Vibration compensation method for atomic absolute gravimeter based on generalized regression neural network

Abstract

This invention discloses a vibration compensation method for an atomic absolute gravimeter based on a generalized regression neural network. The method collects three-component vibration data and true vibration phase under different vibration environments; constructs a sample; establishes a generalized regression neural network model and a loss function; searches for a smoothing factor within a set range to obtain a generalized regression neural network with the optimal smoothing factor and network parameters; establishes a vibration noise compensation model, and performs gravity acceleration compensation based on the vibration noise compensation model. The invention introduces a smoothing factor to optimize the training process of the generalized regression neural network model, obtaining an optimized generalized regression neural network model. Based on the measured three-component vibration data, the vibration phase can be predicted, and the compensated gravity acceleration can be further calculated.

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, including geodesy, earth science, resource exploration, and military research. The cold atom absolute gravimeter is a gravity measurement technology based on atomic interferometry that enables high-precision measurement of gravitational acceleration. It offers advantages such as long-term stability, high sensitivity, and high stability.

[0003] Atom interferometry absolute gravimeters calculate gravitational acceleration based on the atomic interference fringes formed by three Raman laser pulses during a free-falling cluster of atoms. In actual measurements, Raman mirrors are susceptible to vibration noise, which couples into the interferometric trajectory of the falling object, preventing effective interference fringes and affecting the accurate measurement of gravitational acceleration.

[0004] Currently, vibration noise is typically suppressed through vibration isolation or compensation. Vibration isolation platforms can reduce vibration interference during measurements, but they present a number of challenges, including bulk, system complexity, and operational difficulties. Vibration compensation measures the vibration of the Raman mirror, removes the phase shift caused by the vibration, and reconstructs the fringes. However, the vibration measured by the vibration sensor is not identical to the vibration of the Raman mirror, making it difficult to estimate the transfer function between the sensor and the Raman mirror. Summary of the Invention

[0005] The purpose of the present invention is to address the above-mentioned deficiencies in the existing technology and provide a vibration compensation method for an atomic absolute gravimeter based on a generalized regression neural network, thereby improving 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 and test sets. Each sample corresponds to a true vibration phase, and the true vibration phase corresponding to the sample is used as the sample label.

[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 the minimized loss function value, and obtain the network parameters of the generalized regression neural network corresponding to the minimized loss function value;

[0013] Step 6: Search for a smoothing factor within the set range. Under the searched smoothing factor condition, execute step 5 to obtain the smoothing factor corresponding to the minimum value of the minimization loss function as the optimal smoothing 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: Use the generalized regression neural network with the optimal smoothing factor and optimal network parameters determined in step 6 to establish a vibration noise compensation model;

[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 is calculated in step 1 as follows:

[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 above, the generalized regression neural network model includes an input layer, a pattern layer, a summation layer and an output layer. The sample is 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 offset is 0.01.

[0021] The calculation of the absolute gravity value in step 8 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] Obtain the compensated gravity acceleration, where α0 is the background chirp rate.

[0031] A computer device includes 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 above-mentioned atomic absolute gravimeter vibration compensation method when executed by a processor.

[0033] A computer program product includes a computer program, which implements the above-mentioned atomic absolute gravimeter vibration compensation method when executed by a processor.

[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 22 is a structural diagram of a generalized regression neural network 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 embodiments 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 vibration compensation method of the atomic absolute gravimeter based on the generalized regression neural network includes the following steps:

[0040] Vibration phase acquisition scheme design: Atomic gravimeters calculate gravitational acceleration by measuring the phase of interference fringes. In fact, atomic gravimeters measure the population of interference fringes to obtain 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] Wherein, the values ​​of A and B are constants with small variations, which have little impact on the measurement results. The values ​​of A and B can be determined by performing multiple static measurements in a laboratory environment.

[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] Where 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] The vibration phase Φ can be derived from formulas (1) and (2): v The expression:

[0047]

[0048] Therefore, when measuring at the absolute gravity point, that is, when 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 true vibration phase of the corresponding three-component vibration data.

