CN108804766A - The recognition methods of damping parameter - Google Patents
The recognition methods of damping parameter Download PDFInfo
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Abstract
The present invention provides a kind of recognition methods of damping parameter, including：According to the physical model of damping system structure and the relevant finite element model of damping parameter；Modal parameter sensitive to damping parameter variation in finite element model is known according to Sensitivity Analysis Method；Identical exciting force is applied respectively to physical model and finite element model, obtains the modal parameter of physical model and the modal parameter of finite element model；It determines the correlation between the modal parameter of physical model and the modal parameter of finite element model, and object function is built according to the error meeting correlation and the modal parameter sensitive between damping parameter variation；Damping parameter when making object function stable convergence is determined according to optimization algorithm, as the actual damping parameter of the damping system.Object function stable convergence can be achieved in the present invention, and the statics testing method or dynamic testing machine test method of the prior art are substantially better than in efficiency.
Description
Technical Field
The invention relates to the technical field of structural dynamics, in particular to a damping parameter identification method.
Background
Modal analysis is a method for researching the dynamic characteristics of a structure and is generally applied to the field of engineering vibration. The modes refer to the natural vibration characteristics of the mechanical structure, and each mode has a specific natural frequency, a specific damping ratio and a specific mode shape. The process of analyzing these modalities is called modality analysis. According to the calculation method, the modal analysis can be divided into calculation modal analysis and test modal analysis. The finite element calculation method is used for obtaining calculation modal analysis, and the acquired system input and output signals are subjected to parameter identification through a test to obtain test modal analysis. Each order of the modal analysis corresponds to a mode, and each order has modal parameters such as specific frequency and damping ratio.
In the field of rail transportation, a rubber member is often used as a damping means in order to reduce vehicle vibration and improve ride comfort. The academic researches of the finite element analysis-based work developed around the motor train, such as modal calculation, noise calculation, dynamic response calculation and the like, are relatively extensive. Meanwhile, the rubber block is independently used as a research object, a finite element model of the rubber block is established, the rigidity damping parameter of the rubber block is obtained by inquiring related documents, empirical formulas or quasi-static mechanics tests, and then the mechanical property of the rubber block is researched. In the rubber block in the existing report, if the damping parameters are obtained by inquiring documents, the accuracy of the established model is limited due to the difference of material batches and manufacturers; if the damping parameters are obtained through a quasi-static mechanics test, the dynamic characteristics of the actual rubber block cannot be well reflected by the model established by the damping parameters.
Disclosure of Invention
The present invention provides a method of identifying a damping parameter that overcomes or at least partially solves the above mentioned problems.
According to an aspect of the present invention, there is provided a method for identifying a damping parameter, including:
constructing a finite element model related to damping parameters according to the entity model of the damping system;
acquiring modal parameters which are sensitive to the damping parameter change in the finite element model according to a sensitivity analysis method;
respectively applying the same excitation force to the solid model and the finite element model to obtain the modal parameters of the solid model and the modal parameters of the finite element model;
determining the correlation between the modal parameters of the entity model and the modal parameters of the finite element model, and constructing a target function according to the error between the modal parameters which meet the correlation and are sensitive to the damping parameter change;
and determining a damping parameter when the target function is stably converged according to an optimization algorithm, wherein the damping parameter is used as the actual damping parameter of the damping system.
Preferably, the modal parameters sensitive to the damping parameter change in the finite element model are obtained according to a sensitivity analysis method, specifically:
changing the damping parameters in the finite element model within a preset range to obtain the variation of the damping parameters;
calculating the variation of the modal parameters in the finite element model according to a perturbation method, and regarding any modal parameter, taking the variation of the modal parameter and the variation of the damping parameter as the sensitivity of the modal parameter;
constructing a sensitivity matrix according to the sensitivity of each modal parameter to the damping parameter;
and acquiring modal parameters which are sensitive to the damping parameter change in the finite element model according to the sensitivity matrix.
Preferably, the same excitation force is applied to the solid model and the finite element model respectively to obtain the modal parameters of the solid model and the modal parameters of each order of the finite element model, specifically:
applying an excitation force to the entity model, collecting an excitation signal and a response signal at the same time, and carrying out experimental modal analysis on a test signal of the entity model to obtain modal parameters of the entity model;
loading the excitation signal into the finite element model, calculating a response signal of the finite element model, and performing calculation modal analysis on the response signal of the finite element model to obtain modal parameters of the finite element model.
Preferably, the constructing an objective function according to the error between the modal parameters having correlation and sensitive to the damping parameter change includes:
determining a modal parameter which has correlation and is sensitive to the damping parameter change as a target modal parameter;
setting the weight corresponding to each target modal parameter according to a preset rule;
the objective function is constructed according to the following formula:
wherein,representing the ith target modal parameter in the finite element model,representing sums in a solid modelCorresponding ith target modal parameter,. DELTA.siRepresenting the error between the ith target modal parameter in the finite element model and the solid model, wiRepresents the weight corresponding to the ith target modal parameter, TminRepresenting the objective function.
Preferably, the determining of the correlation between the modal parameters of the solid model and the modal parameters of the finite element model specifically includes:
and (3) evaluating the correlation of modal shape by adopting a modal confidence criterion:
wherein,respectively representing the ith order vibration mode of the solid model and the jth order vibration mode of the finite element model;
if MACijIf the parameter is larger than the preset threshold value, the ith order modal parameter and the limit of the solid model are determinedThe j-th order modal parameters of the meta-model have a correlation.
