CN113836621A - Structure state/parameter/load joint identification method based on unscented transformation - Google Patents

Structure state/parameter/load joint identification method based on unscented transformation Download PDF

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CN113836621A
CN113836621A CN202111054039.8A CN202111054039A CN113836621A CN 113836621 A CN113836621 A CN 113836621A CN 202111054039 A CN202111054039 A CN 202111054039A CN 113836621 A CN113836621 A CN 113836621A
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王婷
万志敏
曹健
施水娟
陆琼晔
张朝晖
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Nantong Vocational College
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Abstract

The invention discloses a structure state/parameter/load joint identification method based on unscented transformation, which comprises the steps of firstly, constructing an augmented state vector containing a structure modal state and an uncertain structure parameter, and establishing a state transfer equation and an observation equation of a linear system; establishing a modal state transfer equation and an observation equation of the time discretization of the linear system containing the process noise; establishing an improved GDF filter fusing strain response and acceleration response based on the non-linear system processing idea of unscented transformation; identifying a structure augmentation state and an unknown load by improving a GDF filter; and fifthly, identifying the modal state as a structural state in a physical space. The invention improves the traditional GDF algorithm, enables the GDF algorithm to be directly applied to nonlinear system filtering, processes the nonlinearity in the system based on the unscented transformation method, improves the identification precision to be more than the second order, improves the calculation efficiency and relieves the false low-frequency drift problem of displacement/load identification signals.

Description

Structure state/parameter/load joint identification method based on unscented transformation
Technical Field
The invention belongs to the technical field of structural health monitoring, and particularly relates to a structure state/parameter/load joint identification method based on unscented transformation.
Background
The first inverse problem in the field of structure dynamics is parameter identification, which means that easily measured structural response data (such as displacement, velocity, acceleration or strain signals) are used in combination with known dynamic loads to solve structural parameters. The second inverse problem is load identification, which means the use of easily measured structural response data in combination with known system characteristics to reverse the dynamic load. In recent years, the structure dynamic response reconstruction has received attention of a plurality of scholars, and is particularly applied to the technical field of structural health monitoring, and the meaning of the reconstruction is that all position responses of a structure are completely identified according to structural loads and system characteristics by using a structure response which is easy to measure. However, the above three single identification problems are difficult to implement in engineering practice, because the possible loads or some parameters of the structural system are unknown, and therefore, it is of great practical significance to perform joint identification of the structural state (displacement, velocity)/parameters/loads by using a small number of measurement signals.
Although some kalman-like filtering methods are used for joint identification of structural states/parameters/loads, the first-order linearization idea based on taylor expansion in extended kalman filtering is basically adopted, and the identification precision is only one order, so that the prior art needs to be further improved to improve the identification precision.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a structure state/parameter/load joint identification method based on unscented transformation, which solves the technical problems that the structure state/parameter/load joint identification method in the prior art is used for structure state/parameter/load joint identification, but basically adopts the Taylor expansion first-order linearization idea based on the extended Kalman filtering, the identification precision is only first order, the identification precision is low, and the false low-frequency drift of displacement and load identification is caused.
