CN111125889B - Probability sensor measuring point optimization method based on structural component importance index - Google Patents
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Abstract
The invention provides a probability sensor measuring point optimization method based on a structural component importance index, which comprises the following steps: determining structural feature parameters and a structural damage identification inversion matrix required by structural damage identification; obtaining uncertainty distribution of structural characteristic parameters by using a quantification method; constructing a functional relation between structural damage parameters and structural characteristic parameters according to the structural damage identification inversion matrix; obtaining uncertainty distribution of structural damage parameters according to the uncertainty distribution and the functional relation of the structural feature parameters; determining a change curve of service performance parameters in the process of changing damage parameters of each component of the structure; obtaining importance indexes of each component according to the change curve; constructing a weighted standard deviation norm according to uncertainty distribution and importance indexes of structural damage parameters; and constructing an optimization model according to the weighted standard deviation norm so as to optimize the probability sensor measuring points. The invention can improve the identification precision of the key structural elements so as to realize the optimal layout of the measuring points of the probability sensor.
Description
Technical Field
The invention relates to the technical field of sensor measuring point optimization, in particular to a probability sensor measuring point optimization method based on structural component importance indexes.
Background
In practical engineering, in the process of measuring structural damage, various sensors are generally arranged on a structure to perform measurement. However, because the structure of actual measurement is mostly complex, and the limitation of measurement conditions is combined, the sensors can be arranged on limited degrees of freedom, thus the measurement data is incomplete, and researchers research a method for optimizing the sensor arrangement under the limited degrees of freedom.
However, the current sensor arrangement optimization method is not directly oriented to the structural parameter identification error, and the importance of the influence of the damage parameters of each structural component on the service performance of the structural system is not considered, so that the accuracy of the structural parameter identification is not high.
Disclosure of Invention
The present invention aims to solve at least to some extent one of the technical problems in the above-described technology. Therefore, the invention aims to provide a probability sensor measuring point optimization method based on the importance index of the structural components, which can fully consider the importance of each structural component affecting the structural service performance, thereby improving the identification precision of the key structural components and realizing the optimal layout of the probability sensor measuring points.
In order to achieve the above objective, the embodiment of the present invention provides a method for optimizing a measurement point of a probability sensor based on an importance index of a structural element, including the steps of: determining structural feature parameters and a structural damage identification inversion matrix required by structural damage identification; obtaining uncertainty distribution of the structural feature parameters by using a quantification method; constructing a functional relation between structural damage parameters and the structural feature parameters according to the structural damage identification inversion matrix; obtaining the uncertainty distribution of the structural damage parameters according to the uncertainty distribution of the structural feature parameters and the functional relation; determining a change curve of service performance parameters in the process of changing damage parameters of each component of the structure; obtaining importance indexes of each component of the structure according to the change curve; constructing a weighted standard deviation norm according to the uncertainty distribution of the structural damage parameters and the importance index; constructing an optimization model of the probability sensor layout according to the weighted standard deviation norm; and optimizing the probability sensor measuring points according to the optimization model.
According to the probability sensor measuring point optimization method based on the structural component importance index, firstly, structural feature parameters required by structural damage identification and a structural damage identification inversion matrix are determined, uncertainty distribution of the structural feature parameters is obtained by utilizing a quantification method, secondly, functional relation between the structural damage parameters and the structural feature parameters is built according to the structural damage identification inversion matrix, uncertainty distribution of the structural damage parameters is obtained according to the uncertainty distribution and the functional relation of the structural feature parameters, then a change curve of service performance parameters in the structural component damage parameter change process is determined, importance indexes of the structural components are obtained according to the change curve, a weighted standard deviation norm is further built according to the uncertainty distribution and the importance indexes of the structural damage parameters, and finally, an optimization model of probability sensor layout is built according to the weighted standard deviation norm, so that the probability sensor measuring point is optimized, importance of structural service performance influence of the structural components can be fully considered, identification accuracy of the key structural components is improved, and the optimal layout of the probability sensor measuring point is achieved.
