Intelligent compensation method for coupling error of dynamic gravimeter

Abstract

An intelligent compensation method for coupling errors of a dynamic gravimeter comprises the following steps: selecting typical environment interference influencing the dynamic gravimeter in a complex measurement environment, and analyzing an influence mechanism of each typical environment interference on the measurement accuracy of the dynamic gravimeter; according to the influence mechanism under each typical environment interference, analyzing a coupling error influence mechanism between the typical environment interferences; based on the coupling error influence mechanism, constructing a coupling error comprehensive compensation model; adding the coupling effect loss into a data-driven loss function, and defining a model coefficient constrained by physical information; and performing model training by using the training data, and calculating the total loss of the verification set on the obtained model to obtain a final coupling error comprehensive compensation model. According to the invention, the coupling error of the dynamic gravimeter in a complex environment is compensated based on coupling error mechanism analysis and a physical constraint long-short-term memory model, and the measurement precision and environmental adaptability of the dynamic gravimeter under complex multi-factor interference conditions are improved.

Description

Technical Field

[0001] This application relates to the field of dynamic gravity measurement, and in particular to an intelligent compensation method and system for coupling errors of a dynamic gravimeter. Background Technology

[0002] Dynamic gravimeters, relying on a mobile platform, can rapidly, accurately, and efficiently determine the distribution of the Earth's gravitational field in field environments, comparable to performing a "CT scan" of the Earth to reveal its underground structure. They have extremely important applications in economic construction, national defense, basic scientific research, and social development, such as bridge and tunnel engineering, earthquake prediction, and resource exploration. The zero-length spring-type relative gravimeter, typified by the domestically produced CHZ-II gravimeter, has advantages such as small zero deviation, high accuracy, and strong reliability, and its measurement accuracy has reached the international advanced level. However, under complex and noisy field conditions, vibration, temperature changes, and the mobility of the carrier environment greatly affect its measurement accuracy and reliability, and significant and difficult-to-understand coupling errors exist among multiple interfering factors.

[0003] To improve the measurement accuracy of dynamic gravimeters, numerous scholars have made significant efforts. For error suppression in vibration environments, the vibration transmission process is often simplified into a time-delay gain model, and optimization algorithms such as sparrow search, two-dimensional golden section algorithm, correlation analysis, and PSO are used to search for the model's coefficients, resulting in a significant improvement in gravity measurement accuracy under complex vibration environments. Vibration isolation offers higher accuracy on stable platforms, but its bulky structure, high cost, difficult implementation, and poor anti-interference capabilities make it unsuitable for use in complex vibration environments. Li Xinyu proposed a two-step temperature compensation model based on a combination of polynomials and BP neural networks for the temperature-varying environment of zero-length spring gravimeters, effectively suppressing the impact of environmental temperature changes on measurement accuracy. Another effective approach to temperature error suppression is temperature control of the gravimeter's core sensitive components. However, this method requires constant temperature control for several hours or even longer before measurement, which not only increases the operating cost and energy consumption of the gravimeter, but the lengthy preparation process also severely limits the rapid response of gravity measurements, making it difficult to meet the more demanding requirements of practical applications. Huang Motao addressed the prevalent problem of dynamic environmental effects in current operations by proposing a general model applicable to compensating for residual errors caused by various dynamic effects, effectively eliminating the impact of highly dynamic measurement environmental effects. Cai Shaokun, through mechanism analysis of strapdown dynamic errors, proposed a general model to compensate for dynamic errors in strapdown gravity measurements, effectively suppressing dynamic errors in gravity measurements. Existing research mostly focuses on independently analyzing specific error interference factors and proposing suppression strategies. However, in complex environments, multiple influencing factors such as vibration, temperature changes, and carrier mobility inevitably coexist, and these factors exhibit strong coupling relationships characterized by nonlinearity, time-varying nature, and mutual modulation. Compensation for a single factor is insufficient to completely solve the problem; therefore, a system-level compensation model integrating multi-sensor fusion is necessary to fundamentally improve the measurement accuracy of dynamic gravimeters.

[0004] Therefore, in-depth analysis of the coupled influence of multiple factors in complex environments, effective suppression of complex coupled interference from vibration, temperature change and carrier mobility during dynamic gravimeter measurement, and construction of a long short-term memory model considering coupling constraints for system-level error compensation are the technical challenges that urgently need to be solved in the field of dynamic gravimeter measurement error compensation based on machine learning models. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this application aims to provide an intelligent compensation method and system for coupling errors of dynamic gravimeters. In complex measurement environments, this method solves the practical problem that considering only a single error factor is insufficient for practical measurement environments. It effectively suppresses strong coupling errors caused by vibration, temperature changes, carrier mobility, and the nonlinear, time-varying, and mutually modulated errors between them, thereby fundamentally improving the measurement accuracy and adaptability of dynamic gravimeters to complex environments.

[0006] To achieve the above objectives, the present invention provides an intelligent compensation method for coupling errors of a dynamic gravimeter, comprising: We selected typical environmental disturbances that affect the dynamic gravimeter under complex measurement conditions and analyzed the impact mechanism of each typical environmental disturbance on the measurement accuracy of the dynamic gravimeter. Based on the influence mechanism of each typical environmental disturbance, analyze the influence mechanism of coupling error between typical environmental disturbances; Based on the aforementioned mechanism of coupling error, a comprehensive compensation model for coupling error is constructed. The coupling effect loss is incorporated into the data-driven loss function, and the model coefficients constrained by physical information are defined. The model is trained using the training data, and the total loss of the validation set on the obtained model is calculated to obtain the final coupled error comprehensive compensation model.

[0007] Furthermore, the step of selecting typical environmental disturbances that affect the dynamic gravimeter under complex measurement conditions and analyzing the impact mechanism of each typical environmental disturbance on the measurement accuracy of the dynamic gravimeter also includes: selecting three typical environmental disturbances that have the most significant impact on the dynamic gravimeter under complex measurement conditions: vibration, temperature change, and carrier mobility. The error influence mechanism of vibration environment, temperature change environment, and carrier mobility is analyzed.

