CN111125889A - Probability sensor measuring point optimization method based on structural component importance indexes - Google Patents

Probability sensor measuring point optimization method based on structural component importance indexes Download PDF

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CN111125889A
CN111125889A CN201911242885.5A CN201911242885A CN111125889A CN 111125889 A CN111125889 A CN 111125889A CN 201911242885 A CN201911242885 A CN 201911242885A CN 111125889 A CN111125889 A CN 111125889A
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structural
parameters
damage
measuring point
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CN111125889B (en
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石庆贺
胡可军
朱福先
薛荣洁
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Jiangsu University of Technology
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Abstract

The invention provides a probability sensor measuring point optimization method based on structural component importance indexes, which comprises the following steps: determining structural characteristic parameters and a structural damage identification inversion matrix required by structural damage identification; obtaining uncertainty distribution of the structural characteristic parameters by using a quantification method; constructing a functional relation between the structural damage parameters and the structural characteristic parameters according to the structural damage identification inversion matrix; obtaining the uncertainty distribution of the structural damage parameters according to the uncertainty distribution and the functional relation of the structural characteristic parameters; determining a change curve of service performance parameters in the change process of damage parameters of all components of the structure; obtaining the importance indexes of all the components according to the change curve; constructing a weighted standard deviation norm according to the uncertainty distribution and the importance index of the structural damage parameter; and constructing an optimization model according to the weighted standard deviation norm to optimize the probability sensor measuring point. The invention can improve the identification precision of key structural elements so as to realize the optimal layout of the measuring points of the probability sensor.

Description

Probability sensor measuring point optimization method based on structural component importance indexes
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 actual engineering, when measuring structural damage, various sensors are usually arranged on the structure for measurement. However, because the actual measurement structure is mostly complex, and due to the limitation of the measurement conditions, the sensors can be mostly arranged only in the limited degree of freedom, which causes the imperfection of the measurement data, and researchers have developed a method for optimizing the sensor arrangement in the limited degree of freedom.
However, the current sensor layout optimization method is not directly oriented to structural parameter identification errors, and the importance of the damage parameters of all structural components on the service performance of a structural system is not considered, so that the accuracy of structural parameter identification is not high.
Disclosure of Invention
The present invention is directed to solving, at least to some extent, one of the technical problems in the art described above. Therefore, the invention aims to provide a probability sensor measuring point optimization method based on the importance indexes of the structural components, which can fully consider the importance of the influence of each structural component on the service performance of the structure, thereby improving the identification precision of the key structural components and realizing the optimal layout of the probability sensor measuring point.
In order to achieve the above purpose, the embodiment of the present invention provides a method for optimizing a measuring point of a probability sensor based on an importance index of a structural component, which includes the steps of: determining structural characteristic parameters and a structural damage identification inversion matrix required by structural damage identification; obtaining uncertainty distribution of the structural characteristic parameters by using a quantification method; constructing a functional relation between the structural damage parameters and the structural characteristic 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 characteristic parameters and the functional relation; determining a change curve of service performance parameters in the change process of damage parameters of each component of the structure; obtaining importance indexes of all components 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 indexes; constructing an optimization model of the probability sensor layout according to the weighted standard deviation norm; and optimizing the probability sensor measuring point according to the optimization model.
According to the probability sensor measuring point optimization method based on the structural component importance indexes, firstly, structural characteristic parameters and a structural damage identification inversion matrix required by structural damage identification are determined, uncertainty distribution of the structural characteristic parameters is obtained by a quantification method, secondly, a functional relation between the structural damage parameters and the structural characteristic parameters is established according to the structural damage identification inversion matrix, thirdly, uncertainty distribution of the structural damage parameters is obtained according to the uncertainty distribution and the functional relation of the structural characteristic parameters, thirdly, a change curve of service performance parameters in the change process of the damage parameters of all components of the structure is determined, importance indexes of all components of the structure are obtained according to the change curve, fourthly, a weighted standard deviation norm is established according to the uncertainty distribution and the importance indexes of the structural damage parameters, and lastly, an optimization model of the probability sensor layout is established according to the weighted standard deviation norm, the probability sensor measuring point is optimized, so that the influence of each component of the structure on the service performance of the structure can be fully considered, the identification precision of the key structural components is improved, and the optimal layout of the probability sensor measuring point is realized.
