Atomic absolute gravimeter vibration compensation method based on simulated annealing algorithm

Abstract

The invention discloses an atomic absolute gravimeter vibration compensation method based on a simulated annealing algorithm. The method comprises the following steps: introducing a correction coefficient to correct the vibration acceleration of a Raman reflector; a simulated annealing-adaptive particle swarm optimization algorithm is utilized to efficiently search an optimal correction coefficient by minimizing a fitting root-mean-square error of interference fringes; and the interference phase difference is compensated by using the optimal correction coefficient. Compared with a traditional method, the method has the advantages that the vibration compensation speed is remarkably increased, the requirement for real-time measurement of the high-precision atom absolute gravimeter in a complex vibration environment is met, additional expensive equipment is not needed, and the compensation cost is reduced.

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 simulated annealing algorithm. Background Art

[0002] Cold atom physics has shown great potential in the field of precision measurement by cooling atoms to extremely low temperatures to make them exhibit quantum behavior. As an important experimental device, the atomic absolute gravimeter can accurately measure the absolute value of the earth's gravity by measuring the acceleration of atoms in free fall, and has important applications in geological exploration, basic physics research and other fields.

[0003] However, in practical applications, cold atom experiments are extremely sensitive to environmental vibrations. Even tiny vibrations can have a significant impact on experimental accuracy, limiting their application in high-precision measurements. During the measurement of the atomic absolute gravimeter, environmental vibrations mainly come from low-frequency ground vibrations, high-frequency mechanical vibrations, and other environmental disturbances in the platform or measurement environment. They are coupled to the atomic interference signal through the Raman reflector of the atomic absolute gravimeter, causing the phase on the interferometer path to change. This change causes a deviation in the measured gravitational acceleration, thereby reducing the measurement accuracy.

[0004] Although domestic and foreign scholars have developed a variety of vibration compensation technologies to improve the measurement accuracy of atomic absolute gravimeters, there are still problems such as large amount of calculation and time consumption. Therefore, how to effectively suppress vibration interference, especially in dynamic and complex scenes such as mobile platforms, aerospace, etc., to achieve efficient, real-time and reliable vibration compensation still faces 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, aiming to effectively reduce the influence of environmental vibration on the accuracy of gravity measurement.

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

[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, so that the atomic wave packets interfere with each other. 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 interference 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 RMS error of the interference fringes and find the corresponding correction coefficient F as the optimal correction coefficient F. best , and use the optimal correction factor 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] Among them, A, B and C are fitting parameters, P represents the population number, and ΔΦ represents the interference phase difference;

[0019] Then, the interference phase difference calculation value ΔΦ corresponding to each chirp rate α is ex Substitute them into the right side of the fitting formula to get the corresponding population number 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] The above-mentioned step 2 specifically includes the following steps:

[0022] 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;

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

[0024] 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;

[0025] 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 are kept unchanged;

[0026] 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;

[0027] 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 the global best fitness respectively; otherwise, the global best position and the global best fitness are kept unchanged;

[0028] In the first round of 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 in the global best fitness in this iteration compared to the previous iteration is less than the fitness change threshold, 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 taken as the best correction coefficient F best If the fitness is the same, 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 at 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] As mentioned above, step 2.5 specifically includes the following operations:

[0033] Step 2.5.1, the particle velocity is represented by the change step of the random solution of the correction coefficient F, and the updated velocity and updated position of each particle are calculated;

[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, 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, 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, select whether to use the position to be updated as the new current position;

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

[0037] As mentioned above, the updated speed and updated 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] In the formula, is the updated velocity of the ith particle at the (k+1)th iteration, is the velocity of the ith particle at the kth 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 end of 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] In the formula, is the position to be updated of the i-th particle in the (k+1)th iteration.

[0045] As described above, 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:

[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 1st 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 current position of the particle is updated to the fitness of the position to be updated; if R>ω, the current position of the particle and the corresponding fitness are kept 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 represent the temperatures in the kth iteration and the k+1th iteration respectively, r is the cooling rate, 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 the computer program, when executed by a processor, implements step 2 of the vibration compensation method according to any one of claims 1 to 7.

