A working condition transmission path analysis method

Abstract

The present application relates to the field of signal processing of mechanical system, and particularly relates to a working condition transmission path analysis method, comprising the following steps: establishing a finite element model at the passive end of a machine; arranging acceleration sensors and strain sensors at a reference point and a target point of the machine, and obtaining acceleration and strain information of the reference point and the target point respectively under the operating condition of the machine, and constructing a target point response matrix; estimating optimal state variables according to the acceleration and strain information of the reference point, wherein the optimal state variables contain interface forces 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 transmission rate function; and calculating total contribution of each transmission path. The present application can eliminate the influence of crosstalk to a certain extent, and improve the accuracy and stability of the transmission rate function.

Description

Technical Field

[0001] This invention relates to the field of signal processing in mechanical systems, and more specifically to a method for analyzing the transmission path of operating conditions. Background Technology

[0002] To identify vibration / noise sources in mechanical systems, analyze their contribution to target points, and guide the improvement and optimization of NVH parameters, transfer path analysis (TPA) has been proposed and widely used in this field. Traditional transfer path analysis (CTPA) was the earliest proposed method, boasting the highest accuracy and widest application, often serving as a benchmark for other TPA methods. However, it requires decoupling the mechanical system when measuring the frequency response function (FRF), consuming significant time and effort. Operational transfer path analysis (OTPA), on the other hand, replaces the original interface forces with the reference point response generated by interface forces and replaces the FRF with the transmissibility function (TF). It eliminates the need for decoupling, is highly efficient, and preserves boundary conditions.

[0003] However, the input to OTPA has no actual physical meaning; it is not a force but rather the response at a reference point. Therefore, the response at the target point is not directly related to it. The response at the reference point is likely the result of multiple forces acting together, which implies the presence of crosstalk. Therefore, a new method for transferring operating conditions is needed. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a method for analyzing the transmission path of operating conditions, the specific technical solution of which is as follows.

[0005] A method for analyzing the transmission path of operating conditions, characterized by comprising the following steps:

[0006] Establish a finite element model at the passive end of the machine;

[0007] Accelerometers and strain sensors are placed at the machine reference point and the target point. Acceleration and strain information at the reference point and the target point are acquired respectively under the condition of machine operation, and the target point response matrix Y(t) is constructed.

[0008] The optimal state variables are estimated based on the acceleration and strain information of the reference point. These optimal state variables include the interfacial forces at the reference point, and the interfacial force matrix X(t) is constructed.

[0009] The target point response matrix and the interface force matrix are subjected to fast Fourier transform to obtain Y(w) and X(w), thus converting the time domain information into the frequency domain information;

[0010] Construct the transfer rate function T(w) λ , Where, T(w) = Y(w)X(w) -1 Improve regularization parameters The standardization parameter λ is obtained by adopting the GVV criterion. The calculation shows that I is the identity matrix;

[0011] The total contribution of each transmission path, Y(w) = T(w), is calculated based on the transfer rate function. λ X(w) completes the working condition transmission path analysis.

[0012] Furthermore, the step of estimating the optimal state variables based on the acceleration and strain information of the reference point includes:

[0013] Constructing a linear state-space model of the structural dynamics system: Among them Let C be the state variable, D be the observation matrix of the state-space model, A be the system matrix of the state-space model, B be the control matrix of the state-space model, w(t) be the process noise considering model uncertainties, v(t) be the measurement noise considering measurement uncertainties, and q(t) be the modal displacement. Here, u(t) represents the modal velocity, u(t) represents the unknown force, and y(t) represents the information measured by the sensor.

[0014] Establish a random walk model of interface forces: w u (t) represents the input force model noise on the derivative of the force parameter, indicating that the force derivative or force increment is a completely random process, and extending the random walk model of interface forces to state variables. In this process, a new linear state-space model is obtained: in H * =[CD],

[0015] use Discretizing the new linear state-space model using the sampling rate yields a discrete linear state-space model: Among them in y k =y(kΔt), v k =v(kΔt), k = 1,...,N;

[0016] The optimal state estimation vector is obtained by performing Kalman filtering. It includes an unknown force u(t) and an interface force with the unknown force u(t) as the reference point.

