A gravity acceleration dynamic measurement method and system based on PSO-VMD

Abstract

The application belongs to the field of gravity measurement, and relates to a gravity acceleration dynamic measurement method and system based on PSO-VMD, a survey line survey point is designed, and original gravity acceleration data of each survey point output by an atomic gravimeter is obtained; data is extracted from each survey point, abnormal data is removed according to a 3sigma rule, and pretreatment data is obtained; an optimal parameter combination of a modal number K and a penalty factor alpha is found by using a particle swarm optimization algorithm, the pretreatment data is decomposed into multiple modes by using VMD decomposition according to the optimal parameter combination, a low-frequency mode is selected from the multiple modes, and a mean value of the low-frequency mode is taken as a signal component of denoised gravity acceleration; signal components of gravity acceleration of all survey points are reconstructed, and gravity acceleration of a to-be-measured place is obtained. The application can adaptively denoise various gravimeter dynamic measurement data, and can make up for the limitation of limited data processing effect of an original method and artificial parameter adjustment of traditional VMD decomposition.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of gravity measurement, and relates to a gravity acceleration dynamic measurement method and system based on PSO-VMD. BACKGROUND

[0002] An atomic gravimeter is a high-precision gravity acceleration measurement tool, which is currently widely used in fields such as geophysical exploration, seismic wave detection, climate monitoring and the like. Compared with traditional gravimeters, the atomic gravimeter can realize very accurate gravity change detection by virtue of its measurement mode based on the quantum interference principle, and the judgment precision can usually reach the microgal (μGal) level, and the atomic gravimeter has extremely high sensitivity and long-term stability.

[0003] However, one of the main problems in the process of applying the atomic gravimeter for field dynamic measurement is the interference of the instrument intrinsic noise and the environmental noise on the measurement signal. Due to the equivalence principle, it is impossible to distinguish the gravity acceleration and the acceleration caused by vibration, so there is a deviation between the measurement data and the local true gravity acceleration, which reduces the measurement reliability and precision, and seriously affects the application effect in actual engineering.

[0004] Since the periodic fluctuation of gravity acceleration caused by the tidal effect has a long period, the gravity acceleration measured at the same position in a short time can be regarded as a low-frequency signal with very small amplitude change. The conventional method is to take the mean value of all gravity acceleration data of the measurement point to eliminate the influence of accidental errors, but in fact, the errors caused by various noises to the gravity acceleration measurement value have not been completely eliminated. At the same time, different experimental environments have different influences on the gravity dynamic measurement data, therefore, it still faces many challenges to realize an efficient and reliable adaptive denoising algorithm. SUMMARY

[0005] The embodiment of the application provides a gravity acceleration dynamic measurement method and system based on PSO-VMD, which aims to effectively reduce the noise in the process of gravity dynamic measurement.

[0006] According to the gravity acceleration dynamic measurement method based on PSO-VMD provided by the first aspect of the application, the following steps are included.

[0007] Designing a measurement line and measurement points, running an atomic gravimeter at each measurement point, and obtaining gravity acceleration original data of each measurement point output by the atomic gravimeter;

[0008] Extracting data from each measurement point, removing abnormal data according to the 3σ criterion, and obtaining pretreatment data;

[0009] The optimal parameter combination of the mode number K and the penalty factor a is found by using a particle swarm optimization algorithm, and the preprocessed data is decomposed into multiple modes by using VMD decomposition according to the optimal parameter combination; the mean value of a low-frequency mode selected from the multiple modes is taken as the signal component of the gravity acceleration after denoising.

[0010] The signal components of the gravity acceleration of all measuring points are reconstructed to obtain the gravity acceleration of the to-be-measured earth.

[0011] Further, the modes are time-domain signals and spectrums arranged in ascending order of frequency, and the low-frequency mode is selected from the multiple modes, which meets the following conditions: modes with a frequency lower than a set frequency threshold are selected, the amplitude variation of the selected modes is calculated, and a mode with an amplitude variation lower than a set amplitude variation is taken as the final selected low-frequency mode for signal reconstruction.

