CN113128053A - Nonlinear system parameter identification method, device, equipment and medium - Google Patents
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Abstract
The invention discloses a nonlinear system parameter identification method, a device, equipment and a medium, wherein the method comprises the following steps: acquiring a linear natural frequency, a damping coefficient and a nonlinear stiffness coefficient of the system, and constructing a nonlinear system equation of the structure; constructing a calculation formula and a measured value of a response power spectral density function according to the nonlinear system equation; acquiring a parameter initial value and a response sensitivity matrix of a structure; and carrying out iterative processing according to the measured value, the parameter initial value and the response sensitivity matrix to determine a nonlinear system parameter. The method can reduce model errors caused by over-simplified modeling of the system, improve the reliability of the structural health monitoring technology, and can be widely applied to the technical field of data processing.
Description
Technical Field
The invention relates to the technical field of data processing, in particular to a nonlinear system parameter identification method, a nonlinear system parameter identification device, equipment and a medium.
Background
With the development of society, a large number of civil engineering and construction structures including conventional buildings, roads and bridges and a plurality of large-scale complex structures appear all over the country and all over the world. The advent of these civil engineering and construction structures has facilitated people's productive life, but has also led to some possible safety issues due to various factors. For example, various environmental climate factors such as typhoon, earthquake, tsunami, debris flow, etc. may adversely affect the structure, and overload, traffic accident, etc. may cause damage to the road and bridge structure. These situations are ubiquitous, and it is very important to monitor the health of civil structures and obtain the state changes in time so as to ensure the safety of people's lives and properties. Therefore, health monitoring has also attracted attention from numerous scholars and researchers in recent years.
At present, for monitoring the health condition of a structure, a structure is generally modeled into a linear dynamic system, the damage of the structure and related key attributes are parameterized, the related parameters of the system are identified by using response data (such as displacement, speed, acceleration data and the like) of a period of time collected by sensors arranged on the structure, and the health condition of an engineering structure is monitored and diagnosed by monitoring the change of the related parameters. Indeed, modeling the structure as a linear dynamics system does greatly simplify the practical engineering problems, successfully solves many problems, and promotes the development of the structural health monitoring field. However, in engineering practice, the nonlinearity is ubiquitous, including the inherent nonlinearity of materials, geometric nonlinearity caused by large structural deformation, and the like, and neglecting the nonlinearity factors, simplifying the engineering structure and handling many times can also cause significant errors. Because the dynamic behavior of the nonlinear system is quite different from that of the linear system, phenomena such as bifurcation, chaos, limit cycle and the like are commonly present in the nonlinear system, but do not appear in the linear system at all. Therefore, it is very necessary to consider non-linearity factors when modeling an engineering structure. Furthermore, considering the engineering practice, the effects to which civil engineering structures are subjected are generally uncertain, such as wind loads, seismic loads, loads generated by passing vehicles due to uneven road and bridge surfaces, and the like, which are typical random loads. For random loads, the form of the random loads cannot be determined in advance, and only relevant statistical characteristics (mean, variance and the like) of the random loads can be mastered, but the random loads widely exist in engineering practice.
Disclosure of Invention
In view of this, embodiments of the present invention provide a method, an apparatus, a device and a medium for identifying nonlinear system parameters, so as to improve the reliability of structural health monitoring.
The invention provides a nonlinear system parameter identification method in a first aspect, which comprises the following steps:
acquiring a linear natural frequency, a damping coefficient and a nonlinear stiffness coefficient of the system, and constructing a nonlinear system equation of the structure;
constructing a calculation formula and a measured value of a response power spectral density function according to the nonlinear system equation;
acquiring a parameter initial value and a response sensitivity matrix of a structure;
performing iterative processing according to the measured value, the parameter initial value and the response sensitivity matrix to determine a nonlinear system parameter;
wherein the non-linear system parameters are used for structural health monitoring.