Preferably, the optimization algorithm is one of a sequence quadratic programming algorithm, an ant colony algorithm, a genetic algorithm, a simulated annealing algorithm and a particle swarm algorithm.
Preferably, the damping system comprises a damping unit, the lower part of the damping unit is fixedly connected to the supporting surface, and a mass block is fixed above the damping unit;
correspondingly, the constructing of the finite element model related to the damping parameters according to the solid model of the damping system specifically includes:
and establishing a mass point model of the mass block by using a concentrated mass point unit in finite element analysis software, meshing the damping units by using a connecting unit in the finite element analysis software, and establishing the finite element model according to the mass point model and the meshed damping units.
Preferably, the applying the same excitation force to the solid model and the finite element model respectively further comprises:
the acceleration sensor is adhered to the surface of the mass block, and a plurality of test points are vertically arranged on the mass block, so that an excitation signal is vertically generated when an excitation force is applied.
According to another aspect of the present invention, there is also provided an electronic apparatus, including:
at least one processor; and
at least one memory communicatively coupled to the processor, wherein:
the memory stores program instructions executable by the processor, and the processor calls the program instructions to execute the identification method of the damping parameter of the embodiment of the invention and the method of any optional embodiment thereof.
According to another aspect of the present invention, there is also provided a non-transitory computer readable storage medium, characterized in that the non-transitory computer readable storage medium stores computer instructions for causing the computer to execute the method for identifying a damping parameter of an embodiment of the present invention and the method of any optional embodiment thereof.
According to the damping parameter identification method provided by the invention, the damping parameters can be identified more efficiently by adjusting the modal parameters sensitive to the damping parameter change, then the objective function is constructed according to the modal parameters which are relevant and sensitive to the damping parameter change in the entity model and the finite element model, and the value of the damping parameters in the finite element model is optimized through the optimization algorithm, so that the modal parameters corresponding to the optimized finite element model are very close to the modal parameters corresponding to the entity model, and the effect that the optimized finite element model can truly reflect the entity model is achieved. It should be noted that, when the calculation method of the embodiment of the present invention is practically applied, it is found that stable convergence of the target function can be achieved only by performing optimization iteration for 5 to 15 times, and the efficiency is obviously superior to that of the static test method or the dynamic test method in the prior art.
Drawings
Fig. 1 is a schematic flow chart of a damping parameter identification method according to an embodiment of the present invention;
FIG. 2 is a schematic flow chart illustrating a process of obtaining a modal parameter sensitive to a change in the damping parameter in the finite element model according to a sensitivity analysis method according to an embodiment of the present invention;
FIG. 3 is a functional block diagram of a damping parameter identification system according to an embodiment of the present invention;
FIG. 4 is a functional block diagram of a sensitivity analysis module according to an embodiment of the present invention;
FIG. 5 is a functional block diagram of an objective function unit according to an embodiment of the present invention;
FIG. 6 is a schematic diagram of a frame of an electronic device according to an embodiment of the invention;
FIG. 7 is a graph of convergence of imaginary part errors of modal eigenvalues in an example in accordance with the present invention;
FIG. 8 is a graph of convergence of real part errors of modal eigenvalues in an example in accordance with the present invention;
FIG. 9 is a graph of the convergence of the damping parameters in one example according to the invention.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
In order to overcome the above defects in the prior art, an embodiment of the present invention provides a method for identifying a damping parameter, and fig. 1 is a schematic flow chart of the method for identifying a damping parameter in an embodiment of the present invention, including:
101. and constructing a finite element model related to the damping parameters according to the solid model of the damping system.
It should be noted that the damping system refers to a system including a damping unit, and the damping (english: damping) refers to a characteristic that the amplitude of vibration of any vibration system is gradually reduced in vibration due to an external effect or a reason inherent to the system, and a quantitative representation of the characteristic. The damping unit is a device which provides resistance to movement and reduces movement energy. The embodiments of the invention do not limit the damping system and the specific form and connection relationship of the damping units included in the damping system, and the finite element model is composed of nodes and elements. The finite element model of the embodiment of the invention is constructed by adopting two methods according to the complexity of the damping system: if the damping system is simpler, the nodes and the units are directly established according to the geometric shape of the mechanical structure; if the damping system is complex, a finite element model is established through points, lines, surfaces and volumes, and then solid mesh division is carried out to complete establishment of the finite element model.
102. And acquiring modal parameters which are sensitive to the damping parameter change in the finite element model according to a sensitivity analysis method.
In the embodiment of the present invention, the type of the damping parameter to be identified is at least one, for example: damping coefficient and damping ratio of the material. In the embodiment of the present invention, the modal parameters may be modal frequency, modal shape, modal damping, modal stiffness, modal mass, etc., each of the modal parameters has a concept of order, for example, the modal frequency is used as a modal parameter, the modal frequency is arranged from small to large, the smallest modal frequency is called as a first order, and for the modal shape, the modal shapes of different orders have different shapes. The total order of the modal parameters required in the identification process can be adjusted according to the actual situation.