[0017] Furthermore, the Kalman filtering process includes time updates and test updates; the time update formula is as follows: The test update formula is as follows: Among them It is the posterior state estimate at time k-1. It is the prior state estimate at time k. Q is the covariance matrix of the model, K k y is the Kalman gain at time k, R is the covariance matrix of the measurement noise, and y is the Kalman gain at time k. k The corresponding matrix Y of the target point n×r (t) contains information about n response points at time t = kΔt; Let the prior estimate of the covariance at time k be . Let be the posterior estimated covariance at time k.

[0018] Furthermore, the arrangement of the acceleration sensor and strain sensor at the machine reference point and target point includes the following steps:

[0019] Constructing the sensor pool: Randomly select nodes and elements for acceleration / strain measurement in the finite element model;

[0020] Training: Perform finite element model simulations with static and dynamic loads of different directions, amplitudes, and frequencies, and identify the loads given the known excitation input locations;

[0021] Coarse screening: First, remove sensors with low signal-to-noise ratios during training; second, remove sensors that are too similar to each other and of the same type.

[0022] Observability screening: Sensors are screened for observability based on the PBH standard.

[0023] A d Let ω be the discretized system matrix of system matrix A. d For the discretized system matrix A d eigenvalues, C d The discretized observation matrix is ​​the observation matrix C;

[0024] The sensor positions in the finite element model are located in the actual physical structure.

[0025] Furthermore, the process of locating the sensor positions in the finite element model within the actual physical structure includes:

[0026] Use cameras to identify sensor locations and define an uncertainty region for each sensor;

[0027] The strain of each element in the uncertain region along the measurement direction is measured using sensors. The optimal state variables are estimated, and the set of elements whose calculated load and actual load are minimized is found.

[0028] Beneficial effects: The working condition transfer path analysis method provided by this invention estimates the optimal state variables based on the acceleration and strain information of a reference point, thereby estimating the interface force at the reference point. This gives the input end a real physical meaning, eliminates the influence of crosstalk to a certain extent, and improves the accuracy and stability of the transfer rate function. Furthermore, it can dynamically adjust the magnitude of the regularization parameter of the transfer rate function according to different frequencies and response orders, while taking into account both the accuracy and stability of the transfer rate function. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of the process of the present invention. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0031] Example

[0032] This embodiment provides a method for analyzing the transmission path of operating conditions, which specifically includes the following steps:

[0033] Includes the following steps:

[0034] S1. Establish a finite element model at the passive end of the machine;

[0035] S2. Accelerometers and strain sensors are placed at the machine reference point and target point. Under the condition of machine operation, the acceleration and strain information of the reference point and target point are obtained respectively, and the target point response matrix Y(t) is constructed.

[0036] S3. Estimate the optimal state variables based on the acceleration and strain information of the reference point. The optimal state variables include the interfacial forces at the reference point, and construct the interfacial force matrix X(t).

[0037] S4. Perform a fast Fourier transform on the target point response matrix and the interface force matrix to obtain Y(w) and X(w), and convert the time domain information into frequency domain information.

[0038] S5. Construct the transfer rate function T(w) λ , Where, T(w) = Y(w)X(w) -1 Improve regularization parameters The standardization parameter λ is obtained by adopting the GVV criterion. The calculation shows that I is the identity matrix;

[0039] S6. Calculate the total contribution of each transmission path Y(w) = T(w) based on the transmission rate function. λ X(w) completes the working condition transmission path analysis.

[0040] Specifically, in steps S2 and S3, there are m unknown forces and n response points, thus there are n×m transmission paths. When the machine runs r times, the target point response matrix Y is constructed by collecting time-domain data through sensors. n×r (w) and the interfacial force matrix X m×r (t); for example, at t = t N time: x m×r (t N ) represents the m-th force and the r-th test t N Size at any given time; y n×r (t N ) represents the nth response and the rth test. N Size at any given moment.

[0041] In step S4, the target point corresponding matrix Y is... n×r (w) and the interfacial force matrix X m×r (t) Perform a Fourier transform to convert to the frequency domain to obtain X. m×r (w) and Y n×r (w); for example:

[0042] In w = w N frequency:

[0043] x m×r (w N ) represents the m-th force and the r-th test w N Magnitude at frequency;

[0044] y n×r (w N ) represents the nth response and the rth test. N Magnitude at frequency.