In addition, the probability sensor measuring point optimization method based on the structural component importance index provided by the embodiment of the invention can also have the following additional technical characteristics:
according to one embodiment of the invention, the structural damage identification inversion matrix is:
wherein, the liquid crystal display device comprises a liquid crystal display device,
as partial differential sign, α= [ α ] 1 ,α 2 ，…,α m ] T For the damage parameter vector to be identified, m is the number of damage parameters, and x= [ x ] 1 ,x 2 ，…,x n ] T Is the structural response vector, n is the number of responses.
Further, the uncertainty distribution of the structural feature parameter is:
x＝x c *(1+X x )
wherein, superscript "c" represents the corresponding true value, 1= [1, ], 1.] T ，X x ＝{X xi I=1, 2, …, n represents the relative error of the measured response value, and x represents the structural feature parameter vector with the error.
Further, the functional relationship between the structural damage parameter and the structural feature parameter is:
α＝S x
s is a damage identification inversion matrix, and alpha is a structural damage parameter vector.
Further, the uncertainty distribution of the structural damage parameter is:
wherein m represents the number of structural damage parameters, n represents the number of uncertainty variables, and Cov (·, ·) represents covariance.
Further, the change curve of the service performance parameter in the damage parameter change process of each component in the structure is as follows:
wherein D is i To accumulate the residual intensity index, a=min {1, srf i * }，SRF i * For the allowable degree of damage of the ith component, "1" represents that the component loses all rigidity.
Further, the importance index of each component in the structure is as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,
further, the weighted standard deviation norm is:
WSDN＝||(σ*DEWI)||
where σ is the standard deviation of the uncertainty distribution of the structural damage parameter, (·) is the Hadamard product.
Further, the optimization model is:
wherein, the liquid crystal display device comprises a liquid crystal display device,
represents the position of the ith probability sensor in the jth probability sensor layout, m is the number of probability sensors, n is the number of probability sensor schemes, Γ 0 Representing alternative possibilities for the probability sensor layout.
Further, optimizing the probability sensor measurement points according to the optimization model includes: if the number of the probability sensor schemes is limited, solving the optimization model by adopting a traversal method; and if the calculated amount of the probability sensor exceeds the calculation capacity range, solving the optimization model by adopting an intelligent optimization algorithm.
Drawings
FIG. 1 is a flow chart of a probabilistic sensor measurement point optimization method based on a structural component importance index according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a variation curve of service performance parameters during a variation of damage parameters of each component of a structure according to an embodiment of the present invention;
FIG. 3 is a schematic illustration of a simply supported beam according to one embodiment of the invention
FIG. 4 is a graph showing the trend of the maximum displacement of each unit of a simply supported beam according to an embodiment of the present invention as the damage degree of each unit structure increases;
FIG. 5 (a) is a schematic diagram of a sensor station arrangement employing condition number criteria for a different number of sensors in accordance with one embodiment of the present invention;
FIG. 5 (b) is a schematic diagram of a sensor station arrangement employing information entropy criteria for different numbers of sensors in accordance with one embodiment of the present invention;
FIG. 5 (c) is a schematic diagram of a sensor station arrangement employing standard deviation norm criteria for a different number of sensors in accordance with an embodiment of the present invention;
FIG. 5 (d) is a schematic diagram of a sensor station arrangement employing weighted standard deviation norm criteria for a different number of sensors in accordance with an embodiment of the present invention;
FIG. 6 is a diagram of weighted standard deviation norms obtained for different sensor numbers for condition number indicators, information entropy indicators, standard deviation norms, and importance indicators according to an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
FIG. 1 is a flow chart of a probabilistic sensor measurement point optimization method based on a structural component importance index according to an embodiment of the present invention.
As shown in fig. 1, the probability sensor measuring point optimization method based on the structural element importance index in the embodiment of the invention comprises the following steps:
s1, determining structural characteristic parameters and a structural damage identification inversion matrix required by structural damage identification.
Specifically, the structural damage parameter identification method can be determined, so that the structural characteristic parameters required by the structural damage identification and the structural damage identification inversion matrix are determined.
The structural damage parameter identification method can be determined as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,
is a partial differential symbol, phi is a mode shape, and alpha is a damage parameter to be identified.