The modal parameters and the damping parameters belong to inherent characteristics of a mechanical structure, and after a finite element model is built, in order to enable the modal parameters and the damping parameters in the finite element model to be as close to a solid model as possible, the modal parameters and the damping parameters need to be continuously fine-tuned. Since the modal parameters and the damping parameters are associated with each other, that is, the damping parameters are necessarily changed after the modal parameters are adjusted, but since the associations between different modal parameters and different damping parameters are large or small, in order to identify the damping parameters more accurately, the modal parameters sensitive to the damping parameter change need to be found out, and thus the damping parameters can be identified more efficiently by adjusting the modal parameters sensitive to the damping parameter change. In the embodiment of the invention, the modal parameters which are sensitive to the damping parameter change in the finite element model are obtained through a sensitivity analysis method, and the sensitivity analysis method is a method for researching and analyzing the sensitivity degree of the state or output change of a system (or a model) to the system parameter or ambient condition change.
103. And respectively applying the same excitation force to the solid model and the finite element model to obtain the modal parameters of the solid model and the modal parameters of the finite element model.
It should be noted that, by applying an excitation force to the solid model, an acceleration response of the solid model may be acquired, and by analyzing the acceleration response, modal parameters of each order of the solid model and the finite element model may be identified. The same excitation force in the embodiment of the present invention means that the position, the magnitude and the direction of the applied excitation force are the same.
104. And determining the correlation between the modal parameters of the entity model and the modal parameters of the finite element model, and constructing an objective function according to the error between the modal parameters which meet the correlation and are sensitive to the damping parameter change.
It can be known from the prior art that it is only meaningful to compare modal parameters belonging to the same mode shape, and therefore, after obtaining modal parameters of each level of the solid model and the finite element model, the correlation between the modal parameters of the solid model and the finite element model needs to be determined. Currently, there are two main methods for determination: one method is to look similar to the same order by visual observation, and this method is intuitive but has no quantitative index. The other method is to judge through a Mode Assessment Criterion (MAC), and the MAC method has the advantage of high precision.
The modal parameters meeting the correlation and sensitive to the damping parameter change in the embodiment of the invention are as follows: on one hand, the selected modal parameters are sensitive to the change of the damping parameters, so that the damping parameters send tiny changes, and the target function can also obviously change; on the other hand, the selected modal parameters need to have a correlation, for example, a modal frequency of 2 nd order is selected in the solid model, and a modal frequency of 3 rd order is selected in the finite element model, because the mode shape of 2 nd order of the solid model is consistent with the mode shape of 3 rd order of the finite element model, so the mode frequency of 2 nd order in the task solid model and the mode shape of 3 rd order in the finite element model are correlated.
105. And determining a damping parameter when the target function is stably converged according to an optimization algorithm, wherein the damping parameter is used as the actual damping parameter of the damping system.
It should be noted that, the value of the damping parameter in the finite element model is optimized through the optimization algorithm, so that the modal parameter corresponding to the optimized finite element model is very close to the modal parameter corresponding to the solid model, and the effect that the optimized finite element model can truly reflect the solid model is achieved. It should be noted that, when the calculation method of the embodiment of the present invention is practically applied, it is found that stable convergence of the target function can be achieved only by performing optimization iteration for 5 to 15 times, and the efficiency is obviously superior to that of the static test method or the dynamic test method in the prior art.
Fig. 2 is a schematic flow chart illustrating a process of obtaining a modal parameter sensitive to a change of the damping parameter in the finite element model according to a sensitivity analysis method in an embodiment of the present invention, where as shown in fig. 2, the process specifically includes:
201. changing the damping parameters in the finite element model within a preset range to obtain the variation of the damping parameters;
it should be noted that, in the embodiment of the present invention, an adjustment range of the damping parameter is preset, and the damping parameter is adjusted within the preset range each time the damping parameter is adjusted.
202. And calculating the variable quantity of the modal parameters in the finite element model according to a perturbation method, and regarding any modal parameter, taking the variable quantity of the modal parameter and the variable quantity of the damping parameter as the sensitivity of the modal parameter.
for example, when the damping parameter is ξ before being changed, the ith modal parameter is A, the damping parameter is Δ ξ + ξ after being changed, and the modal parameter is A ', the sensitivity of the modal parameter is (A' -A)/Δ ξ.
203. And constructing a sensitivity matrix according to the sensitivity of each modal parameter to the damping parameter.
In addition, the ith row and the j column of the sensitivity matrix D are DijDenotes the ith order modal parameterSensitivity of the number to the jth damping parameter. Obviously, if only the damping parameters are to be identified, j is 1. For example, in a damping system, the sensitivities of the first 6 modal frequencies to a damping parameter are 0.01,0.02,0.03, 0.01, respectively. The sensitivity matrix thus constructed is: [0.01,0.02,0.03,0.03,0.01,0.01]。
204. And acquiring modal parameters which are sensitive to the damping parameter change in the finite element model according to the sensitivity matrix.
It should be noted that, since each row of the sensitivity matrix represents the sensitivity of each order of modal parameter to a change of a certain damping parameter, in order to obtain the modal parameter that is sensitive to a change of a certain damping parameter, only a certain number of modal parameters with higher sensitivity need to be selected from a row of elements corresponding to the damping parameter in the sensitivity matrix. Taking the sensitivity matrix as an example, it can be seen that the values of the elements in the 3 rd column and the 4 th column are the highest and are 0.03, so that the modal frequencies of the 3 rd order and the 4 th order are selected as the modal parameters sensitive to the damping parameter change.