[0045] In step S5, the transfer rate function is calculated using an improved regularization method. Where λ wThis is an improved regularization parameter. For different frequencies, the condition number of the interfacial force PSD matrix varies. When the condition number cond(X) is too large, the inversion becomes ill-conditioned. In this case, the improved regularization parameter method automatically adjusts the regularization parameter using the formula above, increasing the regularization parameter. That is, increasing cond(X) leads to an increase in the improved regularization parameter λ. w As the regularization method described above increases, a larger regularization parameter is beneficial to the stability of the solution.

[0046] Specifically, for the formula Y(w)=T(w) λ X(w), in matrix form:

[0047]

[0048] The total contribution of the nth response point in the rth test is:

[0049] 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), and thus according to the transfer rate function T(w) λ The total contribution of the transmission path is obtained, thus completing the working condition transmission path analysis.

[0050] This embodiment provides a working condition transfer path analysis method that estimates the optimal state variables based on the acceleration and strain information of a reference point, thereby estimating the interfacial force at the reference point. This gives the input end a real physical meaning, eliminates the influence of crosstalk to a certain extent, and improves the accuracy and stability of the transfer rate function. Furthermore, it can dynamically adjust the magnitude of the regularization parameter of the transfer rate function according to different frequencies and response orders, while taking into account both the accuracy and stability of the transfer rate function.

[0051] Specifically, the step of estimating the optimal state variables based on the acceleration and strain information of the reference point in step S4 includes:

[0052] Constructing a linear state-space model of the structural dynamics system: in Let C be the state variable, D be the observation matrix of the state-space model, A be the system matrix of the state-space model, B be the control matrix of the state-space model, w(t) be the process noise considering model uncertainties, v(t) be the measurement noise considering measurement uncertainties, and q(t) be the modal displacement. Here, u(t) represents the modal velocity, u(t) represents the unknown force, and y(t) represents the information measured by the sensor.

[0053] Establish a random walk model of interface forces: w u (t) represents the input force model noise on the derivative of the force parameter, indicating that the force derivative or force increment is a completely random process, and extending the random walk model of interface forces to state variables. In this process, a new linear state-space model is obtained: in H * =[CD],

[0054] use Discretizing the new linear state-space model using the sampling rate yields a discrete linear state-space model: in in y k =y(kΔt), v k =v(kΔt), k = 1,...,N;

[0055] The optimal state estimation vector is obtained by performing Kalman filtering. It includes an unknown force u(t) and an interface force with the unknown force u(t) as the reference point.

[0056] Interface force refers to the excitation force generated at the active end of a machine under operating conditions. This excitation force, generated at the active-passive interface, affects the target point at the passive end. For example, the excitation force generated by a car engine creates an interface force through the engine mount. This interface force, the force at the connection point between the engine mount and the chassis, is the unknown force u(t) to be determined. This force affects the target point on the chassis. Therefore, by using the above process to perform optimal state estimation, the unknown force u(t) can be obtained, and this unknown force can be used as the interface force.

[0057] The Kalman filtering process includes time updates and test updates; the time update formula is as follows: The test update formula is as follows: in It is the posterior state estimate at time k-1. It is the prior state estimate at time k. Q is the covariance matrix of the model, K k y is the Kalman gain at time k, R is the covariance matrix of the measurement noise, and y is the Kalman gain at time k. k The corresponding matrix Y of the target point n×r (t) contains information about n response points at time t = kΔt; Let the prior estimate of the covariance at time k be . Let be the posterior estimated covariance at time k. Defined as: The Kalman gain K is determined by minimizing its trace (minimizing the sum of variances) to minimize the error. k .

[0058] Specifically, the placement of the acceleration sensor and strain sensor at the machine reference point and target point includes the following steps:

[0059] Constructing the sensor pool: Randomly select nodes and elements for acceleration / strain measurement in the finite element model;

[0060] Training: Perform finite element model simulations with static and dynamic loads of different directions, amplitudes, and frequencies, and identify the loads given the known excitation input locations;

[0061] Coarse screening: First, remove sensors with low signal-to-noise ratios during training; second, remove sensors that are too similar to each other and of the same type.