Optionally, the obtaining a linear natural frequency, a damping coefficient, and a nonlinear stiffness coefficient of the system, and constructing a nonlinear system equation of the structure includes:
taking the obtained system linear natural frequency, damping coefficient and nonlinear stiffness coefficient as system parameters to be identified;
constructing a nonlinear system equation according to the system parameters to be identified;
wherein the expression of the nonlinear system equation is:
wherein, ω isnRepresents the system linear natural frequency; beta represents a damping coefficient; epsilon represents a nonlinear stiffness coefficient; (t) represents a nonlinear system equation;
represents system acceleration;
represents the system speed; x represents the system displacement.
Optionally, the constructing a calculation and a measurement of the response power spectral density function according to the nonlinear system equation comprises:
determining an external excitation frequency and an integral variable;
performing equivalent linearization processing on the nonlinear system equation according to the external excitation frequency and the integral variable to obtain a calculation formula of the response power spectral density function;
calculating according to the calculation formula to obtain the measured value;
wherein the response power spectral density function is calculated as:
wherein S isxx(ω) represents a response power spectral density function; e is a natural constant, and omega is an external excitation frequency; xi is an integral variable; k is a constant; d xi represents the differential of xi; beta represents the damping coefficient.
Optionally, the obtaining of the initial values of the parameters of the structure and the response sensitivity matrix includes:
acquiring an updated value of a system parameter;
obtaining a difference between the measured response and the calculated response;
and carrying out sensitivity analysis according to the system parameter update value and the difference value to obtain the response sensitivity matrix.
Optionally, the method further comprises the step of constructing an objective function of the parameter identification problem, the step comprising:
performing linearization treatment on a weighted nonlinear least square problem in the parameter identification problem;
and iteratively solving the result after the linearization processing by a method of enhancing response sensitivity.
Optionally, the iteratively solving the linearized result by the enhanced response sensitivity method includes:
and optimizing the regularization parameters by a confidence domain limiting method, and determining the system parameter update value in the iteration step by a least square method with regularization according to the regularization parameters obtained by optimization.
A second aspect of the present invention provides a nonlinear system parameter identification apparatus, including:
the first module is used for acquiring the linear natural frequency, the damping coefficient and the nonlinear stiffness coefficient of the system and constructing a nonlinear system equation of the structure;
a second module for constructing a calculation and a measurement of a response power spectral density function according to the nonlinear system equation;
the third module is used for acquiring a parameter initial value and a response sensitivity matrix of the structure;
a fourth module, configured to perform iterative processing according to the measurement value, the initial parameter value, and the response sensitivity matrix, and determine a nonlinear system parameter;
wherein the non-linear system parameters are used for structural health monitoring.
A third aspect of the invention provides an electronic device comprising a processor and a memory;
the memory is used for storing programs;
the processor executes the program to implement the method as described above.
A fourth aspect of the invention provides a computer readable storage medium storing a program for execution by a processor to perform a method as described above.
The embodiment of the invention also discloses a computer program product or a computer program, which comprises computer instructions, and the computer instructions are stored in a computer readable storage medium. The computer instructions may be read by a processor of a computer device from a computer-readable storage medium, and the computer instructions executed by the processor cause the computer device to perform the foregoing method.
The embodiment of the invention firstly obtains the linear natural frequency, the damping coefficient and the nonlinear stiffness coefficient of the system, and constructs the nonlinear system equation of the structure; then, according to the nonlinear system equation, a calculation formula and a measured value of a response power spectral density function are constructed; then, acquiring a parameter initial value and a response sensitivity matrix of the structure; and finally, carrying out iterative processing according to the measured value, the parameter initial value and the response sensitivity matrix to determine a nonlinear system parameter. The embodiment of the invention can reduce the model error caused by over-simplified modeling of the system and improve the reliability of the structural health monitoring technology.