The technical scheme adopted by the invention is as follows:
a structure state/parameter/load joint identification method based on unscented transformation comprises the following steps:
s1: introducing modal coordinate transformation, constructing an augmented state vector containing structural modal states and uncertain structural parameters, and establishing a state transfer equation and an observation equation of a linear system; the method comprises the following specific steps:
s101: introducing a modal coordinate transformation p (t) ═ q (t), where Φ is a modal shape matrix, q (t) is a node displacement vector with respect to time t, and p (t) is a modal displacement vector with respect to time t;
s102: constructing augmented state vectors containing structural states and uncertain structural parameters
Figure BDA0003240456420000021
Wherein the structural state includes displacement and velocity, α ═ α1 α2 … αα]TAn uncertainty parameter representing a structure;
s103, establishing a state transfer equation and an observation equation of the linear system, wherein the equation is as follows:
Figure BDA0003240456420000022
Figure BDA0003240456420000023
wherein the content of the first and second substances,
Figure BDA0003240456420000024
is a modal velocity vector with respect to time t,
Figure BDA0003240456420000025
For the modal acceleration vector over time t, Λ is a normalized modal frequency matrix, Γ is a modal damping matrix, u (t) is the external load excitation over time t, BuIs the position influence matrix of the external load vector, y (t) denotes the acceleration measurement response with respect to time t, H [ -H [ ]0ΦΛ -H0ΦΓ]，D＝H0ΦΦTBu，H0The method comprises the steps of representing a position influence matrix of an acceleration measurement signal for system identification, wherein a matrix D is a reversible matrix, and a superscript T represents the transpose of the matrix or a vector;
s2: establishing a modal state transfer equation and an observation equation of the linear system time discretization containing the process noise, wherein the following equations are shown:
zk+1＝f(zk,uk)+wk；k＝1,2…N；
yk＝h(zk)+Dkuk+vk；k＝1,2…N；
wherein the subscript k denotes the kth sampling instant, N is a positive integer, zkAn augmented state vector, u, representing the kth sampling instantkRepresenting the excitation of the external load at the kth sampling instant, ykRepresenting the acceleration measurement response at the kth sampling instant, wkRepresenting the system noise at the k-th sampling instant, the mean and variance are set to 0 and G, respectivelykThe mean and variance are assumed to be 0 and G, respectivelyk；vkRepresenting the observed noise at the kth sampling instant, with the mean and variance set to 0 and R, respectivelyk；f(zk,uk) With respect to vector z in the transfer equation representing modal statek、ukA non-linear function of h (z)k) Representing z in an observation equation with respect to a vectorkA non-linear function of (d);
s3: setting an initial value and a variance value of an augmentation state vector, and establishing an improved GDF filter fusing strain response and acceleration response based on a nonlinear system processing idea of unscented transformation;
the unscented transformation does not perform a linear approximation to the non-linear equations f and h in step S2 at the estimation points, but determines sampling points near the estimation points using the unscented transformation, and approximates the probability density function of the state with the gaussian density represented by these sampling points.
S4: according to the structure dynamic acceleration response and the strain response measured in real time, identifying a structure augmentation state and an unknown load through an improved GDF filter fusing the strain response and the acceleration response;
s5: transformation of p by modal coordinatesk|k＝Φqk|kThe modal state is identified as a structural state in physical space.
The applicant earlier filed a Chinese patent, the name of the invention is: a structure state/parameter/load combined identification method based on expanded GDF is disclosed in the application number: 2021103547265, the application optimizes on this basis. Compared with the method for processing the nonlinearity in the system by adopting Taylor expansion first-order linearization in the prior patent application, the method obviously has higher precision and reaches more than second-order precision. In addition, the strain response and acceleration response fusion strategy is simple and convenient to operate in practical application, the problem of false low-frequency drift of displacement and load can be effectively solved, and the identification precision is improved.
Further optimization, in step S3, based on the non-linear system processing idea of the unscented transformation, an improved GDF filter is established that fuses the strain response and the acceleration response, including the following four steps:
step S301: defining a vector
Figure BDA0003240456420000031
Respectively true value zk、ukIn the observation vector (y)0,y1,y2,…,yk) The posterior estimate of the state variance matrix is assumed to be
Figure BDA0003240456420000032
Giving an initial value of an augmented state vector
Figure BDA0003240456420000033
Sum variance value
Figure BDA0003240456420000034
Step S302: and a load identification step, which comprises the following formula:
Figure BDA0003240456420000035
πi,k|k-1＝h(zi,k|k-1)；
Figure BDA0003240456420000036
Figure BDA0003240456420000037
Figure BDA0003240456420000041
Figure BDA0003240456420000042
Figure BDA0003240456420000043
Figure BDA0003240456420000044
wherein z isk|k-1Is composed of
Figure BDA0003240456420000045
2L +1 Sigma point sets sampled after unscented transformation, L denotes the dimension of the state, zi,k|k-1Namely the ith Sigma point; λ and κ are two different scaling parameters, respectively, where λ ═ θ2(L + κ) -L to reduce the overall prediction error; matrix array
Figure BDA0003240456420000046
Is a semi-positive definite matrix; the choice of θ controls the distribution of the sampling points and is usually set to a small positive number, such as 0.001.