[0050] The vibration sensing system includes a Titan triaxial accelerometer with a DC to 430Hz acquisition frequency, collecting vibration data in the three axes: X, Y, and Z. Due to cross-coupling effects in complex environments and installation errors, the vertical direction may not strictly align with the direction of gravity. Therefore, using both horizontal and vertical vibration data measured by the vibration sensor to jointly train the network model can further improve measurement accuracy.

[0051] To maximize the acquisition of vibration source data across all frequency bands, three-component vibration data were collected in various vibration environments, including quiet laboratories, buildings, roads, and areas with pedestrians. Without any vibration isolation or compensation, a full day of atomic transition probability P and accelerometer three-component vibration data was collected in each vibration environment. It's worth noting that multiple different types of vibration sensors can be placed on the ground, and data fusion methods can be used to integrate data from these different sources to obtain more accurate and comprehensive three-component vibration data.

[0052] Repeated measurements are performed at the measuring point to obtain accurate gravitational acceleration values ​​at different measuring points. The effects of tides, ocean currents, and air pressure on gravitational acceleration should be deducted during this step. The vibration environment at the measuring point is changed to perform absolute gravity measurements to obtain three-component vibration data and atomic transition probabilities. The vibration phase is calculated from the atomic transition probabilities using formula (3) and used 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 a training set and a test set. 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 a sample 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 corresponding labels are used as training sets, and 20% of the samples and 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, where i=1, 2, ..., N, and j=1, 2, ..., K.

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

[0057] Step 4. In a generalized regression neural network, the loss function measures the difference between the model's predictions and the actual targets. It plays a crucial role in model training, guiding the adjustment of model parameters to minimize prediction error. In this case, the root mean square error (RMSE) 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 a 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 predictions. Choosing an appropriate smoothing factor is crucial to model performance. In this case, a cross-validation method is used to search for a smoothing factor between 0.01 and 1 in steps of 0.01. Under the searched smoothing factor, step 5 is executed to obtain the smoothing factor that minimizes the loss function value (root mean square error) as the optimal smoothing factor. The network parameters of the generalized regression neural network that minimize the loss function value (root mean square error) are then obtained as the optimal network parameters.

[0060] Step 7: Establish a vibration noise compensation model using the generalized regression neural network with the optimal smoothing factor and optimal network parameters determined in step 6.

[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 Gets the compensated gravity acceleration.

[0062] The algorithm was verified at different points with known absolute gravity values. During the measurement process, all vibration compensation devices were disabled, and only the three-component vibration data obtained by the vibration sensing system was collected. The measured three-component vibration data was used as the predicted three-component vibration data and input into the vibration noise compensation model established in step 7 for calculation. The output was 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 , calculate the phase ΔΦ of the interference fringes when affected by 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 when affected by vibration) as the horizontal coordinate, and the calculated atomic transition probability P as the vertical coordinate to obtain the corrected interference fringes.

[0064] The corrected interference fringes are fitted to a standard cosine signal (y = a1 + b1 cos(x - c1)) using a least-squares algorithm. x represents the compensated interference fringe phase, and y represents the transition probability. The desired fitted fringe pattern is obtained when the residuals of parameters a1, b1, and c1 are minimized. The standard deviation of the fitted residuals is calculated and found to be over 30 times lower than that of measurements 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 α0 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. The memory stores a computer program, 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] Those skilled in the art will 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 illustrative of the spirit of the present invention. Persons skilled in the art may make various modifications, additions, or substitutions to the described specific embodiments without departing from the spirit of the present invention or exceeding the scope of 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 and test sets. Each sample corresponds to a true vibration phase, and the true vibration phase corresponding to the sample is used as the sample label. 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 the minimized loss function value, and obtain the network parameters of the generalized regression neural network corresponding to the minimized loss function value; Step 6: Search for a smoothing factor within the set range. Under the searched smoothing factor condition, execute step 5 to obtain the smoothing factor corresponding to the minimum value of the minimization loss function as the optimal smoothing 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: Use the generalized regression neural network with the optimal smoothing factor and optimal network parameters determined in step 6 to establish a vibration noise compensation model; 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, 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 sample is 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, 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, characterized in that: The calculation of the absolute gravity value in step 8 includes 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: Obtain the compensated gravity acceleration, where α0 is the background chirp rate.

6. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: 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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