Method for predicting impact acceleration of rocket sled based on linear time invariant

Abstract

The invention relates to a method for predicting the impact acceleration of a rocket sled based on linear time invariance, and the method comprises the steps: constructing a time domain output response function of an impact sensor of a rocket sled measurement system, and obtaining a discretized frequency domain output response function; obtaining a replacement vector based on the frequency domain complex transfer function; obtaining an impact acceleration true value based on the L excitation signals, and obtaining an impact acceleration measurement value based on the L response values; and constructing an optimization function, solving the optimization function to obtain an estimated value of a parameter in the frequency domain output response function, and obtaining an estimated value of a time domain output response function parameter through the replacement vector and the estimated value, and obtaining the predicted impact acceleration of the impact sensor of the measurement system through the time domain output response function and the estimated values of the parameters thereof. According to the method, the problem that the full-scale calibration value of the impact acceleration cannot be obtained during field calibration of the rocket sled measurement system is solved.

Description

Technical Field

[0001] The invention relates to the field of dynamic characteristic calibration, and in particular to a method for predicting rocket sled impact acceleration based on linear time invariance. Background Art

[0002] Rocket sleds are mainly used to test the performance indicators of the object being tested during flight. With the rapid development of aerospace and other fields, the speed and accuracy requirements for rocket sleds are becoming higher and higher. Therefore, in order to enable the measurement system on the rocket sled to provide high-precision measurement results, how to accurately calibrate it has become one of the key issues that need to be solved in the development of hypersonic rocket sled test technology.

[0003] At present, the calibration of rocket sled measurement system usually adopts the inspection method, that is, calibration is carried out in the laboratory and then installed on the rocket sled. However, the placement position, installation torque and on-site environment of the rocket sled measurement system sensor will have a great influence on the measurement results, resulting in large errors in the measurement results after the measurement system is calibrated.

[0004] To solve the above problems, the rocket sled measurement system can be calibrated on site. However, during the on-site calibration, the impact acceleration of the rocket sled measurement system sensor cannot obtain the full-scale calibration value due to the influence of environmental factors, so that the impact acceleration of the rocket sled cannot be fully calibrated. Summary of the invention

[0005] In view of the above analysis, the present invention aims to provide a method for predicting the impact acceleration of a rocket sled based on linear time invariance, so as to solve the problem that the impact acceleration of the sensor of the rocket sled measurement system cannot obtain the full-scale calibration value during on-site calibration.

[0006] The present invention provides a method for predicting rocket sled impact acceleration based on linear time invariance, the method comprising the following steps:

[0007] Apply L different excitation signals to the rocket sled measurement system to obtain L response values ​​of the impact sensor of the measurement system;

[0008] Based on the linear time-invariant system principle, a time-domain output response function of the impact sensor of the measurement system is constructed, and a discretized frequency-domain output response function is obtained;

[0009] Obtaining a replacement vector for each parameter in the frequency domain output response function based on the frequency domain complex transfer function of the frequency domain output response function;

[0010] Obtaining the shock acceleration true value based on the L excitation signals, and obtaining the shock acceleration measurement value based on the L response values; constructing a truth value matrix based on the shock acceleration true value, and constructing a measurement shock acceleration matrix containing uncertainty based on the shock acceleration measurement value;

[0011] An optimization function is constructed based on the measured impact acceleration matrix and the truth value matrix, and the least squares method is used to solve the optimization function to obtain the estimated values ​​of the parameters in the frequency domain output response function. The estimated values ​​of the time domain output response function parameters are obtained by replacing the vector and the estimated values. The predicted impact acceleration of the impact sensor of the measurement system is obtained by the estimated values ​​of the time domain output response function and its parameters.

[0012] Furthermore, the time domain output response function of the impact sensor of the measurement system is:

[0013]

[0014] Where y(t) is the output value of the impact sensor, is the first-order derivative of the output value of the shock sensor, is the second-order derivative of the output value of the shock sensor, δ is the damping coefficient of the shock sensor, ω0 is the installation resonant frequency of the shock sensor, ε is the inherent characteristic constant of the shock sensor, and x(t) is the input value of the shock sensor.

