\frac{{\mathrm{\λ}}_j^{*}}{{\mathrm{\λ}}_i},$ $C_M={\left({\mathrm{\Φ}}_i\right)}^{T}M{\mathrm{\Φ}}_j^{*},$ $C_K={\left({\mathrm{\Φ}}_i\right)}^{T}K{\mathrm{\Φ}}_j^{*},$ K and M represent the stiffness matrix and the mass matrix of structure, K respectively _nThe element stiffness matrix of representing n unit, M _nThe element mass matrix of representing n unit, Φ _i,

The Mode Shape that refers to structural finite element model and empirical model respectively, λ _iWith

Be the eigenwert of structural finite element model and empirical model, the rigidity correction factor α that COMPUTER CALCULATION is gone out _n, the mass modified factor beta _nSubstitution respectively $K^{*}=K+\underset{n=1}{\overset{N_K}{\mathrm{\Σ}}}{\mathrm{\α}}_n{K}_n$ With $M^{*}=M+\underset{n=1}{\overset{N_M}{\mathrm{\Σ}}}{\mathrm{\β}}_n{M}_n$ In, obtain revised structural finite element model.

Described structural experiment structure of models dynamic response data, itself or acceleration, and/or be speed, and/or be displacement.

Compared with prior art, advantage of the present invention and good effect are: the present invention adjusts by stiffness matrix and mass matrix to finite element model, makes its kinematic behavior and practical structures coupling.Therefore for each unit of finite element model, its stiffness matrix and mass matrix have two correction factor α and β: the α stiffness difference at each unit of works respectively; β changes at each element quality of works.Relatively calculating by to structure finite element numerical model and experiment realistic model obtains the correction factor of each unit, thereby stiffness matrix and mass matrix is revised, and reaches the purpose of model correction.The present invention has the advantage of direct matrix and indirect physical characteristics adjustment method concurrently, does not need iteration, saves computing time, has improved work efficiency, and can keep the physics contiguity of structural model.In addition, the needed actual measurement vibration shape does not need quality normalization in this method, combines with the Modal Parameter Identification technology that responds based on output, can carry out the offshore platform structure model correction under the environmental excitation, thereby this method has more actual application value.

Description of drawings

Fig. 1 is: three-dimensional frame structure finite element model figure of the present invention;

Fig. 2 is: three-dimensional frame structure analytical model and empirical model are preset correction factor;

Fig. 3 is: default coefficient and correction result factor alpha _nThe comparison of (rigidity);

Fig. 4 is: default coefficient and correction result factor beta _nThe comparison of (quality).

Embodiment

The present invention is further detailed explanation below in conjunction with the drawings and specific embodiments.

One. specific algorithm is derived as follows:

For K and M and relevant i rank eigenvalue _iWith proper vector Φ _i, have:

KΦ _i＝λ _iMΦ _i (1)

Suppose the stiffness matrix K of empirical model ^*Can be expressed as:

$K^{*}=K+\underset{n=1}{\overset{N_e}{\mathrm{\Σ}}}{\mathrm{\α}}_n{K}_n---\left(2\right)$

In the formula, K _nThe element stiffness matrix of representing n unit, N _eBe unit number, α _nIt is the correction factor that to determine.Here for simplicity, suppose that all there is a corrected parameter each unit, such as the elastic modulus of each unit.

Same, mass matrix M ^*Also can write:

$M^{*}=M+\underset{n=1}{\overset{N_e}{\mathrm{\Σ}}}{\mathrm{\β}}_n{M}_n---\left(3\right)$

M _nThe element mass matrix of representing n unit, β _nIt is the correction factor that to determine.All there is a corrected parameter each unit of same supposition, such as the density of each unit.

For K ^*And M ^*And relevant j rank eigenwert

And proper vector

Have

$K^{*}{\mathrm{\Φ}}_j^{*}={\mathrm{\λ}}_j^{*}{M}^{*}{\mathrm{\Φ}}_j^{*}---\left(4\right)$

Hereinafter,

With

The data that record in the expression experiment.

