Atomic absolute gravimeter vibration compensation method based on generalized regression neural network

Abstract

The invention discloses an atomic absolute gravimeter vibration compensation method based on a generalized regression neural network. The method comprises the following steps: acquiring three-component vibration data and real vibration phases in different vibration environments; constructing a sample; establishing a generalized regression neural network model and a loss function; smooth factors are searched in a set range, the generalized regression neural network with the optimal smooth factors and the optimal network parameters is obtained, a vibration noise compensation model is established, and gravitational acceleration compensation is carried out based on the vibration noise compensation model. According to the method, the smooth factor is introduced to optimize the training process of the generalized regression neural network model, the optimized generalized regression neural network model is obtained, the vibration phase can be predicted based on the measured three-component vibration data, and the compensated gravitational acceleration is obtained through further calculation.

Description

Technical Field

[0001] The invention belongs to the field of gravity measurement and relates to a vibration compensation method of an atomic absolute gravimeter based on a generalized regression neural network. Background Art

[0002] Absolute gravity measurement has a wide range of applications in scientific research and engineering technology fields such as geodesy, earth science, resource exploration, and military. The cold atom absolute gravimeter is a gravity measurement technology based on atomic interference to achieve high-precision measurement of gravitational acceleration, with the advantages of long-term stability, high sensitivity, and high stability.

[0003] The atomic interferometric absolute gravimeter calculates the gravitational acceleration based on the atomic interference fringes formed by three Raman laser pulses during the free fall of the atomic group. In actual measurement, the Raman reflector is easily affected by vibration noise, which causes the vibration noise to couple into the falling motion trajectory of the interferometric measurement, making it impossible to obtain effective interference fringes, affecting the accurate measurement of gravitational acceleration.

[0004] At present, vibration noise is usually suppressed by vibration isolation or compensation. Vibration isolation platforms can reduce vibration interference in measurements, but they have a series of problems such as large size, complex system, and difficult processing. Vibration compensation is to reconstruct the fringes by measuring the vibration of the Raman mirror and removing the phase shift caused by the vibration. However, the vibration measured by the vibration sensor is not equal to the vibration of the Raman mirror, and it is not easy to estimate the transfer function between the sensor and the Raman reflector. Summary of the invention

[0005] The purpose of the present invention is to provide an atomic absolute gravimeter vibration compensation method based on a generalized regression neural network to improve the environmental adaptability of the atomic gravimeter and the measurement accuracy of the gravitational acceleration value.

[0006] In order to achieve the above object, the technical solution steps of the present invention are as follows:

[0007] The vibration compensation method of atomic absolute gravimeter based on generalized regression neural network includes the following steps:

[0008] Step 1: Collect atomic transition probabilities without vibration isolation and vibration compensation under different vibration environments, calculate the vibration phase, collect three-component vibration data under the above different vibration environments, and use the calculated vibration phase as the true vibration phase of the corresponding three-component vibration data;

[0009] Step 2: Normalize the three-component vibration data and use them as samples to construct training sets and test sets. Each sample corresponds to a true vibration phase, and the true vibration phase corresponding to the sample is used as the label of the sample.

[0010] Step 3: Establish a generalized regression neural network model;

[0011] Step 4: Construct loss function;

[0012] Step 5: Input the samples in the training set into the generalized regression neural network, train the generalized regression neural network based on minimizing the loss function value, and obtain the network parameters of the generalized regression neural network corresponding to the minimizing loss function value;

[0013] Step 6: Search for a smooth factor within the set range. Under the searched smooth factor condition, execute step 5 to obtain the smooth factor corresponding to the minimum value of the minimization loss function as the optimal smooth factor, and obtain the network parameters of the generalized regression neural network corresponding to the minimum value of the minimization loss function as the optimal network parameters;

[0014] Step 7: Establish a vibration noise compensation model using the generalized regression neural network with the best smoothing factor and the best network parameters determined in step 6;

[0015] Step 8: Input the normalized three-component vibration data to be predicted into the vibration noise compensation model established in the previous step, denormalize the output simulated vibration phase as the predicted vibration phase, and further calculate the compensated gravity acceleration.