[0062] Observability screening: Sensors are screened for observability based on the PBH standard.

[0063] A d Let ω be the discretized system matrix of system matrix A. d For the discretized system matrix A d eigenvalues, C d The discretized observation matrix is ​​the observation matrix C;

[0064] The sensor positions in the finite element model are located in the actual physical structure.

[0065] The process of locating the sensor positions in the finite element model within the actual physical structure includes: first, using a ProCam camera to identify the sensor positions, and considering the measurement accuracy of the instrument and the geometric accuracy of the finite element model, defining an uncertainty region for each sensor; second, evaluating the strain of each element along the measurement direction within the uncertainty region, and finding the element that minimizes the error between a set of training values ​​and experimental data.

[0066] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method of operating deflection path analysis, characterized by, The method comprises the following steps: establishing a finite element model at the passive end of the machine; Acceleration sensors and strain sensors are arranged at a machine reference point and a target point, acceleration and strain information of the reference point and the target point are respectively acquired under a condition of machine operation, and a target point response matrix is constructed ; Estimating optimal state variables including interface forces of the reference points from acceleration and strain information of the reference points, and constructing an interface force matrix ; Fast Fourier Transforming the target point response matrix and the interface force matrix to obtain and converts time domain information into frequency domain information; Constructing the delivery rate function , where, , improving the regularization parameter ; standard regularization parameter is calculated by using the GCV criterion , I is the identity matrix; calculating the total contribution of each transmission path according to the transmission rate function , completing the working condition transmission path analysis; 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 the structural dynamics system: ,in Let C be the state variable, D be the observation matrix of the state-space model, A be the system matrix of the state-space model, and B be the control matrix of the state-space model. This is process noise added to account for model uncertainties. This is measurement noise added to account for measurement uncertainties. It is modal displacement. It is modal velocity. It is an unknown force. It is information measured by the sensor; A random walk model of the interfacial force is established: , is the input force model noise on the force parameter derivative, indicating that the force derivative or force increment is a completely random process, and the random walk model of the interfacial force is extended to the state variable , a new linear state space model is obtained: , , , , ; Using the sampling rate of 1000 Hz, the new linear state space model is discretized to obtain a discrete linear state space model: where where , , , , ; The optimal state estimation vector is obtained by performing Kalman filtering. It contains unknown forces. and with unknown force Interface force as a reference point.

2. A method of operating deflection path analysis according to claim 1, wherein, The Kalman filtering process comprises time update and test update; the time update formula is ; the test update formula is: , wherein is the posterior state estimation at k-1, is the prior state estimation at k, , is the covariance matrix of the model, is the Kalman gain at k, is the covariance matrix of the measurement noise; is the target point response matrix , wherein is the information of n response points when is the prior estimation covariance at k, is the posterior estimation covariance at k.

3. The operational transfer path analysis method of claim 1, wherein, The step of arranging acceleration sensors and strain sensors at the machine reference point and the target point comprises the following steps: Constructing a sensor pool: randomly selecting acceleration / strain measurement nodes and elements in the finite element model; Training: finite element model simulation under different directions, amplitudes and frequencies of static and dynamic loads, load identification under the premise of known excitation input position; Coarse screening: firstly, delete the sensors with low signal-to-noise ratio in training, and secondly, delete the sensors that are too close to each other and of the same type; Observability screening: screening the sensors based on the PBH criterion, , is a discretized system matrix for the system matrix A, is a discretized system matrix is an eigenvalue of the discretized system matrix is a discretized observation matrix for the observation matrix C; Positioning the sensor positions in the finite element model in the actual physical structure.

4. A method of operating deflection path analysis according to claim 3, wherein, The process of positioning the sensor positions in the finite element model in the actual physical structure comprises: Identifying the sensor positions by using a camera, defining an uncertainty area for each sensor; Measuring the strain of each element in the uncertainty area in the measurement direction by using the sensor, estimating the optimal state variable, and finding a set of elements with the smallest calculation load and true load.

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