With formula (1) premultiplication

Formula (4) premultiplication (Φ _i) ^T, obtain

${\left({\mathrm{\Φ}}_j^{*}\right)}^{T}K{\mathrm{\Φ}}_i={\mathrm{\λ}}_i{\left({\mathrm{\Φ}}_j^{*}\right)}^{T}M{\mathrm{\Φ}}_i---\left(5\right)$

${\left({\mathrm{\Φ}}_i\right)}^T{K}^{*}{\mathrm{\Φ}}_j^{*}={\mathrm{\λ}}_j^{*}{\left({\mathrm{\Φ}}_i\right)}^T{M}^{*}{\mathrm{\Φ}}_j^{*}---\left(6\right)$

Because M is a symmetric matrix, then ${\left[{\left({\mathrm{\Φ}}_j^{*}\right)}^{T}M{\mathrm{\Φ}}_i\right]}^T={\left({\mathrm{\Φ}}_i\right)}^{T}M{\mathrm{\Φ}}_j^{*},$ In addition, the transposition of scalar equals itself, as ${\left[{\left({\mathrm{\Φ}}_j^{*}\right)}^{T}M{\mathrm{\Φ}}_i\right]}^T={\left({\mathrm{\Φ}}_j^{*}\right)}^{T}M{\mathrm{\Φ}}_i,$ Can obtain

${\left({\mathrm{\Φ}}_j^{*}\right)}^{T}M{\mathrm{\Φ}}_i={\left({\mathrm{\Φ}}_i\right)}^{T}M{\mathrm{\Φ}}_j^{*}---\left(7\right)$

Same, because K is a symmetric matrix, also have

${\left({\mathrm{\Φ}}_j^{*}\right)}^{T}K{\mathrm{\Φ}}_i={\left({\mathrm{\Φ}}_i\right)}^{T}K{\mathrm{\Φ}}_j^{*}---\left(8\right)$

Then,, obtain divided by formula (5) with formula (6)

$\frac{{\left({\mathrm{\Φ}}_i\right)}^T{K}^{*}{\mathrm{\Φ}}_j^{*}}{{\left({\mathrm{\Φ}}_i\right)}^{T}K{\mathrm{\Φ}}_j^{*}}=\frac{{\mathrm{\λ}}_j^{*}{\left({\mathrm{\Φ}}_i\right)}^T{M}^{*}{\mathrm{\Φ}}_j^{*}}{{\mathrm{\λ}}_i{\left({\mathrm{\Φ}}_i\right)}^{T}M{\mathrm{\Φ}}_j^{*}}---\left(9\right)$

With formula (2) and (3) substitution following formula,

$1+\underset{n=1}{\overset{N_e}{\mathrm{\Σ}}}{\mathrm{\α}}_n{C}_{n,\mathrm{ij}}=\frac{{\mathrm{\λ}}_j^{*}}{{\mathrm{\λ}}_i}(1+\underset{n=1}{\overset{N_e}{\mathrm{\Σ}}}{\mathrm{\β}}_n{D}_{n,\mathrm{ij}})---\left(10\right)$

Wherein

$C_{n,\mathrm{ij}}={\left({\mathrm{\Φ}}_i\right)}^T{K}_n{\mathrm{\Φ}}_j^{*}{C}_M---\left(11\right)$

$D_{n,\mathrm{ij}}={\left({\mathrm{\Φ}}_i\right)}^T{M}_n{\mathrm{\Φ}}_j^{*}{C}_K---\left(12\right)$

$C_M={\left({\mathrm{\Φ}}_i\right)}^{T}M{\mathrm{\Φ}}_j^{*}---\left(13\right)$

$C_K={\left({\mathrm{\Φ}}_i\right)}^{T}K{\mathrm{\Φ}}_j^{*}---\left(14\right)$

Replace ij with a new label m, formula (10) becomes

$1+\underset{n=1}{\overset{N_e}{\mathrm{\Σ}}}{\mathrm{\α}}_n{C}_{n,m}=b_m(1+\underset{n=1}{\overset{N_e}{\mathrm{\Σ}}}{\mathrm{\β}}_n{D}_{n,m})---\left(15\right)$

In the formula

$b_m=\frac{{\mathrm{\λ}}_j^{*}}{{\mathrm{\λ}}_i}---\left(16\right)$

Rearrangement formula (15) can obtain

$\underset{n=1}{\overset{N_e}{\mathrm{\Σ}}}{\mathrm{\α}}_n{C}_{n,m}-b_m\underset{n=1}{\overset{N_e}{\mathrm{\Σ}}}{\mathrm{\β}}_n{D}_{n,m}=b_m-1---\left(17\right)$

Or

$\underset{n=1}{\overset{N_e}{\mathrm{\Σ}}}{\mathrm{\α}}_n{C}_{n,m}+\underset{n=1}{\overset{N_e}{\mathrm{\Σ}}}{\mathrm{\β}}_n{E}_{n,m}=f_m---\left(18\right)$