On the basis of the above embodiment, the applying the same excitation force to the solid model and the finite element model respectively to obtain the modal parameters of the solid model and the modal parameters of the finite element model specifically includes:
applying an excitation force to the entity model, collecting an excitation signal and a response signal at the same time, and carrying out experimental modal analysis on a test signal of the entity model to obtain modal parameters of the entity model;
loading the excitation signal into the finite element model, calculating a response signal of the finite element model, and performing calculation modal analysis on the response signal of the finite element model to obtain modal parameters of the finite element model.
As can be understood by those skilled in the art, the positions of the nodes for calculating the vibration signals in the finite element model are consistent with the positions of the measured points for collecting the vibration signals in the solid model, so that the vibration signals at the same positions are calculated.
On the basis of the above embodiments, the constructing an objective function according to the error between the modal parameters that have correlation and are sensitive to the damping parameter change according to the embodiments of the present invention specifically includes:
determining a modal parameter which has correlation and is sensitive to the damping parameter change as a target modal parameter;
it should be noted that, in the embodiment of the present invention, firstly, modal parameters that are sensitive to damping parameter changes, such as 2-order modal frequency, 3-order modal damping, 2-order modal stiffness, and the like, can be known according to sensitivity analysis, then, correlation analysis is performed on the modal parameters of the solid model and the modal parameters of the finite element model obtained based on the same excitation force, and the modal frequency related to the 2-section modal frequency of the solid model, the modal damping related to the 3-section modal damping of the solid model, and the modal stiffness related to the 2-order modal stiffness of the solid model are found from the finite element model, that is, the target modal parameters are obtained.
Setting the weight corresponding to each target modal parameter according to a preset rule;
it should be noted that, because different target modal parameters may have different sensitivities to the change of the damping parameter, and at the same time, different target modal parameters also have different influences on the damping parameter, a corresponding weight may be set for each target modal parameter according to experience.
The objective function is constructed according to the following formula:
wherein,representing the ith target modal parameter in the finite element model,representing sums in a solid modelCorresponding ith target modal parameter,. DELTA.siRepresenting the error between the ith target modal parameter in the finite element model and the solid model, wiRepresents the weight corresponding to the ith target modal parameter, TminAnd expressing the target function, namely taking the minimum value of the product of the error and the weight between the target modal parameters in the finite element model and the solid model and then summing as a target value.
On the basis of the above embodiment, determining the correlation between the modal parameters of the solid model and the modal parameters of the finite element model specifically includes:
and (3) evaluating the correlation of modal shape by adopting a modal confidence criterion:
wherein,respectively representing the ith order vibration mode of the solid model and the jth order vibration mode of the finite element model; in actually calculating the mode shape, the MAC calculation may be performed with coordinates of a series of points in the mode shape.
If MACijAnd if the value is larger than the preset threshold (for example, 0.7), determining that the ith order modal parameter of the solid model and the jth order modal parameter of the finite element model have correlation.
On the basis of the above embodiments, the optimization algorithm is one of a sequence quadratic programming algorithm, an ant colony algorithm, a genetic algorithm, a simulated annealing algorithm, and a particle swarm algorithm. In a preferred embodiment, the optimization algorithm is a sequential quadratic programming method, and is verified, and the solution of a constraint equation set can be quickly converted into a constraint optimization problem by adopting the sequential quadratic programming method and the optimization method of sensitivity analysis, so that the equivalent precision of the model is ensured, and the speed of iterative computation is also ensured.
On the basis of the embodiment, the damping system comprises a damping unit, the lower part of the damping unit is fixedly connected to a supporting surface, and a mass block is fixed above the damping unit;
correspondingly, the constructing of the finite element model related to the damping parameters according to the solid model of the damping system specifically includes:
and establishing a mass point model of the mass block by using a concentrated mass point unit in finite element analysis software, meshing the damping units by using a connecting unit in the finite element analysis software, and establishing the finite element model according to the mass point model and the meshed damping units.
It should be noted that the finite element model is established by converting a mechanical structure into multiple nodes and connecting the multiple nodes with a unit, where a node is a coordinate of a point in the mechanical structure, and a number and a coordinate position are specified. After the nodes are built, proper units are needed to be used for connecting the mechanical structures into units according to the nodes, and the finite element model is completed. Whether the unit selection is correct or not will determine the final analysis result. Finite element analysis software (e.g., ANSYS) provides a number of cells of different properties and types, each cell having a fixed number, e.g., LINK is cell number 1 and SOLID is cell number 45. In the embodiment of the invention, the damping system is subjected to grid division by a MASS concentration point unit (MASS), and a MASS block is regarded as a MASS concentration point by using the MASS, so that the effects of simplifying a model, reducing the calculation amount and accelerating the calculation speed can be achieved; the damping units are subjected to grid division by a connecting unit (BUSH), and damping parameters of the damping units can be defined by the BUSH.
In an optional embodiment, by changing the size of the mass block above the damping unit, a system with different mass points and the same damping unit can be obtained, and by identifying the system, the problem that a single model cannot describe the frequency domain damping nonlinearity of the damping unit can be solved.