[0012] Further, the optimal parameter combination of the mode number K and the penalty factor a is found by using a particle swarm optimization algorithm, which includes the following steps: the sample entropy sum of each mode obtained by VMD decomposition, the Pearson correlation coefficient between the original signal and the sum of each mode signal, and the aggregation algebra are used to calculate the fitness as follows: , The fitness is denoted as fitness;

[0013] The low-frequency mode is assigned a high weight, and the high-frequency mode is assigned a low weight.

[0014] The position with the optimal fitness in the history of each particle is recorded as the individual optimal position, and the position with the optimal fitness in the history of the entire population is recorded as the global optimal solution.

[0015] Further, the optimal parameter combination of the mode number K and the penalty factor a is found by using a particle swarm optimization algorithm, which further includes the following steps:

[0016] In the initial iteration, the preprocessed data is decomposed into multiple modes by using VMD decomposition with the initial parameter combination;

[0017] The particle swarm optimization algorithm calculates the fitness of the multiple modes, and the individual optimal position and the global optimal solution are updated according to the fitness.

[0018] Further, the preprocessed data is decomposed into multiple modes by using VMD decomposition, which includes the following steps: the preprocessed data is decomposed by VMD according to the parameter combination output by the current particle swarm algorithm, it is judged whether the frequency and the amplitude variation of a mode are lower than the set minimum frequency and the set minimum amplitude variation, and the fitness is calculated; the particle position and the speed are updated according to the fitness until the frequency of a mode is lower than the set minimum frequency, the amplitude variation of the mode is lower than the set minimum amplitude variation, and the fitness is minimum. Further, the minimum amplitude variation is higher than the amplitude variation caused by tides in a tidal period.

[0019] According to the second aspect of the embodiment of the application, a PSO-VMD-based dynamic gravity acceleration measurement system comprises:

[0020] The acquisition device comprises a plurality of atomic gravimeters, and a design survey line survey point is designed, an atomic gravimeter is operated at each survey point, and original gravity acceleration data of each survey point is obtained;

[0021] The host computer extracts data from each survey point, removes abnormal data according to the 3σ criterion to obtain pretreatment data, uses a particle swarm optimization algorithm to find an optimal parameter combination of the mode number K and the penalty factor α, decomposes the pretreatment data into a plurality of modes according to the optimal parameter combination, selects a low-frequency mode from the plurality of modes, and takes the mean value of the low-frequency mode as a signal component of the gravity acceleration after denoising; and the signal components of the gravity acceleration of all survey points are reconstructed to obtain the gravity acceleration of the surveyed area.

[0022] Compared with the prior art, the application has the beneficial effects that the application can effectively reduce the influence of various noises on the gravity measurement accuracy in the gravity dynamic measurement process, can adaptively denoise various gravity dynamic measurement data, and can make up for the limited data processing effect of the original method and the limitations of the traditional VMD decomposition artificial parameter adjustment. BRIEF DESCRIPTION OF DRAWINGS

[0023] Figure 1 A flowchart of a PSO-VMD-based gravity acceleration dynamic measurement method provided by the embodiment of the application is shown in the figure.

[0024] Figure 2 A block diagram of a PSO-VMD-based gravity acceleration dynamic measurement system provided by the embodiment of the application is shown in the figure. DETAILED DESCRIPTION

[0025] In order to make the purpose, technical scheme and advantages of the application more clear, the application is further described in detail below with reference to the embodiments. It should be understood that the specific embodiments described herein are only used to explain the application and do not limit the application.