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In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present application, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a flowchart illustrating the overall steps provided by an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
To solve the problems in the prior art, an embodiment of the present invention provides a nonlinear system parameter identification method, as shown in fig. 1, the method includes:
acquiring a linear natural frequency, a damping coefficient and a nonlinear stiffness coefficient of the system, and constructing a nonlinear system equation of the structure;
constructing a calculation formula and a measured value of a response power spectral density function according to the nonlinear system equation;
acquiring a parameter initial value and a response sensitivity matrix of a structure;
performing iterative processing according to the measured value, the parameter initial value and the response sensitivity matrix to determine a nonlinear system parameter;
wherein the non-linear system parameters are used for structural health monitoring.
Optionally, the obtaining a linear natural frequency, a damping coefficient, and a nonlinear stiffness coefficient of the system, and constructing a nonlinear system equation of the structure includes:
taking the obtained system linear natural frequency, damping coefficient and nonlinear stiffness coefficient as system parameters to be identified;
constructing a nonlinear system equation according to the system parameters to be identified;
wherein the expression of the nonlinear system equation is:
wherein, ω isnRepresents the system linear natural frequency; beta represents a damping coefficient; epsilon represents a nonlinear stiffness coefficient; (t) represents a nonlinear system equation;
represents system acceleration;
represents the system speed; x represents the system displacement.
Optionally, the constructing a calculation and a measurement of the response power spectral density function according to the nonlinear system equation comprises:
determining an external excitation frequency and an integral variable;
performing equivalent linearization processing on the nonlinear system equation according to the external excitation frequency and the integral variable to obtain a calculation formula of the response power spectral density function;
calculating according to the calculation formula to obtain the measured value;
wherein the response power spectral density function is calculated as:
wherein S isxx(ω) represents a response power spectral density function; e is a natural constant, and omega is an external excitation frequency; xi is an integral variable; k is a constant; d xi represents the differential of xi; beta represents the damping coefficient.
Optionally, the obtaining of the initial values of the parameters of the structure and the response sensitivity matrix includes:
acquiring an updated value of a system parameter;
obtaining a difference between the measured response and the calculated response;
and carrying out sensitivity analysis according to the system parameter update value and the difference value to obtain the response sensitivity matrix.
Optionally, the method further comprises the step of constructing an objective function of the parameter identification problem, the step comprising:
performing linearization treatment on a weighted nonlinear least square problem in the parameter identification problem;
and iteratively solving the result after the linearization processing by a method of enhancing response sensitivity.
Optionally, the iteratively solving the linearized result by the enhanced response sensitivity method includes:
optimizing the regularization parameters by a confidence domain limiting method, and determining the system parameter update value in the iteration step by a least square method with regularization according to the regularization parameters obtained by optimization
A second aspect of the present invention provides a nonlinear system parameter identification apparatus, including:
the first module is used for acquiring the linear natural frequency, the damping coefficient and the nonlinear stiffness coefficient of the system and constructing a nonlinear system equation of the structure;
a second module for constructing a calculation and a measurement of a response power spectral density function according to the nonlinear system equation;
the third module is used for acquiring a parameter initial value and a response sensitivity matrix of the structure;
a fourth module, configured to perform iterative processing according to the measurement value, the initial parameter value, and the response sensitivity matrix, and determine a nonlinear system parameter;
wherein the non-linear system parameters are used for structural health monitoring.
A third aspect of the invention provides an electronic device comprising a processor and a memory;
the memory is used for storing programs;
the processor executes the program to implement the method as described above.
A fourth aspect of the invention provides a computer readable storage medium storing a program for execution by a processor to perform a method as described above.
The embodiment of the invention also discloses a computer program product or a computer program, which comprises computer instructions, and the computer instructions are stored in a computer readable storage medium. The computer instructions may be read by a processor of a computer device from a computer-readable storage medium, and the computer instructions executed by the processor cause the computer device to perform the foregoing method.