In addition, the probability sensor measuring point optimization method based on the structural component importance index provided by the above embodiment of the invention can also have the following additional technical features:
according to one embodiment of the present invention, the structural damage identification inversion matrix is:
Figure BDA0002306744310000021
wherein the content of the first and second substances,
Figure BDA0002306744310000022
is a partial differential sign, α ═ α12,…,αm]TFor the damage parameter vector to be identified, m is the number of damage parameters, x ═ x1,x2,…,xn]TIs a structural response vector, and n is the number of responses.
Further, the uncertainty distribution of the structural feature parameters is:
x=xc*(1+Xx)
where the superscript "c" represents the corresponding true value, 1 ═ 1,1]T,Xx={XxiI-1, 2, …, n representing the relative error of the measured response values, and x representing the erroneous structural feature parameter vector.
Further, the functional relationship between the structural damage parameter and the structural feature parameter is:
α=S x
wherein S is a damage identification inversion matrix, and α is a structural damage parameter vector.
Further, the uncertainty distribution of the structural damage parameter is:
Figure BDA0002306744310000031
where m represents the number of structural damage parameters, n represents the number of uncertainty variables, and Cov (·,) represents the covariance.
Further, the change curve of the service performance parameter in the change process of the damage parameter of each component in the structure is as follows:
Figure BDA0002306744310000032
wherein D isiTo accumulate the residual intensity index, a ═ min {1, SRFi *},SRFi *For the allowable damage level of the ith component, "1" represents that the component loses all of its rigidity.
Further, the importance indexes of each component in the structure are as follows:
Figure BDA0002306744310000033
wherein the content of the first and second substances,
Figure BDA0002306744310000034
further, the weighted standard deviation norm is:
WSDN=||(σ*DEWI)||
wherein σ is the standard deviation of the uncertainty distribution of the structural damage parameter, (. cndot.) is the Hadamard product.
Further, the optimization model is as follows:
Figure BDA0002306744310000041
wherein the content of the first and second substances,
Figure BDA0002306744310000042
representing the position of the ith probability sensor in the jth probability sensor layout, m being the number of probability sensors, n being the number of probability sensor schemes, Γ0Representing alternative possibilities for the layout of the probabilistic sensor.
Further, optimizing the probabilistic sensor stations based on 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 probability sensor measuring point optimization method based on structural component importance indexes according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a change curve of service performance parameters in a damage parameter change process of each component of the structure according to an embodiment of the present invention;
FIG. 3 is a schematic view of a simply supported beam according to an embodiment of the present invention
FIG. 4 is a diagram illustrating a trend of maximum displacement of each unit of the 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 layout of sensor measuring points using condition number criteria for different numbers of sensors according to an embodiment of the present invention;
FIG. 5(b) is a schematic diagram of a sensor measuring point arrangement scheme using information entropy criterion under different numbers of sensors according to an embodiment of the present invention;
FIG. 5(c) is a schematic diagram of a layout of sensor measuring points using the norm of standard deviation for different numbers of sensors according to an embodiment of the present invention;
FIG. 5(d) is a diagram illustrating a layout of sensor points using a weighted norm of standard deviation for different numbers of sensors in accordance with an embodiment of the present invention;
FIG. 6 is a diagram illustrating a condition number indicator, an information entropy indicator, a standard deviation norm indicator, and a weighted standard deviation norm obtained by the importance indicator of the present invention under different sensor numbers according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
FIG. 1 is a flowchart of a probabilistic sensor measuring point optimization method based on structural component importance indicators according to an embodiment of the present invention.
As shown in FIG. 1, the method for optimizing the measuring point of the probabilistic sensor based on the importance index of the structural component in the embodiment of the invention comprises the following steps:
and S1, determining structural characteristic parameters and a structural damage identification inversion matrix required by structural damage identification.
