A vibration compensation method for an atomic absolute gravimeter based on a simulated annealing algorithm

Abstract

The application discloses a vibration compensation method for an atomic absolute gravimeter based on a simulated annealing algorithm, introduces a correction coefficient to correct vibration acceleration of a Raman mirror, uses a simulated annealing-adaptive particle swarm optimization algorithm to minimize fitting root mean square error of interference fringes, efficiently searches for optimal correction coefficients, and then uses the optimal correction coefficients to compensate for interference phase difference. Compared with a traditional method, the application has a significant improvement in vibration compensation speed, meets the demand of real-time measurement of a high-precision atomic absolute gravimeter in a complex vibration environment, and reduces compensation cost without additional expensive equipment.

Description

Technical Field

[0001] The invention belongs to the field of gravity measurement and relates to a vibration compensation method for an atomic absolute gravimeter based on a simulated annealing algorithm. Background Art

[0002] Cold atom physics, which cools atoms to extremely low temperatures, causing them to exhibit quantum behavior, has demonstrated tremendous potential in the field of precision measurement. The atomic absolute gravimeter, a key experimental device, can precisely measure the absolute value of Earth's gravity by measuring the acceleration of atoms in free fall. This has important applications in geological exploration, fundamental physics research, and other fields.

[0003] However, in practical applications, cold atom experiments are extremely sensitive to environmental vibrations. Even tiny vibrations can significantly affect experimental accuracy, limiting their application in high-precision measurements. During atomic absolute gravimeter measurements, environmental vibrations primarily originate from low-frequency ground vibrations, high-frequency mechanical vibrations, and other environmental disturbances within the platform or measurement environment. These vibrations are coupled into the atomic interferometer signal via the atomic absolute gravimeter's Raman reflectors, causing phase shifts along the interferometer path. These shifts cause deviations in the measured gravitational acceleration, reducing measurement accuracy.

[0004] Although researchers at home and abroad have developed a variety of vibration compensation techniques to improve the measurement accuracy of atomic absolute gravimeters, they still face challenges such as large computational complexity and time-consuming computations. Therefore, effectively suppressing vibration interference, especially in dynamic and complex scenarios such as mobile platforms and aerospace, and achieving efficient, real-time, and reliable vibration compensation still face many technical challenges. Summary of the Invention

[0005] To solve the above problems, the present invention proposes a vibration compensation method for an atomic absolute gravimeter based on a simulated annealing algorithm, which aims to effectively reduce the impact of environmental vibration on the accuracy of gravity measurement.

[0006] In order to achieve the above object, the technical solution of the present invention comprises the following steps:

[0007] A vibration compensation method for an atomic absolute gravimeter based on a simulated annealing algorithm comprises the following steps:

[0008] Step 1: Install an accelerometer on the Raman reflector of the atomic absolute gravimeter, operate the atomic absolute gravimeter, and use π / 2 Raman pulses, π Raman pulses, and π / 2 Raman pulses to sequentially split, reflect, and combine the atomic wave packets in the atomic absolute gravimeter to cause interference of the atomic wave packets. The time interval between adjacent Raman pulses is T. During this process, the accelerometer output voltage U continuously output by the accelerometer is collected. acce (t);

[0009] At the same time, in each interferometric cycle of the atomic absolute gravimeter, the chirp rate α is scanned and the atomic population corresponding to each chirp rate α is detected, which is recorded as the measured population value P ex ;

[0010] Step 2: Minimize the root mean square error of the interference fringes and find the corresponding correction coefficient F as the optimal correction coefficient F. best , and use the optimal correction coefficient F best Compensate for interference phase difference;

[0011] The fitting root mean square error of the interference fringes is calculated by the following steps:

[0012] Convert the value of the correction coefficient F and the accelerometer output voltage into the acceleration coefficient K acce , accelerometer output voltage U acce (t), sensitivity function g of the atomic absolute gravimeter a Substitute (t) into the right side of the following formula to calculate the vibration phase Φ v Recorded as the vibration phase calculation value

[0013]

[0014] Where t represents time, k eff is the effective wave vector;

[0015] The vibration phase calculated value Add the initial phase value Φ corresponding to each chirp rate α α , and obtain the corresponding interference phase difference calculation value ΔΦ ex ;

[0016] The calculated interference phase difference ΔΦ corresponding to different chirp rates α ex The corresponding population number P ex Perform cosine fitting, the fitting formula is as follows:

[0017] P=A+B cos(ΔΦ+C)

[0018] Where A, B, and C are fitting parameters, P represents the population, and ΔΦ represents the interference phase difference;

[0019] Then, the interference phase difference calculation value ΔΦ corresponding to each chirp rate α is calculated ex Substitute them into the right side of the fitting formula to get the corresponding population fitting value P fit ;

[0020] Population number fitting value P fit and the measured population value P exThe root mean square error between them is the fitting root mean square error of the interference fringes corresponding to the correction coefficient F.