On the basis of the above embodiments, the applying the same excitation force to the solid model and the finite element model respectively further includes:
the acceleration sensor is adhered to the surface of the mass block, and a plurality of test points are vertically arranged on the mass block, so that excitation signals are sequentially generated along the vertical direction when excitation force is applied. It should be noted that, because the working direction of the actual rubber shock absorber is vertical, the vertical excitation mode is more beneficial to identify the damping parameters of the actual rubber shock absorber.
Fig. 3 shows a functional block diagram of a damping parameter identification system according to an embodiment of the present invention, and as shown in fig. 3, the identification system includes:
a finite element model module 301, configured to construct a finite element model related to the damping parameters according to the solid model of the damping system.
It should be noted that the damping system refers to a system including a damping unit, and the damping (english: damping) refers to a characteristic that the amplitude of vibration of any vibration system is gradually reduced in vibration due to an external effect or a reason inherent to the system, and a quantitative representation of the characteristic. The damping unit is a device which provides resistance to movement and reduces movement energy. The embodiments of the invention do not limit the damping system and the specific form and connection relationship of the damping units included in the damping system, and the finite element model is composed of nodes and elements. The finite element model of the embodiment of the invention is constructed by adopting two methods according to the complexity of the damping system: if the damping system is simpler, the nodes and the units are directly established according to the geometric shape of the mechanical structure; if the damping system is complex, a finite element model is established through points, lines, surfaces and volumes, and then solid mesh division is carried out to complete establishment of the finite element model.
And a sensitivity analysis module 302, configured to obtain a modal parameter, which is sensitive to the damping parameter change, in the finite element model according to a sensitivity analysis method.
In the embodiment of the present invention, the type of the damping parameter to be identified is at least one, for example: damping coefficient and material damping ratio. In the embodiment of the invention, the modal parameters are a general name, each order of modal parameters comprises a modal frequency, a modal shape, modal damping, modal rigidity, modal quality and the like, the modal frequencies are arranged from small to large, the smallest order is called as a first-order mode, and the order of the modal parameters required in the identification process can be adjusted according to the actual situation.
The modal parameters and the damping parameters belong to inherent characteristics of a mechanical structure, and after a finite element model is built, in order to enable the modal parameters and the damping parameters in the finite element model to be as close to a solid model as possible, the modal parameters and the damping parameters need to be continuously fine-tuned. Since the modal parameters and the damping parameters are associated with each other, that is, the damping parameters are necessarily changed after the modal parameters are adjusted, but since the associations between different modal parameters and different damping parameters are large or small, in order to identify the damping parameters more accurately, the modal parameters sensitive to the damping parameter change need to be found out, and thus the damping parameters can be identified more efficiently by adjusting the modal parameters sensitive to the damping parameter change. In the embodiment of the invention, the modal parameters which are sensitive to the damping parameter change in the finite element model are obtained through a sensitivity analysis method, and the sensitivity analysis method is a method for researching and analyzing the sensitivity degree of the state or output change of a system (or a model) to the system parameter or ambient condition change.
And the excitation module 303 is configured to apply the same excitation force to the solid model and the finite element model respectively to obtain a modal parameter of the solid model and a modal parameter of the finite element model.
It should be noted that, by applying an excitation force to the solid model, an acceleration response of the solid model may be acquired, and by analyzing the acceleration response, modal parameters of each order of the solid model and the finite element model may be identified. The same excitation force in the embodiment of the present invention means that the position, the magnitude and the direction of the applied excitation force are the same.
And the target function module 304 is used for determining the correlation between the modal parameters of the solid model and the modal parameters of the finite element model, and constructing a target function according to the error between the modal parameters which meet the correlation and are sensitive to the damping parameter change.
It can be known from the prior art that it is only meaningful to compare modal parameters belonging to the same mode shape, and therefore, after obtaining modal parameters of each level of the solid model and the finite element model, the correlation between the modal parameters of the solid model and the finite element model needs to be determined. Currently, there are two main methods for determination: one method is to look similar to the same order by visual observation, and this method is intuitive but has no quantitative index. The other method is to judge through a Mode Assessment Criterion (MAC), and the MAC method has the advantage of high precision.
The modal parameters meeting the correlation and sensitive to the damping parameter change in the embodiment of the invention are as follows: on one hand, the selected modal parameters are sensitive to the change of the damping parameters, so that the damping parameters send tiny changes, and the target function can also obviously change; on the other hand, the selected modal parameters need to have a correlation, for example, a modal frequency of 2 nd order is selected in the solid model, and a modal frequency of 3 rd order is selected in the finite element model, because the mode shape of 2 nd order of the solid model is consistent with the mode shape of 3 rd order of the finite element model, so the mode frequency of 2 nd order in the task solid model and the mode shape of 3 rd order in the finite element model are correlated.
And an optimizing module 305, configured to determine, according to an optimizing algorithm, a damping parameter when the objective function is converged stably, as an actual damping parameter of the damping system.
It should be noted that, the value of the damping parameter in the finite element model is optimized through the optimization algorithm, so that the modal parameter corresponding to the optimized finite element model is very close to the modal parameter corresponding to the solid model, and the effect that the optimized finite element model can truly reflect the solid model is achieved. It should be noted that, when the calculation method of the embodiment of the present invention is practically applied, it is found that stable convergence of the target function can be achieved only by performing optimization iteration for 5 to 15 times, and the efficiency is obviously superior to that of the static test method or the dynamic test method in the prior art.