[0016] The vibration phase calculated in step 1 above is based on the following formula:

[0017]

[0018] Among them, Φ v is the vibration phase, P is the atomic transition probability, A and B are constants, k eff is the effective wave vector, α is the scanning chirp rate, and T is the Raman pulse time interval.

[0019] As described in step 3, the generalized regression neural network model includes an input layer, a pattern layer, a summation layer and an output layer. The samples are input to the input layer, and the output layer outputs the simulated vibration phase.

[0020] As described above, the setting range of the smoothing factor in step 6 is 0.01 to 1, and the search compensation is 0.01.

[0021] The calculation of the absolute gravity value in step 8 as described above includes the following steps:

[0022] The predicted vibration phase is used as the vibration phase Φ caused by the vibration noise v , the phase ΔΦ of the interference fringes when affected by vibration is calculated based on the following formula:

[0023] ΔΦ=(k eff g-2πα)T2 +Φ v

[0024] Among them, k eff is the effective wave vector, g is the acceleration due to gravity, α is the scanning chirp rate, and T is the Raman pulse duration;

[0025] The atomic transition probability P is calculated based on the following formula,

[0026] P=A+B cos(ΔΦ)

[0027] Among them, A and B are constants,

[0028] The calculated phase ΔΦ of the interference fringes is used as the horizontal coordinate, and the calculated atomic transition probability P is used as the vertical coordinate to obtain the corrected interference fringes. The phase difference ΔΦ obtained from the corrected interference fringes is substituted into the following formula:

[0029]

[0030] Get the compensated gravity acceleration, where α 0 is the background chirp rate.

[0031] A computer device comprises a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the above-mentioned atomic absolute gravimeter vibration compensation method when executing the computer program.

[0032] A computer-readable storage medium stores a computer program, which implements the atomic absolute gravimeter vibration compensation method when executed by a processor.

[0033] A computer program product comprises a computer program, and when the computer program is executed by a processor, the vibration compensation method of the atomic absolute gravimeter is realized.

[0034] Compared with the prior art, the present invention has the following beneficial effects:

[0035] From the perspective of machine learning, the present invention trains a generalized regression neural network model based on the three-component vibration data and the true vibration phase measured under different vibration environments, and introduces a smoothing factor to optimize the training process of the generalized regression neural network model to obtain an optimized generalized regression neural network model. The vibration phase can be predicted based on the measured three-component vibration data, and the compensated gravity acceleration can be further calculated. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 is a flow chart of the present invention;

[0037] Figure 2Schematic diagram of the generalized regression neural network structure in an embodiment of the present invention. DETAILED DESCRIPTION

[0038] In order to facilitate those skilled in the art to understand and implement the present invention, the present invention is further described in detail below in conjunction with embodiments. It should be understood that the implementation examples described herein are only used to illustrate and explain the present invention and are not used to limit the present invention.

[0039] like Figure 1 As shown, the atomic absolute gravimeter vibration compensation method based on generalized regression neural network includes the following steps:

[0040] Vibration phase acquisition scheme design: The atomic gravimeter calculates the gravitational acceleration by measuring the phase of the interference fringes. In fact, the atomic gravimeter measures the population of the interference fringes to obtain the atomic transition probability. The relationship between the phase ΔΦ of the interference fringes and the atomic transition probability P satisfies:

[0041] P=A+B cos(ΔΦ) (1)

[0042] In the formula, the values ​​of A and B are constants with small variations, which have little impact on the measurement results. Multiple static measurements can be performed in a laboratory environment to determine the values ​​of A and B.

[0043] The vibration phase caused by vibration noise is expressed as Φ v , the phase of the interference fringes of the atomic interferometer can be expressed by the following formula:

[0044] ΔΦ=(k eff g-2πα)T 2 +Φ v (2)

[0045] In the formula, k eff is the effective wave vector, g is the acceleration due to gravity, α is the scanning chirp rate, and T is the Raman pulse duration.