[0021] Step 2 specifically comprises the following steps:

[0022] Step 2.1, set the search range F of the correction coefficient F range , and set a specified number of random solutions of the correction coefficient F in the search range F range , a random solution is recorded as a particle, and the initial value corresponding to the random solution is recorded as the initial position of the particle;

[0023] Step 2.2, for each particle, calculate the corresponding fitness according to the current position of the particle, and the fitness is the fitting root mean square error of the interference fringes;

[0024] In the first iteration, the current position of each particle is the initial position of the particle, and the current position of the particle represents the value of the random solution in the current iteration;

[0025] Step 2.3, for each particle, if the fitness of the current position is less than the historical best fitness of the same particle, the current position of the particle is taken as the best position of the particle, and the fitness of the current position is taken as the historical best fitness; otherwise, the best position and the historical best fitness of the particle are kept unchanged;

[0026] In the first iteration, the historical best fitness of each particle is infinite, and the best position of the particle is the initial position of the particle;

[0027] If in all particles, there is a particle whose fitness of the current position is less than the global best fitness, the current position and the fitness of the particle corresponding to the minimum fitness in all particles are taken as the global best position and the global best fitness respectively; otherwise, the global best position and the global best fitness are kept unchanged;

[0028] In the first iteration, the global best position is the initial position of a particle, and the global best fitness is infinite;

[0029] Step 2.4, if the number of iterations is greater than the preset maximum number of iterations, and the change of the global best fitness is less than the fitness change threshold compared with the last iteration, terminate the iteration; and the finally recorded global best position is taken as the best correction coefficient F best , and the global best fitness is taken as the best correction coefficient F best , execute step 2.6; otherwise, execute step 2.5;

[0030] Step 2.5, update the current position of each particle, and calculate the fitness of the particle in the new current position; return to step 2.3;

[0031] Step 2.6: Set the optimal correction coefficient F best The corresponding interference phase difference calculated value ΔΦ ex As the compensated interference phase difference.

[0032] Step 2.5 as described above specifically includes the following operations:

[0033] Step 2.5.1. Use the particle velocity to represent the step size of the random solution of the correction coefficient F, and calculate the updated velocity and position of each particle.

[0034] Step 2.5.2, calculate the fitness of each particle's position to be updated;

[0035] Step 2.5.3: For each particle, if the fitness of the position to be updated is less than the fitness of the current position, then the position to be updated is used as the new current position; if the fitness of the position to be updated is greater than or equal to the fitness of the current position, then based on the difference ΔE between the fitness of the position to be updated and the fitness of the current position and the temperature in the current iteration, whether to use the position to be updated as the new current position is selected;

[0036] Step 2.5.4: Cool down and return to step 2.3.

[0037] As mentioned above, the updated velocity and position of each particle in step 2.5.1 are calculated as follows:

[0038] The current iteration is recorded as the kth iteration;

[0039] The update speed is calculated according to the following formula:

[0040]

[0041] Where, is the updated velocity of the i-th particle at the (k+1)th iteration, is the velocity of the i-th particle at the k-th iteration; is the current position of the i-th particle at the k-th iteration; w is the inertia weight; c1 and c2 are learning factors, and r1 and r2 are random numbers in the range [0,1]; is the optimal position of the i-th particle at the k-th iteration; is the global optimal position up to the kth iteration; in the first iteration, the speed of all particles is the initialized speed value;

[0042] The position to be updated is calculated according to the following formula:

[0043]

[0044] Where, is the position of the i-th particle to be updated in the (k+1)th iteration.

[0045] In step 2.5.3, based on the difference ΔE between the fitness of the position to be updated and the fitness of the current position and the temperature in the current iteration, it is determined whether to use the position to be updated as the new current position. Specifically, the following steps are included:

[0046] Get a random number R, which is a randomly generated number in the interval [0, 1];

[0047] The probability ω is calculated according to the following formula:

[0048]

[0049] Where ΔE is the difference between the fitness of the position to be updated and the fitness of the current position; Te k is the temperature in the kth iteration, and the temperature Te1 in the first iteration is the preset value;

[0050] If R≤ω, the position to be updated is used as the new current position, and the fitness of the particle's current position is updated to the fitness of the position to be updated; if R>ω, the particle's current position and corresponding fitness remain unchanged.

[0051] Cooling is performed as described in step 2.5.4, based on the following rules:

[0052] Te k =Te k ·r 2

[0053] In the formula, Te k and Te k+1 denote the temperatures at the kth iteration and the k+1th iteration, respectively, r is the cooling rate, and r<1.

[0054] The initial position of each particle in step 2.1 is the search range F range A random number within .