Fig. 4 shows a functional block diagram of a sensitivity analysis module according to an embodiment of the present invention, and as shown in the figure, the sensitivity analysis module includes:
a damping parameter adjusting unit 401, configured to change a damping parameter in the finite element model within a preset range, so as to obtain a variation of the damping parameter;
it should be noted that, in the embodiment of the present invention, an adjustment range of the damping parameter is preset, and the damping parameter is adjusted within the preset range each time the damping parameter is adjusted.
A sensitivity obtaining unit 402, configured to calculate a variation of a modal parameter in the finite element model according to a perturbation method, and regarding any modal parameter, take the variation of the modal parameter and the variation of the damping parameter as a sensitivity of the modal parameter.
for example, when the damping parameter is ξ before being changed, the ith modal parameter is A, the damping parameter is Δ ξ + ξ after being changed, and the modal parameter is A ', the sensitivity of the modal parameter is (A' -A)/Δ ξ.
A sensitivity matrix obtaining unit 403, configured to construct a sensitivity matrix according to the sensitivity of each modal parameter to the damping parameter.
In addition, the ith row and the j column of the sensitivity matrix D are DijAnd the sensitivity of the ith order modal parameter to the jth damping parameter is shown. Obviously, if only the damping parameters are to be identified, j is 1. For example, in a damping system, the first 6 modal frequencies damp a certain dampingThe sensitivity of the parameters was 0.01,0.02,0.03, 0.01, respectively. The sensitivity matrix thus constructed is: [0.01,0.02,0.03,0.03,0.01,0.01]。
A modal parameter obtaining unit 404, configured to obtain a modal parameter sensitive to the damping parameter change in the finite element model according to the sensitivity matrix.
It should be noted that, since each row of the sensitivity matrix represents the sensitivity of each order of modal parameter to a change of a certain damping parameter, in order to obtain the modal parameter that is sensitive to a change of a certain damping parameter, only a certain number of modal parameters with higher sensitivity need to be selected from a row of elements corresponding to the damping parameter in the sensitivity matrix. Taking the sensitivity matrix as an example, it can be seen that the values of the elements in the 3 rd column and the 4 th column are the highest and are 0.03, so that the modal frequencies of the 3 rd order and the 4 th order are selected as the modal parameters sensitive to the damping parameter change.
On the basis of the above embodiments, the excitation module specifically includes:
the entity excitation unit is used for applying excitation force to the entity model, acquiring an excitation signal and a response signal at the same time, and performing test modal analysis on a test signal of the entity model to obtain modal parameters of the entity model;
and the model excitation unit is used for loading the excitation signal into the finite element model, calculating a response signal of the finite element model, and performing computational modal analysis on the response signal of the finite element model to obtain modal parameters of the finite element model.
As can be understood by those skilled in the art, the positions of the nodes for calculating the vibration signals in the finite element model are consistent with the positions of the measured points for collecting the vibration signals in the solid model, so that the vibration signals at the same positions are calculated.
On the basis of the foregoing embodiments, the objective function module according to the embodiments of the present invention specifically includes: the correlation determining unit is used for determining the correlation between the modal parameters of the solid model and the modal parameters of the finite element model; and the target function unit is used for constructing a target function according to the error between the modal parameters which meet the correlation and are sensitive to the damping parameter change.
Wherein the correlation determination unit is specifically configured to:
and (3) evaluating the correlation of modal shape by adopting a modal confidence criterion:
wherein,respectively representing the ith order vibration mode of the solid model and the jth order vibration mode of the finite element model;
if MACijAnd if the parameter is larger than the preset threshold, determining that the ith order modal parameter of the solid model and the jth order modal parameter of the finite element model have correlation.
FIG. 5 shows a functional block diagram of an objective function unit of an embodiment of the present invention, as shown in FIG. 5, the objective function unit further includes:
a target modal parameter subunit 501, configured to determine a modal parameter that has a correlation and is sensitive to a change of the damping parameter, as a target modal parameter;
it should be noted that, in the embodiment of the present invention, firstly, modal parameters that are sensitive to damping parameter changes, such as 2-order modal frequency, 3-order modal damping, 2-order modal stiffness, and the like, can be known according to sensitivity analysis, then, correlation analysis is performed on the modal parameters of the solid model and the modal parameters of the finite element model obtained based on the same excitation force, and the modal frequency related to the 2-section modal frequency of the solid model, the modal damping related to the 3-section modal damping of the solid model, and the modal stiffness related to the 2-order modal stiffness of the solid model are found from the finite element model, that is, the target modal parameters are obtained.
A weight resetting stator unit 502, configured to set a weight corresponding to each target modal parameter according to a preset rule;
it should be noted that, because different target modal parameters may have different sensitivities to the change of the damping parameter, and at the same time, different target modal parameters also have different influences on the damping parameter, a corresponding weight may be set for each target modal parameter according to experience.
An objective function constructing subunit 503, configured to construct an objective function according to the following formula:
wherein,representing the ith target modal parameter in the finite element model,representing sums in a solid modelCorresponding ith target modal parameter,. DELTA.siRepresenting the error between the ith target modal parameter in the finite element model and the solid model, wiRepresents the weight corresponding to the ith target modal parameter, TminAnd expressing the target function, namely taking the minimum value of the product of the error and the weight between the target modal parameters in the finite element model and the solid model and then summing as a target value.