In the formula (I), the compound is shown in the specification,
Figure BDA0003240456420000047
and is
Figure BDA0003240456420000048
The ith column representing the square root of the matrix;
Figure BDA0003240456420000049
respectively, the weight values corresponding to the sampled Sigma points, vεkStrain epsilon for the kth sampling instantkWith variance of Rεk，DkFor the load position influence matrix at the kth sampling instant, the following is calculated:
Figure BDA00032404564200000410
ε＝Hεp＝HεΦq；
Figure BDA00032404564200000411
wherein, the superscript m is the mean value, and c is the covariance; the candidate parameter beta is not less than 0 and is a non-negative weight coefficient; hεIs a strain-displacement transfer matrix; the subscript l indicates the amount of measured strain and the subscript udof indicates the amount of unknown load;
step S303: and a measurement updating step, which comprises the following formula:
Figure BDA00032404564200000412
Figure BDA00032404564200000413
Lk＝Kk(I-DkJk)；
Figure BDA0003240456420000051
Figure BDA0003240456420000052
Figure BDA0003240456420000053
Figure BDA0003240456420000054
wherein the content of the first and second substances,
Figure BDA0003240456420000055
the variance matrix for the augmented state at the kth sampling instant,
Figure BDA0003240456420000056
a covariance matrix of the load and the augmented state at the kth sampling moment;
step S304: the time updating step comprises the following formula:
Figure BDA0003240456420000057
Figure BDA0003240456420000058
Figure BDA0003240456420000059
the UT conversion implementation method comprises the steps of selecting a plurality of sampling points in original state distribution according to a certain rule, and enabling the mean value and the covariance of the sampling points to be equal to the mean value and the covariance of the original state distribution; and substituting the points into a nonlinear function to correspondingly obtain a nonlinear function value point set, and solving the mean value and the covariance after transformation through the point set. The resulting nonlinear transformed mean and covariance accuracies have at least 2 nd order accuracy (Taylor sequence expansion). For a gaussian distribution, a 3 rd order accuracy can be achieved. The selection of its sampling points is based on the correlation columns of the square root of the prior mean and prior covariance matrices.
Further optimization, in step S302, k is another scaling parameter, generally taking the value of 0 or 3-L, and it should be ensured that the matrix is
Figure BDA00032404564200000510
Is a semi-positive definite matrix. ,
the candidate parameter β ≧ 0 is a non-negative weight coefficient, which can incorporate the moments of the higher-order terms in the equation, so as to include the influence of the higher-order terms, which is 2 in the case of gaussian distribution.
Further preferably, in step S4, the structure augmentation state vector is identified by the improved GDF filter that combines the strain response and the acceleration response according to the structure dynamic acceleration response and the strain response measured in real time
Figure BDA0003240456420000061
And unknown load
Figure BDA0003240456420000062
The structure augmented state vector contains modal state and uncertainty structure parameters; vector quantity
Figure BDA0003240456420000063
Is the true value zkIn the observation vector (y)0,y1,y2,…,yk) A posterior estimate of;
Figure BDA0003240456420000064
is the true value ukIn the observation vector (y)0,y1,y2,…,yk) The posterior estimates of the following.
Compared with the prior art, the invention has the following beneficial effects:
1. compared with the prior art that the nonlinearity in the system is processed by adopting a Taylor expansion first-order linearization mode, the method obviously has higher precision and reaches more than second-order precision.
2. The strain response and acceleration response fusion strategy is simple and convenient to operate in practical application, the problem of false low-frequency drift of displacement and load can be effectively solved, and the identification precision is improved.
3. The application of the modal reduction method improves the calculation efficiency and is suitable for practical engineering application.