[0015] Furthermore, the discretized frequency domain output response function is:

[0016] y k +c1y k-1 +C2y k-2 = b(a k +2a k-1 +a k-2 ),

[0017] Among them, y k is the output of the impact sensor at time k; a k is the input of the shock sensor at time k, b, c1, c2 are the parameters of the discretized frequency domain output response function.

[0018] Furthermore, the formula of the replacement vector is:

[0019] ν T =[ν1, v2, v3] = [1 / b, c1 / b, c2 / b],

[0020] Among them, ν T is the replacement vector.

[0021] Furthermore, the measured impact acceleration matrix is:

[0022]

[0023] Among them, y is the measured impact acceleration matrix, Re is the real part, Im is the imaginary part, G Lis the Lth response value after adding uncertainty, exp is an exponential function with e as the base, j is an imaginary number, is the phase of the Lth response value after adding uncertainty.

[0024] Furthermore, the uncertainty vector is obtained by the following method:

[0025]

[0026] Among them, u i is the standard uncertainty corresponding to the i-th response value, G` i is the ith response value, is the phase of the i-th response value, σ is the shock acceleration amplitude random variable of the normal distribution, and ∈ is the phase random variable of the normal distribution.

[0027] Furthermore, the truth matrix is:

[0028]

[0029] Among them, H is the truth matrix, a(ω L ) is the true value of the impact acceleration of the Lth excitation signal.

[0030] Furthermore, the optimization function is:

[0031]

[0032] in, is the estimated value of the parameters in the frequency domain output response function, and A is the transposed matrix of the true value matrix.

[0033] Furthermore, the estimated values ​​of the time domain output response function parameters are:

[0034]

[0035] Where T is the sampling interval.

[0036] Furthermore, before applying the excitation signal through the excitation source, it is necessary to determine the boundary conditions of the rocket sled measurement system. The boundary conditions of the rocket sled measurement system include: the impact sensor of the rocket sled measurement system and the standard sensor of the excitation source use the same installation torque, and the same screws are used to fix the two sensors separately for rigid connection; so that the boundary conditions of the measurement system are solidified.

[0037] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0038] 1. The present invention solidifies the boundary conditions of the rocket sled measurement system, thereby constructing the time domain output response function of the rocket sled measurement system sensor based on the principle of linear time invariant system, and takes into account the structural characteristics of the sensor itself through the parameters of the time domain output response function, thereby providing a basis for accurately predicting the impact acceleration of the rocket sled.

[0039] 2. The present invention constructs an optimization function and uses the least squares method to solve the optimization function to obtain estimated values ​​of parameters in the frequency domain output response function, and obtains the predicted impact acceleration of the measurement system sensor based on the estimated values ​​of the parameters, thereby solving the problem that the impact acceleration of the rocket sled measurement system sensor cannot obtain the full-scale calibration value during on-site calibration.

[0040] 3. The present invention obtains L response values ​​of the rocket sled measurement system sensor through L different excitation signals, that is, the impact acceleration is predicted based on the true value and the measured value obtained in the field environment, thereby improving the prediction accuracy.

[0041] 4. The present invention takes uncertainty into account when constructing the impact acceleration measurement matrix, so that the uncertainty is taken into account when predicting the impact acceleration, thereby improving the accuracy of the prediction.

[0042] In the present invention, the above-mentioned technical solutions can also be combined with each other to achieve more preferred combination solutions. Other features and advantages of the present invention will be described in the subsequent description, and some advantages can become obvious from the description, or can be understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained through the contents particularly pointed out in the description and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] The drawings are only for the purpose of illustrating specific embodiments and are not to be considered limiting of the present invention. Like reference symbols denote like components throughout the drawings.

[0044] Figure 1 It is a flow chart of a method for predicting rocket sled impact acceleration based on linear time invariance according to an embodiment of the present invention;

[0045] Figure 2 4 is a block diagram of a rocket sled measurement system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0046] The preferred embodiments of the present invention are described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not used to limit the scope of the present invention.