Specifically, the structural characteristic parameters and the structural damage identification inversion matrix required by structural damage identification can be determined by determining a structural damage parameter identification method.
The identification method for determining the structural damage parameters comprises the following steps:
Figure BDA0002306744310000051
wherein the content of the first and second substances,
Figure BDA0002306744310000052
is the partial differential sign, phi is the mode shape, α is the damage parameter to be identified.
Further, the structural damage identification inversion matrix may be determined as:
Figure BDA0002306744310000061
wherein the content of the first and second substances,
Figure BDA0002306744310000062
is a partial differential sign, α ═ α12,…,αm]TFor the damage parameter vector to be identified, m is the number of damage parameters, x ═ x1,x2,…,xn]TIs a structural response vector, and n is the number of responses.
And S2, obtaining the uncertainty distribution of the structural characteristic parameters by using a quantification method.
Specifically, uncertainty distribution of the structural characteristic parameters can be obtained by using an uncertainty quantification method, and the uncertainty distribution of the structural characteristic parameters is as follows:
x=xc*(1+Xx)
where the superscript "c" represents the corresponding true value, 1 ═ 1,1]T,Xx={XxiI-1, 2, …, n representing the relative error of the measured response values, and x representing the erroneous structural feature parameter vector.
By describing the uncertain distribution of the structural characteristic parameters by using an uncertainty quantification method, the identification of the structural damage parameters can have physical significance.
And 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
wherein S is a damage identification inversion matrix, and α 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 characteristic parameters.
Specifically, the uncertainty distribution of the structural damage parameter is:
Figure BDA0002306744310000071
where m represents the number of structural damage parameters, n represents the number of uncertainty variables, and Cov (·,) represents the covariance.
And S5, determining the change curve of the service performance parameters in the change process of the damage parameters of each component of the structure.
Specifically, the structure can be divided into a limited number of components, the damage parameters of the components of the structure are changed one by one, and finally, a change curve of the service performance parameters 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 accumulatediCharacterizing service performance parameters, namely attention of stiffness parameter errors, in the process of changing damage parameters of all components of the structure:
Figure BDA0002306744310000072
wherein, a is min {1, SRFi *},SRFi *For the allowable damage level of the ith component, "1" represents that the component loses all of its rigidity.
It should be noted that when the residual intensity index D is accumulatediThe larger the value is, the rigidity coefficient a of the i-th component is expressediThe less the influence on the structural properties, and on aiThe identification requirement of (2) is low; conversely, the stiffness coefficient a of the ith component is expressediHas a large influence on the structural performance, and is aiThe recognition requirements are high.
And S6, obtaining importance indexes of the components of the structure according to the change curve.
Specifically, can be to { DiCarrying out normalization treatment:
Figure BDA0002306744310000073
further, the importance indexes of the components of the structure can be constructed according to the result after normalization treatment:
Figure BDA0002306744310000074
it should be noted that when the importance index DEWIiThe larger the component is, the more important the ith component is to the service performance of the structure; conversely, it means that the ith element is less important to fabric commissioning performance.
And S7, constructing a weighted standard deviation norm according to the uncertainty distribution and the importance index of the structural damage parameters.
Specifically, the weighted standard deviation norm is:
WSDN=||(σ*DEWI)||
wherein σ is the standard deviation of the uncertainty distribution of the structural damage parameter, (. cndot.) is the Hadamard product. The influence of the identification error of the structural damage parameter on the service performance evaluation of the structure can be represented by the weighted standard deviation norm.
And S8, constructing an optimization model of the probability sensor layout according to the weighted standard deviation norm.
Specifically, the optimization model is:
Figure BDA0002306744310000081
wherein the content of the first and second substances,
Figure BDA0002306744310000082
representing the position of the ith probability sensor in the jth probability sensor layout, m being the number of probability sensors, n being the number of probability sensor schemes, Γ0Representing alternative possibilities for the layout of the probabilistic sensor.
And S9, optimizing the probability sensor measuring point according to the optimization model.