Drawings
FIG. 1 is a schematic flow chart of a structure state/parameter/load joint identification method based on unscented transformation according to the present invention;
fig. 2 is a schematic view of a truss in an embodiment of the invention: wherein, fig. 2(a) is a schematic diagram of a plane truss structure, and fig. 2(b) is a schematic diagram of a truss finite element model and sensor arrangement;
FIG. 3 shows the method of the invention for a load u1(t) the result of the recognition; wherein, FIG. 3(a) loads u1FIG. 3(b) is a partial enlarged view of 13-13.25s in FIG. 3 (a);
FIG. 4 shows the method of the invention for a load u2The result of the recognition of (1); wherein, FIG. 4(a) shows the load u2(t) recognition results, FIG. 4(b) is a partial enlarged view of 12-12.05s in FIG. 4 (a);
FIG. 5 shows the theoretical value and the identification value of the vertical displacement of the node 6 according to the method of the present invention; fig. 5(a) shows a theoretical value and an identification value of the vertical displacement of the node 6, and fig. 5(b) shows a theoretical value and an identification value of the vertical velocity of the node 6.
Detailed Description
In order to make the purpose and technical solution of the present invention clearer, the following will clearly and completely describe the technical solution of the present invention with reference to the embodiments of the present invention.
Example 1:
as shown in fig. 1, a structure state/parameter/load joint identification method based on unscented transformation includes the following steps:
step S1, introducing modal coordinate transformation p (t) ═ Φ q (t), where Φ is a modal shape matrix, q (t) is a node displacement vector with respect to time t, and p (t) is a modal displacement vector with respect to time t;
constructing augmented state vectors containing structural states and uncertain structural parameters
Figure BDA0003240456420000071
Wherein the structural state includes displacement and velocity, α ═ α1 α2 … αα]TAn uncertainty parameter representing a structure;
establishing a state transfer equation and an observation equation of a linear system, wherein the following formulas are shown:
Figure BDA0003240456420000072
Figure BDA0003240456420000073
wherein the content of the first and second substances,
Figure BDA0003240456420000076
is a modal velocity vector with respect to time t,
Figure BDA0003240456420000075
For the modal acceleration vector over time t, Λ is a normalized modal frequency matrix, Γ is a modal damping matrix, u (t) is the external load excitation over time t, BuIs the position influence matrix of the external load vector, y (t) denotes the acceleration measurement response with respect to time t, H [ -H [ ]0ΦΛ -H0ΦΓ]，D＝H0ΦΦTBu，H0The method comprises the steps of representing a position influence matrix of an acceleration measurement signal for system identification, wherein a matrix D is a reversible matrix, and a superscript T represents the transpose of the matrix or a vector;
step S2, establishing a modal state transfer equation and an observation equation of the linear system time discretization containing process noise, as shown in the following formulas:
zk+1＝f(zk,uk)+wk；k＝1,2…N；
yk＝h(zk)+Dkuk+vk；k＝1,2…N；
wherein the subscript k denotes the kth sampling instant, N is a positive integer, zkAn augmented state vector, u, representing the kth sampling instantkRepresenting the excitation of the external load at the kth sampling instant, ykRepresenting the acceleration measurement response at the kth sampling instant, wkRepresenting the system noise at the k-th sampling instant, the mean and variance are set to 0 and G, respectivelykThe mean and variance are assumed to be 0 and G, respectivelyk；vkRepresenting the observed noise at the kth sampling instant, with the mean and variance set to 0 and R, respectivelyk；f(zk,uk) With respect to vector z in the transfer equation representing modal statek、ukA non-linear function of h (z)k) Representing z in an observation equation with respect to a vectorkA non-linear function of (d);
step S3, establishing an improved GDF filter that fuses strain response and acceleration response: the method comprises the following four steps:
step S301: vector quantity
Figure BDA0003240456420000081
Is the true value zkIn the observation vector (y)0,y1,y2,…,yk) A posterior estimate of;
Figure BDA0003240456420000082
is the true value ukIn the observation vector (y)0,y1,y2,…,yk) A posterior estimate of;
the state variance matrix is assumed to be
Figure BDA0003240456420000083
Giving an initial value of an augmented state vector
Figure BDA0003240456420000084
Sum variance value
Figure BDA0003240456420000085
Step S302, load identification step: the formula includes:
Figure BDA0003240456420000086
πi,k|k-1＝h(zi,k|k-1)；
Figure BDA0003240456420000087
Figure BDA0003240456420000088
Figure BDA0003240456420000089
Figure BDA00032404564200000810
Figure BDA00032404564200000811
Figure BDA00032404564200000812
wherein z isk|k-1Is composed of
Figure BDA00032404564200000813
2L +1 Sigma point sets sampled after unscented transformation, L denotes the dimension of the state, zi,k|k-1I.e. the ith Sigma point, λ ═ θ2(L + κ) -L is a scaling parameter used to reduce the overall prediction error. The choice of θ controls the distribution of the sampling points and is usually set to a small positive number, such as 0.001. Kappa is another scaling parameter, typically 0 or 3-L, which should ensure that the matrix is
Figure BDA00032404564200000814
Is a semi-positive definite matrix. In the formula (I), the compound is shown in the specification,
Figure BDA00032404564200000815
and is
Figure BDA00032404564200000816
The ith column representing the square root of the matrix.