[0046] From formulas (1) and (2), the vibration phase Φ can be derived: v The expression is:

[0047]

[0048] Therefore, when measuring at the absolute gravity point, that is, the gravitational acceleration g is known, the vibration phase Φ can be derived according to formula (3): v .

[0049] Step 1: Use the cold atom absolute gravimeter to collect the atomic transition probability P without any vibration isolation and vibration compensation under different vibration environments, and further calculate the vibration phase Φ v, using the three-component vibration data measured by the vibration sensing system, the calculated vibration phase Φ v As the actual vibration phase of the corresponding three-component vibration data.

[0050] The vibration sensing system includes an accelerometer, the model of which is Titan accelerometer, which is a three-axis accelerometer with a collection frequency of DC to 430Hz, and is used to collect three-component vibration data in the three directions of X, Y and Z. Due to the cross-coupling effect of the vibration sensor itself in a complex environment, as well as the installation error of the vibration sensor, the vertical direction cannot strictly coincide with the gravity direction. Therefore, the vibration data in the horizontal and vertical directions measured by the vibration sensor are used to jointly train the network model to further improve the measurement accuracy.

[0051] In order to collect as much vibration source data as possible covering each frequency band, three-component vibration data are collected in different vibration environments, including quiet laboratories, buildings, roads, people walking, etc. Without any vibration isolation and vibration compensation, one day of atomic transition probability P and three-component vibration data of accelerometer are collected in each vibration environment. It is worth mentioning that multiple different types of vibration sensors can be placed on the ground, and data fusion methods can be used to integrate different source data to obtain more accurate and comprehensive three-component vibration data.

[0052] Repeated measurements are performed at the measuring point to obtain accurate gravity acceleration values ​​at different measuring points. In this step, the influence of tide, sea tide, air pressure, etc. on gravity acceleration should be deducted. The vibration environment of the measuring point is changed to perform absolute gravity measurement to obtain three-component vibration data and atomic transition probability. The vibration phase is calculated from the atomic transition probability using formula (3) as the true vibration phase corresponding to the three-component vibration data.

[0053] Step 2. Normalize the three-component vibration data and use them as samples to construct training sets and test sets. In order to eliminate the dimensional differences between different three-component vibration data, the three-component vibration data is normalized to between [-1,1], and the normalized three-component vibration data is used as samples for training. The number of groups of three-component vibration data is K, and each group of three-component vibration data is used as a sample. Each group of three-component vibration data contains N X-direction vibration data, N Y-direction vibration data, and N Z-direction vibration data. Each sample corresponds to a true vibration phase, and the true vibration phase corresponding to the sample is used as the label of the sample; in this embodiment, 80% of the samples and the corresponding labels are used as training sets, and 20% of the samples and the corresponding labels are used as test sets;

[0054] Step 3, establish a generalized regression neural network model. In this case, a generalized regression neural network (GRNN) is used. It is a four-layer feedforward neural network, including an input layer, a pattern layer, a summation layer, and an output layer. The input layer inputs samples (normalized three-component vibration data in the X, Y, and Z directions collected by the vibration sensing system). The number of groups of three-component vibration data is K. Each group of three-component vibration data is a sample. Each group of three-component vibration data contains N X-direction vibration data, N Y-direction vibration data, and N Z-direction vibration data. Each sample corresponds to a real vibration phase, and each sample corresponds to a real vibration phase as the label of the sample. The number of samples and labels to be trained is K. The network structure diagram is shown below. Figure 2 The first sample is The second sample is The Kth sample is

[0055] X of the above sample ij , Y ij , Z ij They are respectively the X-direction vibration data, Y-direction vibration data, and Z-direction vibration data of the i-th component vibration data of the j-th sample, i=1, 2,…, N, j=1, 2,…, K.

