CN115809575A - Working condition transmission path analysis method - Google Patents

Working condition transmission path analysis method Download PDF

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CN115809575A
CN115809575A CN202211443236.3A CN202211443236A CN115809575A CN 115809575 A CN115809575 A CN 115809575A CN 202211443236 A CN202211443236 A CN 202211443236A CN 115809575 A CN115809575 A CN 115809575A
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matrix
force
model
reference point
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何智成
朱雨
周恩临
谭刚
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Hunan University
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Abstract

The invention relates to the field of signal processing of mechanical systems, in particular to a working condition transmission path analysis method, which comprises the following steps: establishing a finite element model at a passive end of a machine; arranging an acceleration sensor and a strain sensor at a machine reference point and a target point, respectively acquiring acceleration and strain information of the reference point and the target point under the condition of machine operation, and constructing a target point response matrix; estimating an optimal state variable according to the acceleration and the strain information of the reference point, wherein the optimal state variable comprises the interface force of the reference point, and constructing an interface force matrix; performing fast Fourier transform on the target point response matrix and the interface force matrix; constructing a transfer rate function; the total contribution of each transfer path is calculated. The invention can eliminate the influence of crosstalk to a certain extent and improve the accuracy and stability of the transfer rate function.

Description

Working condition transmission path analysis method
Technical Field
The invention relates to the field of signal processing of mechanical systems, in particular to a working condition transmission path analysis method.
Background
In order to identify the vibration/noise source of the mechanical system, analyze its contribution to the target point, and further guide the improvement and optimization of NVH parameters of the mechanical system, a Transfer Path Analysis (TPA) method is proposed and widely used in this field. The Traditional Transfer Path Analysis (CTPA) method is firstly proposed, has the highest precision and the most extensive application, and is often used as a standard rod of other TPA methods. However, since it is necessary to decouple the mechanical system when measuring the Frequency Response Function (FRF), a lot of time and effort costs are consumed. The operating condition Transfer Path Analysis (OTPA) method replaces the original interface force with the reference point response generated by the interface force, replaces the FRF with the Transfer Function (TF), does not need decoupling, has extremely high efficiency, and retains the boundary condition.
However, the input to the OTPA has no practical physical meaning, it is not a force, but a reference point response of the force, and therefore there is no direct relationship between the response of the target point and it, the reference point response is likely to be a co-action of multiple forces, which means that there is a cross-talk effect. Therefore, a new method for transmitting the operating condition path is needed.
Disclosure of Invention
In order to solve the technical problems, the invention provides a working condition transmission path analysis method, and the specific technical scheme is as follows.
A working condition transmission path analysis method is characterized by comprising the following steps:
establishing a finite element model at a passive end of a machine;
arranging an acceleration sensor and a strain sensor at a machine reference point and a target point, respectively acquiring acceleration and strain information of the reference point and the target point under the condition of machine operation, and constructing a target point response matrix Y (t);
estimating an optimal state variable according to the acceleration and the strain information of the reference point, wherein the optimal state variable comprises the interface force of the reference point, and constructing an interface force matrix X (t);
performing fast Fourier transform on the target point response matrix and the interface force matrix to obtain Y (w) and X (w), and converting time domain information into frequency domain information;
construction of the transfer Rate function T (w) λ ，
Figure BDA0003947865820000021
Wherein, T (w) = Y (w) X (w) -1 Improving regularization parameters
Figure BDA0003947865820000022
Standard regularization parameter λ is determined by applying the GVV criterion
Figure BDA0003947865820000023
Calculating to obtain I as a unit matrix;
calculating a total contribution Y (w) = T (w) of each transfer path according to the transfer rate function λ And X (w), completing the analysis of the working condition transmission path.