The following describes in detail a specific implementation process of the method according to the embodiment of the present invention:
first, in the field of structural health monitoring, the following problems mainly exist:
most of the prior art simplifies the system into a linear power system, does not consider the influence of nonlinear factors such as material nonlinearity, geometric nonlinearity and the like, has larger access with the structure in the actual engineering, and can misjudge the health condition of the structure to cause property and life safety problems; the existing technology also rarely considers the influence of various uncertainties and random factors in engineering practice, simply considers the input of the system according to the deterministic load, and has low practicability.
Therefore, an object of the present invention is to provide a structural health monitoring technique that can be widely applied to engineering practice. The technology has the following characteristics: the technology considers a nonlinear system, reduces model errors caused by over-simplified modeling of the system as far as possible, and improves the reliability of the structural health monitoring technology. The technology fully considers the influence of various uncertain factors on the structure in the engineering practice, and explores the method for identifying the key parameters of the system under the random excitation action with certain statistical characteristics.
The following describes in detail the implementation principle of various technical features of the present invention:
nonlinear system control equations and response power spectral density functions:
for a nonlinear system with random excitation, the general form of the governing equation is as follows:
wherein m is the mass of the system,
for system nonlinear forces, f (t) is random excitation.
The duffing system is a typical nonlinear system which is ubiquitous and has wide attention, and the invention takes a parameter identification method of the duffing system as an example to show a nonlinear system parameter identification process of random excitation. The daphen system control equation is as follows:
in the system (2), ωnAnd beta and epsilon are respectively a system linear natural frequency, a damping coefficient and a nonlinear stiffness coefficient which are used as system parameters to be identified and are expressed as p ═ omegan,β,ε]＝[p1,p2,p3]. Miles et al non-linear by the formula (2)Equivalent linearization is carried out on the linear system, and a response power spectral density function S of the linear system under the excitation of Gaussian white noise is obtainedxxThe following were used:
where e is a natural constant, ω is an independent variable, i.e., the external excitation frequency, SfAs a function of the power spectral density of the white gaussian noise excitation, ξ is an additionally introduced integral variable (which can be eliminated after integration),
where k is a constant determined by the following nonlinear algebraic equation:
secondly, identifying an objective function of the problem by parameters:
the parameter identification problem is generally modeled as a weighted nonlinear least squares problem, as follows:
wherein the content of the first and second substances,
is the parameter domain, | | | purple2Representing a two-norm, W is a weight matrix (usually an identity matrix), r (p) is calculated response data obtained by equation (3),
and response power spectral density function measurement data is obtained by performing spectral density estimation on the displacement response data obtained by the sensor measurement.
Enhanced response sensitivity method for solving objective function
For the non-linear least squares problem of equation (5), it is usually solved iteratively by linearizing it and then using the enhanced response sensitivity method. The linearization process is as follows:
wherein Δ p is the system parameter update, Δ R is the difference between the calculated response and the measured response, and S is the sensitivity matrix of the response power spectral density to the system parameters, which can be obtained by performing sensitivity analysis by equation (3), as follows:
since the partial derivative analytical formula of the formula (7) is difficult to directly obtain, each partial derivative is obtained by a difference method.
After the target function (5) is linearized by the equation (6), the system parameter update Δ p in the iterative step can be obtained by the least square method with regularization in consideration of the least square problem of linearization that may not be suitable, as shown below:
wherein λ is a regularization parameter, and the selection is generally obtained by an L-curve method. Considering that the algorithm convergence performance is not strong due to the fact that the regularization parameter lambda obtained by the L curve method is usually small, a more appropriate regularization parameter lambda can be selected through confidence domain limitation, and therefore the convergence performance of the algorithm is enhanced. Confidence domain constraints guide the selection of regularization parameter λ by introducing a consistency indicator ρ as shown below
Good consistency index rho is not less than rhocr(ρcrTypically 0.5), while increasing the regularization parameter λ increases the conformity indicator ρ, so regularization can be increasedAnd obtaining a proper regularization parameter lambda until the consistency index meets the condition.