[0056] The output layer outputs the simulated vibration phase. The simulated vibration phase corresponding to the jth sample is represented by P j .

[0057] Step 4. In a generalized regression neural network, the loss function is a function used to measure the difference between the model's prediction results and the actual target. It plays a vital role in the model training process, guiding the adjustment of model parameters to minimize the prediction error. In this case, the root mean square error is used as the loss function.

[0058] Step 5: Input the samples in the training set into the generalized regression neural network, train the generalized regression neural network based on minimizing the loss function value, and obtain the network parameters of the generalized regression neural network corresponding to the minimizing loss function value.

[0059] Step 6. In the generalized regression neural network, the smoothing factor determines the width of the radial basis function in the GRNN. The size of the smoothing factor directly affects the smoothness of the model and the accuracy of the prediction. Selecting an appropriate smoothing factor is crucial to the model performance. In this case, the cross-validation method is used to set the smoothing factor to a value between 0.01 and 1 with a step length of 0.01 for searching. Under the searched smoothing factor condition, step 5 is executed to obtain the smoothing factor corresponding to the minimum loss function value (root mean square error) as the optimal smoothing factor, and the network parameters of the generalized regression neural network corresponding to the minimum loss function value (root mean square error) are obtained as the optimal network parameters.

[0060] Step 7: Use the generalized regression neural network with the best smoothing factor and the best network parameters determined in step 6 to establish a vibration noise compensation model.

[0061] Step 8: Input the normalized three-component vibration data to be predicted into the vibration noise compensation model established in the previous step, and denormalize the output simulated vibration phase to obtain the predicted vibration phase. The predicted vibration phase is used as the vibration phase Φ caused by the vibration noise. v , calculate the phase ΔΦ of the interference fringes under the influence of vibration based on formula (2), calculate the atomic transition probability P based on formula (1), take the calculated phase ΔΦ of the interference fringes (atomic phase under the influence of vibration) as the horizontal coordinate, and the calculated atomic transition probability P as the vertical coordinate to obtain the corrected interference fringes. Substitute the phase difference ΔΦ obtained from the corrected interference fringes into Get the compensated gravity acceleration.

[0062] The algorithm is verified at different known points of absolute gravity values. During the measurement process, all vibration compensation devices are turned off, and only the three-component vibration data obtained by the vibration sensing system are collected. The measured three-component vibration data is used as the three-component vibration data to be predicted and input into the vibration noise compensation model established in step 7 for calculation, and the output is the predicted vibration phase.

[0063] According to the predicted vibration phase, the predicted vibration phase is used as the vibration phase Φ caused by the vibration noise v , the phase ΔΦ of the interference fringes affected by vibration is calculated based on formula (2), and the atomic transition probability P is calculated based on formula (1). The calculated phase ΔΦ of the interference fringes (atomic phase when affected by vibration) is used as the horizontal coordinate, and the calculated atomic transition probability P is used as the vertical coordinate to obtain the corrected interference fringes.

[0064] The least squares algorithm is used to fit the corrected interference fringes with the standard cosine signal y=a1+b1 cos(x-c1), where x represents the phase of the compensated interference fringes and y represents the transition probability. When the residual values ​​of parameters a1, b1 and c1 are the smallest, the required fitting fringes are obtained. The standard deviation of the fitting residuals of the fitting fringes is calculated, which is more than 30 times lower than the measurement results without vibration compensation.

[0065] Substitute the phase difference ΔΦ (corresponding to c1) obtained by fitting the corrected interference fringes into the calculation formula of gravitational acceleration: Where α 0 is the background chirp rate, and the compensated gravity acceleration is obtained.

[0066] In one embodiment, a computer device is further provided, including a memory and a processor, wherein a computer program is stored in the memory, and the processor implements the steps in the above method embodiments when executing the computer program.

[0067] In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps in the above-mentioned method embodiments are implemented.

[0068] In one embodiment, a computer program product is provided, including a computer program, which implements the steps in the above method embodiments when executed by a processor.

[0069] A person of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing related hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods.