[0055] A computer device comprises a memory and a processor, wherein the memory stores a computer program, and the processor implements step 2 of the vibration compensation method according to any one of claims 1 to 7 when executing the computer program.

[0056] A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, step 2 of the vibration compensation method according to any one of claims 1 to 7 is implemented.

[0057] A computer program product comprises a computer program, wherein when the computer program is executed by a processor, step 2 of the vibration compensation method according to any one of claims 1 to 7 is implemented.

[0058] Compared with the prior art, the present invention has the following beneficial effects:

[0059] The present invention discloses a vibration compensation method for an atomic absolute gravimeter based on a simulated annealing algorithm, which can effectively reduce the interference of environmental vibrations on measurement results and improve the accuracy and stability of gravity measurements. Furthermore, the method does not require expensive isolation equipment and can achieve efficient vibration compensation in different vibration environments at low cost through algorithm optimization. The present invention utilizes a simulated annealing-adaptive particle swarm optimization algorithm to efficiently search for the optimal correction coefficient by minimizing the root mean square error of the interference fringes. Compared with traditional methods, the present invention significantly improves the speed of vibration compensation, meeting the requirements for real-time measurement of high-precision atomic absolute gravimeters in complex vibration environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 It is the iterative flow chart of the simulated annealing-adaptive particle swarm optimization algorithm;

[0061] Figure 2 Comparison diagram of the fitted fringe patterns before and after compensation of a set of data points of the measured interference phase difference-population value according to an embodiment of the present invention; (a) is the fitted fringe pattern before compensation; (b) is the fitted fringe pattern after compensation;

[0062] Figure 3 A graph showing changes in the global optimal position versus the number of iterations in the iteration of the simulated annealing-adaptive particle swarm optimization algorithm according to an embodiment of the present invention;

[0063] Figure 4 A graph showing the variation of the root mean square error of the interference fringes fitting with the number of iterations in the simulated annealing-adaptive particle swarm optimization algorithm according to an embodiment of the present invention;

[0064] Figure 5 150 sets of interference phase difference-population number measured value data points after compensation according to an embodiment of the present invention;

[0065] Figure 6 This is a comparison diagram of the RMS error of the interference fringes fitted before and after compensation for 150 sets of interference phase difference-population number measured values ​​according to an embodiment of the present invention. DETAILED DESCRIPTION

[0066] 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 with reference to the embodiments. It should be understood that the embodiments described herein are only used to illustrate and explain the present invention and are not intended to limit the present invention.

[0067] A vibration compensation method for an atomic absolute gravimeter based on a simulated annealing algorithm is based on the following principles:

[0068] (1) Vibration compensation principle:

[0069] The interference fringes of the atomic absolute gravimeter are represented by the population numbers of atoms in different energy states. There is a cosine relationship between the population number P of atoms in the ground state or excited state after the interference is completed and the interference phase difference ΔΦ.

[0070] In an atomic absolute gravimeter, vibration introduces additional phase noise, affecting the measurement accuracy. The expression for the interferometric phase difference ΔΦ taking into account the phase noise is:

[0071] ΔΦ=(k eff g-2πα)T 2 +Φ v (1)

[0072] Where k eff is the effective wave vector, g is the acceleration due to gravity, α is the chirp rate, T is the time interval between adjacent Raman pulses, Φ v It is the vibration phase, which characterizes the interference phase change caused by vibration noise and is a quantity that requires vibration compensation.

[0073] An accelerometer is installed on the Raman reflector to accurately measure the vibration signal of the Raman reflector. v The solution formula is:

[0074]

[0075] g a (t) is the sensitivity function of the atomic absolute gravimeter, a r (t) is the vibration acceleration of the Raman reflector, t represents time, and the sensitivity function g of the atomic absolute gravimeter is a (t) satisfies the following formula,

[0076]

[0077] Where, Ω R is the Rabi frequency, and τ is the pulse time length of π / 2.

[0078] Introducing the correction factor F to improve the compensation effect:

[0079] Due to a combination of vibration noise, system sensitivity errors, installation deviations, and environmental factors, there may be inconsistencies between the acceleration sensed by the Raman reflector and the acceleration measured by the accelerometer. To address this issue, a correction factor F is introduced to more accurately reflect the actual acceleration, thereby improving measurement accuracy and reliability.

[0080] a r (t) = F·K acce ·U acce (t) (4)

[0081] Where a r (t) is the vibration acceleration of the Raman reflector; F represents the correction factor; K acce It is the coefficient of converting the accelerometer output voltage into acceleration, which represents the accelerometer output voltage U acce (t) is proportional to the monitored acceleration.