The specific steps of the response sensitivity method of the present invention are described in detail below:
firstly, setting a system parameter initial value p, and giving a weight matrix W; setting convergence criterion error tolerance tol (e.g., take 10-6) (ii) a Setting a maximum number of iterations Nmax(for example, take 1000); setting confidence domain parameter rhocr(e.g., take 0.5) and γ (e.g., take 2); setting the maximum cycle number N of the confidence domain process of each step of iterationtr(for example, take 20); importing measurement data
According to the preset parameter values, executing the following algorithm:
importing measurement data
for k＝1:Nmax
Obtaining R (p) from formula (3)k)
Calculating residual error
The sensitivity matrix S (p) is obtained from equation (7)k)
Obtaining regularization parameter initial value lambda by using L curve methodL(pk)
for i＝1:Ntr
λ＝γi-1λL(pk)
Calculating a parameter update value Δ p ═ S (S)T(pk)WS(pk)+λI)-1·ST(pk)WΔR
If it is not
Continue to use
Obtaining R (p) from formula (3)k+Δp)
Calculating a consistency index
If rho is not less than rhocrOut of circulation
end for
Updating the parameter pk+1＝pk+Δp
If | | | | | p | |k+1Less than or equal to tol, jump out of the circulation
end for
The following describes the implementation of the present invention with reference to a specific numerical example:
wherein the measured data
And (3) solving the displacement response obtained by the formula (2) and then carrying out spectral density estimation to obtain the target. Considering that measurement noise (error) always exists in the measurement data, the displacement response data adds noise by:
wherein x is displacement data obtained by numerical simulation, std (x) represents the standard deviation of x, enoiseAs noise level, RandnIs a vector (dimension size is same as x) composed of random numbers which obey standard normal distribution.
Let the system unknown parameter be pu＝[ωn,β,ε]＝[1.0,0.04,0.1]Considering p asuThe magnitude of different parameters is different, and the reference value p of the parameters is set0＝[1.0,0.1,1]A 1 is to puIs divided by p one by one0The normalized parameter p to be identified is obtained as [1.0,0.4,0.1 ] according to the parameter reference value of the corresponding position]. Assuming a Gaussian white noise excitation power spectral density function of Sf1, selecting omega epsilon [0.8,1.8 ∈ ]]Response power spectral density values in range as measurement data for calculation
Four conditions as in table 2 were considered to explore the initial values of parameter iteration and the influence of measurement noise on the algorithm. In addition, considering that the system input is random excitation and the influence of measurement noise is considered, the monte carlo simulation of 100 tests is performed for all the working conditions of the example, and the average value of the 100 test results is taken as the final identification result and is summarized in table 3.
TABLE 2 parameter identification conditions
TABLE 3 identification results of the respective working conditions
Note that, the data in parentheses in table 3 represents the relative error of the recognition result.
As can be seen from the identification results of the working condition 1 and the working condition 2 (or the working condition 3 and the working condition 4) in the table 3, the maximum relative error is not more than 10%, and the results which can be accepted in the engineering practice can still be obtained by setting the iteration initial values of different parameters, which indicates that the algorithm of the invention has good convergence performance and the selectable range of the iteration initial values is relatively large. In addition, according to the comparison of the identification results of the working condition 1 and the working condition 3 (or the working condition 2 and the working condition 4), the identification results have small difference under different measurement noise levels, and the algorithm has good noise resistance and robustness and can effectively overcome the measurement error in engineering practice.
In summary, the invention has the following advantages:
1. high accuracy: the considered engineering structure system model is a nonlinear power system, and deviation and even errors caused by model errors brought by simple linearization processing of the engineering structure model are avoided.
2. High universality: the excitation of the engineering structure system is set as random excitation, and the influence of various uncertain factors and random factors on the structure health monitoring in the engineering practice is considered.
3. The algorithm has good convergence performance: and confidence domain limitation is introduced when a sensitivity method is applied, so that the algorithm obtains stronger convergence performance.