[0008] Furthermore, the error influence mechanism of the vibration environment is analyzed using the following formula: , in, x The mass block deviates from its original equilibrium position and undergoes displacement. The change in gravitational acceleration ， The natural circular frequency of the sensitive component, k e The equivalent coefficient of the elastic sensitive element, M The mass of the mass block. , and These represent the amplitude, frequency, and initial phase of the vertical disturbance acceleration, respectively. The damping coefficient is... t This is the time flag bit for the vibration interference signal; The error mechanism of temperature-changing environment is analyzed using the following formula: , In the formula, x Let the displacement be that of the zero-length metal spring. This is the change in gravitational acceleration. k This is the spring stiffness coefficient.m For the mass block mass.

[0009] The error influence mechanism of the carrier's maneuverability environment is analyzed using the following formula: , in, To account for the measurement error of approximate gravity anomalies, k 1 to k 9 represents the model coefficients related to each error. v e and v n These are the eastward and northward velocities of the carrier, respectively. The latitude of the location of the carrier. a e and a n These are the eastward and northward accelerations of the carrier, respectively. g m These are gravity measurements from a platform-type gravimeter. f x and f y They are respectively x shaft and y The specific force output of the horizontal accelerometer along the axial direction. This is to correct the platform tilt caused by the movement of the carrier.

[0010] Furthermore, the step of analyzing the error mechanism of the temperature change environment also includes: The following formula is used to analyze the mechanism of influence of internal temperature environment: , In the formula, The error in the gravimeter output is due to internal temperature. P c is a positive constant. T in Internal temperature, The integral constant is related to the internal temperature, which refers to the temperature at which the zero-length metal spring is directly exposed to the space in which it is located; The following formula is used to analyze the mechanism of influence of external temperature environment: , In the formula, The error in the gravimeter output is caused by external temperature. B and C are respectively Model coefficients v Indicates the velocity of the mass block. λ The viscosity coefficient of silicone oil, k Let be the spring constant of a zero-length metal spring. T out For external temperature, The integral constant related to the external temperature. K c The calibration coefficient for minute displacement and the output voltage of the capacitive sensor is related to the gravimeter's manufacturing process and the materials used. K G This refers to the output voltage and the scale coefficient of the gravimeter output.

[0011] Furthermore, the step of analyzing the coupling error influence mechanism between typical environmental disturbances based on the influence mechanism of each typical environmental disturbance also includes: Analysis of the coupling effect between temperature and vibration; Analysis of the coupling effect between vibration and carrier mobility; Analysis of the coupled effects of carrier mobility and temperature; Analysis of the combined effects of temperature, vibration and carrier mobility.

[0012] Furthermore, the step of constructing a comprehensive compensation model for coupling error based on the coupling error influence mechanism further includes: fitting the comprehensive compensation model for coupling error using a machine learning method based on a long short-term memory model; and, according to the analyzed coupling error influence mechanism, listing the inputs of each model together as the input for coupling error compensation, with the model output being the true value of gravity.

[0013] Furthermore, the step of constructing a comprehensive compensation model for coupling error based on the aforementioned coupling error influence mechanism further includes: Define the data loss function of the coupling error integrated compensation model. : In the formula, These are the model parameters during training. S test For the test dataset, N To test the length of the dataset, x For input data, Output values ​​for the model. y The true value of the model; Physical information loss function constrained by the comprehensive coupling error between temperature, vibration, and carrier maneuverability for: In the formula, , , , These are the weighting coefficients, T in Internal temperature, Output values ​​for the model. a vFor vibration acceleration, a For the acceleration of the carrier motion, In mathematics, this is the operator for finding partial derivatives.

[0014] Furthermore, the step of training the model using training data and calculating the total loss of the validation set on the obtained model to obtain the final coupling error comprehensive compensation model further includes: Data was collected and processed according to the specifications of the model training dataset, and then input into the coupling error compensation model to perform coupling error compensation, thereby obtaining the measurement results of the dynamic gravimeter under various typical environmental disturbances.

[0015] To achieve the above objectives, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor is configured to execute the computer program stored in the memory to implement the intelligent compensation method for dynamic gravimeter coupling error as described above.

[0016] To achieve the above objectives, the present invention also provides a computer-readable storage medium storing a computer program, which is loaded and executed by a processor to implement the intelligent compensation method for dynamic gravimeter coupling error as described above.

[0017] The intelligent compensation method for coupling error of dynamic gravimeters provided by this invention has the following advantages compared with the prior art: (1) The coupling error mechanism analysis of dynamic gravimeter in complex application scenarios proposed in this invention comprehensively considers the influence of various environmental interferences and their coupling effects on measurement accuracy, effectively improves the measurement accuracy of dynamic gravimeter under complex multi-factor interference conditions, and thus enhances its environmental adaptability and practicality.

[0018] (2) By designing the coupling effects of multiple environmental disturbances as physical constraints and embedding them into the data-driven loss function, the physical information long short-term memory model is formed. This ensures that the model not only performs well in data fitting, but more importantly, it captures the inherent physical mechanism of multi-physics coupling, which greatly reduces the model's requirements for the scale and quality of training data, and significantly improves the measurement accuracy in complex application scenarios.

[0019] (3) The proposed technical solution has certain feasibility, stability and robustness. It has important value in the theoretical level of machine learning model construction and the engineering level of dynamic gravity measurement. It can be extended to the measurement and error compensation process of marine, underwater and airborne dynamic gravimeters.

[0020] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. Attached Figure Description

[0021] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings: Figure 1 The flowchart is shown below for the intelligent compensation method for coupling error of dynamic gravimeter according to Embodiment 1 of the present invention. Figure 2 This is a schematic diagram of the measurement results before coupling error compensation in Embodiment 2 of this application; Figure 3 This is a schematic diagram of the measurement results after coupling error compensation in Embodiment 2 of this application; Figure 4 This is a diagram showing the measurement results before coupling error compensation in Embodiment 3 of this application; Figure 5 This is a schematic diagram of the measurement results after coupling error compensation in Embodiment 3 of this application; Figure 6 This is a schematic diagram of the electronic device structure according to Embodiment 4 of the present invention. Detailed Implementation

[0022] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0023] Embodiments of the present invention will now be described in more detail with reference to the accompanying drawings. While some embodiments of the invention are shown in the drawings, it should be understood that the invention can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of the invention. It should be understood that the accompanying drawings and embodiments are for illustrative purposes only and are not intended to limit the scope of protection of the invention.