[0082] Therefore, formula (2) can be written as,

[0083]

[0084] By collecting the accelerometer output voltage U acce (t), combined with the correction coefficient F, the vibration phase Φ can be calculated using formula (5) v The calculated value (recorded as the vibration phase calculated value) ); further combined with formula (1), the vibration phase can be calculated Calculate the calculated value corresponding to the interference phase difference ΔΦ (denoted as the calculated interference phase difference ΔΦ ex ); According to the cosine relationship between the population number P and the interference phase difference ΔΦ, the value ΔΦ can be calculated by the interference phase difference ex Calculate the fitted value of the population number P (denoted as the fitted population number P fit ); If the optimal value of the correction coefficient F is found (denoted as the optimal correction coefficient F best ), then the optimal correction coefficient F best The corresponding interference phase difference calculated value ΔΦ ex The calculated population fitting value P fit , and the actual collected value of the population number P (denoted as the measured population number P ex ) are consistent or close.

[0085] (2) By calculating the RMS error of the interference fringes, and taking minimizing the RMS error of the interference fringes as the goal, the optimal value of the correction coefficient F is found:

[0086] Since there is a cosine relationship between the population number P and the interference phase difference ΔΦ, and since the correction coefficient F in formula (1) and formula (5) also has a one-to-one correspondence with the interference phase difference ΔΦ, the actual acquisition value of the corresponding population number P can be obtained by scanning the chirp rate α and detecting (denoted as the population number measured value P ex ), thus obtaining the measured population value P corresponding to the sequence of chirp rate α exThen, the goal is to minimize the root mean square error of the interference fringes, find the optimal value of the corresponding correction coefficient F, and take the value of the correction coefficient F when the root mean square error of the interference fringes is the smallest as the optimal correction coefficient F best , for a value of the correction coefficient F, obtaining the corresponding interference fringe fitting root mean square error, specifically including the following steps:

[0087] Convert the value of the correction coefficient F and the accelerometer output voltage into the acceleration coefficient K acce , accelerometer output voltage U acce (t), sensitivity function g of the atomic absolute gravimeter a Substituting (t) into the right side of formula (5), the vibration phase Φ is calculated v Recorded as the vibration phase calculation value

[0088] In order to obtain interference fringes, a cyclic scanning method is used to scan the chirp rate α, and each chirp rate α corresponds to an initial phase value Φ α . Vibration phase calculation value Add the initial phase value Φ corresponding to each chirp rate α α , and obtain the corresponding interference phase difference calculation value ΔΦ ex .

[0089] The calculated interference phase difference ΔΦ corresponding to different chirp rates α ex The corresponding population number P ex Perform cosine fitting and determine the cosine fitting parameters. The fitting formula is as follows:

[0090] P=A+B cos(ΔΦ+C) (6)

[0091] Where A, B, and C are fitting parameters, P represents the population, and ΔΦ represents the interference phase difference.

[0092] After obtaining the fitting parameters A, B and C through cosine fitting, the interference phase difference ΔΦ corresponding to each chirp rate α is calculated. ex Substitute them into the right side of the fitted formula (6) to obtain the corresponding population number P, which is recorded as the population number fitting value P fit ;

[0093] Calculate the population fitting value P fit and the measured population value P ex The root mean square error (RMSE) between them is the fitting root mean square error of the interference fringes corresponding to the correction coefficient F.

[0094] Example 1

[0095] To find the optimal correction factor F best, the root mean square error of the interference fringes corresponding to each preset correction coefficient F can be calculated by traversal method, and then the correction coefficient F with the smallest root mean square error of the interference fringes can be found as the optimal correction coefficient F best , but the efficiency is low. This embodiment provides a vibration compensation method for an atomic absolute gravimeter based on a simulated annealing algorithm. The simulated annealing-adaptive particle swarm optimization algorithm is used to iteratively calculate the minimum value of the root mean square error of the interference fringes to obtain the optimal correction coefficient F best . In the simulated annealing algorithm, the adaptive particle swarm optimization algorithm is integrated, and the global search capability of the simulated annealing algorithm and the local search capability of the adaptive particle swarm optimization algorithm are utilized to adaptively adjust the search strategy according to the quality of the solution during the search process. The algorithm controls the randomness and convergence speed of the search process by introducing an annealing temperature parameter, and uses the swarm intelligence of the particle swarm optimization algorithm to guide the search direction, thereby achieving a balance between global and local searches. Vibration compensation based on the simulated annealing-adaptive particle swarm optimization algorithm specifically includes the following steps:

[0096] Step 1: Use the atomic absolute gravimeter to realize atomic wave packet interferometry and perform data acquisition.