[0047] A specific embodiment of the present invention discloses a method for predicting the impact acceleration of a rocket sled based on linear time invariance. Figure 1As shown, the method comprises the following steps:

[0048] Step S1, applying L different excitation signals to the rocket sled measurement system to obtain L response values ​​of the impact sensor of the measurement system;

[0049] Step S2, constructing a time domain output response function of the impact sensor of the measurement system based on the linear time-invariant system principle, and obtaining a discretized frequency domain output response function;

[0050] Step S3, obtaining a replacement vector of each parameter in the frequency domain output response function based on the frequency domain complex transfer function of the frequency domain output response function;

[0051] Step S4, obtaining the shock acceleration true value based on the L excitation signals, and obtaining the shock acceleration measurement value based on the L response values; constructing a truth value matrix based on the shock acceleration true value, and constructing a measurement shock acceleration matrix containing uncertainty based on the shock acceleration measurement value;

[0052] Step S5, constructing an optimization function based on the measured impact acceleration matrix and the truth matrix, using the least squares method to solve the optimization function to obtain estimated values ​​of the parameters in the frequency domain output response function, obtaining estimated values ​​of the time domain output response function parameters by replacing the vector and the estimated values, and obtaining the predicted impact acceleration of the impact sensor of the measurement system by the estimated values ​​of the time domain output response function and its parameters.

[0053] Specifically, in step S1, Figure 2 As shown, the rocket sled measurement system includes a trigger device, a data acquisition system, a signal conditioning unit and an impact sensor. When the excitation source applies an excitation signal to the rocket sled, the trigger device triggers the data acquisition system, so that the data acquisition system starts to record the response of the impact sensor. At this time, the impact sensor outputs a corresponding response signal according to the excitation generated by the excitation source, and the response signal is converted into a voltage signal by the signal conditioning unit and then input into the data acquisition system.

[0054] Furthermore, before applying the excitation signal through the excitation source, it is necessary to determine the boundary conditions of the rocket sled measurement system. The boundary conditions of the rocket sled measurement system include: the impact sensor of the rocket sled measurement system and the standard sensor of the excitation source use the same installation torque, and the two sensors are fixed separately with the same screws to make a rigid connection; so that the boundary conditions of the measurement system and the excitation source are solidified.

[0055] It can be understood that the measurement system and the excitation source are in the same environmental conditions. When their boundary conditions are solidified by the above method, they constitute a linear time-invariant system. For a linear time-invariant system, a sufficient condition for the stability of its input and output states is that its zero input system is stable. When the impact sensor of the rocket sled measurement system and the standard sensor of the excitation source use the same installation torque and installation method, the zero input system of the measurement system and the excitation source is stable.

[0056] Specifically, the excitation source is a pulsed impact excitation, and L excitation signals are applied to the rocket sled measurement system at different frequencies and amplitudes in sequence to obtain L response values ​​of the impact sensor of the measurement system.

[0057] It can be understood that the present invention obtains L response values ​​of the rocket sled measurement system sensor through L different excitation signals, that is, the impact acceleration is predicted based on the true value and the measured value obtained in the field environment, thereby improving the prediction accuracy.

[0058] Specifically, in step S2, the time domain output response function of the impact sensor of the measurement system is:

[0059]

[0060] Where y(t) is the output value of the impact sensor, is the first-order derivative of the output value of the shock sensor, is the second-order derivative of the output value of the shock sensor, δ is the damping coefficient of the shock sensor, ω0 is the installation resonant frequency of the shock sensor, ε is the inherent characteristic constant of the shock sensor, and x(t) is the input value of the shock sensor.

[0061] It can be understood that based on the linear time-invariant system principle, a mathematical model is used to describe the input-output characteristics of the impact sensor, that is, the time-domain output response function. In addition, considering the structural characteristics of the impact sensor itself, a set of parameters of the model is used to represent the structural characteristics of the sensor. The present invention solidifies the boundary conditions of the rocket sled measurement system, thereby constructing the time-domain output response function of the rocket sled measurement system sensor based on the linear time-invariant system principle, and takes into account the structural characteristics of the sensor itself through the parameters of the time-domain output response function, providing a basis for accurately predicting the impact acceleration of the rocket sled.