[0024] The term "comprising" and its variations as used in this invention are open-ended, meaning "including but not limited to". The term "based on" means "at least partially based on". The term "one embodiment" means "at least one embodiment"; the term "another embodiment" means "at least one additional embodiment"; the term "some embodiments" means "at least some embodiments". Definitions of other terms will be given in the description below.

[0025] It should be noted that the concepts of "first" and "second" may be mentioned in this invention only to distinguish different devices, components or parts, and are not used to limit the order of the functions performed by these devices, components or parts or their interdependence.

[0026] It should be noted that the terms "one" and "multiple" used in this invention are illustrative rather than restrictive. Those skilled in the art should understand that, unless explicitly stated otherwise in the context, they should be understood as "one or more". "Multiple" should be understood as two or more.

[0027] The intelligent compensation method for dynamic gravimeter coupling error in this application includes: The influence of vibration, temperature and carrier mobility on the measurement accuracy of dynamic gravimeter is analyzed in depth. The coupling error when multiple factors coexist in complex environments is comprehensively considered, and the coupling error is intelligently fitted based on the long short-term memory model. The coupling effect process obtained from the analysis is established as a physical constraint condition to design a new loss function to construct a physical information model for error compensation.

[0028] Example 1 Figure 1 The flowchart below shows the intelligent compensation method for dynamic gravimeter coupling error according to Embodiment 1 of the present invention. Figure 1 The embodiments of the present invention will be described in further detail.

[0029] First, in step S1, the influence mechanism of a single environmental disturbance is analyzed.

[0030] In this embodiment, three typical environmental disturbances that have the most significant impact on dynamic gravimeters under complex measurement environments—vibration, temperature change, and carrier mobility—are selected for in-depth analysis of their respective impact mechanisms on the measurement accuracy of dynamic gravimeters under single conditions.

[0031] In this embodiment, the application scenario is the dynamic measurement of a zero-length spring gravimeter in a complex field environment. For the three typical environmental disturbances that have a significant impact, namely vibration, temperature change and carrier mobility, the mechanism of their respective influence on gravity measurement is first analyzed.

[0032] Step S1.1, the error influence mechanism of the vibration environment The basic principle of gravity measurement follows Newton's second law, which states that the gravitational force acting on the mass is equal to the spring force. When gravity changes, the mass deviates from its original equilibrium position and undergoes displacement. x High-precision capacitive displacement sensor x Precise detection is used to achieve relative measurement of gravity. Based on the principle of torque balance, if the tension in each wire is... T Then the tension on both springs is 3. T.like Figure 2 As shown, the mass block has shifted. x Afterwards, the wire drawing and spring tension will produce a size of α Small-angle rotation. Displacement. x Generally, these are small quantities, and the force balance equations satisfy: In the formula, k 0 represents the spring constant of a zero-length spring. L The wire drawing length, M The mass of the mass block. This is the change in gravitational acceleration. k e The equivalent coefficient of the elastic sensitive element. The gravimeter uses a strong damping environment formed by the balance feedback of silicone oil and electromagnetic force to improve the smoothness of the mass block's motion, and can initially suppress disturbance acceleration. Considering the damping structure of the system, the equation of motion of the mass block is: In the formula, a r The vertical disturbance acceleration experienced by the mass block is measured using an accelerometer-type vibration sensor. and Representing displacement x The first and second derivatives, and Let represent the damping force and inertial force acting on the mass block, respectively. The above equation can be transformed into: In the formula, To determine the natural circular frequency of the sensitive component, a sinusoidal signal is typically used to simulate the vertical disturbance acceleration. a r The specific form can be expressed as: In the formula, , and Let represent the amplitude, frequency, and initial phase of the vertical disturbance acceleration, respectively. Then, under vibration conditions, the displacement of the mass block... x The steady-state solution is: In the formula, Under the strong damping effect of silicone oil damping and electromagnetic force compensation, the damping coefficient is The above formula can be simplified to: (The formula is very large.) In the formula, t This is the time flag bit for the vibration interference signal.

[0033] This shows that the gravimeter is sensitive not only to changes in gravitational acceleration, but also to vertical disturbance acceleration introduced by vibration.

[0034] Step S1.2, Error Influence Mechanism of Temperature Variation Environment The measurement principle of this type of gravimeter is based on Newton's second law. Initially, the gravity acting on the mass is balanced by the tension of the zero-length spring. When the acceleration due to gravity changes, the sensitive mass deviates from its original position to reach a new equilibrium. Let the displacement generated at this time be x, then: In the formula, This is the change in gravitational acceleration. k This is the spring stiffness coefficient. m Since the mass of the mass block is determined, the minute displacement of the zero-length spring is detected. x The relative measurement of gravitational acceleration is achieved by changing the magnitude of the acceleration.