[0097] The collected data includes the accelerometer output voltage U acce (t) and atomic population (denoted as the measured population value P ex ). Specifically:

[0098] An accelerometer is installed on the Raman reflector of the atomic absolute gravimeter. The atomic absolute gravimeter is operated and the atomic wave packets in the atomic absolute gravimeter are sequentially split, reflected and combined using π / 2 Raman pulses, π Raman pulses and π / 2 Raman pulses to cause interference of the atomic wave packets. The time interval between adjacent Raman pulses is T. During this process, the accelerometer output voltage U continuously output by the accelerometer is collected. acce (t), accelerometer output voltage U acce (t) is used to compensate for vibration noise. In this embodiment, a Titan accelerometer is used to collect the vertical output signal of the Raman reflector, and the collection frequency is DC to 430 Hz.

[0099] At the same time, in each interferometric cycle of the atomic absolute gravimeter, the chirp rate α is scanned and the atomic population corresponding to each chirp rate α is detected, which is recorded as the measured population value P ex , thus obtaining the measured population value P corresponding to the sequence of chirp rate α ex In this embodiment, the chirp rate α values ​​corresponding to the initial phase value Φ are used for each scan. α The interference fringes are obtained by a 4π cyclic scanning strategy.

[0100] Step 2: Use the simulated annealing-adaptive particle swarm optimization algorithm to minimize the root mean square error of the interference fringes and find the corresponding correction coefficient F as the optimal correction coefficient F. best , and use the optimal correction coefficient F best To compensate for the interference phase difference ΔΦ, the process is as follows Figure 1 shown.

[0101] Step 2.1, Initialize relevant parameters

[0102] Set the search range F corresponding to the correction coefficient F range , in the search range F range A specified number of random solutions of the correction coefficient F are set in it, one random solution is recorded as a particle, and the initial value of the corresponding random solution is recorded as the initial position of the particle;

[0103] Initialization of particle position: The initial position of each particle is the search range F range A random number within , which ensures the numerical diversity of the random solutions of the correction coefficient F by randomly generating the initial positions of the particles;

[0104] Step 2.2, traverse each particle and calculate the corresponding fitness of each particle based on the current position of the particle. The fitness is the root mean square error of the interference fringes.

[0105] In the first round of iteration, the current position of each particle is the initial position of the particle, and the current position of the particle represents the value of the random solution in the current round of iteration;

[0106] Steps 2.3 to 2.5 enter the iterative cycle of simulated annealing-adaptive particle swarm optimization, and determine whether the preset iteration cutoff condition is met through fitness evaluation.

[0107] Step 2.3: Perform fitness evaluation:

[0108] For each particle, if the fitness of the current position is less than the historical best fitness of the same particle, the best position and the historical best fitness of the particle are updated, that is, the current position of the particle is taken as the best position of the particle, and the fitness of the current position is taken as the historical best fitness; otherwise, the best position and the historical best fitness corresponding to the particle are kept unchanged;

[0109] In the first round of iteration, the historical best fitness of each particle is infinite, and the best position of the particle is the initial position of the particle;

[0110] If among all particles, there is a particle whose current position fitness is less than the global best fitness, then the current position and fitness of the particle with the smallest corresponding fitness among all particles are taken as the global best position and global best fitness respectively; otherwise, the global best position and global best fitness remain unchanged;

[0111] In the first round of iteration, the global optimal position is the initial position of a particle, and the global optimal fitness is infinite; in this embodiment, the global optimal position of the first round of iteration is the initial position of the first particle;

[0112] Step 2.4, check the convergence condition: if the number of iterations is greater than the preset maximum number of iterations, and the global best fitness change in this round of iteration is less than the fitness change threshold compared to the previous round of iteration, then terminate the iteration; and use the final recorded global best position as the best correction coefficient F best , the global best fitness is used as the best correction coefficient F best The corresponding fitness; execute step 2.6; otherwise (i.e., the number of iterations is less than or equal to the maximum number of iterations, or the change in the global best fitness in this iteration compared to the previous iteration is greater than or equal to the fitness change threshold), execute step 2.5;

[0113] Step 2.5: Update the current position of each particle and calculate the fitness of the particle at the new current position; return to step 2.3 for the next round of iteration. The specific steps are as follows:

[0114] Step 2.5.1. Use the particle velocity to represent the step size of the random solution of the correction coefficient F, and calculate the updated velocity and position of each particle. The calculation method is as follows:

[0115] The current iteration is recorded as the kth iteration;

[0116] The update speed is calculated according to the following formula:

[0117]

[0118] Where, is the updated velocity of the i-th particle at the (k+1)th iteration, is the velocity of the i-th particle at the k-th iteration; is the current position of the i-th particle at the k-th iteration; w is the inertia weight; c1 and c2 are learning factors that control the tendency of the particle to move towards its own optimal position and the global optimal position respectively; r1 and r2 are random numbers in the range [0,1] to increase the randomness of the search; is the optimal position of the i-th particle at the k-th iteration; is the global optimal position up to the kth iteration; in the first iteration, the speed of all particles is the initialized speed value. In the first iteration of this embodiment, the speed of all particles is set to zero, that is,

[0119] The position to be updated is calculated according to the following formula:

[0120]

[0121] Where, is the position of the i-th particle to be updated at the (k+1)th iteration.