[0062] Specifically, for the linear time-invariant system, its transfer function can be obtained based on the above function formula, and the transfer function is inversely calculated, Z-transformed, and sampled to obtain a discretized frequency domain output response function.

[0063] The transfer function is:

[0064]

[0065] Where H() is the complex transfer function, i is the imaginary unit, S() is the amplitude function of the transfer function, φ() is the phase function of the transfer function, and ω is the response frequency.

[0066] Taking the inverse of the transfer function yields:

[0067]

[0068] Where G() is the inverse of the complex transfer function and s is the Laplace factor.

[0069] The Laplace factor s in the above formula is z-transformed by the following method:

[0070]

[0071] Where z is the z-transform factor and T is the sampling interval.

[0072] Furthermore, the discretized frequency domain output response function is:

[0073] y k +c1y k-1 +c2y k-2 = b(a k +2a k-1 +a k-2 ),

[0074] Among them, y k is the output of the impact sensor at time k; a k is the input of the shock sensor at time k, b, c1, c2 are the parameters of the discretized frequency domain output response function.

[0075] Specifically, the parameters of the discretized frequency domain output response function are obtained by the following method:

[0076]

[0077] It is understandable that the full scale of impact acceleration is usually 20g to 10000g. The above parameters can be determined by rigidly mounting the impact sensor on a pneumatic impact standard device in the laboratory and measuring the linearity of the impact amplitude within the full scale range. It can be seen from the discretized frequency domain output response function that the above parameters are closely related to the sampling interval. According to the sampling law, in order to prevent the influence of uncertainty caused by the first-order resonant frequency of the impact sensor, the sampling frequency should be higher than 5 times the first-order resonant frequency. Preferably, the sampling frequency is higher than 10 times the first-order resonant frequency.

[0078] Specifically, in step S3, since the main frequency component of the impact sensor is a high-frequency signal, its frequency domain complex transfer function can be obtained based on the frequency domain output response function. The frequency domain complex transfer function of the frequency domain output response function is:

[0079]

[0080] Where, Ω = ω / f s =ωT is the angular frequency after sampling and normalization.

[0081] Taking the inverse of the frequency domain complex transfer function yields:

[0082]

[0083] Furthermore, by comparing the above two formulas, a replacement vector can be obtained, and the formula of the replacement vector is:

[0084] v T =[v1, v2, v3] = [1 / b, c1 / b, c2 / b],

[0085] Among them, ν T is the replacement vector.

[0086] Specifically, in step S4, the true value a of the impact acceleration is obtained based on the L excitation signals in step S1. T =[a1, a2, …, a L ], where a L is the true value of the impact acceleration of the Lth excitation signal. The excitation source is connected to the standard sensor, and the standard sensor outputs a corresponding response signal to the excitation signal. The response signal is converted into a voltage signal by the signal conditioning unit. The voltage signal is the true value of the impact acceleration, including amplitude and phase information.

[0087] Furthermore, the truth matrix is:

[0088]

[0089] Among them, H is the truth matrix, a(ω L ) is the true value of the impact acceleration of the Lth excitation signal.

[0090] Specifically, based on the L response values ​​in step S1, the impact acceleration measurement value G(ω)=[G1, G2, ..., G L ]; From step S1, it can be seen that the impact sensor of the rocket sled measurement system outputs a corresponding response signal according to the excitation generated by the excitation source, and the response signal is converted into a voltage signal by the signal conditioning unit. The voltage signal is the measured value of the impact acceleration, including amplitude and phase information. According to the historical experience value, the corresponding uncertainty is set to uω =[u1,u2,…,u L ], where u L is the standard uncertainty of the Lth response value.

[0091] Furthermore, the measured impact acceleration matrix is:

[0092]

[0093] Among them, y is the measured impact acceleration matrix, Re is the real part, Im is the imaginary part, G L is the Lth response value after adding uncertainty, exp is an exponential function with e as the base, j is an imaginary number, is the phase of the Lth response value after adding uncertainty.