[0035] Step S1.2.1, Analysis of the Mechanism of Internal Temperature Influence Internal temperature refers to the temperature of the space directly exposed to the zero-length metal spring. Because the zero-length spring cavity has insulating properties, it effectively prevents sudden changes in internal temperature with ambient temperature; therefore, there is a significant difference between external and internal temperatures. In fact, the influence of internal temperature on the gravimeter output is closely related to the influence of temperature on the stiffness coefficient of the zero-length spring. From the measurement principle of the metal zero-length spring relative to the gravimeter, it is known that the influence of temperature on the spring elongation determines the influence of temperature on the gravimeter output. The derivative of the spring elongation with respect to internal temperature yields: Stiffness coefficient of the zero-length metal spring used in a gravimeter k The calculation formula is: In the formula, G is the elastic modulus of metallic materials; n The number of turns of the wire wound into the spring; d m The diameter of the metal wire; D The diameter of the coil when the metal wire is wound into a spring. D Significantly greater than d m Taking the partial derivative of the above equation with respect to internal temperature yields: The metal material used in the gravimeter is a material with a constant elastic modulus, therefore G It is a constant value; d m and DThe partial derivative with respect to temperature can be equated to the coefficient of linear expansion of metallic materials. α Therefore, the above formula can be simplified to: Based on the above analysis, the relationship between the change in the gravimeter output and the change in internal temperature satisfies: Integrating the above equation, we can obtain the gravimeter output error caused by internal temperature. for: In the formula, P c The meaning is a positive constant. This is the integral constant related to the internal temperature. Therefore, it can be seen that once the material of the gravimeter is determined, the output error of the gravimeter is linearly positively correlated with the internal temperature.

[0036] Step S1.2.2, Analysis of the Mechanism of External Temperature Influence External temperature refers to the temperature of the space surrounding the other components of the gravimeter. Since the gravimeter casing lacks thermal insulation, the external temperature is nearly identical to the ambient temperature. Changes in external temperature alter the viscosity coefficient of the silicone oil, thus affecting the mobility of the mass block. This is the key to understanding the impact of external temperature on the gravimeter's output. The motion of the mass block is a typical second-order motion system, and its equation of motion, according to Newton's second law, is as follows: In the formula, λ This is the viscosity coefficient of silicone oil, and its value is related to temperature. v and a These represent the velocity and acceleration of the mass block, respectively. λv This represents the resistance experienced by the mass block in the silicone oil. Taking the partial derivative of the above equation with respect to external temperature yields: Viscosity coefficient characterizes the degree of viscosity of a fluid and is a measure of its resistance to flow. Viscosity originates from the thermal motion of molecules and the interaction of intermolecular forces, and is closely related to temperature. When the external temperature increases, the interaction between silicone oil molecules weakens, increasing flowability, meaning the viscosity of silicone oil decreases. Conversely, when the temperature decreases, the viscosity of silicone oil increases. Based on theoretical analysis and scientific experiments, different authors have proposed a series of viscosity-temperature relationship models. The Jane equation, which has high fitting accuracy and is widely accepted, is as follows: A , B , CThese are model coefficients, related to the degree of polymerization of the silicone oil type, and obtained by fitting experimental data. For example, the coefficients for #500 methyl silicone oil... A = -4.2263, B = 2452.38, C = 0.00734. Differentiating the above equation with respect to temperature yields: Based on the above analysis, the relationship between the change in the gravimeter output and the change in external temperature satisfies: Due to constant B Much larger C Therefore, the right side of the equation is less than 0, indicating that the gravimeter output error is negatively correlated with the external temperature. Integrating the equation yields the gravimeter output error caused by the external temperature. for: In the formula, This is the integral constant related to the external temperature. Therefore, the gravimeter output error is related to the first and negative first-order terms of the external temperature.

[0037] Furthermore, considering the temperature change characteristics and the uneven temperature gradient between the inside and outside (temperature difference between inside and outside) dT The hysteresis effect generated can also affect the measurement accuracy of the gravimeter. Therefore, the internal and external temperature change rate and temperature gradient are also used as key input parameters for temperature error compensation.

[0038] Step S1.3, Error Influence Mechanism of Carrier Mobility The dynamic gravimeter relies on a high-precision gyroscope and its servo mechanism to provide an inertial stabilization platform, precisely maintaining the accelerometer along the z-axis aligned with the local gravity vector. According to Newton's second law in a non-inertial frame, the specific force measured by the accelerometer is actually the vector difference between the vehicle's acceleration and the acceleration due to gravity. The fundamental equation for gravity measurement in the vertical direction is: In the formula, g This is a gravity measurement value. f z This is the specific force measurement value from the vertical accelerometer. a z Let be the vertical acceleration of the carrier. Dynamic gravity measurements, in addition to satisfying the above equation, also require applying an error correction term introduced by the carrier's motion and subtracting the normal gravity value of the Earth model to obtain gravity anomaly information. The mathematical model for gravity anomalies obtained from platform-type gravimeter measurements is as follows: In the formula, γ For normal gravity correction, and These are the Etford correction and platform tilt correction caused by carrier motion, respectively.

[0039] The formula for calculating normal gravity comes from the WGS-84 model, and its value depends only on the position of the carrier. In the formula, The latitude of the location of the carrier. h For the height of the carrier, R M and R N These are the radius of curvature of the Earth's meridian and the radius of curvature of the zonal circle, respectively.

[0040] The Eötvös correction is a necessary correction term due to the additional centrifugal force generated by the vehicle's motion relative to the Earth. Since the vehicle's speed on the Earth's surface is relatively slow, the approximate formula under the assumption of a rotating ellipsoid can meet the needs of practical applications.

[0041] In the formula, The angular velocity of Earth's rotation. v e and v n These represent the eastward and northward velocities of the carrier, respectively.

[0042] Due to the limitations of the dynamic operating environment of the carrier and the performance of the stable platform control technology, inertial platforms inevitably exhibit a certain degree of tilt. The non-horizontal state of the inertial platform means that the output of the gravity sensor is not the true vertical acceleration, necessitating compensation and correction. According to the principle of rotation invariance, the magnitude of the acceleration felt by any object does not change with the rotation of the orthogonal coordinate system, and the horizontal disturbance acceleration is much smaller than the gravitational acceleration. g The formula for calculating platform tilt correction is as follows: In the formula, f x and f y for x and y The specific force output of the horizontal accelerometer along the axial direction. a e and a n The eastward and northward accelerations of the carrier. g m This is the gravity measurement value of the platform-type gravimeter.