On the basis of the above embodiments, the optimization algorithm used by the optimization module is one of a sequence quadratic programming algorithm, an ant colony algorithm, a genetic algorithm, a simulated annealing algorithm, and a particle swarm algorithm. In a preferred embodiment, the optimization algorithm is a sequential quadratic programming method, and is verified, and the solution of a constraint equation set can be quickly converted into a constraint optimization problem by adopting the sequential quadratic programming method and the optimization method of sensitivity analysis, so that the equivalent precision of the model is ensured, and the speed of iterative computation is also ensured.
On the basis of the embodiment, the damping system comprises a damping unit, the lower part of the damping unit is fixedly connected to a supporting surface, and a mass block is fixed above the damping unit;
accordingly, the finite element model module is specifically configured to: and establishing a mass point model of the mass block by using a concentrated mass point unit in finite element analysis software, meshing the damping units by using a connecting unit in the finite element analysis software, and establishing the finite element model according to the mass point model and the meshed damping units.
It should be noted that the finite element model is established by converting a mechanical structure into multiple nodes and connecting the multiple nodes with a unit, where a node is a coordinate of a point in the mechanical structure, and a number and a coordinate position are specified. After the nodes are built, proper units are needed to be used for connecting the mechanical structures into units according to the nodes, and the finite element model is completed. Whether the unit selection is correct or not will determine the final analysis result. Finite element analysis software (e.g., ANSYS) provides a number of cells of different properties and types, each cell having a fixed number, e.g., LINK is cell number 1 and SOLID is cell number 45. In the embodiment of the invention, the damping system is subjected to grid division by a MASS concentration point unit (MASS), and a MASS block is regarded as a MASS concentration point by using the MASS, so that the effects of simplifying a model, reducing the calculation amount and accelerating the calculation speed can be achieved; the damping units are subjected to grid division by a connecting unit (BUSH), and damping parameters of the damping units can be defined by the BUSH.
In an optional embodiment, by changing the size of the mass block above the damping unit, a system with different mass points and the same damping unit can be obtained, and by identifying the system, the problem that a single model cannot describe the frequency domain damping nonlinearity of the damping unit can be solved.
On the basis of the above embodiments, the excitation module is further configured to, before applying the same excitation force to the solid model and the finite element model, respectively: the acceleration sensor is adhered to the surface of the mass block, and a plurality of test points are vertically arranged on the mass block, so that excitation signals are sequentially generated along the vertical direction when excitation force is applied. It should be noted that, because the working direction of the actual rubber shock absorber is vertical, the vertical excitation mode is more beneficial to identify the damping parameters of the actual rubber shock absorber.
Fig. 6 shows a schematic diagram of a framework of an electronic device of an embodiment of the invention.
Referring to fig. 6, the electronic device includes: a processor (processor)601, a memory (memory)602, and a bus 603;
wherein, the processor 601 and the memory 602 complete the communication with each other through the bus 603;
the processor 601 is configured to call program instructions in the memory 602 to perform the methods provided by the above-mentioned method embodiments, for example, including: constructing a finite element model related to damping parameters according to the entity model of the damping system; acquiring modal parameters which are sensitive to the damping parameter change in the finite element model according to a sensitivity analysis method; respectively applying the same excitation force to the solid model and the finite element model to obtain the modal parameters of the solid model and the modal parameters of the finite element model; determining the correlation between the modal parameters of the entity model and the modal parameters of the finite element model, and constructing a target function according to the error between the modal parameters which meet the correlation and are sensitive to the damping parameter change; and determining a damping parameter when the target function is stably converged according to an optimization algorithm, wherein the damping parameter is used as the actual damping parameter of the damping system.
Another embodiment of the invention provides a non-transitory computer-readable storage medium storing computer instructions that cause the computer to perform a method provided by the above method embodiments, for example, comprising: constructing a finite element model related to damping parameters according to the entity model of the damping system; acquiring modal parameters which are sensitive to the damping parameter change in the finite element model according to a sensitivity analysis method; respectively applying the same excitation force to the solid model and the finite element model to obtain the modal parameters of the solid model and the modal parameters of the finite element model; determining the correlation between the modal parameters of the entity model and the modal parameters of the finite element model, and constructing a target function according to the error between the modal parameters which meet the correlation and are sensitive to the damping parameter change; and determining a damping parameter when the target function is stably converged according to an optimization algorithm, wherein the damping parameter is used as the actual damping parameter of the damping system.
In order to more intuitively show the technical effect of the method for calculating the damping parameter according to the embodiment of the present invention, an example will be described. In the present example, the damping system comprises a rubber block with a vertical stiffness of about 15N/mm, a 9.5kg mass block is fixed above the rubber block by screws, a mass block is fixed below the rubber block on the foundation by screws, and in finite element software, the rubber block is simulated by a push unit and the mass block is simulated by concentrated mass points. One end of the push unit is fixedly supported, and the other end of the push unit is connected with the quality point through node superposition. The finite element model is established as 1 Bush unit and 1 Lumped mass unit. In the implementation process of the example, the modal characteristic values are found to be most sensitive to the damping value change, so that the target function is constructed by the error between the modal characteristic values of the solid model and the finite element model. In the initial finite element model, the damping value was set to 4.5 Ns/mm, and after identification, it was 4.5 Ns/mm. Fig. 7 shows a convergence curve of the imaginary part error of the modal eigenvalue in the present example, fig. 8 shows a convergence curve of the real part error of the modal eigenvalue in the present example, and fig. 9 shows a convergence curve of the damping parameter (i.e., damping value) in the present example. As can be seen from fig. 7-9, the damping parameters tend to be stable after 12 iterations, indicating that the optimization is complete and the efficiency is extremely high.