Specifically, 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. By respectively adopting the traversal method and the intelligent optimization algorithm according to different conditions, the influence of the identification error of the structural damage parameter on the structural performance evaluation can be effectively quantified, and the optimization model can be efficiently and stably solved.
According to the probability sensor measuring point optimization method based on the structural component importance indexes provided by the embodiment of the invention, firstly, the structural characteristic parameters and the structural damage identification inversion matrix required by structural damage identification are determined, the uncertainty distribution of the structural characteristic parameters is obtained by using a quantification method, secondly, the functional relation between the structural damage parameters and the structural characteristic parameters is constructed according to the structural damage identification inversion matrix, thirdly, the uncertainty distribution of the structural damage parameters is obtained according to the uncertainty distribution and the functional relation of the structural characteristic parameters, thirdly, the change curve of the service performance parameters in the change process of the damage parameters of each component of the structure is determined, the importance indexes of each component of the structure are obtained according to the change curve, fourthly, the weighted standard deviation norm is constructed according to the uncertainty distribution and the importance indexes of the structural damage parameters, and finally, the optimization model of the probability sensor layout is constructed according to the weighted standard deviation norm, the probability sensor measuring point is optimized, so that the influence of each component of the structure on the service performance of the structure can be fully considered, the identification precision of the key structural components is improved, and the optimal layout of the probability sensor measuring point is realized.
The following takes the example of optimizing the layout of the sensor measuring points on the simply supported beam by the method for optimizing the measuring points of the probability sensor based on the importance indexes of the structural components, and further explains the adaptability of the method for optimizing the measuring points of the probability sensor based on the importance indexes of the structural components.
Specifically, as shown in fig. 3, the simple beams are selected to have node numbers 1,2, and 21, each node has two degrees of freedom, i.e., a normal translational degree of freedom and a rotational degree of freedom, and the simple beams have unit numbers ①, ②, and
Figure BDA0002306744310000091
each unit is an Euler beam unit, the cross beam section of the simply supported beam is rectangular, and the cross sectional area is A, b, h, 0.02, 0.005m2. In addition, the simply supported beam had a length of 1m and a material density of 7860kg/m3The elastic modulus was 210 GPa.
Further, it is assumed that a load with a uniform pressure of 0.01N/mm is applied to the simply supported beam, and a maximum displacement of each unit in the simply supported beam is set to 4mm, and then structural damage parameters of each unit in the simply supported beam are reduced one by one, and a displacement of each unit in the simply supported beam is calculated.
Specifically, as shown in fig. 4, the maximum displacement of each unit in the simply supported beam increases as the degree of structural damage of each unit, i.e., SRF, increases. The importance indicators dehi of all the units in the simply supported beam are further listed in table 1, wherein the larger the importance indicator dehi of one unit in the simply supported beam is, the more important the service performance of the simply supported beam of the unit is, and the more important the damage identification result of the unit is to the service performance evaluation of the simply supported beam.
Figure BDA0002306744310000101
TABLE 1
Further, sensor measuring points in the simply supported beam are optimized by adopting a condition number criterion, namely a CN criterion, an information entropy criterion, namely an IE criterion, a standard deviation norm criterion, namely an SDN criterion, and a weighted standard deviation norm criterion, namely a WSDN criterion, so that sensor measuring point arrangement schemes shown in fig. 5(a), 5(b), 5(c) and 5(d) are obtained correspondingly, and structural damage parameters of the simply supported beam are further identified by utilizing the previous 8-order modal information. By comparing the sensor measuring point arrangement schemes shown in fig. 5(a), fig. 5(b), fig. 5(c) and fig. 5(d), it can be seen that the sensor measuring point arrangement schemes obtained by the standard deviation norm criterion SDN and the weighted standard deviation norm criterion WSDN are basically symmetrical.
Further, as shown in fig. 6, the condition number index, that is, the CN index, the information entropy index, that is, the IE index, the standard deviation norm index, that is, the SDN index, and the importance index, that is, the weighted standard deviation norm WSDN obtained by the DEWI index respectively under different sensor numbers are compared. Compared with the prior art, the importance index, 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 importance index of the structural elements are shown, meanwhile, the weighted standard deviation norm WSDN is reduced along with the increase of the number of the sensors through the graph 6, and the phenomenon is mainly caused by the fact that the identification error of structural damage parameters is reduced due to the increase of the number of the sensors.