[0043] Variational calculations were performed on the fundamental principle of dynamic gravity measurement to obtain its error model. In the formula, This is due to measurement errors related to gravity anomalies. This is the measurement error of the vertical specific force. This is within the normal gravity calculation error range. This represents the error in the vertical acceleration measurement. and The errors are respectively the Etford correction error and the platform tilt correction error, which can be calculated in the following specific forms: In the formula, Taking the position, velocity, and acceleration of the moving vehicle as core variables, and considering the errors of the navigation system, the specific force measurement error, and other variables in the above two equations, an approximate error analysis equation can be obtained: , In the formula, To account for the measurement error of approximate gravity anomalies, k 1 to k 9 represents the model coefficients related to each error. v e and v n These are the eastward and northward velocities of the carrier, respectively. The latitude of the location of the carrier. a e and a n These are the eastward and northward accelerations of the carrier, respectively. g m These are gravity measurements from a platform-type gravimeter. f x and f y They are respectively x shaft and y The specific force output of the horizontal accelerometer along the axial direction. This is to correct the platform tilt caused by the movement of the carrier.

[0044] In step S2, the coupling effects of multiple factors are analyzed.

[0045] In this embodiment of the application, based on the influence mechanism under various typical environmental disturbances, the coupling influence mechanism existing in complex measurement environment is systematically analyzed, and the strong coupling relationship between multiple factors that is nonlinear and mutually modulated is comprehensively sorted out.

[0046] In this embodiment of the application, in order to systematically analyze the coupled influence relationship between vibration, temperature change and carrier mobility on the measurement accuracy of dynamic gravimeter, the coupling influence mechanism between various factors is comprehensively sorted out.

[0047] Step S2.1, Analysis of the Coupled Influence of Temperature and Vibration Internal temperature directly affects the elastic coefficient k of a zero-length spring, while external temperature causes a change in the silicone oil damping coefficient λ. Both k and λ are closely related to vibration compensation. In addition, temperature changes can also alter the natural frequency of the material, thereby changing the frequency characteristics of the vibration response and thus altering the characteristics of the vibration transfer function.

[0048] Step S2.2, Analysis of the Coupled Influence of Vibration and Carrier Mobility The movement of the carrier itself generates vibrations, and acceleration, deceleration, and turning introduce additional vibrations. These vibrations may be multi-frequency and random. These vibrations, combined with the inherent vibrations of the carrier, make the vibration environment more complex. In addition, the total transfer function of vibration error will change under high carrier mobility, and the horizontal error factor of the zero-length spring of the gravimeter also needs to be taken into account.

[0049] Step S2.3, Analysis of the Coupled Influence of Carrier Mobility and Temperature Temperature changes affect the gravimeter's measurements, which in turn affect the compensation effect for vehicle maneuverability errors. Similarly, vehicle maneuverability also affects the gravimeter's measurements, thus influencing temperature compensation. However, it should be noted that there is no mutually modulating coupling effect between these two influencing factors.

[0050] Step S2.4, Analysis of the common coupling effects among the three. In actual dynamic gravity measurements, vibration, temperature, and carrier mobility coexist and influence each other. Key parameters of the dynamic gravimeter during measurement may change with variations in temperature, vibration, and carrier mobility, exhibiting cross-sensitivity. Therefore, compensating for each factor individually may not be sufficient to completely eliminate errors.

[0051] In step S3, the model architecture is determined. Based on the analyzed coupling error impact mechanism, a comprehensive compensation model for coupling error is constructed based on the Long Short-Term Memory (LSTM) model. The model's input and output are defined, and all input data are normalized using the Z-score method. The Sigmoid function is used as the activation function, and the Adam optimizer is used for training. A fully connected layer is used for the model output. Then, the model parameters are initialized, including the number of network layers (layers), the number of neurons (Num), the number of training epochs (Epochs), the training batch size (BatchSize), the initial learning rate (LR), the learning rate decrease factor (DecayFactor), and the dropout rate (DropoutRate).

[0052] In this embodiment, due to the complexity and unknowability of the coupling factors, a machine learning method based on a long short-term memory model is used to fit the coupling model. Based on the analyzed mechanism of coupling error, the inputs of each model are combined as the input for coupling error compensation, and the model output is the true value of gravity. Therefore, the input of the constructed comprehensive coupling error compensation model is 21-dimensional, consisting of the vibration sensor outputs... a f , internal temperature T in external temperature T out Internal temperature change rate K Tin external temperature change rate K Tout Temperature gradient dT Attitudes in three directions att E , att N , att U Velocity in three directions v E , v N and v U 3D position coordinates λ , , h acceleration a E , a N and a U The specific force output of the horizontal accelerometer f x , f y and the raw output value of the gravimeter g m The coupled error comprehensive compensation model outputs a one-dimensional, environmentally undisturbed true gravity value. To avoid the influence of data scale inconsistencies on the training process, all input data are normalized using the Z-score method.

[0053] The coupled error comprehensive compensation model architecture is configured by using the Sigmoid function as the activation function, training with the Adam optimizer, and passing a fully connected layer for model output. Model parameters are initialized with three network layers, each with 8, 12, and 10 neurons respectively; 100 training epochs; a batch size of 64; an initial learning rate (LR) of 0.001; a learning rate decrease factor (DecayFactor) of 0.5; and a dropout rate of 0.2. The loss function used for model training is a weighted sum of data loss and physical information constraints; details are provided in step S4.

[0054] In step S4, the loss function for physical information constraints is designed. Based on the physical laws governing the influence of coupling errors, a coupling effect loss is designed and incorporated into the data-driven loss function. Furthermore, the model coefficients for physical information constraints are defined, effectively integrating the advantages of both data-driven and physical information constraints. This allows the model to pay more attention to coupling effects during training.

[0055] In this embodiment, the designed coupling constraint term aims to capture the influence of the interaction between different physical factors (temperature, vibration, and carrier mobility) on the gravity measurement error. Specifically, the coupling constraint term forces the model to learn these cross-effects by calculating the mixed partial derivatives of the model output with respect to multiple physical quantities. The design process of the total loss function is as follows: Step S4.1, the model's data loss function It can be defined as: In the formula, These are the model parameters during training. S test For the test dataset, N To test the length of the dataset, x For input data, Output values ​​for the model. y This represents the true value of the model.