4. The noise resistance is good: and an objective function is constructed by utilizing frequency domain data, namely a response power spectral density function value, so that the algorithm has good noise immunity and robustness.
In alternative embodiments, the functions/acts noted in the block diagrams may occur out of the order noted in the operational illustrations. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality/acts involved. Furthermore, the embodiments presented and described in the flow charts of the present invention are provided by way of example in order to provide a more thorough understanding of the technology. The disclosed methods are not limited to the operations and logic flows presented herein. Alternative embodiments are contemplated in which the order of various operations is changed and in which sub-operations described as part of larger operations are performed independently.
Furthermore, although the present invention is described in the context of functional modules, it should be understood that, unless otherwise stated to the contrary, one or more of the described functions and/or features may be integrated in a single physical device and/or software module, or one or more functions and/or features may be implemented in a separate physical device or software module. It will also be appreciated that a detailed discussion of the actual implementation of each module is not necessary for an understanding of the present invention. Rather, the actual implementation of the various functional modules in the apparatus disclosed herein will be understood within the ordinary skill of an engineer, given the nature, function, and internal relationship of the modules. Accordingly, those skilled in the art can, using ordinary skill, practice the invention as set forth in the claims without undue experimentation. It is also to be understood that the specific concepts disclosed are merely illustrative of and not intended to limit the scope of the invention, which is defined by the appended claims and their full scope of equivalents.
The functions, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
The logic and/or steps represented in the flowcharts or otherwise described herein, e.g., an ordered listing of executable instructions that can be considered to implement logical functions, can be embodied in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, processor-containing system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions. For the purposes of this description, a "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device.
More specific examples (a non-exhaustive list) of the computer-readable medium would include the following: an electrical connection (electronic device) having one or more wires, a portable computer diskette (magnetic device), a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM). Additionally, the computer-readable medium could even be paper or another suitable medium upon which the program is printed, as the program can be electronically captured, via for instance optical scanning of the paper or other medium, then compiled, interpreted or otherwise processed in a suitable manner if necessary, and then stored in a computer memory.
It should be understood that portions of the present invention may be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, the various steps or methods may be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, any one or combination of the following techniques, which are known in the art, may be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application specific integrated circuit having an appropriate combinational logic gate circuit, a Programmable Gate Array (PGA), a Field Programmable Gate Array (FPGA), or the like.
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 do not necessarily 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.
While embodiments of the invention have been shown and described, it will be understood by those of ordinary skill in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.
While the preferred embodiments of the present invention have been illustrated and described, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (9)
1. The nonlinear system parameter identification method is characterized by comprising the following steps:
acquiring a linear natural frequency, a damping coefficient and a nonlinear stiffness coefficient of the system, and constructing a nonlinear system equation of the structure;
constructing a calculation formula and a measured value of a response power spectral density function according to the nonlinear system equation;
acquiring a parameter initial value and a response sensitivity matrix of a structure;
performing iterative processing according to the measured value, the parameter initial value and the response sensitivity matrix to determine a nonlinear system parameter;
wherein the non-linear system parameters are used for structural health monitoring.
2. The nonlinear system parameter identification method according to claim 1, wherein the obtaining of the system linear natural frequency, the damping coefficient and the nonlinear stiffness coefficient, and the constructing of the nonlinear system equation of the structure comprise:
taking the obtained system linear natural frequency, damping coefficient and nonlinear stiffness coefficient as system parameters to be identified;
constructing a nonlinear system equation according to the system parameters to be identified;
wherein the expression of the nonlinear system equation is:
wherein, ω isnRepresents the system linear natural frequency; beta represents a damping coefficient; epsilon represents a nonlinear stiffness coefficient; f (t) represents a non-lineA sexual system equation;
represents system acceleration;
represents the system speed; x represents the system displacement.