[0026] Participation Figure 1 The PSO-VMD-based gravity acceleration dynamic measurement method shown in the figure comprises:

[0027] S1 design survey line survey points, operate atomic gravimeters at each survey point, and obtain gravity acceleration original data of each survey point output by the atomic gravimeter;

[0028] S2 extracts data from each survey point, removes abnormal data according to the 3σ criterion to obtain pretreatment data;

[0029] S3 finds the optimal parameter combination of the modal number K and the penalty factor a by using the particle swarm optimization algorithm, and according to the optimal parameter combination, the preprocessed data is decomposed into multiple modes by using VMD decomposition, a low-frequency mode is selected from the multiple modes, and the mean value of the low-frequency mode is taken as the signal component of the denoised gravity acceleration;

[0030] S4 reconstructs the signal components of the gravity acceleration of all measuring points to obtain the gravity acceleration of the measured earth.

[0031] In S1, a measuring line is designed for the measured earth, measuring points are set at equal intervals on the measuring line, an atomic gravimeter is operated at the measuring points, and initial data of the atomic gravimeter at the measuring points are obtained, and the operation is repeated at other measuring points. The gravity acceleration raw data of each measuring point is obtained.

[0032] The data from each measuring point is extracted, and the abnormal data is removed according to the 3σ criterion to obtain the preprocessed data. The 3σ criterion refers to the characteristics based on normal distribution, and the distribution of data values around the mean value can be measured by standard deviation σ. According to the 3σ criterion, any data point outside the mean value standard deviation is considered as an abnormal value or outlier. After removing the abnormal value or outlier, the preprocessed data is obtained for the next step of processing. Here is the process of preliminary denoising of the gravity acceleration raw data of each measuring point.

[0033] In S3, VMD decomposition aims to decompose complex preprocessed data into several intrinsic mode functions with different frequency characteristics. The core idea is to introduce the augmented Lagrange equation to convert the model optimization problem into a variational problem for solving based on the variational constraint theory, and to constrain the bandwidth of each decomposition mode, so that each mode is closely connected with the center frequency, thereby accurately extracting the low-frequency and high-frequency components in the signal.

[0034] Applying Variational Mode Decomposition (VMD) requires manually setting the number of modes K and the penalty factor α, both of which directly affect the VMD decomposition effect. The number of modes K refers to the desired number of modes during VMD decomposition. Each mode corresponds to a signal component with a specific frequency bandwidth. If the chosen number of modes K is too small, VMD will attempt to decompose the signal into fewer modes, often resulting in low-frequency components dominating and high-frequency components being merged into a single mode, failing to effectively identify details or noise in the signal. If the number of modes K is too large, VMD will decompose into even more modes, potentially leading to an excessive number of modes with small bandwidths for each mode. The final modes may contain little signal information, or even simply capture noise. The penalty factor α controls the strength of the penalty applied to frequency smoothing during signal decomposition, affecting the bandwidth of each mode. When the penalty factor α is small, VMD imposes looser restrictions on the frequency bandwidth of the modes, potentially resulting in a wider frequency range. In this case, VMD may merge multiple frequency components into the same mode, making it difficult to effectively distinguish different frequency components in the signal. If the penalty factor α is too large, it may lead to over-refinement of the modes, resulting in overfitting or excessive noise components.

[0035] The number of modes K and the penalty factor α are interrelated, and their selection usually needs to be balanced. Especially for gravitational acceleration, if the chosen number of modes K is too small, low-frequency components will dominate, and high-frequency components will be merged into a single mode, making it impossible to distinguish gravitational acceleration variations caused by tides from those caused by other noise. If the number of modes K is too large, VMD will decompose into more modes, potentially leading to an excessive number of modes with small bandwidth per mode, resulting in the acquisition of only noise.

[0036] The optimal combination of mode number K and penalty factor α is found using the particle swarm optimization algorithm and mapped to a two-dimensional optimization space. The search range and maximum number of iterations for the mode number K and penalty factor α are set, and the initial positions of the particles are randomly generated in the search space. In the first iteration, the current position of each particle is randomly generated within the search range, and the position of the particle represents the random solution of the current parameters.