[0122] Step 2.5.2: Calculate the fitness of each particle at the position to be updated.

[0123] Step 2.5.3: For each particle, compare the fitness of the position to be updated with the fitness of the current position. If the fitness of the position to be updated is less than the fitness of the current position, then use the position to be updated as the new current position. If the fitness of the position to be updated is greater than or equal to the fitness of the current position, then determine whether to use the position to be updated as the new current position based on the following simulated annealing probability acceptance mechanism. The specific operation is as follows:

[0124] 1) Obtain a random number R, which is a randomly generated number in the interval [0, 1];

[0125] 2) Calculate the probability ω according to the following formula:

[0126]

[0127] Where ΔE is the difference between the fitness of the position to be updated and the fitness of the current position; Te k is the temperature in the kth iteration, and the temperature Te1 in the 1st iteration is a preset value.

[0128] 3) If R ≤ ω, the position to be updated is used as the new current position, and the fitness of the particle's current position is updated to the fitness of the position to be updated; if R > ω, the particle's current position and corresponding fitness remain unchanged. Introducing the random number R allows the algorithm to escape local optima during the search process, increasing the chance of finding the global optimal solution.

[0129] Step 2.5.4: Then, a cooling process is performed to shift the algorithm from global search to local search, thereby performing a more refined search when approaching the optimal solution, and then returning to step 2.3.

[0130] The temperature update strategy of the square cooling rate is adopted in the cooling process, which enables rapid cooling in the early stage of the simulated annealing algorithm, thereby accelerating the convergence process of the algorithm. The temperature update formula can be expressed as:

[0131] Te k+1 =Te k ·r 2

[0132] In the formula, Te k and Te k+1 They represent the temperature in the kth iteration and the (k+1)th iteration respectively, r is the cooling rate, r<1, and the temperature Te1 in the first iteration is the preset temperature value. k As the probability of accepting a worse solution decreases, the algorithm will gradually tend to accept a better solution until it finally converges to a satisfactory solution.

[0133] In the iterative cycle, the optimal solution of the correction coefficient F is found by minimizing the fitting root mean square error of the interference fringes.

[0134] Step 2.6: Set the optimal correction coefficient F best The corresponding interference phase difference calculated value ΔΦ ex As the compensated interference phase difference.

[0135] The present invention integrates the adaptive particle swarm optimization algorithm into the simulated annealing algorithm and introduces a fitness function based on the root mean square error of the interference fringes to accurately evaluate the quality of the solution and find the optimal solution of the correction coefficient F. Through this process, the optimal correction coefficient F is efficiently searched. best , to compensate for vibration noise and improve measurement accuracy and reliability.

[0136] The vibration compensation effect of this embodiment based on the simulated annealing algorithm is shown as follows:

[0137] Figure 2 The figure shows the comparison of the fitted fringes of a set of interference phase difference-population number data points before and after compensation. It can be seen that the uncompensated data points (for uncompensated data points, the horizontal axis corresponds to the calculated interference phase difference ΔΦ corresponding to the chirp rate α when the correction coefficient F is not introduced, and the vertical axis corresponds to the corresponding measured population number P) ex ) is relatively scattered and has obvious deviation from the cosine fitting curve, indicating that the fitting effect is poor. The data points after vibration compensation (for the data points after vibration compensation, the corresponding value of the horizontal axis is the introduction of the optimal correction coefficient F best Calculated interference phase difference ΔΦ corresponding to the chirp rate α ex The vertical axis corresponds to the measured value of the corresponding population number P ex) distribution significantly improved, becoming closer to the cosine fitting curve, demonstrating that the compensation measures effectively improved fitting accuracy. Calculating the RMS error of the interference fringes before and after compensation revealed that the RMS error was 1.2248 before compensation and decreased to 0.5057 after compensation, demonstrating the effectiveness of the vibration compensation method.

[0138] Figure 3 and Figure 4 The results show how the global optimal position and the corresponding root mean square error (i.e., fitness) of the interference fringes fit during the optimization process of the simulated annealing-adaptive particle swarm optimization algorithm change with the number of iterations. It can be observed that as the iterations progress, the root mean square error of the interference fringes fit shows a continuous downward trend, and quickly converges to the optimal solution at the 6th iteration. This result fully demonstrates the efficiency of the simulated annealing-adaptive particle swarm optimization algorithm in solving vibration compensation problems. In addition, the total running time of the simulated annealing-adaptive particle swarm optimization algorithm in this experiment is only 1.81 seconds. This data further emphasizes the high efficiency of the simulated annealing-adaptive particle swarm optimization algorithm. In addition, the simulated annealing-adaptive particle swarm optimization algorithm is used to perform vibration compensation on 150 sets of continuously collected data points, and the optimal correction coefficient F is searched. best like Figure 5 As shown, it can be seen that the optimal correction coefficient F corresponding to different measurement points best In order to optimize the measurement results, it is necessary to perform the best correction coefficient F for each independent measurement point. best Therefore, the optimal correction coefficient F is improved best The search efficiency is crucial to improving the overall measurement performance.