3. The nonlinear system parameter identification method of claim 2, wherein constructing the calculated and measured values of the response power spectral density function according to the nonlinear system equation comprises:
determining an external excitation frequency and an integral variable;
performing equivalent linearization processing on the nonlinear system equation according to the external excitation frequency and the integral variable to obtain a calculation formula of the response power spectral density function;
calculating according to the calculation formula to obtain the measured value;
wherein the response power spectral density function is calculated as:
wherein S isxx(ω) represents a response power spectral density function; e is a natural constant, and omega is an external excitation frequency; xi is an integral variable; k is a constant; d xi represents the differential of xi; beta represents the damping coefficient.
4. The nonlinear system parameter identification method of claim 1, wherein the obtaining of the initial value of the parameter of the structure and the response sensitivity matrix comprises:
acquiring an updated value of a system parameter;
obtaining a difference between the measured response and the calculated response;
and carrying out sensitivity analysis according to the system parameter update value and the difference value to obtain the response sensitivity matrix.
5. The nonlinear system parameter identification method in accordance with claim 4, further comprising the step of constructing an objective function of a parameter identification problem, the step comprising:
performing linearization treatment on a weighted nonlinear least square problem in the parameter identification problem;
and iteratively solving the result after the linearization processing by a method of enhancing response sensitivity.
6. The nonlinear system parameter identification method of claim 5, wherein the iteratively solving the linearized result by the enhanced response sensitivity method comprises:
and optimizing the regularization parameters by a confidence domain limiting method, and determining the system parameter update value in the iteration step by a least square method with regularization according to the regularization parameters obtained by optimization.
7. The nonlinear system parameter identification device is characterized by comprising:
the first module is used for acquiring the linear natural frequency, the damping coefficient and the nonlinear stiffness coefficient of the system and constructing a nonlinear system equation of the structure;
a second module for constructing a calculation and a measurement of a response power spectral density function according to the nonlinear system equation;
the third module is used for acquiring a parameter initial value and a response sensitivity matrix of the structure;
a fourth module, configured to perform iterative processing according to the measurement value, the initial parameter value, and the response sensitivity matrix, and determine a nonlinear system parameter;
wherein the non-linear system parameters are used for structural health monitoring.
8. An electronic device comprising a processor and a memory;
the memory is used for storing programs;
the processor executing the program realizes the method of any one of claims 1-6.
9. A computer-readable storage medium, characterized in that the storage medium stores a program, which is executed by a processor to implement the method according to any one of claims 1-6.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113472251A (en) * | 2021-08-06 | 2021-10-01 | 中山大学 | Motor parameter identification method |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20030114995A1 (en) * | 2001-12-18 | 2003-06-19 | Hong Su | Fatigue sensitivity determination procedure |
| CN107357980A (en) * | 2017-06-29 | 2017-11-17 | 中山大学 | A kind of damnification recognition method of axial functionally gradient beam |
| CN110472315A (en) * | 2019-07-30 | 2019-11-19 | 中山大学 | Structural parameter identification method based on ERSA algorithm |
-
2021
- 2021-04-21 CN CN202110432448.0A patent/CN113128053A/en active Pending
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20030114995A1 (en) * | 2001-12-18 | 2003-06-19 | Hong Su | Fatigue sensitivity determination procedure |
| CN107357980A (en) * | 2017-06-29 | 2017-11-17 | 中山大学 | A kind of damnification recognition method of axial functionally gradient beam |
| CN110472315A (en) * | 2019-07-30 | 2019-11-19 | 中山大学 | Structural parameter identification method based on ERSA algorithm |
Non-Patent Citations (3)
| Title |
|---|
| R.N.MILES: "An approximate solution for the spectral response of Duffing"s oscillator with random input", 《JOURNAL OF SOUND AND VIBRATION》 * |
| 刘广 等: "基于时域响应灵敏度分析的非线性系统参数识别", 《振动与冲击》 * |
| 郑泽栋 等: "基于功率谱灵敏度分析的结构损伤识别方法", 《振动与冲击》 * |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113472251A (en) * | 2021-08-06 | 2021-10-01 | 中山大学 | Motor parameter identification method |
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