The above-described embodiments of the apparatus are merely illustrative, and the units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment. One of ordinary skill in the art can understand and implement it without inventive effort.
Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware. With this understanding in mind, the above-described technical solutions may be embodied in the form of a software product, which can be stored in a computer-readable storage medium such as ROM/RAM, magnetic disk, optical disk, etc., and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the methods described in the embodiments or some parts of the embodiments.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.
Claims (10)
1. A method for identifying a damping parameter, comprising:
constructing a finite element model related to damping parameters according to the entity model of the damping system;
acquiring modal parameters which are sensitive to the damping parameter change in the finite element model according to a sensitivity analysis method;
respectively applying the same excitation force to the solid model and the finite element model to obtain the modal parameters of the solid model and the modal parameters of the finite element model;
determining the correlation between the modal parameters of the entity model and the modal parameters of the finite element model, and constructing a target function according to the error between the modal parameters which meet the correlation and are sensitive to the damping parameter change;
and determining a damping parameter when the target function is stably converged according to an optimization algorithm, wherein the damping parameter is used as the actual damping parameter of the damping system.
2. The identification method according to claim 1, wherein the modal parameters of the finite element model that are sensitive to the damping parameter change are obtained according to a sensitivity analysis method, specifically:
changing the damping parameters in the finite element model within a preset range to obtain the variation of the damping parameters;
calculating the variation of the modal parameters in the finite element model according to a perturbation method, and regarding any modal parameter, taking the ratio of the variation of the modal parameter to the variation of the damping parameter as the sensitivity of the modal parameter;
constructing a sensitivity matrix according to the sensitivity of each modal parameter to the damping parameter;
and acquiring modal parameters which are sensitive to the damping parameter change in the finite element model according to the sensitivity matrix.
3. The identification method according to claim 1, wherein the same excitation force is applied to the solid model and the finite element model respectively to obtain modal parameters of the solid model and modal parameters of each order of the finite element model, and specifically:
applying an excitation force to the entity model, collecting an excitation signal and a response signal at the same time, and carrying out experimental modal analysis on a test signal of the entity model to obtain modal parameters of the entity model;
loading the excitation signal into the finite element model, calculating a response signal of the finite element model, and performing calculation modal analysis on the response signal of the finite element model to obtain modal parameters of the finite element model.
4. The identification method according to claim 1, wherein the constructing of the objective function from the correlated error between the modal parameters sensitive to the damping parameter variation is:
determining a modal parameter which has correlation and is sensitive to the damping parameter change as a target modal parameter;
setting the weight corresponding to each target modal parameter according to a preset rule;
the objective function is constructed according to the following formula:
wherein,representing the ith target modal parameter in the finite element model,representing sums in a solid modelCorresponding ith target modal parameter,. DELTA.siRepresenting the error between the ith target modal parameter in the finite element model and the solid model, wiRepresents the weight corresponding to the ith target modal parameter, TminRepresenting the objective function.
5. The identification method according to claim 1, wherein the determining of the correlation between the modal parameters of the solid model and the modal parameters of the finite element model comprises:
and (3) evaluating the correlation of modal shape by adopting a modal confidence criterion:
wherein,respectively representing the ith order vibration mode of the solid model and the jth order vibration mode of the finite element model;
if MACijAnd if the parameter is larger than the preset threshold, determining that the ith order modal parameter of the solid model and the jth order modal parameter of the finite element model have correlation.
6. The identification method of claim 1, wherein the optimization algorithm is one of a sequential quadratic programming algorithm, an ant colony algorithm, a genetic algorithm, a simulated annealing algorithm, and a particle swarm algorithm.
7. The identification method according to claim 1, wherein the damping system comprises a damping unit, the lower part of the damping unit is fixedly connected to the supporting surface, and a mass block is fixed on the upper part of the damping unit;
correspondingly, the constructing of the finite element model related to the damping parameters according to the solid model of the damping system specifically includes:
and establishing a mass point model of the mass block by using a concentrated mass point unit in finite element analysis software, meshing the damping units by using a connecting unit in the finite element analysis software, and establishing the finite element model according to the mass point model and the meshed damping units.
8. The identification method of claim 7, wherein said applying the same excitation force to said solid model and finite element model, respectively, further comprises:
the acceleration sensor is adhered to the surface of the mass block, and a plurality of test points are vertically arranged on the mass block, so that excitation signals are sequentially generated along the vertical direction when excitation force is applied.
9. An electronic device, comprising:
at least one processor; and
at least one memory communicatively coupled to the processor, wherein:
the memory stores program instructions executable by the processor, the processor invoking the program instructions to perform the method of any of claims 1 to 8.
10. A non-transitory computer-readable storage medium storing computer instructions for causing a computer to perform the method according to any one of claims 1 to 8.
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