Further, the step of estimating the optimal state variable according to the acceleration and strain information of the reference point includes:
constructing a linear state space model of a structural dynamics system:
Figure BDA0003947865820000024
wherein
Figure BDA0003947865820000025
Is a state variable, C is an observation matrix of a state space model, D is a direct transfer matrix of the state space model, A is a system matrix of the state space model, B is a control matrix of the state space model, w (t) is process noise added in consideration of model uncertainty, v (t) is measurement noise added in consideration of measurement uncertainty, q (t) is modal displacement,
Figure BDA0003947865820000026
is modal velocity, u (t) is unknown force, y (t) is information measured by the sensor;
random walk mode for establishing interface forceType (2):
Figure BDA0003947865820000027
w u (t) is the input force model noise on the force parameter derivatives, representing a process where the force derivatives or force increments are completely random, and extending the random walk model of the interfacial force to state variables
Figure BDA0003947865820000028
Obtaining a new linear state space model:
Figure BDA0003947865820000029
wherein
Figure BDA00039478658200000210
H * ＝[C D]，
Figure BDA00039478658200000211
Use of
Figure BDA00039478658200000212
The new linear state space model is discretized by the sampling rate to obtain a discrete linear state space model:
Figure BDA00039478658200000213
wherein
Figure BDA00039478658200000214
Wherein
Figure BDA00039478658200000215
y k ＝y(kΔt)，v k ＝v(kΔt)，k＝1,...,N；
Performing Kalman filtering to obtain optimal state estimation vector
Figure BDA00039478658200000216
Including the unknown force u (t) and the interfacial force with the unknown force u (t) as a reference point.
Further, the Kalman filtering processManaging comprises updating time and updating test; the time update formula is
Figure BDA00039478658200000217
The test update formula is:
Figure BDA00039478658200000218
wherein
Figure BDA00039478658200000219
Is an a posteriori state estimate at time k-1,
Figure BDA0003947865820000031
is an a priori state estimate at time k,
Figure BDA0003947865820000032
q is the covariance matrix of the model, K k Is the Kalman gain at time k, R is the covariance matrix of the measurement noise, y k For the target point corresponding matrix Y n×r Information of n response points at t = k Δ t in (t);
Figure BDA0003947865820000033
the covariance is estimated a priori for time instance k,
Figure BDA0003947865820000034
covariance is estimated for the a posteriori at time k.
Further, the arranging of the acceleration sensor and the strain sensor at the machine reference point and the target point includes the steps of:
constructing a sensor pool: randomly selecting nodes and units for acceleration/strain measurement in a finite element model;
training: carrying out finite element model simulation on static and dynamic loads with different directions, amplitudes and frequencies, and carrying out load identification on the premise of knowing an excitation input position;
coarse screening: firstly, sensors with low signal-to-noise ratio in training are deleted, and secondly, sensors which are too close to each other and have the same type are deleted;
observability screening: observability screening of sensors based on PBH criteria,
Figure BDA0003947865820000035
A d discretized system matrix, ω, for system matrix A d For discretizing the system matrix A d Characteristic value of (C) d A discretized observation matrix that is an observation matrix C;
the sensor locations in the finite element model are located in the actual physical structure.
Further, the process of locating the sensor position in the finite element model in the actual physical structure includes:
identifying sensor locations using a camera, defining an uncertainty region for each sensor;
and measuring the dependent variable of each unit in the uncertain region along the measuring direction by using a sensor, estimating an optimal state variable, and finding a group of units with the minimum calculated load and the minimum real load. .
Has the advantages that: according to the method for analyzing the working condition transmission path, the optimal state variable is estimated according to the acceleration and the strain information of the reference point, so that the interface force of the reference point is estimated, the input end has actual physical significance, the influence of crosstalk is eliminated to a certain extent, and the accuracy and the stability of a transfer rate function are improved. The regularization parameter of the transfer rate function can be dynamically adjusted along with different frequencies and response orders, and meanwhile, the accuracy and the stability of the transfer rate function are considered.
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FIG. 1 is a schematic flow chart of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Examples
The embodiment provides a working condition transmission path analysis method, which specifically comprises the following steps:
the method comprises the following steps:
s1, establishing a finite element model at a passive end of a machine;
s2, arranging an acceleration sensor and a strain sensor at a machine reference point and a target point, respectively acquiring acceleration and strain information of the reference point and the target point under the condition of machine operation, and constructing a target point response matrix Y (t);
s3, estimating an optimal state variable according to the acceleration and strain information of the reference point, wherein the optimal state variable comprises the interface force of the reference point, and constructing an interface force matrix X (t);
s4, performing fast Fourier transform on the target point response matrix and the interface force matrix to obtain Y (w) and X (w), and converting time domain information into frequency domain information;
s5, constructing a transfer rate function T (w) λ ，
Figure BDA0003947865820000041
Wherein, T (w) = Y (w) X (w) -1 Improving regularization parameters
Figure BDA0003947865820000042
Standard regularization parameter λ is determined by applying the GVV criterion
Figure BDA0003947865820000043
Calculating to obtain I as a unit matrix;
s6, calculating the total contribution Y (w) = T (w) of each transfer path according to the transfer rate function λ And X (w), completing the analysis of the working condition transmission path.