Figure BDA00032404564200000817
Respectively, the weight values corresponding to the sampled Sigma points, vεkStrain epsilon for the kth sampling instantkWith variance of Rεk，DkFor the load position influence matrix at the kth sampling instant, the following is calculated:
Figure BDA0003240456420000091
ε＝Hεp＝HεΦq；
Figure BDA0003240456420000092
where the superscript m is the mean and c is the covariance. The candidate parameter β ≧ 0 is a non-negative weight coefficient, which can combine the moments of the higher-order terms in the equation, so as to include the influence of the higher-order terms, and in general, for gaussian distribution, β ═ 2 is taken. HεIs a strain-displacement transfer matrix. The subscript l indicates the amount of measured strain and the subscript udof indicates the amount of unknown load.
Step S303 measurement update step: the formula includes:
Figure BDA0003240456420000093
Figure BDA0003240456420000094
Lk＝Kk(I-DkJk)；
Figure BDA0003240456420000095
Figure BDA0003240456420000096
Figure BDA0003240456420000097
Figure BDA0003240456420000098
wherein the content of the first and second substances,
Figure BDA0003240456420000099
is the k-thA variance matrix of the augmented state for each sampling instant,
Figure BDA00032404564200000910
a covariance matrix of the load and the augmented state at the kth sampling moment;
step S304 time update step: the formula includes:
Figure BDA00032404564200000911
Figure BDA0003240456420000101
Figure BDA0003240456420000102
step S4, identifying a structure augmentation state vector through an improved GDF filter fusing strain response and acceleration response according to the structure dynamic acceleration response and strain response measured in real time
Figure BDA0003240456420000103
And unknown load
Figure BDA0003240456420000104
The structure augmented state vector contains modal state and uncertainty structure parameters; vector quantity
Figure BDA0003240456420000105
Is the true value zkIn the observation vector (y)0,y1,y2,…,yk) A posterior estimate of;
Figure BDA0003240456420000106
is the true value ukIn the observation vector (y)0,y1,y2,…,yk) A posterior estimate of;
step S5, changing according to the modal coordinateTrade pk|k＝Φqk|kThe modal state is identified as a structural state in physical space.
Comparative example 1:
comparative example 1, in order to identify the state/parameter/load of the structure using only a part of the acceleration signal as the measurement response, is different from the present invention in step 3, and the other steps are the same as in example 1.
Step 3 of comparative example 1: the method comprises the following four steps of giving an initial value and a variance value of an augmentation state vector, and establishing an improved GDF filter under the condition of only adopting partial acceleration measurement signals:
step S301 (initialization): defining a vector
Figure BDA0003240456420000107
Respectively true value zk、ukIn the observation vector (y)0,y1,y2,…,yk) The posterior estimate of the state variance matrix is assumed to be
Figure BDA0003240456420000108
Giving an initial value of an augmented state vector
Figure BDA0003240456420000109
Sum variance value
Figure BDA00032404564200001010
Step S302 (load identification step): the formula includes:
Figure BDA00032404564200001011
πi,k|k-1＝h(zi,k|k-1)；
Figure BDA00032404564200001012
ek＝h(zk|k-1)-E[h(zk|k-1)]+vk；
Figure BDA0003240456420000111
Figure BDA0003240456420000112
Figure BDA0003240456420000113
Figure BDA0003240456420000114
step S303 measurement update step: the formula includes:
Figure BDA0003240456420000115
Figure BDA0003240456420000116
Lk＝Kk(I-DkJk)；
Figure BDA0003240456420000117
Figure BDA0003240456420000118
Figure BDA0003240456420000119
Figure BDA00032404564200001110
wherein the content of the first and second substances,
Figure BDA00032404564200001111
the variance matrix for the augmented state at the kth sampling instant,
Figure BDA00032404564200001112
a covariance matrix of the load and the augmented state at the kth sampling moment;
step S304 time update step: the formula includes:
Figure BDA00032404564200001113
Figure BDA00032404564200001114
Figure BDA00032404564200001115
comparative example 2:
in this embodiment, the technical solution with the application number of 2021103547265, named as a structure state/parameter/load joint identification method based on expanded GDF, is adopted, and details are not repeated.