[0139] Furthermore, the changes in the fitting root mean square error of the interference fringes before and after compensation are analyzed, as shown in Figure 2. Figure 6 As shown in the figure, the RMS error of the interference fringes after compensation is significantly lower than that before compensation. Calculating the average RMS error of the interference fringes before and after compensation shows that the average RMS error before compensation is 0.9868, while the average RMS error after compensation is reduced to 0.4991. This result strongly demonstrates the effectiveness of vibration compensation in reducing system errors and improving measurement accuracy. This method not only verifies its effectiveness but also demonstrates excellent performance and stability. The robustness of the simulated annealing algorithm and its ability to effectively explore the optimal solution in a vast search space make it a fast and reliable method for solving complex optimization problems.

[0140] Example 2

[0141] A vibration compensation device for an atomic absolute gravimeter based on a simulated annealing algorithm, using the vibration compensation method for an atomic absolute gravimeter based on a simulated annealing algorithm described in Example 1, comprising:

[0142] The compensation module is used to implement step 2 of the embodiment 1.

[0143] Example 3

[0144] A computer device includes a memory and a processor, wherein a computer program is stored in the memory, and the processor implements step 2 in the above embodiment 1 when executing the computer program.

[0145] Example 4

[0146] A computer-readable storage medium stores a computer program, which implements step 2 in the above embodiment 1 when executed by a processor.

[0147] Example 5

[0148] A computer program product includes a computer program, which implements step 2 in the above embodiment 1 when executed by a processor.

[0149] The technical content described herein is merely illustrative of the spirit of the present invention. Persons skilled in the art may make various modifications, additions, or substitute similar methods for the specific technical solutions described herein. However, these modifications and additions 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 an atomic absolute gravimeter based on a simulated annealing algorithm, characterized in that: The following steps are involved: Step 1: Install an accelerometer on the Raman reflector of the atomic absolute gravimeter, operate the atomic absolute gravimeter, and use π / 2 Raman pulses, π Raman pulses, and π / 2 Raman pulses to sequentially split, reflect, and combine the atomic wave packets in the atomic absolute gravimeter to cause interference of the atomic wave packets. The time interval between adjacent Raman pulses is T. During this process, the accelerometer output voltage U continuously output by the accelerometer is collected. acce (t); At the same time, in each interferometric cycle of the atomic absolute gravimeter, the chirp rate α is scanned and the atomic population corresponding to each chirp rate α is detected, which is recorded as the measured population value P ex ; Step 2: Minimize the root mean square error of the interference fringes and find the corresponding correction coefficient F as the optimal correction coefficient F. best , and use the optimal correction coefficient F best Compensate for interference phase difference; The fitting root mean square error of the interference fringes is calculated by the following steps: Convert the value of the correction coefficient F and the accelerometer output voltage into the acceleration coefficient K acce , accelerometer output voltage U acce (t), sensitivity function g of the atomic absolute gravimeter a Substitute (t) into the right side of the following formula to calculate the vibration phase Φ v Recorded as the vibration phase calculation value Where t represents time, k eff is the effective wave vector; The vibration phase calculated value Add the initial phase value Φ corresponding to each chirp rate α α , and obtain the corresponding interference phase difference calculation value ΔΦ ex ; The calculated interference phase difference ΔΦ corresponding to different chirp rates α ex The corresponding population number P ex Perform cosine fitting, the fitting formula is as follows: P=A+B cos(ΔΦ+C) Where A, B, and C are fitting parameters, P represents the population, and ΔΦ represents the interference phase difference; Then, the interference phase difference calculation value ΔΦ corresponding to each chirp rate α is calculated ex Substitute them into the right side of the fitting formula to get the corresponding population fitting value P fit ; Population number fitting value P fit and the measured population value P ex The root mean square error between them is the fitting root mean square error of the interference fringes corresponding to the correction coefficient F.