Specifically, in steps S2 and S3, there are m unknown forces and n response points, so that there are n × m transmission paths, and when the machine century runs r times, a time domain data structure is acquired by a sensorEstablishing a corresponding matrix Y of target points n×r (w) and interfacial force matrix X m×r (t); e.g. at t = t N Time:
Figure BDA0003947865820000044
x m×r (t N ) Represents the mth force, the mth test t N The size at the moment;
Figure BDA0003947865820000045
y n×r (t N ) Representing the nth response, the r test t N The size at the moment.
In step S4, the target points are mapped to a matrix Y n×r (w) and interfacial force matrix X m×r (t) Fourier transform and conversion to the frequency domain to obtain X m×r (w) and Y n×r (w); for example:
at w = w N Frequency:
Figure BDA0003947865820000051
x m×r (w N ) Represents the m-th force, the r-th test w N A magnitude at frequency;
Figure BDA0003947865820000052
y n×r (w N ) Representing the nth response the nth test w N Magnitude at frequency.
In step S5, a transfer rate function is calculated using an improved regularization method. Wherein λ is w The improved regularization parameter is that the condition numbers of the interface force PSD matrix are different for different frequencies, and when the condition number cond (X) is too large, the inversion is ill-conditioned, and then the improved regularization parameter method automatically adjusts the above formula to make the regularization parameter larger, that is, cond (X) is larger to result in the improved regularization parameter lambda being larger w Becoming larger, large regularization parameters favor solution stability according to the regularization methods described previously.
Specifically, for formula Y (w) = T (w) λ X (w), matrix form:
Figure BDA0003947865820000053
the total contribution of the nth response point, the nth test, is:
y n×r (w)＝T n×1 (w)x 1×r (w)+T n×2 (w)x 2×r (w)+…T n×m (w)x m×r (w) according to a transfer rate function T (w) λ And obtaining the total contribution of the transmission path, thereby completing the analysis of the working condition transmission path.
According to the method for analyzing the working condition transmission path, the optimal state variable is estimated according to the acceleration and the strain information of the reference point, so that the interface force of the reference point is estimated, the input end has actual physical significance, the influence of crosstalk is eliminated to a certain extent, and the accuracy and the stability of a transfer rate function are improved. The regularization parameter of the transfer rate function can be dynamically adjusted along with different frequencies and response orders, and meanwhile, the accuracy and the stability of the transfer rate function are considered.
Specifically, the step of estimating the optimal state variable from the acceleration and strain information of the reference point in step S4 includes:
constructing a linear state space model of a structural dynamics system:
Figure BDA0003947865820000054
wherein
Figure BDA0003947865820000055
Is a state variable, C is an observation matrix of a state space model, D is a direct transfer matrix of the state space model, A is a system matrix of the state space model, B is a control matrix of the state space model, w (t) is process noise added in consideration of model uncertainty, v (t) is measurement noise added in consideration of measurement uncertainty, q (t) is modal displacement,
Figure BDA0003947865820000061
is the speed of the mode shape,u (t) is the unknown force, y (t) is the information measured by the sensor;
establishing a random walk model of interface force:
Figure BDA0003947865820000062
w u (t) is the input force model noise on the force parameter derivatives, representing a process where the force derivatives or force increments are completely random, and extending the random walk model of the interfacial force to state variables
Figure BDA0003947865820000063
Obtaining a new linear state space model:
Figure BDA0003947865820000064
wherein
Figure BDA0003947865820000065
H * ＝[C D]，
Figure BDA0003947865820000066
Use of
Figure BDA0003947865820000067
The new linear state space model is discretized by the sampling rate to obtain a discrete linear state space model:
Figure BDA0003947865820000068
wherein
Figure BDA0003947865820000069
Wherein
Figure BDA00039478658200000610
y k ＝y(kΔt)，v k ＝v(kΔt)，k＝1,...,N；
Performing Kalman filtering to obtain optimal state estimation vector
Figure BDA00039478658200000611
Including an unknown force u (t) andthe unknown force u (t) is the interfacial force at the reference point.