The following example analyses were carried out for example 1 and comparative examples 1, 2:
as shown in FIG. 2, the object is a plane truss, as shown in FIG. 2(a), which comprises 31 rod units, and the cross-sectional dimension of each rod is uniform, the length of the rod unit arranged horizontally is 2m, and the length of the rod unit arranged at an angle of 45 degrees is
Figure BDA0003240456420000121
The common structural parameters for all rods are as follows: the cross-sectional area of the rod unit was 8.95X 10-5m2The modulus of elasticity is 2X 107Pa, density 7.85X 103kg/m3. Each rod unit in this example is a lumped mass unit, consisting of two nodes, each node having 2 degrees of freedom in the lateral and longitudinal directions, and nodes 1 and 17 being fixed constraints. The damping of the structural system is assumed to be proportional C ═ γ M + δ K, and the damping coefficients γ ═ 0.1523 and δ ═ 4.6203 × 10, respectively-4. Two external loads act on the node 4 and the node 9 respectively and are vertical forces, i.e. a load u1Using a double sinusoidal excitation pattern
u1(t)＝40sin(10πt)+30sin(20πt)；
And the load u2(t) takes the form of random excitation.
The black squares in fig. 2(b) represent the positions of the acceleration sensor arrangements, and 6 acceleration sensor arrangements are arranged at the nodes of 2, 3, 5, 7, 8, and 10, respectively. The stiffness values of the 6 rod units 5, 7, 10, 14, 15 and 17 are uncertain and need to be identified in association with the external load, assuming initial values of 759.5, 633.0, 1342.5, 1163.5, 759.5, 633.0N/m, respectively. The first 7 dominant modes are used for load/state/parameter identification of the structure. And 7 acceleration measurement signals and 2 strains are selected to participate in identification calculation, namely vertical acceleration response signals of nodes 2, 3, 5, 7, 8 and 10, horizontal acceleration response signals of a node 9 and vertical strain responses of units 6 and 17. 5% of the ambient noise is added to all measured responses.
Using the extended GDF filter of step 3 of example 1, two external loads u were obtained1(t) and u2The recognition results of (t) are shown in FIGS. 3 to 4, respectively, in which FIG. 3(a) shows the load u1(t) recognition results, FIG. 3(b) is a partial enlarged view of 13-13.25s in FIG. 3 (a); FIG. 4(a) shows the load u2(t), FIG. 4(b) is a partial enlarged view of 129-12.05s in FIG. 4 (a); from these 4 figures it can be seen that the load identification value curve is close to the true value. The state values (displacement and velocity responses) of all nodes are also identified, as shown in fig. 5, which is a graph comparing the theoretical values and the identified values of the vertical displacement and the velocity of the node 6, wherein fig. 5(a) is the theoretical value and the identified value of the vertical displacement of the node 6, and fig. 5(b) is the theoretical value and the identified value of the vertical velocity of the node 6. As is apparent from the figuresThe displacement and speed identification values are good in result, relative errors are small, and the phenomenon of false low-frequency drift caused by load and displacement when only acceleration measurement response is adopted for identification does not occur.