[0094] Furthermore, the uncertainty vector is obtained by the following method:

[0095]

[0096] Among them, u i is the standard uncertainty corresponding to the i-th response value, G` i is the ith response value, is the phase of the i-th response value, σ is the shock acceleration amplitude random variable of the normal distribution, and ∈ is the phase random variable of the normal distribution.

[0097] It is understandable that according to public literature and historical experience data, it can be found that the response of the impact sensor obeys a normal distribution, and the standard deviation is the standard uncertainty of its response. The present invention takes uncertainty into account when constructing the impact acceleration measurement matrix, so that the uncertainty is taken into account when predicting the impact acceleration, thereby improving the accuracy of the prediction.

[0098] Specifically, in step S5, the optimization function is:

[0099]

[0100] in, Outputs estimates of the parameters in the frequency-domain response function.

[0101] Specifically, the covariance matrix of the parameter estimation values ​​in the frequency domain output response function, that is, the uncertainty of the parameter estimation values, is obtained by the following method:

[0102]

[0103] in, for The covariance matrix, H T is the transformed rank of the truth matrix, V yis the covariance matrix of y, V y -1 V y The inverse matrix of .

[0104] It can be understood that the estimated values ​​of the parameters in the frequency domain output response function can be obtained by solving the optimization function using the least square method.

[0105] Specifically, after solving the estimated values ​​of each parameter in the frequency domain, the estimated values ​​of v1, v2, and ν3 are obtained using the replacement vector, and then the estimated values ​​of each parameter in the time domain output response function are obtained by the following formula.

[0106] Furthermore, the estimated values ​​of the time domain output response function parameters are:

[0107]

[0108] Where T is the sampling interval.

[0109] It can be understood that the estimated values ​​of the parameters in the frequency domain output response function are replaced by the replacement vector to obtain the estimated values ​​of the parameters in the time domain output response function. Substituting the estimated values ​​of the parameters in the time domain output response function into the time domain output response function, the predicted optimal impact acceleration of the impact sensor of the measurement system can be obtained. The present invention obtains the estimated values ​​of the parameters in the frequency domain output response function by constructing an optimization function and solving the optimization function using the least squares method, and obtains the predicted impact acceleration of the measurement system sensor based on the estimated values ​​of the parameters, thereby solving the problem that the impact acceleration of the rocket sled measurement system sensor cannot obtain the full-scale calibration value during on-site calibration.

[0110] Compared with the prior art, the method for predicting rocket sled impact acceleration based on linear time invariance provided by the present invention has the following beneficial effects:

[0111] 1. The present invention solidifies the boundary conditions of the rocket sled measurement system, thereby constructing the time domain output response function of the rocket sled measurement system sensor based on the principle of linear time invariant system, and takes into account the structural characteristics of the sensor itself through the parameters of the time domain output response function, thereby providing a basis for accurately predicting the impact acceleration of the rocket sled.

[0112] 2. The present invention constructs an optimization function and uses the least squares method to solve the optimization function to obtain estimated values ​​of parameters in the frequency domain output response function, and obtains the predicted impact acceleration of the measurement system sensor based on the estimated values ​​of the parameters, thereby solving the problem that the impact acceleration of the rocket sled measurement system sensor cannot obtain the full-scale calibration value during on-site calibration.

[0113] 3. The present invention obtains L response values ​​of the rocket sled measurement system sensor through L different excitation signals, that is, the impact acceleration is predicted based on the true value and the measured value obtained in the field environment, thereby improving the prediction accuracy.

[0114] 4. The present invention takes uncertainty into account when constructing the impact acceleration measurement matrix, so that the uncertainty is taken into account when predicting the impact acceleration, thereby improving the accuracy of the prediction.

[0115] Those skilled in the art will appreciate that all or part of the processes of the above-mentioned embodiments can be implemented by instructing related hardware through a computer program, and the program can be stored in a computer-readable storage medium, wherein the computer-readable storage medium is a disk, an optical disk, a read-only storage memory, or a random access memory, etc.