[0037] When calling VMD decomposition, the initial parameter combination is used in the first iteration. VMD decomposition decomposes the preprocessed data into multiple modes and calculates the time domain signal and spectrum of each mode in order of frequency from low to high.

[0038] Calculate the sample entropy of each mode, the Pearson correlation coefficient between the original signal and the sum of the signals of each mode, and the aggregation algebra.

[0039] Fitness is calculated using the following formula: ,

[0040] Here, sample entropy represents the complexity of the data after VMD decomposition, Pearson coefficient represents the correlation between the data before and after VMD decomposition, and convergent algebra represents the degree of frequency domain separation of each mode after VMD decomposition. It can be seen that the smaller the fitness value, the better the VMD decomposition effect.

[0041] Since gravitational acceleration data is primarily found in low-frequency modes, the weight of these low-frequency modes is increased here. Specifically, the first two modes are treated as low-frequency modes, and their weights are appropriately increased. The final fitness function is:

[0042] ,

[0043] Here, low-frequency modes are assigned high weights, and high-frequency modes are assigned low weights; the position with the best fitness in the history of each particle is calculated and recorded as the individual's best position, and the position with the best fitness in the history of the entire population is recorded as the global optimal solution.

[0044] In each iteration, particles evaluate the quality of the current solution based on their fitness, updating their individual optimal position and the global optimal solution. The algorithm terminates when the number of iterations reaches a preset maximum, outputting the final optimal parameter combination. If the number of iterations exceeds the preset maximum, and the change in the global optimal fitness compared to the previous iteration is less than a threshold, the iteration terminates; and the final recorded global optimal position is used as the optimal parameter combination for VMD decomposition.

[0045] Based on the velocity and position update formulas of the particle swarm optimization algorithm, the velocity and position of particles are updated in the direction of decreasing fitness; specifically including:

[0046] The velocity of the particles is used to characterize the step size of the random solution of the decomposition parameter combination, and the velocity and position to be updated for each particle are calculated.

[0047] Calculate the fitness of each particle at the position to be updated;

[0048] 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 taken as the new current position. The update velocity and update position of each particle are calculated as follows:

[0049] Calculate the update speed using the following formula: ,

[0050] in, This represents the number of iterations. The inertial weight represents the degree to which a particle inherits the velocity from the previous position, and is used to balance the global optimum and the local optimum. , The acceleration factor represents the degree to which a particle approaches its optimal position and the global optimal solution. , These are random numbers, primarily used to introduce randomness and prevent premature convergence. For particles In the Wei Shang Di The speed of each iteration For particles In the Wei Shang Di The individual's historical best position in the next iteration. For particles In the Wei Shang Di The current position in the next iteration. For the entire particle swarm in the th Wei Shang Di The global optimal position in the next iteration.

[0051] Calculate the position to be updated using the following formula: ,in, It is the first The first particle The position to be updated in the next iteration.

[0052] In one embodiment, VMD decomposition is used to decompose the preprocessed data into multiple modes. This includes: performing VMD decomposition on the preprocessed data according to the parameter combination output by the current particle swarm optimization algorithm; determining whether any mode has a frequency and amplitude variation lower than a set minimum frequency and minimum amplitude variation; simultaneously calculating the fitness; and updating the particle position and velocity accordingly, until a mode simultaneously satisfies both the set minimum frequency and minimum amplitude variation, and has the minimum fitness. This ensures the accuracy of the calculation.

[0053] In one embodiment, the modes are time-domain signals and their spectra arranged from low to high frequency. Low-frequency modes are selected from multiple modes, provided their selection frequency is below a set frequency threshold. The amplitude changes of these modes are calculated, and the modes with amplitude changes below a set threshold are selected as the final low-frequency modes for signal reconstruction. For example, after VMD decomposition, multiple modes are output with different frequencies, arranged from high to low frequency. The first three output modes can be considered as intermediate modes, and then the intermediate mode with an amplitude change below a set minimum amplitude change is selected as the final low-frequency mode.