In addition, Table 1 shows the Relative Error values (Relative Error: RE) of the three methods of example one, comparative example 1 and comparative example 2, which are calculated by
Figure BDA0003240456420000131
Where s represents an identified physical quantity such as load, displacement, parameter, etc. As can be seen from table 1:
(1) the method of comparative example 1 (without strain measurement response) generates obvious low-frequency drift phenomenon because only acceleration measurement response is adopted for the identification system, so that the relative errors of the identified load and displacement values are large, and particularly, the displacements of the load 1 and the node 8 reach 28.91 percent and 32.23 percent respectively; (2) the method adopts the strain response and the acceleration response as the measurement response to identify the system, thereby avoiding the low-frequency drift phenomenon; (3) the accuracy of the method of the present invention is higher compared to the method of comparative example 2 because the present invention uses an unscented transformation to approximate the recognition system nonlinearity, which is higher than using a taylor first order linearized approximation (comparative example 2).
TABLE 1 identification of relative errors for the three methods
Figure BDA0003240456420000132
The embodiments of the present invention are not limited to the specific embodiments described herein, but rather, the embodiments are merely preferred embodiments of the present invention, and are not intended to limit the scope of the present invention. That is, all equivalent changes and modifications made according to the content of the claims of the present invention should be regarded as the technical scope of the present invention.

Claims (4)

1. A structure state/parameter/load joint identification method based on unscented transformation is characterized by comprising the following steps:
s1: introducing modal coordinate transformation, constructing an augmented state vector containing structural modal states and uncertain structural parameters, and establishing a state transfer equation and an observation equation of a linear system; the method comprises the following specific steps:
s101: introducing a modal coordinate transformation p (t) ═ q (t), where Φ is a modal shape matrix, q (t) is a node displacement vector with respect to time t, and p (t) is a modal displacement vector with respect to time t;
s102: constructing augmented state vectors containing structural states and uncertain structural parameters
Figure FDA0003240456410000011
Wherein the structural state includes displacement and velocity, α ═ α1 α2…αα]TAn uncertainty parameter representing a structure;
s103, establishing a state transfer equation and an observation equation of the linear system, wherein the equation is as follows:
Figure FDA0003240456410000012
Figure FDA0003240456410000013
wherein the content of the first and second substances,
Figure FDA0003240456410000014
is a modal velocity vector with respect to time t,
Figure FDA0003240456410000015
For the modal acceleration vector over time t, Λ is a normalized modal frequency matrix, Γ is a modal damping matrix, u (t) is the external load excitation over time t, BuIs a position influence matrix of the external load vector, y (t) representsWith respect to time t acceleration measurement response, H [ -H [ ]0ΦΛ -H0ΦΓ]，D＝H0ΦΦTBu，H0The method comprises the steps of representing a position influence matrix of an acceleration measurement signal for system identification, wherein a matrix D is a reversible matrix, and a superscript T represents the transpose of the matrix or a vector;
s2: establishing a modal state transfer equation and an observation equation of the linear system time discretization containing the process noise, wherein the following equations are shown:
zk+1＝f(zk,uk)+wk；k＝1,2…N；
yk＝h(zk)+Dkuk+vk；k＝1,2…N；
wherein the subscript k denotes the kth sampling instant, N is a positive integer, zkAn augmented state vector, u, representing the kth sampling instantkRepresenting the excitation of the external load at the kth sampling instant, ykRepresenting the acceleration measurement response at the kth sampling instant, wkRepresenting the system noise at the k-th sampling instant, the mean and variance are set to 0 and G, respectivelykThe mean and variance are assumed to be 0 and G, respectivelyk；vkRepresenting the observed noise at the kth sampling instant, with the mean and variance set to 0 and R, respectivelyk；f(zk,uk) With respect to vector z in the transfer equation representing modal statek、ukA non-linear function of h (z)k) Representing z in an observation equation with respect to a vectorkA non-linear function of (d);
s3: setting an initial value and a variance value of an augmentation state vector, and establishing an improved GDF filter fusing strain response and acceleration response based on a nonlinear system processing idea of unscented transformation;
s4: according to the structure dynamic acceleration response and the strain response measured in real time, identifying a structure augmentation state and an unknown load through an improved GDF filter fusing the strain response and the acceleration response;
s5: transformation of p by modal coordinatesk|k＝Φqk|kThe modal state is identified as a structural state in physical space.