[0070] The specific embodiments described herein are merely examples of the spirit of the present invention. Those skilled in the art may make various modifications or additions to the specific embodiments described or replace them in similar ways, but they will not deviate from the spirit of the present invention or exceed the scope defined by the appended claims.

Claims

1. A vibration compensation method for atomic absolute gravimeter based on generalized regression neural network, characterized in that: The following steps are involved: Step 1: Collect atomic transition probabilities without vibration isolation and vibration compensation under different vibration environments, calculate the vibration phase, collect three-component vibration data under the above different vibration environments, and use the calculated vibration phase as the true vibration phase of the corresponding three-component vibration data; Step 2: Normalize the three-component vibration data and use them as samples to construct training sets and test sets. Each sample corresponds to a true vibration phase, and the true vibration phase corresponding to the sample is used as the label of the sample. Step 3: Establish a generalized regression neural network model; Step 4: Construct loss function; Step 5: Input the samples in the training set into the generalized regression neural network, train the generalized regression neural network based on minimizing the loss function value, and obtain the network parameters of the generalized regression neural network corresponding to the minimizing loss function value; Step 6: Search for a smooth factor within the set range. Under the searched smooth factor condition, execute step 5 to obtain the smooth factor corresponding to the minimum value of the minimization loss function as the optimal smooth factor, and obtain the network parameters of the generalized regression neural network corresponding to the minimum value of the minimization loss function as the optimal network parameters; Step 7: Establish a vibration noise compensation model using the generalized regression neural network with the best smoothing factor and the best network parameters determined in step 6; Step 8: Input the normalized three-component vibration data to be predicted into the vibration noise compensation model established in the previous step, denormalize the output simulated vibration phase as the predicted vibration phase, and further calculate the compensated gravity acceleration.

2. The atomic absolute gravimeter vibration compensation method based on generalized regression neural network according to claim 1 is characterized in that: The vibration phase calculated in step 1 is based on the following formula: Among them, Φ v is the vibration phase, P is the atomic transition probability, A and B are constants, k eff is the effective wave vector, α is the scanning chirp rate, and T is the Raman pulse time interval.

3. The atomic absolute gravimeter vibration compensation method based on generalized regression neural network according to claim 1 is characterized in that: In step 3, the generalized regression neural network model includes an input layer, a pattern layer, a summation layer and an output layer. The samples are input to the input layer, and the output layer outputs the simulated vibration phase.

4. The atomic absolute gravimeter vibration compensation method based on generalized regression neural network according to claim 1 is characterized in that: The setting range of the smoothing factor in step 6 is 0.01 to 1, and the search compensation is 0.

01.

5. The atomic absolute gravimeter vibration compensation method based on generalized regression neural network according to claim 1 is characterized in that: The calculation of the absolute gravity value in step 8 comprises the following steps: The predicted vibration phase is used as the vibration phase Φ caused by the vibration noise v , the phase ΔΦ of the interference fringes when affected by vibration is calculated based on the following formula: ΔΦ=(k eff g-2pa)T 2 +F v Among them, k eff is the effective wave vector, g is the acceleration due to gravity, α is the scanning chirp rate, and T is the Raman pulse duration; The atomic transition probability P is calculated based on the following formula, P=A+B cos(ΔΦ) Among them, A and B are constants, The calculated phase ΔΦ of the interference fringes is used as the horizontal coordinate, and the calculated atomic transition probability P is used as the vertical coordinate to obtain the corrected interference fringes. The phase difference ΔΦ obtained from the corrected interference fringes is substituted into the following formula: The compensated gravity acceleration is obtained, where α0 is the background chirp rate.

6. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, the steps of the atomic absolute gravimeter vibration compensation method according to any one of claims 1 to 5 are implemented.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the atomic absolute gravimeter vibration compensation method according to any one of claims 1 to 5 is implemented.

8. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the atomic absolute gravimeter vibration compensation method according to any one of claims 1 to 5 is implemented.

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