[0056] Step S4.2, Coupled constraint design of temperature and vibration; the coupling effect of temperature change and vibration can be expressed as the gravity error with respect to temperature. T and vibration acceleration a vThe mixed partial derivatives are calculated. In actual measurement outputs, temperature changes alter the impact of vibration on gravity errors, resulting in non-zero mixed partial derivatives. However, in real physical processes, the coupling effect between the true gravity value and the changes in the complex environment is small; therefore, the mixed partial derivatives of the real physical process can be considered zero. We embed this coupling relationship by ensuring that the mixed partial derivatives of the model output match those of the real physical process. Therefore, in the loss function, we design coupling constraint terms by calculating the mixed partial derivatives of the model output with respect to the coupled environmental variables and constraining these mixed partial derivatives to be as small as possible. We also control the strength of the coupling effect by adjusting the regularization coefficient.

[0057] Regarding the coupling of temperature and vibration, the main change is in the internal temperature, thus allowing for the construction of... T in · a v We then calculate the partial derivatives of the error-compensated model output with respect to these interaction features. After full error compensation, the coefficients of these interaction features should be very small. Therefore, when designing coupling constraints, we tend to use interaction features like these as inputs and allow the model to automatically learn the coupling effects, while avoiding overfitting through regularization. Thus, the coupling constraints can be designed as follows: In the formula, the first term is the partial derivative of the output after gravity measurement compensation with respect to vibration factors, and then the partial derivative with respect to internal temperature, which reflects the change in the sensitivity of the gravity measurement output to vibration with respect to temperature; the second term reflects the sensitivity of the gravity measurement output to the cross-coupling effect of temperature and vibration environment.

[0058] Step S4.3, design of coupling constraints between vibration and carrier mobility; vibration can be collected by vibration sensors. a v This reflects the vehicle's mobility and the magnitude of its acceleration. a To characterize this. Based on the coupling influence relationship and the basic idea of ​​coupling constraint design analyzed above, the coupling error constraint term between the vibration environment and the carrier's mobility factors can be designed as follows: In the formula, the first term is the partial derivative of the output after gravity measurement compensation with respect to vibration factors, and then the partial derivative with respect to the carrier acceleration. It reflects the change in the sensitivity of the vibration to the gravity measurement output as the carrier maneuverability changes. The second term reflects the sensitivity of the gravity measurement output to the cross-coupling effect of the carrier acceleration and the vibration environment.

[0059] Step S4.4: Under the complex environment of temperature, vibration, and carrier maneuverability measurements, the design of the coupling terms becomes more complex. Considering the actual situation, there is no significant coupling effect between temperature changes and carrier maneuverability, and the influence between the two is not considered in the coupling term constraints. Therefore, the physical information loss function of the comprehensive coupling error constraint can be designed as follows: In the formula, the first two terms reflect the synergistic effect between temperature change and vibration environment on the gravity measurement output, while the third and fourth terms reflect the synergistic effect between vehicle mobility and vibration environment on the gravity measurement output. The coefficients before each term represent the weighting coefficients of each coupling term. Taking into account the strength of each constraint term, the weighting coefficients are defined as 0.3, 0.2, 0.4, and 0.1, respectively.

[0060] The designed method can minimize the cross-rate of change of the gravity error prediction value learned by the model with respect to different physical quantities. Such coupling constraint design has physical consistency, forces the model to follow the real physical laws, can still make accurate predictions without experiencing coupling conditions, improves the model's generalization ability, reduces dependence on large coupling experimental data, and enhances the model's interpretability and data efficiency.

[0061] In step S5, the coupling error comprehensive compensation model is trained and error compensation is performed. The model is trained using training data, and the total loss of the validation set on the obtained model is calculated. After training, the obtained model is the final coupling error comprehensive compensation model. In subsequent measurement experiments, data is collected and processed according to the specifications of the model training set, and input into the obtained error compensation model to implement comprehensive compensation of coupling errors. The model output is the high-precision dynamic gravity measurement result under the suppression of coupling interference in complex environments.

[0062] In this embodiment of the application, the detailed process of model training and error compensation is as follows: Step S5.1: Collect and preprocess experimental data according to the data specifications of the constructed model to construct the model training dataset, and divide the training set and validation set in a 5:1 ratio.

[0063] Step S5.2: Use the constructed training dataset to train the model and calculate the total loss of the validation set on the obtained model. The model obtained after training is the final coupling error compensation model.

[0064] Step S5.3: In subsequent measurement experiments, data is collected and processed according to the specifications of the model training set, and input into the obtained error compensation model to implement coupling error compensation. The model output is the measurement result of the high-precision dynamic gravimeter under the suppression of coupling interference in complex environment.

[0065] Example 2 To make the objectives, technical solutions, and advantages of the present invention clearer, the dynamic gravimeter coupling error compensation method of the present invention will be further described in detail below with reference to specific embodiments.

[0066] This embodiment aims to demonstrate the complete process and significant effects of the method described in Embodiment 1 in practical applications through a specific application scenario.

[0067] The test vehicle is equipped with a dual-axis laser strapdown inertial navigation system, GNSS facilities, an odometer, and a barometric altimeter. Through combined navigation calculations, it provides high-precision navigation data, acquiring the vehicle's attitude, velocity, and position information. The vehicle's acceleration is obtained by first-order difference from the calculated velocity. In addition, a CHZ-II dynamic gravimeter is equipped to dynamically measure gravity anomalies. This gravimeter features a temperature control device and switch, allowing for autonomous control of the temperature-controlled environment. An electromagnetic vibration table is also installed on the test vehicle to generate controllable vibration conditions, and an acceleration-type vibration sensor is used to sensitively measure these vibration conditions.