2. The method for joint structural state/parameter/load identification based on unscented transformation according to claim 1, wherein in step S3, the step of establishing the modified GDF filter with fused strain response and acceleration response comprises the following four steps:
step S301: defining a vector
Figure FDA0003240456410000021
Respectively true value zk、ukIn the observation vector (y)0,y1,y2,…,yk) The posterior estimate of the state variance matrix is assumed to be
Figure FDA0003240456410000022
Giving an initial value of an augmented state vector
Figure FDA0003240456410000023
Sum variance value
Figure FDA0003240456410000024
Step S302: and a load identification step, which comprises the following formula:
Figure FDA0003240456410000025
πi,k|k-1＝h(zi,k|k-1)；
Figure FDA0003240456410000026
Figure FDA0003240456410000027
Figure FDA0003240456410000028
Figure FDA0003240456410000031
Figure FDA0003240456410000032
Figure FDA0003240456410000033
wherein z isk|k-1Is composed of
Figure FDA0003240456410000034
2L +1 Sigma point sets sampled after unscented transformation, L denotes the dimension of the state, zi,k|k-1Namely the ith Sigma point; λ and κ are two different scaling parameters, respectively, where λ ═ θ2(L + κ) -L to reduce the overall prediction error; matrix array
Figure FDA0003240456410000035
Is a semi-positive definite matrix; theta is a positive number;
in the formula (I), the compound is shown in the specification,
Figure FDA0003240456410000036
and is
Figure FDA0003240456410000037
The ith column representing the square root of the matrix;
Figure FDA0003240456410000038
respectively, the weight values corresponding to the sampled Sigma points, vεkStrain epsilon for the kth sampling instantkWith variance of Rεk，DkIs the k-thAnd (3) a load position influence matrix at the sampling moment is calculated as follows:
Figure FDA0003240456410000039
ε＝Hεp＝HεΦq；
Figure FDA00032404564100000310
wherein, the superscript m is the mean value, and c is the covariance; the candidate parameter beta is not less than 0 and is a non-negative weight coefficient; hεIs a strain-displacement transfer matrix; the subscript l indicates the amount of measured strain and the subscript udof indicates the amount of unknown load;
step S303: and a measurement updating step, which comprises the following formula:
Figure FDA00032404564100000311
Figure FDA00032404564100000312
Lk＝Kk(I-DkJk)；
Figure FDA0003240456410000041
Figure FDA0003240456410000042
Figure FDA0003240456410000043
Figure FDA0003240456410000044
wherein the content of the first and second substances,
Figure FDA0003240456410000045
the variance matrix for the augmented state at the kth sampling instant,
Figure FDA0003240456410000046
a covariance matrix of the load and the augmented state at the kth sampling moment;
step S304: the time updating step comprises the following formula:
Figure FDA0003240456410000047
Figure FDA0003240456410000048
Figure FDA0003240456410000049
3. the method for jointly recognizing structural states/parameters/loads based on unscented transformation according to claim 2, wherein in step S302, k is 0 or 3-L, and β is 2.
4. The method for joint structural state/parameter/load identification based on unscented transformation as claimed in claim 3, wherein in step S4, the structural augmented state vector is identified by the modified GDF filter fusing the strain response and the acceleration response according to the structural dynamic acceleration response and the strain response measured in real time
Figure FDA00032404564100000410
And unknown load
Figure FDA00032404564100000411
The structure augmented state vector contains modal state and uncertainty structure parameters; vector quantity
Figure FDA00032404564100000412
Is the true value zkIn the observation vector (y)0,y1,y2,…,yk) A posterior estimate of;
Figure FDA00032404564100000413
is the true value ukIn the observation vector (y)0,y1,y2,…,yk) The posterior estimates of the following.
CN202111054039.8A 2021-08-31 2021-08-31 Structure state/parameter/load joint identification method based on unscented transformation Withdrawn CN113836621A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114610224A (en) * 2022-01-25 2022-06-10 清华大学 Structural dynamic load identification method and virtual keyboard

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