Further, the structural damage identification inversion matrix may be determined as:
wherein, the liquid crystal display device comprises a liquid crystal display device,
as partial differential sign, α= [ α ] 1 ,α 2 ，…,α m ] T For the damage parameter vector to be identified, m is the number of damage parameters, and x= [ x ] 1 ,x 2 ，…,x n ] T Is the structural response vector, n is the number of responses.
S2, obtaining uncertainty distribution of the structural characteristic parameters by using a quantification method.
Specifically, an uncertainty quantification method can be used to obtain an uncertainty distribution of the structural feature parameters, where the uncertainty distribution of the structural feature parameters is:
x＝x c *(1+X x )
wherein, superscript "c" represents the corresponding true value, 1= [1, ], 1.] T ，X x ＝{X xi I=1, 2, …, n represents the relative error of the measured response value, and x represents the structural feature parameter vector with the error.
By describing the uncertain distribution of the structural feature parameters by using an uncertainty quantification method, the identification of the structural damage parameters can have physical significance.
S3, constructing a functional relation between the structural damage parameters and the structural characteristic parameters according to the structural damage identification inversion matrix.
Specifically, the functional relationship between the structural damage parameter and the structural feature parameter is:
α＝S x
s is a damage identification inversion matrix, and alpha is a structural damage parameter vector.
And S4, obtaining the uncertainty distribution of the structural damage parameters according to the uncertainty distribution and the functional relation of the structural feature parameters.
Specifically, the uncertainty distribution of structural damage parameters is:
wherein m represents the number of structural damage parameters, n represents the number of uncertainty variables, and Cov (·, ·) represents covariance.
S5, determining a change curve of the service performance parameter in the process of changing the damage parameters of each component of the structure.
Specifically, the structure can be divided into a limited number of components, then the damage parameters of the components of the structure are changed one by one, and finally the change curve of the service performance parameter of the structure along with the change of the damage parameters of the components of the structure is calculated.
More specifically, as shown in FIG. 2, the residual intensity index D may be accumulated by i Characterizing service performance parameters, namely the attention of stiffness parameter errors, in the structural component damage parameter change process:
wherein a=min {1, srf i * }，SRF i * For the allowable degree of damage of the ith component, "1" represents that the component loses all rigidity.
When the remaining intensity index D is accumulated i The larger the value, the stiffness coefficient a of the i-th component is represented i The less the impact on structural performance and on a i The recognition requirement of (2) is lower; conversely, the stiffness coefficient a of the ith component i Has a great influence on structural performance and on a i Is more demanding.
S6, obtaining importance indexes of each component of the structure according to the change curve.
In particular, can be applied to { D i Normalization processing:
further, the importance index of each component of the structure can be constructed according to the normalized result:
when the importance index is DEWI i The larger the i-th component is, the more important the structural service performance is; conversely, the less important the ith component is to structure service performance.
S7, constructing weighted standard deviation norms according to uncertainty distribution and importance indexes of the structural damage parameters.
Specifically, the weighted standard deviation norm is:
WSDN＝||(σ*DEWI)||
where σ is the standard deviation of the uncertainty distribution of the structural damage parameter, (·) is the Hadamard product. The influence of the structural damage parameter identification error on the structural service performance evaluation can be represented by the weighted standard deviation norm.
S8, constructing an optimization model of the probability sensor layout according to the weighted standard deviation norm.
Specifically, the optimization model is:
wherein, the liquid crystal display device comprises a liquid crystal display device,
represents the position of the ith probability sensor in the jth probability sensor layout, m is the number of probability sensors, n is the number of probability sensor schemes, Γ 0 Representing alternative possibilities for the probability sensor layout.
And S9, optimizing the probability sensor measuring points according to the optimization model.
Specifically, if the number of probability sensor schemes is limited, solving an optimization model by adopting a traversal method; and if the calculated amount of the probability sensor exceeds the calculation capacity range, solving the optimization model by adopting an intelligent optimization algorithm. By adopting a traversal method and an intelligent optimization algorithm aiming at different conditions, the influence of the structural damage parameter identification error on structural performance evaluation can be effectively quantified, and the optimization model can be efficiently and robustly solved.