[0068] The experiment was conducted on a closed road. Before collecting dynamic measurement data, discrete gravity anomaly values ​​were obtained by static measurement every 2 km along the measurement line using a CG-5 high-precision relative gravimeter. Interpolation and fitting were then used to obtain the gravity anomaly values ​​along the measurement line as the model output for the training dataset. The temperature control of the gravimeter was turned off, allowing the dynamic gravimeter to be sensitive to changes in ambient temperature and the rise in internal temperature during instrument operation. An electromagnetic vibration table was turned on to generate random vibration experimental conditions, and an accelerometer-type vibration sensor was used to sense vibration acceleration in real time. Then, the vehicle entered a driving state and underwent turning, undulation, acceleration, and deceleration along the measurement line to conduct dynamic gravity measurements. The collected experimental data were preprocessed according to the data specifications of the proposed coupling error compensation method, forming a 21-dimensional model input and a 1-dimensional model output, which together constituted the training dataset for training the error compensation model.

[0069] The model obtained after training is the coupling error compensation model under complex environment. After dynamic gravity measurement is carried out, the data is collected and preprocessed according to the data specifications and then input into the model. The model output is the high-precision dynamic gravimeter measurement result after coupling error compensation.

[0070] The dynamic gravimeter was placed in a natural environment with the temperature control system turned off to allow it to acclimatize to natural temperature changes before being mounted on the electromagnetic vibration table on the experimental vehicle. After gravity measurements began, the vibration table was activated to apply a random vibration environment, and the vehicle simultaneously began a round trip dynamic measurement along the measurement line. All sensors operated normally, collecting experimental data. After collecting and preprocessing the experimental data according to data specifications, a model dataset was constructed and divided into training, validation, and test sets in a 4:1:1 ratio. This embodiment, based on the coupling error compensation model obtained after training on the training and validation sets, uses the test set to verify the effectiveness of the proposed coupling error model. The experimental results before and after coupling error compensation are as follows: Figure 2 and Figure 3 As shown in Table 1, the internal and external conformity accuracy of repeated measurement lines are statistically analyzed, and the percentage improvement in accuracy after error compensation relative to before compensation is calculated.

[0071] Table 1. Statistical table of measurement accuracy before and after coupling error compensation in Example 2.

[0072] Experimental results show that although the overall trend of the measurement results before coupling error compensation is in good agreement with the reference value, the interference from vibration, temperature change, and carrier mobility during the measurement process is also significant. The internal and external coincidence accuracies before coupling error compensation are 14.89 mGal and 33.56 mGal, respectively, severely affecting the measurement accuracy of the dynamic gravimeter. Such an accuracy level is clearly unsuitable for practical engineering applications. After applying the proposed coupling error compensation model in this embodiment, the internal and external coincidence accuracies reach 1.46 mGal and 1.88 mGal, respectively, representing improvements of 90.19% and 94.40% compared to before compensation. The measurement accuracy of the dynamic gravimeter is significantly improved, effectively demonstrating the effectiveness of the proposed coupling error compensation model.

[0073] Example 3 This embodiment is used to evaluate the practical application effect of the dynamic gravimeter coupling error compensation model under complex and extreme working conditions. After the model training is completed, a dynamic measurement experiment with more severe environmental disturbances is carried out again on the experimental measurement line of Embodiment 2. When the ambient temperature is low, the temperature control facility of the gravimeter is turned on and its temperature is controlled at 60°C. After the measurement experiment begins, the temperature control switch is immediately turned off, exposing it to the low-temperature external environment, giving the gravimeter a rapid temperature change. An electromagnetic vibration test bench is set up, and a vibration environment with more significant vibration amplitude and frequency is applied. During the dynamic measurement, the experimental vehicle undergoes more rapid acceleration, deceleration, and start-stop changes, exciting more significant carrier maneuvering characteristics. The equipment used in the experiment is the same as in Section 4.1.1. The results of two repeated measurement lines running back and forth on the measurement line are used to evaluate the internal consistency accuracy of the results. Similarly, the CG-5 is used to statically measure the true value of gravity anomalies every 2km on the measurement line in advance. The interpolated and fitted values ​​are used as the gravity anomaly benchmark on the measurement line for evaluating the external consistency accuracy of the dynamic measurement results.

[0074] After preprocessing the experimental data under extreme conditions to construct a training dataset, it is input into the coupled error compensation model obtained after training. The output result is the dynamic gravity measurement result after coupling error compensation, and the measurement data on each measurement line are processed in sequence.

[0075] In this embodiment, the results before and after gravity measurement coupling error compensation are as follows: Figure 4 and Figure 5 As shown, the accuracy index of the calculated results is shown in Table 2.

[0076] Experimental results show that the coupling effect of complex environments under extreme conditions is more significant, with internal and external coincidence accuracies of only 59.05 mGal and 73.01 mGal, respectively, indicating a more urgent need for error compensation. After applying the coupling error compensation model proposed in this invention, the internal and external coincidence accuracies improved by 96.56% and 95.96%, respectively, reaching 2.03 mGal and 2.95 mGal. This demonstrates that under extreme conditions, the proposed coupling error compensation model achieves a greater improvement in accuracy, but the compensated measurement accuracy is still lower than that under more stable experimental conditions. The model compensation effect decreases under complex and rapidly changing coupling experimental environments because the design of the coupling constraint terms is not perfect. Considering factors such as temperature change rate and carrier attitude will yield better results.

[0077] Table 2. Statistical table of measurement accuracy before and after coupling error compensation in Example 3.

[0078] Example 4 In embodiments of the present invention, an electronic device is also provided. Figure 6This is a schematic diagram of the structure of an electronic device according to an embodiment of the present invention, such as... Figure 6 As shown, the electronic device of the present invention includes a processor 601 and a memory 602, wherein, The memory 602 stores a computer program, which, when read and executed by the processor 601, performs the steps described above in the embodiment of the intelligent compensation method for dynamic gravimeter coupling error.

[0079] Example 5 In embodiments of the present invention, a computer-readable storage medium is also provided, wherein a computer program is stored in the computer program, wherein the computer program is configured to execute the steps in the embodiments of the intelligent compensation method for dynamic gravimeter coupling error as described above when running.

[0080] In this embodiment, the aforementioned computer-readable storage medium may include, but is not limited to, various media capable of storing computer programs, such as USB flash drives, read-only memory (ROM), random access memory (RAM), portable hard drives, magnetic disks, or optical disks.