[0116] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for predicting rocket sled impact acceleration based on linear time invariance, characterized in that: The method comprises the following steps: Apply L different excitation signals to the rocket sled measurement system to obtain L response values ​​of the impact sensor of the measurement system; Based on the linear time-invariant system principle, a time-domain output response function of the impact sensor of the measurement system is constructed, and a discretized frequency-domain output response function is obtained; Obtaining a replacement vector for each parameter in the frequency domain output response function based on the frequency domain complex transfer function of the frequency domain output response function; Obtaining the shock acceleration true value based on the L excitation signals, and obtaining the shock acceleration measurement value based on the L response values; constructing a truth value matrix based on the shock acceleration true value, and constructing a measurement shock acceleration matrix containing uncertainty based on the shock acceleration measurement value; An optimization function is constructed based on the measured impact acceleration matrix and the truth value matrix, and the least squares method is used to solve the optimization function to obtain the estimated values ​​of the parameters in the frequency domain output response function. The estimated values ​​of the time domain output response function parameters are obtained by replacing the vector and the estimated values. The predicted impact acceleration of the impact sensor of the measurement system is obtained by the time domain output response function and the estimated values ​​of its parameters.

2. The method for predicting rocket sled impact acceleration based on linear time invariance according to claim 1 is characterized in that: The time domain output response function of the impact sensor of the measurement system is: Where y(t) is the output value of the impact sensor, is the first-order derivative of the output value of the shock sensor, is the second-order derivative of the output value of the shock sensor, δ is the damping coefficient of the shock sensor, ω0 is the installation resonant frequency of the shock sensor, ε is the inherent characteristic constant of the shock sensor, and x(t) is the input value of the shock sensor.

3. The method for predicting rocket sled impact acceleration based on linear time invariance according to claim 1, characterized in that: The discretized frequency domain output response function is: y k +c1y k-1 +c2y k-2 =b(a k +2a k-1 +a k-2 ), Among them, y k is the output of the shock sensor at time k; ak is the input of the shock sensor at time k, b, c1, c2 are the parameters of the discretized frequency domain output response function.

4. The method for predicting rocket sled impact acceleration based on linear time invariance according to claim 1, characterized in that: The formula for the replacement vector is: v T =[ν1,ν2,v3]=[1 / b,c1 / b,c2 / b], Among them, ν T is the replacement vector.

5. The method for predicting rocket sled impact acceleration based on linear time invariance according to claim 1, characterized in that: The measured impact acceleration matrix is: Among them, y is the measured impact acceleration matrix, Re is the real part, Im is the imaginary part, G L is the Lth response value after adding uncertainty, exp is an exponential function with e as the base, j is an imaginary number, is the phase of the Lth response value after adding uncertainty.

6. The method for predicting rocket sled impact acceleration based on linear time invariance according to claim 1, characterized in that: The uncertainty vector is obtained by the following method: i=1, 2, 3, 4..., L, Among them, u i is the standard uncertainty corresponding to the i-th response value, is the ith response value, is the phase of the i-th response value, σ is the shock acceleration amplitude random variable of the normal distribution, and ∈ is the phase random variable of the normal distribution.

7. The method for predicting rocket sled impact acceleration based on linear time invariance according to claim 1, characterized in that: The truth matrix is: Among them, H is the truth matrix, a(ω L ) is the true value of the impact acceleration of the Lth excitation signal.

8. The method for predicting rocket sled impact acceleration based on linear time invariance according to claim 1, characterized in that: The optimization function is: in, is the estimated value of the parameters in the frequency domain output response function, and A is the transposed matrix of the true value matrix.

9. The method for predicting rocket sled impact acceleration based on linear time invariance according to claim 1, characterized in that: The estimated values ​​of the time domain output response function parameters are: Where T is the sampling interval.

10. The method for predicting rocket sled impact acceleration based on linear time invariance according to claim 1, characterized in that: Before applying the excitation signal through the excitation source, it is necessary to determine the boundary conditions of the rocket sled measurement system. The boundary conditions of the rocket sled measurement system include: the impact sensor of the rocket sled measurement system and the standard sensor of the excitation source use the same installation torque, and the two sensors are fixed separately with the same screws to make a rigid connection; so that the boundary conditions of the measurement system and the excitation source are solidified.

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