According to the probability sensor measuring point optimization method based on the structural component importance index, firstly, structural feature parameters required by structural damage identification and a structural damage identification inversion matrix are determined, uncertainty distribution of the structural feature parameters is obtained by utilizing a quantification method, secondly, functional relation between the structural damage parameters and the structural feature parameters is built according to the structural damage identification inversion matrix, uncertainty distribution of the structural damage parameters is obtained according to the uncertainty distribution and the functional relation of the structural feature parameters, then a change curve of service performance parameters in the structural component damage parameter change process is determined, importance indexes of the structural components are obtained according to the change curve, a weighted standard deviation norm is further built according to the uncertainty distribution and the importance indexes of the structural damage parameters, and finally, an optimization model of probability sensor layout is built according to the weighted standard deviation norm so as to optimize the probability sensor measuring points, and therefore, importance of service performance influence of the structural components can be fully considered, identification accuracy of key structural components is improved, and optimal layout of the probability sensor measuring points is achieved.
The adaptability of the probability sensor measuring point optimizing method based on the structural component importance index of the invention is further described below by taking the layout optimization of the sensor measuring points on the simply supported beams as an example.
Specifically, as shown in fig. 3, the selected simply supported beams have node numbers 1,2, 21, each having two degrees of freedom, i.e., a normal translational degree of freedom and a rotational degree of freedom, and the simply supported beams have unit numbers (1)、②、...、
Each unit is an Euler beam unit, the cross section of the simply supported beam is rectangular, and the cross section area is A=b×h=0.02×0.005m 2 . In addition, the simply supported beam has a length of 1m and a material density of 7860kg/m 3 The elastic modulus was 210GPa.
Further, it is first assumed that a load with a uniform pressure of 0.01N/mm is applied to the simply supported beams, and the maximum displacement of each cell in the simply supported beams is set to 4mm, and then the structural damage parameters of each cell in the simply supported beams are reduced one by one, and the displacement of each cell in the simply supported beams is calculated.
Specifically, as shown in fig. 4, the maximum displacement of each cell in the simply supported beam increases with the degree of structural damage of each cell, i.e., the increase in SRF. Further listed in table 1 are importance indicators DEWI for all of the units in the simply supported beam, wherein a larger importance indicator DEWI for one of the units indicates that the service performance of the simply supported beam for that unit is more important, and the damage identification result of that unit is also more important for the service performance evaluation of the simply supported beam.
TABLE 1
Further, condition number criteria, i.e. CN criteria, information entropy criteria, i.e. IE criteria, standard deviation norm criteria, i.e. SDN criteria, and weighted standard deviation norm criteria, i.e. WSDN criteria, are adopted to respectively optimize the sensor measuring points in the simply supported beams, so as to respectively obtain the sensor measuring point arrangement schemes shown in fig. 5 (a), 5 (b), 5 (c) and 5 (d), and further identify structural damage parameters of the simply supported beams by using the front 8-order modal information. By comparing the sensor point arrangements shown in fig. 5 (a), 5 (b), 5 (c), 5 (d), it can be seen that the sensor point arrangement obtained by the standard deviation norm criterion SDN and the weighted standard deviation norm criterion WSDN is substantially symmetrical.
Further, as shown in fig. 6, the condition number index, i.e., CN index, the information entropy index, i.e., IE index, the standard deviation norm index, i.e., SDN index, and the importance index proposed by the present invention, i.e., DEWI index, are compared to obtain weighted standard deviation norms WSDNs under different sensor numbers, respectively. The importance index provided by the invention, namely the weighted standard deviation norm WSDN obtained by the DEWI index is always minimum, so that the effectiveness and the adaptability of the probability sensor measuring point optimization method based on the structural component importance index are shown, meanwhile, the weighted standard deviation norm WSDN is reduced along with the increase of the number of sensors, and the phenomenon is mainly caused by the fact that the increase of the number of sensors reduces the identification error of structural damage parameters.