[0081] It will be understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A smart compensation method for coupling error of a dynamic gravimeter, comprising: We selected typical environmental disturbances that affect the dynamic gravimeter under complex measurement conditions and analyzed the impact mechanism of each typical environmental disturbance on the measurement accuracy of the dynamic gravimeter. Based on the influence mechanism of each typical environmental disturbance, analyze the influence mechanism of coupling error between typical environmental disturbances; Based on the aforementioned mechanism of coupling error, a comprehensive compensation model for coupling error is constructed. The coupling effect loss is incorporated into the data-driven loss function, and the model coefficients constrained by physical information are defined. The model is trained using the training data, and the total loss of the validation set on the obtained model is calculated to obtain the final coupled error comprehensive compensation model.

2. The intelligent compensation method for coupling error of a dynamic gravimeter according to claim 1, characterized in that, The steps of selecting typical environmental disturbances that affect the dynamic gravimeter under complex measurement conditions and analyzing the impact mechanism of each typical environmental disturbance on the measurement accuracy of the dynamic gravimeter also include: selecting three typical environmental disturbances that have the most significant impact on the dynamic gravimeter under complex measurement conditions: vibration, temperature change, and carrier mobility. The error influence mechanism of vibration environment, temperature change environment, and carrier mobility is analyzed.

3. The intelligent compensation method for coupling error of a dynamic gravimeter according to claim 2, characterized in that, The error influence mechanism of the vibration environment is analyzed using the following formula: ， in, x The mass block deviates from its original equilibrium position and undergoes displacement. The change in gravitational acceleration ， The natural circular frequency of the sensitive component, k e The equivalent coefficient of the elastic sensitive element, M For the mass of the mass block, , and These represent the amplitude, frequency, and initial phase of the vertical disturbance acceleration, respectively. The damping coefficient is... t This is the time flag bit for the vibration interference signal; The error mechanism of temperature-changing environment is analyzed using the following formula: ， In the formula, x Let the displacement be that of the zero-length metal spring. This is the change in gravitational acceleration. k This is the spring stiffness coefficient. m For the mass block mass. The error influence mechanism of the carrier's maneuverability environment is analyzed using the following formula: ， in, To account for the measurement error of approximate gravity anomalies, k 1 to k 9 represents the model coefficients related to each error. v e and v n These are the eastward and northward velocities of the carrier, respectively. The latitude of the location of the carrier. a e and a n These are the eastward and northward accelerations of the carrier, respectively. g m These are gravity measurements from a platform-type gravimeter. f x and f y They are respectively x shaft and y The specific force output of the horizontal accelerometer along the axial direction. This is to correct the platform tilt caused by the movement of the carrier.

4. The intelligent compensation method for coupling error of a dynamic gravimeter according to claim 2, characterized in that, The step of analyzing the error mechanism of temperature change environment further includes: The following formula is used to analyze the mechanism of influence of internal temperature environment: ， In the formula, The error in the gravimeter output is due to internal temperature. P c is a positive constant. T in Internal temperature, The integral constant is related to the internal temperature, which refers to the temperature at which the zero-length metal spring is directly exposed to the space in which it is located; The following formula is used to analyze the mechanism of influence of external temperature environment: ， In the formula, The error in the gravimeter output is caused by external temperature. B and C are respectively Model coefficients v Indicates the velocity of the mass block. λ The viscosity coefficient of silicone oil, k Let be the spring constant of a zero-length metal spring. T out For external temperature, The integral constant related to the external temperature. K c The calibration coefficient for minute displacement and the output voltage of the capacitive sensor is related to the gravimeter's manufacturing process and the materials used. K G This refers to the output voltage and the scale coefficient of the gravimeter output.

5. The intelligent compensation method for coupling error of a dynamic gravimeter according to claim 1, characterized in that, The step of analyzing the coupling error influence mechanism between typical environmental disturbances based on the influence mechanism of each typical environmental disturbance further includes: Analysis of the coupling effect of temperature and vibration; Analysis of the coupling effect between vibration and carrier mobility; Analysis of the coupled effects of carrier mobility and temperature; Analysis of the combined effects of temperature, vibration and carrier mobility.

6. The intelligent compensation method for coupling error of a dynamic gravimeter according to claim 1, characterized in that, The step of constructing a comprehensive compensation model for coupling error based on the coupling error influence mechanism further includes: fitting the comprehensive compensation model for coupling error using a machine learning method based on a long short-term memory model; and, according to the analyzed coupling error influence mechanism, listing the inputs of each model together as the input for coupling error compensation, with the model output being the true value of gravity.

7. The intelligent compensation method for coupling error of a dynamic gravimeter according to claim 1, characterized in that, The step of constructing a comprehensive compensation model for coupling error based on the aforementioned mechanism of coupling error further includes: Define the data loss function of the coupling error integrated compensation model. : In the formula, These are the model parameters during training. S test For the test dataset, N To test the length of the dataset, x For input data, Output values ​​for the model. y The true value of the model; Physical information loss function constrained by the comprehensive coupling error between temperature, vibration, and carrier maneuverability for: In the formula, , , , These are the weighting coefficients, T in Internal temperature, Output values ​​for the model. a v For vibration acceleration, a For the acceleration of the carrier motion, In mathematics, this is the operator for finding partial derivatives.

8. The intelligent compensation method for coupling error of a dynamic gravimeter according to claim 1, characterized in that, The steps of training the model using training data and calculating the total loss of the validation set on the obtained model to obtain the final coupling error comprehensive compensation model further include: Data was collected and processed according to the specifications of the model training dataset, and then input into the coupling error compensation model to perform coupling error compensation, thereby obtaining the measurement results of the dynamic gravimeter under various typical environmental disturbances.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the intelligent compensation method for the coupling error of the dynamic gravimeter as described in any one of claims 1 to 8.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the intelligent compensation method for the coupling error of the dynamic gravimeter as described in any one of claims 1 to 8.

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