[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 vibration on the measurement results and improve the accuracy and stability of gravity measurement; and 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 fitting root mean square error of the interference fringes. Compared with traditional methods, the present invention has a significant improvement in the vibration compensation speed, meeting the needs of 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 simulated annealing-adaptive particle swarm optimization algorithm;

[0061] Figure 2 A comparison diagram of fitted fringes before and after compensation of a set of data points of the measured values ​​of the interference phase difference-population number in an embodiment of the present invention; (a) is the fitted fringe diagram before compensation; (b) is the fitted fringe diagram after compensation;

[0062] Figure 3 A graph showing the change of the global optimal position with 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 fitting root mean square error of interference fringes with the number of iterations in the simulated annealing-adaptive particle swarm optimization algorithm of an embodiment of the present invention;

[0064] Figure 5 This is a distribution diagram of the best correction coefficients after compensation for 150 sets of interference phase difference-population number measured values ​​of the embodiment of the present invention;

[0065] Figure 6 This is a comparison diagram of the fitting root mean square errors of the interference fringes before and after compensation for 150 sets of interference phase difference-population number measured values ​​of the 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 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.

[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. After the interference is completed, there is a cosine relationship between the population number P of atoms in the ground state or excited state and the interference phase difference ΔΦ.

[0070] In an atomic absolute gravimeter, vibration will introduce additional phase noise, affecting the measurement accuracy. The expression of the interference phase difference ΔΦ considering the phase noise is:

[0071] ΔΦ=(k eff g-2πα)T 2 +Φ v (1)

[0072] In the formula, k eff is the effective wave vector, g is the acceleration caused by 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. Vibration phase Φ 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] In the formula, Ω R is the Rabi frequency, and τ is the pulse time length of π / 2.

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

[0079] Due to the combined effects of vibration noise, system sensitivity error, installation deviation, and environmental factors, there may be inconsistency between the acceleration sensed by the Raman reflector and the acceleration measured by the accelerometer. In order to solve this problem, the correction factor F is introduced to more accurately reflect the actual acceleration situation, thereby improving the accuracy and reliability of the measurement.

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

[0081] In the formula, 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 factor 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 (recorded 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 (referred to as the optimal correction coefficient F best ), then the optimal correction coefficient F best The corresponding interference phase difference calculation value ΔΦ ex The calculated population fitting value P fit , and the actual collected value of the population number P (recorded as the measured population number P ex ) are consistent or close.

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

[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 (recorded as the population number measured value P ex ), thus obtaining the measured population value P corresponding to the sequence of chirp rate α exsequence; then the minimum root mean square error of the interference fringes is taken as the goal, the corresponding optimal value of the correction coefficient F is found, and the value of the correction coefficient F when the root mean square error of the interference fringes is the minimum is taken as the optimal correction coefficient F best , for a value of the correction coefficient F, obtaining the corresponding fitting root mean square error of the interference fringes, specifically includes 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 scanning chirp rate α is used for cyclic scanning, 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 number, and ΔΦ represents the interference phase difference.

[0092] After the cosine fitting obtains the fitting parameters A, B and C, the interference phase difference calculation value 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 is found as the optimal correction coefficient F best , but the efficiency is low. This embodiment is 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 fitting 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 group 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 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 interference 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 split, reflected and combined in sequence using π / 2 Raman pulses, π Raman pulses and π / 2 Raman pulses to make the atomic wave packets interfere. 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 interference 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 circular scanning strategy.

[0100] Step 2: Use 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 factor F best To compensate 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 factor 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 according to the current position of the particle, and 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] Step 2.3-Step 2.5 enters the iterative cycle of simulated annealing-adaptive particle swarm optimization, and determines whether the preset iteration cutoff condition is reached 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 the global best fitness respectively; otherwise, the global best position and the global best fitness remain unchanged;

[0111] In the first round of iteration, the global best position is the initial position of a particle, and the global best fitness is infinite; in this embodiment, the global best 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 taken as the best correction coefficient F best Corresponding fitness; execute step 2.6; otherwise (that is, the number of iterations is less than or equal to the maximum number of iterations, or the change of the global best fitness in this round of iteration compared with the previous round of 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, the particle velocity represents the change step of the random solution of the correction coefficient F, and the updated velocity and updated position of each particle are calculated 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] In the formula, is the updated velocity of the ith particle at the (k+1)th iteration, is the velocity of the ith particle at the kth iteration; is the current position of the ith particle at the kth iteration; w is the inertia weight; c1 and c2 are learning factors, which control the tendency of the particle to move to its own optimal position and the global optimal position respectively; r1 and r2 are random numbers in the range of [0,1], which are used to increase the randomness of the search; is the optimal position of the i-th particle at the end of 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] In the formula, 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, 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, determine whether to use the position to be updated as the new current position based on the following simulated annealing probability receiving mechanism. The specific operations are 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. The introduction of the random number R enables the algorithm to jump out of the local optimum during the search process, increasing the chance of finding the global optimal solution.