[0054] Because the periodic fluctuations in gravitational acceleration caused by tidal effects have a relatively long period, the gravitational acceleration measured at the same location over a short period can be considered a low-frequency signal with very small amplitude changes. However, in actual dynamic measurements, gravitational acceleration data is mixed with a series of noise components, such as instrument intrinsic noise, ambient temperature changes, and vibration noise. These noises have higher frequencies and more significant amplitude changes compared to the gravitational acceleration data. Therefore, the low-frequency modes after VMD decomposition can be considered as the effective components of the dynamic measurement data of the atomic gravimeter. By removing noise components from both the frequency and amplitude variation aspects, the low-frequency signal of amplitude variation in the data caused by the periodic fluctuations of gravitational acceleration due to tidal effects is retained.

[0055] In one embodiment, the minimum amplitude variation is higher than the amplitude variation caused by tides within a tidal cycle. Setting the minimum amplitude variation within a tidal cycle preserves the low-frequency signal of amplitude variations in the data caused by the periodic fluctuations in gravitational acceleration due to tidal effects.

[0056] The process of obtaining the amplitude change caused by tides within a tidal cycle includes:

[0057] The gravitational acceleration at the beginning of a tidal cycle at the measurement point is theoretically calculated to obtain theoretical calculation data. The theoretical calculation method is the calculation process of gravitational acceleration by combining Newtonian gravity with the Earth's rotation, ellipticity, elevation, solid tides, and relativistic effects. This is an existing method and will not be elaborated here.

[0058] VMD decomposition was performed on the theoretical calculation data to obtain time-domain signals and spectra of multiple modes;

[0059] Amplitude information is extracted from the spectrum, and the difference between the maximum and minimum amplitude is obtained as the amplitude change caused by the tide within a tidal cycle.

[0060] On the other hand, see Figure 2 As shown, this application provides a PSO-VMD-based dynamic measurement system for gravity acceleration, used to implement the PSO-VMD-based dynamic measurement method for gravity acceleration described in the above embodiments, including:

[0061] The data acquisition device includes multiple atomic gravimeters, with a design of measurement lines and points. The atomic gravimeter is run at each measurement point to obtain the raw data of gravitational acceleration at each measurement point.

[0062] The host computer extracts data from each measuring point, removes outlier data according to the 3σ criterion, and obtains preprocessed data. It uses the particle swarm optimization algorithm to find the optimal combination of mode number K and penalty factor α. Based on the optimal parameter combination, VMD decomposition is used to decompose the preprocessed data into multiple modes. Low-frequency modes are selected from multiple modes, and the mean of the low-frequency modes is taken as the signal component of the denoised gravitational acceleration. The signal components of the gravitational acceleration of all measuring points are reconstructed to obtain the gravitational acceleration of the ground to be measured.

[0063] Data is transmitted between the data acquisition device and the host computer via wired or wireless means. At the same time, the host computer can issue a synchronous acquisition command to control multiple atomic gravimeters to acquire data synchronously.

[0064] After analyzing the data from multiple measuring points within the same location area over the same time period, the host computer reconstructs the signal components of the gravitational acceleration of all measuring points to obtain a gravitational acceleration distribution map at different coordinates. For multiple measuring points with the same altitude and within a certain latitude and longitude range, the average gravitational acceleration within a region is obtained by averaging the gravitational acceleration.