The interfacial force refers to: under the operation condition of the machine, an excitation force is generated at the active end of the machine, and an interface force is generated at the active-passive interface, so that the target point of the passive end is influenced. For example, the excitation force is generated by an automobile engine, the interface force is generated by an engine suspension, and the force at the connecting point of the engine suspension and the frame, namely the unknown force u (t) to be required, influences the frame target point, so that the unknown force u (t) can be obtained by utilizing the process to carry out the optimal state estimation, and the unknown force is taken as the interface force.
Wherein the Kalman filtering process comprises a time update and a test update; the time update formula is
Figure BDA00039478658200000612
The test update formula is:
Figure BDA00039478658200000613
wherein
Figure BDA00039478658200000614
Is an a posteriori state estimate at time k-1,
Figure BDA00039478658200000615
is an a priori state estimate at time k,
Figure BDA00039478658200000616
q is the covariance matrix of the model, K k Is the Kalman gain at time k, R is the covariance matrix of the measurement noise, y k For the target point corresponding matrix Y n×r Information of n response points at (t) where t = k Δ t;
Figure BDA00039478658200000617
the covariance is estimated a priori for time instance k,
Figure BDA00039478658200000618
the covariance is estimated a posteriori for time k,
Figure BDA00039478658200000619
is defined as:
Figure BDA0003947865820000071
the Kalman gain K is found by minimizing its trace (sum of variances) to minimize the error k 。
Specifically, the arrangement of the acceleration sensor and the strain sensor at the machine reference point and the target point includes the steps of:
constructing a sensor pool: randomly selecting nodes and units for acceleration/strain measurement in a finite element model;
training: carrying out finite element model simulation on static and dynamic loads with different directions, amplitudes and frequencies, and carrying out load identification on the premise of knowing an excitation input position;
coarse screening: firstly, sensors with low signal-to-noise ratio in training are deleted, and secondly, sensors which are too close to each other and have the same type are deleted;
observability screening: observability screening of sensors based on PBH criteria,
Figure BDA0003947865820000072
A d discretized system matrix, ω, for system matrix A d For discretizing the system matrix A d Characteristic value of (C) d A discretized observation matrix that is an observation matrix C;
the sensor locations in the finite element model are located in the actual physical structure.
The method comprises the steps that firstly, a ProCam camera is used for identifying the position of a sensor, and an uncertainty area is defined for each sensor by considering the measurement precision of an instrument and the geometric precision of a finite element model; second, the amount of strain in the measurement direction of each cell in the uncertainty region is evaluated, finding the cell that minimizes the error between a set of trained values and the experimental data.
Although the present invention has been described in detail with reference to the foregoing embodiments, 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; 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 (5)

1. A working condition transmission path analysis method is characterized by comprising the following steps:
establishing a finite element model at a passive end of a machine;
arranging an acceleration sensor and a strain sensor at a machine reference point and a target point, respectively acquiring acceleration and strain information of the reference point and the target point under the condition of machine operation, and constructing a target point response matrix Y (t);
estimating an optimal state variable according to the acceleration and the strain information of the reference point, wherein the optimal state variable comprises the interface force of the reference point, and constructing an interface force matrix X (t);
performing fast Fourier transform on the target point response matrix and the interface force matrix to obtain Y (w) and X (w), and converting time domain information into frequency domain information;
construction of the transfer Rate function T (w) λ ，T(w) λ ＝argmin(||T(w)X(w)-Y(w)|| 2 +λ 2 w ||T(w)|| 2 ) Wherein T (w) = Y (w) X (w) -1 Improving regularization parameters
Figure FDA0003947865810000011
Standard regularization parameter λ is determined by applying the GVV criterion
Figure FDA0003947865810000012
Calculating to obtain I as a unit matrix;
calculating a total contribution Y (w) = T (w) of each transfer path according to the transfer rate function λ And X (w), completing the analysis of the working condition transmission path.