In the present invention, unless otherwise expressly specified or limited, the term "coupled" is to be construed broadly, e.g., as meaning either a fixed connection, a removable connection, or an integral part; can be mechanically or electrically connected; either directly or indirectly through intervening media, either internally or in any other relationship. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean 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 invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer 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, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments 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. A probability sensor measuring point optimization method based on structural component importance indexes is characterized by comprising the following steps:
determining structural characteristic parameters and a structural damage identification inversion matrix required by structural damage identification;
obtaining uncertainty distribution of the structural characteristic parameters by using a quantification method;
constructing a functional relation between the structural damage parameters and the structural characteristic 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 characteristic parameters and the functional relation;
determining a change curve of service performance parameters in the change process of damage parameters of each component of the structure;
obtaining importance indexes of all components 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 indexes;
constructing an optimization model of the probability sensor layout according to the weighted standard deviation norm;
and optimizing the probability sensor measuring point according to the optimization model.
2. The method for optimizing the measuring point of the probabilistic sensor based on the importance index of the structural elements as claimed in claim 1, wherein the structural damage identification inversion matrix is:
Figure FDA0002306744300000011
wherein the content of the first and second substances,
Figure FDA0002306744300000012
is a partial differential sign, α ═ α12,…,αm]TFor the damage parameter vector to be identified, m is the number of damage parameters, x ═ x1,x2,…,xn]TIs a structural response vector, and n is the number of responses.
3. The method for optimizing the measuring point of the probabilistic sensor based on the importance index of the structural elements as claimed in claim 2, wherein the uncertainty distribution of the structural characteristic parameters is as follows:
x=xc*(1+Xx)
where the superscript "c" represents the corresponding true value, 1 ═ 1,1]T,Xx={XxiI-1, 2, …, n representing the relative error of the measured response values, and x representing the erroneous structural feature parameter vector.
4. The method of claim 3, wherein the functional relationship between the structural damage parameter and the structural feature parameter is:
α=Sx
wherein S is a damage identification inversion matrix, and α is a structural damage parameter vector.
5. The method for optimizing the measuring points of the probabilistic sensor based on the importance index of the structural elements as claimed in claim 4, wherein the uncertainty distribution of the structural damage parameters is as follows:
Figure FDA0002306744300000021
where m represents the number of structural damage parameters, n represents the number of uncertainty variables, and Cov (·,) represents the covariance.
6. The method for optimizing the measuring point of the probability sensor based on the importance index of the structural elements as claimed in claim 5, wherein the change curve of the service performance parameter in the process of the damage parameter change of each structural element in the structure is as follows:
Di=∫0 a|R-P(SRFi)|d(SRFi)
wherein D isiTo accumulate the residual intensity index, a ═ min {1, SRFi *},SRFi *For the allowable damage level of the ith component, "1" represents that the component loses all of its rigidity.
7. The method for optimizing the measuring point of the probabilistic sensor based on the importance index of the structural elements as claimed in claim 6, wherein the importance index of each element in the structure is:
Figure FDA0002306744300000031
wherein the content of the first and second substances,
Figure FDA0002306744300000032
8. the method for optimizing the measuring point of the probabilistic sensor based on the importance index of the structural element according to claim 7, wherein the weighted standard deviation norm is:
WSDN=||(σ*DEWI)||
wherein σ is the standard deviation of the uncertainty distribution of the structural damage parameter, (. cndot.) is the Hadamard product.
9. The method for optimizing the measuring point of the probabilistic sensor based on the importance index of the structural element according to claim 8, wherein the optimization model is:
Figure FDA0002306744300000033
wherein, { Γi jRepresents 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, Γ0Representing alternative possibilities for the layout of the probabilistic sensor.
10. The method of claim 9, wherein optimizing the probabilistic sensor station based on the structural component importance indicator 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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