[0065] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A dynamic measurement method for gravitational acceleration based on PSO-VMD, characterized in that, include: Design measurement lines and measurement points, run an atomic gravimeter at each measurement point, and obtain the raw data of gravitational acceleration at each measurement point output by the atomic gravimeter; Data is extracted from each measurement point, and outliers are removed according to the 3σ criterion to obtain preprocessed data; The optimal combination of mode number K and penalty factor α is found by using particle swarm optimization algorithm. Based on the optimal parameter combination, VMD decomposition is used to decompose the preprocessed data into multiple modes. Low-frequency modes are selected from multiple modes, and the mean of the low-frequency modes is taken as the signal component of the denoised gravitational acceleration. The modes are time-domain signals and spectra arranged from low to high frequency. Low-frequency modes are selected from multiple modes to meet the following conditions: select modes with frequencies lower than a set frequency threshold, calculate the amplitude change of the selected modes, and take the modes with amplitude changes lower than the set amplitude change as the final selected low-frequency modes for signal reconstruction. The VMD decomposition method is used to decompose the preprocessed data into multiple modes, including: performing VMD decomposition on the preprocessed data according to the parameter combination output by the current particle swarm algorithm, determining whether there are modes whose frequency and amplitude changes are lower than the set minimum frequency and minimum amplitude changes, calculating the fitness, updating the particle position and velocity according to the fitness, until there is a mode that simultaneously satisfies the condition that the frequency and amplitude change are lower than the set minimum frequency and amplitude change, and has the minimum fitness. The gravitational acceleration signal components of all measuring points are reconstructed to obtain the gravitational acceleration of the site to be measured.

2. The dynamic measurement method for gravity acceleration based on PSO-VMD according to claim 1, characterized in that, The optimal combination of mode number K and penalty factor α is found using the particle swarm optimization algorithm, including: calculating the fitness based on the sum of sample entropies of each mode obtained from VMD decomposition, the Pearson correlation coefficient between the original signal and the sum of signals of each mode, and the aggregation algebra. , Indicates fitness; Low-frequency modes are assigned high weights, and high-frequency modes are assigned low weights. The position with the best fitness in the history of each particle is recorded as the individual optimal position, and the position with the best fitness in the history of the entire population is recorded as the global optimal solution.

3. The dynamic measurement method for gravity acceleration based on PSO-VMD according to claim 2, characterized in that, Finding the optimal combination of mode number K and penalty factor α using the particle swarm optimization algorithm also includes: In the initial iteration, using the initial parameter combination, VMD decomposition decomposes the preprocessed data into multiple modes; The particle swarm optimization algorithm calculates the fitness of the particles under the initial combination of parameters and updates the particle velocity and position based on the fitness.

4. The dynamic measurement method for gravity acceleration based on PSO-VMD according to claim 1, characterized in that, The minimum amplitude change is higher than the amplitude change caused by tides within a tidal cycle.

5. A dynamic measurement system for gravity acceleration based on PSO-VMD, characterized in that, include: The data acquisition device includes multiple atomic gravimeters. According to the designed measurement line and measurement points, the atomic gravimeters are run at each measurement point to obtain the raw data of gravitational acceleration at each measurement point. The host computer extracts data from each measuring point, removes outlier data according to the 3σ criterion, and obtains preprocessed data. It then uses particle swarm optimization to find the optimal combination of mode number K and penalty factor α. Based on this optimal combination, VMD decomposition is used to decompose the preprocessed data into multiple modes. Low-frequency modes are selected from these modes, and the average of these low-frequency modes is taken as the signal component of the denoised gravitational acceleration. Finally, the signal components of the gravitational acceleration from all measuring points are reconstructed to obtain the gravitational acceleration of the target location. The modes are time-domain signals and spectra arranged from low to high frequency. Low-frequency modes are selected from multiple modes to meet the following conditions: select modes with frequencies lower than a set frequency threshold, calculate the amplitude change of the selected modes, and take the modes with amplitude changes lower than the set amplitude change as the final selected low-frequency modes for signal reconstruction. VMD decomposition is used to decompose the preprocessed data into multiple modes, including: performing VMD decomposition on the preprocessed data according to the parameter combination output by the current particle swarm algorithm, determining whether there are modes whose frequency and amplitude changes are lower than the set minimum frequency and minimum amplitude changes, calculating fitness, updating particle position and velocity according to fitness, until there is a mode that simultaneously satisfies both the set minimum frequency and the set minimum amplitude change, and has the minimum fitness.

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