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

[0130] The temperature update strategy of the square cooling rate is adopted in the cooling process, so that the temperature can be quickly cooled 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 temperatures 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 calculation 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 the 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 the 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 there is an 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 The calculated interference phase difference ΔΦ corresponding to the chirp rate α ex The vertical coordinate corresponds to the measured value of the corresponding population number P ex) distribution is significantly improved and closer to the cosine fitting curve, which shows that the compensation measures effectively improve the accuracy of the fitting. The root mean square error of the interference fringes before and after compensation is calculated. It can be seen that the root mean square error of the interference fringes before compensation is 1.2248, and the root mean square error of the interference fringes after compensation is reduced to 0.5057, which proves the effectiveness of the vibration compensation method.

[0138] Figure 3 and Figure 4 The simulation results show how the global optimal position and the corresponding root mean square error (i.e., fitness) of the interference fringes change with the number of iterations during the optimization process of the simulated annealing-adaptive particle swarm optimization algorithm. It can be observed that with the advancement of iterations, the root mean square error of the interference fringes 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, in this experiment, the total running time of the simulated annealing-adaptive particle swarm optimization algorithm was only 1.81 seconds, which further emphasizes the high efficiency of the simulated annealing-adaptive particle swarm optimization algorithm. In addition, the simulated annealing-adaptive particle swarm optimization algorithm was used to perform vibration compensation on 150 sets of continuously collected data points, and the optimal correction coefficient F was 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 factor F for each independent measurement point. best Therefore, the optimal correction factor 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, such as Figure 6 As shown in the figure, it can be seen that the RMS error of the interference fringes after compensation is significantly lower than that before compensation. The average RMS error of the interference fringes before and after compensation is calculated, and it can be seen that the average RMS error of the interference fringes before compensation is 0.9868, and the average RMS error of the interference fringes after compensation is reduced to 0.4991. This result strongly proves the effectiveness of vibration compensation measures 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 wide 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, and when the computer program is executed by a processor, step 2 in the above embodiment 1 is implemented.

[0149] The technical contents described herein are merely examples of the spirit of the present invention. Those skilled in the art of the present invention may make various modifications or additions to the specific technical solutions described or replace them in similar ways. However, they will not deviate from the spirit of the present invention or exceed the scope defined by the attached 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, so that the atomic wave packets interfere with each other. 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 interference 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 RMS error of the interference fringes and find the corresponding correction coefficient F as the optimal correction coefficient F. best , and use the optimal correction factor 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) Among them, A, B and C are fitting parameters, P represents the population number, and ΔΦ represents the interference phase difference; Then, the interference phase difference calculation value ΔΦ corresponding to each chirp rate α is ex Substitute them into the right side of the fitting formula to get the corresponding population number 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 vibration compensation method of atomic absolute gravimeter based on 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, the corresponding fitness is calculated according to the current position of the particle, and 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 are kept 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 the global best fitness respectively; otherwise, the global best position and the global best fitness remain unchanged; In the first round of iteration, the global best position is the initial position of a particle, and the global best 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 iteration compared to the previous iteration is less than the fitness change threshold, 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 taken as the best correction coefficient F best If the fitness is the same, execute step 2.6; otherwise, execute 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 vibration compensation method of atomic absolute gravimeter based on simulated annealing algorithm according to claim 2, characterized in that: The step 2.5 specifically includes the following operations: Step 2.5.1, the particle velocity is represented by the change step of the random solution of the correction coefficient F, and the updated velocity and updated position of each particle are calculated; 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, 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, 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, select whether to use the position to be updated as the new current position; Step 2.5.4: Cool down and return to step 2.

3.

4. The vibration compensation method of atomic absolute gravimeter based on simulated annealing algorithm according to claim 3, characterized in that: The updated speed 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: In the formula, is the updated velocity of the ith particle at the (k+1)th iteration, is the velocity of the ith particle at the kth 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 end of 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: In the formula, is the position to be updated of the i-th particle in the (k+1)th iteration.

5. The vibration compensation method of atomic absolute gravimeter based on 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 1st 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 current position of the particle is updated to the fitness of the position to be updated; if R>ω, the current position of the particle and the corresponding fitness are kept unchanged.

6. The vibration compensation method of atomic absolute gravimeter based on 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 represent the temperatures in the kth iteration and the k+1th iteration respectively, r is the cooling rate, r<1.

7. The vibration compensation method of atomic absolute gravimeter 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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