2. The method for compensating an atomic absolute gravimeter for vibration based on a simulated annealing algorithm according to claim 1, characterized in that: The step 2 specifically includes the following steps: Step 2.1, set the search range F corresponding to the correction coefficient F range , in the search range F range A specified number of random solutions of the correction coefficient F are set in it, one random solution is recorded as a particle, and the initial value of the corresponding random solution is recorded as the initial position of the particle; Step 2.2: For each particle, calculate the corresponding fitness based on the current position of the particle. The fitness is the root mean square error of the interference fringes. In the first round of iteration, the current position of each particle is the initial position of the particle, and the current position of the particle represents the value of the random solution in the current round of iteration; Step 2.3: For each particle, if the fitness of the current position is less than the best fitness of the same particle in history, the current position of the particle is taken as the best position of the particle, and the fitness of the current position is taken as the best fitness in history; otherwise, the best position and the best fitness in history of the particle remain unchanged. In the first round of iteration, the historical best fitness of each particle is infinite, and the best position of the particle is the initial position of the particle; If among all particles, there is a particle whose current position fitness is less than the global best fitness, then the current position and fitness of the particle with the smallest corresponding fitness among all particles are taken as the global best position and global best fitness respectively; otherwise, the global best position and global best fitness remain unchanged; In the first round of iteration, the global optimal position is the initial position of a particle, and the global optimal fitness is infinite; Step 2.4: If the number of iterations is greater than the preset maximum number of iterations, and the change in the global best fitness in this round of iteration is less than the fitness change threshold compared to the previous round of iteration, the iteration is terminated; and the final recorded global best position is used as the best correction coefficient F best , the global best fitness is used as the best correction coefficient F best If the fitness is the same as the fitness, go to step 2.6; otherwise go to step 2.5; Step 2.5: Update the current position of each particle and calculate the fitness of the particle at the new current position; return to step 2.3; Step 2.6: Set the optimal correction coefficient F best The corresponding interference phase difference calculated value ΔΦ ex As the compensated interference phase difference.

3. The method for compensating an atomic absolute gravimeter for vibration based on a simulated annealing algorithm according to claim 2, characterized in that: The step 2.5 specifically includes the following operations: Step 2.5.

1. Use the particle velocity to represent the step size of the random solution of the correction coefficient F, and calculate the updated velocity and position of each particle. Step 2.5.2, calculate the fitness of each particle's position to be updated; Step 2.5.3: For each particle, if the fitness of the position to be updated is less than the fitness of the current position, then the position to be updated is used as the new current position; if the fitness of the position to be updated is greater than or equal to the fitness of the current position, then based on the difference ΔE between the fitness of the position to be updated and the fitness of the current position and the temperature in the current iteration, whether to use the position to be updated as the new current position is selected; Step 2.5.4: Cool down and return to step 2.

3.

4. The vibration compensation method for an atomic absolute gravimeter based on a simulated annealing algorithm according to claim 3, characterized in that: The updated velocity and updated position of each particle in step 2.5.1 are calculated as follows: The current iteration is recorded as the kth iteration; The update speed is calculated according to the following formula: Where, is the updated velocity of the i-th particle at the (k+1)th iteration, is the velocity of the i-th particle at the k-th iteration; is the current position of the i-th particle at the k-th iteration; w is the inertia weight; c1 and c2 are learning factors, and r1 and r2 are random numbers in the range [0,1]; is the optimal position of the i-th particle at the k-th iteration; is the global optimal position up to the kth iteration; in the first iteration, the speed of all particles is the initialized speed value; The position to be updated is calculated according to the following formula: Where, is the position of the i-th particle to be updated in the (k+1)th iteration.

5. The vibration compensation method for an atomic absolute gravimeter based on a simulated annealing algorithm according to claim 4, characterized in that: In step 2.5.3, based on the difference ΔE between the fitness of the position to be updated and the fitness of the current position and the temperature in the current iteration, it is determined whether to use the position to be updated as the new current position, which specifically includes the following steps: Get a random number R, which is a randomly generated number in the interval [0, 1]; The probability ω is calculated according to the following formula: Where ΔE is the difference between the fitness of the position to be updated and the fitness of the current position; Te k is the temperature in the kth iteration, and the temperature Te1 in the first iteration is the preset value; If R≤ω, the position to be updated is used as the new current position, and the fitness of the particle's current position is updated to the fitness of the position to be updated; if R>ω, the particle's current position and corresponding fitness remain unchanged.

6. The vibration compensation method for an atomic absolute gravimeter based on a simulated annealing algorithm according to claim 5, characterized in that: The cooling in step 2.5.4 is based on the following rules: yourself k =You k ·r 2 In the formula, Te k and Te k+1 denote the temperatures at the kth iteration and the k+1th iteration, respectively, r is the cooling rate, and r<1.

7. The method for compensating atomic absolute gravimeter vibration based on simulated annealing algorithm according to claim 2, characterized in that: The initial position of each particle in step 2.1 is the search range F range A random number within .

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, step 2 of the vibration compensation method according to any one of claims 1 to 7 is implemented.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, step 2 of the vibration compensation method according to any one of claims 1 to 7 is implemented.

10. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, step 2 of the vibration compensation method according to any one of claims 1 to 7 is implemented.

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