2. The operating condition transmission path analysis method according to claim 1, wherein the step of estimating the optimal state variable according to the acceleration and strain information of the reference point comprises:
constructing a linear state space model of a structural dynamics system:
Figure FDA0003947865810000013
wherein
Figure FDA0003947865810000014
Is a state variable, C is an observation matrix of a state space model, D is a direct transfer matrix of the state space model, A is a system matrix of the state space model, B is a control matrix of the state space model, w (t) is process noise added in consideration of model uncertainty, v (t) is measurement noise added in consideration of measurement uncertainty, q (t) is modal displacement,
Figure FDA0003947865810000015
is modal velocity, u (t) is unknown force, y (t) is information measured by the sensor;
establishing a random walk model of interface force:
Figure FDA0003947865810000016
w u (t) is the input force model noise on the force parameter derivative, representing a process where the force derivative or force increment is completely random, and extending the stochastic walk model of the interfacial force to state variables
Figure FDA0003947865810000017
Obtaining a new linear state space model:
Figure FDA0003947865810000018
wherein
Figure FDA0003947865810000019
H * ＝[C D]，
Figure FDA00039478658100000110
Use of
Figure FDA0003947865810000021
The new linear state space model is discretized by the sampling rate to obtain a discrete linear state space model:
Figure FDA0003947865810000022
wherein
Figure FDA0003947865810000023
Wherein
Figure FDA0003947865810000024
y k ＝y(kΔt)，v k ＝v(kΔt)，k＝1,...,N；
Performing Kalman filtering to obtain optimal state estimation vector
Figure FDA0003947865810000025
Including the unknown force u (t) and the interfacial force with the unknown force u (t) as a reference point.
3. The operating condition transfer path analysis method according to claim 2, wherein the kalman filtering process includes a time update and a test update; the time update formula is
Figure FDA0003947865810000026
The test update formula is:
Figure FDA0003947865810000027
wherein
Figure FDA0003947865810000028
Is an a posteriori state estimate at time k-1,
Figure FDA0003947865810000029
is an a priori state estimate at time k,
Figure FDA00039478658100000210
q is the covariance matrix of the model, K k Is the kalman gain at time k, R is the covariance matrix of the measurement noise; y is k For the target point corresponding matrix Y n×r Information of n response points at t = k Δ t in (t);
Figure FDA00039478658100000211
the covariance is estimated a priori for time instance k,
Figure FDA00039478658100000212
covariance is estimated for the a posteriori at time k.
4. The operating condition transmission path analysis method according to claim 2, wherein the step of arranging acceleration sensors and strain sensors at the machine reference points and the target points comprises the steps of:
constructing a sensor pool: randomly selecting nodes and units for acceleration/strain measurement in a finite element model;
training: carrying out finite element model simulation on static and dynamic loads with different directions, amplitudes and frequencies, and carrying out load identification on the premise of knowing an excitation input position;
coarse screening: firstly, sensors with low signal-to-noise ratio in training are deleted, and secondly, sensors which are too close to each other and have the same type are deleted;
observability screening: observability screening of sensors based on PBH criteria,
Figure FDA00039478658100000213
A d discretized system matrix, ω, for system matrix A d For discretizing the system matrix A d Characteristic value of (C) d To watchMeasuring a discretization observation matrix of the matrix C;
the sensor locations in the finite element model are located in the actual physical structure.
5. The operating condition transmission path analysis method according to claim 4, wherein the process of positioning the sensor position in the finite element model in the actual physical structure comprises:
identifying sensor locations using a camera, defining an uncertainty region for each sensor;
and measuring the dependent variable of each unit in the uncertain region along the measuring direction by using a sensor, estimating an optimal state variable, and finding a group of units with the minimum calculated load and the minimum real load.
CN202211443236.3A 2022-11-17 2022-11-17 Working condition transmission path analysis method Pending CN115809575A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116527060A (en) * 2023-05-29 2023-08-01 北京理工大学 Information compression and anomaly detection method based on event trigger sampling

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116527060A (en) * 2023-05-29 2023-08-01 北京理工大学 Information compression and anomaly detection method based on event trigger sampling
CN116527060B (en) * 2023-05-29 2024-01-05 北京理工大学 Information compression and anomaly detection method based on event trigger sampling

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