E wherein _{N, m}=-b _mD _{N, m}, f _m=b _m-1.When from finite element model, extracting N _iRank mode extracts N from empirical model _jRank mode, formula (18) has just comprised N _m=N _i* N _jIndividual equation.These equations are called cross over model and intersect mode (CMCM) equation, because they are the intersections by two models (finite element and empirical model), and the mode of same order does not intersect to form.Be written as matrix form, have

Cα+Eβ＝f (19)

C and E are respectively N in the formula _m* N _kRank matrix and N _m* N _MThe rank matrix; α and β are N _KAnd N _MThe rank column vector; F is N _mThe rank column vector.Formula (19) can be written as thus

Gγ＝f (20)

In the formula

G＝[C E] (21)

$\mathrm{\γ}=\left\{\begin{array}{c}\mathrm{\α}\\ \mathrm{\β}\end{array}\right\}---\left(22\right)$

If N _mGreater than 2N _e, promptly equation number is more than unknown number, and that γ should solve by least square method:

$\widehat{\mathrm{\γ}}={\left(G^{T}G\right)}^{-1}{G}^{T}f---\left(23\right)$

But notice (G ^TG) order can not be greater than (2N _e-1), so (G ^TG) ^-1Do not exist.In order to address this problem, should add a subsidiary condition equation, for example, quality or rigidity correction term have one to be known.

Two. set up the three-dimensional framework finite element numerical model:

Set up a three-dimensional frame structure, structure is by the beam of level, and vertically pile element is formed, and totally 40 unit are seen shown in Figure 1ly, and it is 1m that the three-dimensional frame structure weak point is striden direction length, and long span direction length is 3m.The member length of all vertical directions is 1m.The elastic modulus E of all members is 2.1 * 10 ¹¹Pa, area of section A=2.825 * 10 ^-3m ², corresponding moment of inertia I=2.89 * 10 ^-6m ⁴

Utilize MATLAB to write finite element program, set up finite element model, as Structural Analysis Model.According to default correction factor, the empirical model of model configuration draws the modal parameter of simulation actual measurement then.According to the canonical form of three dimensions beam element, can calculate element stiffness matrix k _nWith unit (consistent) mass matrix m _nIt is 12 * 12 matrix.In this model, have 40 unit.So, the integral rigidity matrix of analytical model $K={\mathrm{\Σ}}_{n=1}^{40}{K}_n,$ For realistic model $K^{*}={\mathrm{\Σ}}_{n=1}^{40}(1+{\mathrm{\α}}_n)K_n,$ K wherein _nBe the k under the global coordinate system _nSame, the total quality matrix of analytical model and realistic model is respectively: $M={\mathrm{\Σ}}_{n=1}^{40}{M}_n$ With $M^{*}={\mathrm{\Σ}}_{n=1}^{40}(1+{\mathrm{\β}}_n)M_n.$

Three. the structural model correction:

Have 20 nodes in the structure, each node has 6 degree of freedom, so K and M are 120 * 120 matrix.In the CMCM procedure, get 60 rank mode of analytical model, the preceding two rank mode of realistic model---form 120 CMCM equations altogether and separated 80 unknown numbers.Additional is constrained to ${\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="C200610171049E00132.png"\; state="\{\{state\}\}">M</figure-callout>}}_1={\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="C200610171049E00132.png"\; state="\{\{state\}\}">M</figure-callout>}}_1^{*}$ (quality of first unit of analytical model and empirical model does not change) is correction factor β ₁Equal 0.Predefined correction factor α _nAnd β _nAll be random number, α _nBe that a class mean is 0, standard deviation is 0.2 Gaussian number, β _nBe that a class mean is 0, standard deviation is 0.1 Gaussian number, as shown in Figure 2.The mode of the frequency of analytical model and experiment and first three first order mode puts that letter criterion (MAC) value sees Table 1, table 2 before revising.Φ _iWith Φ _jMould model attitude put the letter criterion and be defined as

Preceding 10 order frequencies of table 1 (Hz) are (before revising) relatively

n(Hz)	Finite element numerical model	Empirical model
			1	6.91	6.52
2	9.36	8.88
			3	12.11	11.46
4	23.04	21.86
			5	29.36	28.06
6	38.05	36.57
			7	42.24	39.62
8	44.88	42.70
			9	51.77	48.92
10	52.37	50.40

First three first order mode MAC value of table 2 (before revising)

Mode	1	2	3
				MAC	0.9994	0.9917	0.9977

Can obtain the correction factor α of stiffness matrix after the correction _n(n=1 ... 40) as shown in Figure 3.Absolute error between default correction factor and the correction factor that obtains is 10 ^-7The order of magnitude on, as shown in Figure 4.Same, the correction factor β of revised mass matrix _n(n=1 ... 40) and with the error of default correction factor see Fig. 5 and Fig. 6.Notice because of additional condition, β ₁Error be 0.Above numerical result shows that the correction factor that calculates by the CMCM method can be good at meeting predefined value, and error is enough to neglect.By the correction factor that obtains, can calculate revised stiffness matrix K ^*With mass matrix M ^*, and obtain revising the frequency of back model and the MAC value of first three rank Mode Shape through feature calculation, see Table 3 and table 4.Can be it can be seen from the table, revised model can well be represented the kinetic parameter of empirical model.