In the present invention, unless explicitly specified and limited otherwise, the term "connected" is to be construed broadly, and for example, may be fixedly connected, detachably connected, or integrally formed; can be mechanically or electrically connected; can be directly connected or indirectly connected through an intermediate medium, and can be communicated with the inside of two elements or the interaction relationship of the two elements. The specific meaning of the above terms in the present invention can be understood by those of ordinary skill in the art according to the specific circumstances.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms are not necessarily directed to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, the different embodiments or examples described in this specification and the features of the different embodiments or examples may be combined and combined by those skilled in the art without contradiction.
Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made therein without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (10)
1. The probability sensor measuring point optimizing method based on the structural element importance index is characterized by comprising the following steps of:
determining structural feature parameters and a structural damage identification inversion matrix required by structural damage identification;
obtaining uncertainty distribution of the structural feature parameters by using a quantification method;
constructing a functional relation between structural damage parameters and the structural feature parameters according to the structural damage identification inversion matrix;
obtaining the uncertainty distribution of the structural damage parameters according to the uncertainty distribution of the structural feature parameters and the functional relation;
determining a change curve of service performance parameters in the process of changing damage parameters of each component of the structure;
obtaining importance indexes of each component of the structure according to the change curve;
constructing a weighted standard deviation norm according to the uncertainty distribution of the structural damage parameters and the importance index;
constructing an optimization model of the probability sensor layout according to the weighted standard deviation norm;
and optimizing the probability sensor measuring points according to the optimization model.
2. The probabilistic sensor site optimization method based on structural component importance index of claim 1, wherein the structural damage identification inversion matrix is:
wherein, the liquid crystal display device comprises a liquid crystal display device,
as partial differential sign, α= [ α ] 1 ,α 2 ，...,α m ] T For the damage parameter vector to be identified, m is the number of damage parameters, and x= [ x ] 1 ,x 2 ，...,x n ] T Is the structural response vector, n is the number of responses.
3. The probabilistic sensor site optimization method based on structural component importance index according to claim 2, wherein the uncertainty distribution of the structural feature parameter is:
x＝x c *(1+X x )
wherein, superscript "c" represents the corresponding true value, 1= [1, ], 1.] T ，X x ＝{X xi I=1, 2, ·, n represents the relative error of the measured response value, x represents the structural feature parameter vector with errors.
4. A probabilistic sensor site optimization method based on structural component importance indicators as claimed in claim 3, wherein the functional relationship between the structural damage parameter and the structural feature parameter is:
α＝Sx
s is a damage identification inversion matrix, and alpha is a structural damage parameter vector.
5. The probabilistic sensor site optimization method based on structural component importance index of claim 4, wherein the uncertainty distribution of the structural damage parameters is:
wherein m represents the number of structural damage parameters, n represents the number of uncertainty variables, and Cov (·, ·) represents covariance.
6. The method for optimizing measuring points of a probability sensor based on an importance index of structural elements according to claim 5, wherein a change curve of service performance parameters in a change process of damage parameters of each element in the structure is:
wherein D is i To accumulate the residual intensity index, a=min {1, srf i * }，SRF i * For the allowable degree of damage of the ith component, "1" represents that the component loses all rigidity.
7. The probabilistic sensor site optimization method based on structural component importance index of claim 6, wherein the importance index of each component in the structure is:
wherein, the liquid crystal display device comprises a liquid crystal display device,
8. the method for optimizing a sensor measurement point based on a structural element importance index according to claim 7, wherein the weighted standard deviation norm is:
WSDN＝||(σ*DEWI)||
where σ is the standard deviation of the uncertainty distribution of the structural damage parameter, (·) is the Hadamard product.
9. The probabilistic sensor site optimization method based on structural component importance index of claim 8, wherein the optimization model is:
wherein, the liquid crystal display device comprises a liquid crystal display device,
represents the position of the ith probability sensor in the jth probability sensor layout, m is the number of probability sensors, n is the number of probability sensor schemes, Γ 0 Representing alternative possibilities for the probability sensor layout.
10. The method for optimizing a probabilistic sensor site based on an importance index of a structural component according to claim 9, wherein optimizing the probabilistic sensor site according to the optimization model comprises:
if the number of the probability sensor schemes is limited, solving the optimization model by adopting a traversal method;
and if the calculated amount of the probability sensor exceeds the calculation capacity range, solving the optimization model by adopting an intelligent optimization algorithm.
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