Preceding 10 order frequencies of table 3 (Hz) relatively (are revised the back)

n(Hz)	Correction model	Empirical model
				1	6.52	6.52
2	8.88	8.88
			3	11.46	11.46
4	21.86	21.86
			5	28.06	28.06
6	36.57	36.57
			7	39.62	39.62
8	42.70	42.70
			9	48.92	48.92
10	50.40	50.40

First three first order mode MAC value of table 4 (revising the back)

Mode	1	2	3
				MAC	1.0000	1.0000	1.0000

Claims (3)

1. one kind is utilized cross over model to intersect the structural model modification method of mode, it is characterized in that: may further comprise the steps:

A) set up structural finite element model with computer software;

B) modal parameter of said structure finite element model is calculated and data storage is gone in the private memory;

C) utilize the structural dynamic response data of sensor test empirical model and obtain modal parameter information, be stored in the described private memory by the mode recognition technology;

D) utilize the modal parameter of structural finite element model and empirical model, carry out the structural model correction, that is: from described private memory, read above-mentioned steps b), c) in stored parameters information, and from structural finite element model, extract N _iRank mode extracts N from empirical model _jRank mode, by the intersection of structural finite element model and empirical model, and same order not

Mode intersects to form cross over model intersection modal equations, is written as matrix form, has:

Cα+Eβ＝f

C and E are respectively N in the formula _m* N _kRank matrix and N _m* N _MThe rank matrix; α and β are N _KAnd N _MThe rank column vector; F is N _mThe rank column vector, formula can be written as thus: G γ=f

In the formula: G=[C E]

$\mathrm{\&gamma;}=\left\{\begin{array}{c}\mathrm{\&alpha;}\\ \mathrm{\&beta;}\end{array}\right\}$

Have one to be that γ solves by least square method under the known prerequisite in quality or rigidity correction term: $\widehat{\mathrm{\&gamma;}}={\left(G^{T}G\right)}^{-1}{G}^{T}f,$ Subscript T represents transposition, $C_{n,m}={\left({\mathrm{\&Phi;}}_i\right)}^T{K}_n{\mathrm{\&Phi;}}_j^{*}{C}_M,$ E _{N, m}=-b _mD _{N, m}, f _m=b _m-1, wherein $D_{n,m}={\left({\mathrm{\&Phi;}}_i\right)}^T{M}_n{\mathrm{\&Phi;}}_j^{*}{C}_K,$ $b_m=\frac{{\mathrm{\&lambda;}}_j^{*}}{{\mathrm{\&lambda;}}_i},$ $C_M={\left({\mathrm{\&Phi;}}_i\right)}^{T}M{\mathrm{\&Phi;}}_j^{*},$ $C_K={\left({\mathrm{\&Phi;}}_i\right)}^{T}K{\mathrm{\&Phi;}}_j^{*},$ K and M represent the stiffness matrix and the mass matrix of structure, K respectively _nThe element stiffness matrix of representing n unit, M _nThe element mass matrix of representing n unit, Φ _i,

The Mode Shape that refers to structural finite element model and empirical model respectively, λ _iWith

Be the eigenwert of structural finite element model and empirical model, the rigidity correction factor α that COMPUTER CALCULATION is gone out _n, the mass modified factor beta _nSubstitution respectively $K^{*}=K+\underset{n=1}{\overset{N_K}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_n{K}_n$ With $M^{*}=M+\underset{n=1}{\overset{N_M}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_n{M}_n$ In, obtain revised structural finite element model.

2. the cross over model that utilizes according to claim 1 intersects the structural model modification method of mode, it is characterized in that: the structural dynamic response data of described empirical model, and itself or acceleration, and/or be speed, and/or be displacement.

3. the cross over model that utilizes according to claim 1 intersects the structural model modification method of mode, it is characterized in that: be suitable for carrying out the offshore platform structure model correction under the environmental excitation.

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