Tool face angle prediction method and system for drill string whirling system based on response surface method

Abstract

The application discloses a tool face angle prediction method and system of a drill string whirling system based on a response surface method, and relates to the technical field of tool face angle prediction. The method comprises the following steps: selecting a sampling interval, a motor speed, a maximum motor rotation angle, a drill string length and a moment of inertia as initial parameters, wherein the moment of inertia is obtained through inversion calculation based on no-load operation data of a top drive system; building an experimental bench, adopting orthogonal experimental design to design multiple working conditions, collecting drill string acceleration component data, processing and synthesizing tool face angle related parameters, and determining parameter influence significance through range analysis; constructing multiple prediction models based on a specific response surface design, deploying the optimal model to a hardware platform after variance analysis and residual error analysis, and realizing prediction. The application improves prediction accuracy and adaptability by supplementing key initial parameters, optimizing experimental design and model screening mechanism, solves the problems of incomplete traditional technical parameters and response lag, and provides technical support for parameter optimization of the drill string whirling system and drilling trajectory control.

Description

Technical Field

[0001] This invention relates to the field of tool face angle prediction technology, and specifically to a method and system for predicting tool face angles in a drill string torsion system based on response surface methodology. Background Technology

[0002] In oil and gas drilling engineering, the widespread application of horizontal and directional well technologies places stringent demands on the accuracy of drill string attitude control. The tool face angle, as a core parameter determining the accuracy of the drilling trajectory, is directly related to the wellbore trajectory conformity and drilling efficiency through stable prediction. Drill string torsion systems, driven by servo motors, periodically torsion the drill string, effectively mitigating stuck pipe due to bottom hole differential pressure. However, in actual operations, the tool face angle is easily affected by the coupling of various operating parameters, causing fluctuations. Traditional prediction methods often rely on empirical formulas or single-parameter analysis, making it difficult to fully cover the parameter correlation characteristics under complex operating conditions. With increasing drilling depth and more complex formation conditions, there is an urgent need to establish a precise tool face angle prediction mechanism under multi-parameter coupling to provide technical support for parameter optimization and trajectory control of drill string torsion systems, meeting the demands of efficient and precise drilling operations.

[0003] Existing tool face angle prediction technologies have two significant shortcomings: First, the initial parameter selection is not comprehensive enough, failing to consider the influence of rotational inertia on the tool face angle. Although this parameter cannot be directly measured, it can be obtained through inversion calculations of system dynamic characteristics. Its absence causes the prediction model to fail to fully reflect the dynamic response law of the system, thus affecting the accuracy of the prediction results. Second, the construction and deployment of prediction models lack systematic optimization. Some technologies rely solely on a single experimental design method to obtain data, without selecting the optimal fitting scheme through multi-model comparison. Furthermore, the model deployment does not fully utilize the advantages of hardware parallel computing, resulting in a slow prediction response speed, making it difficult to adapt to the real-time control needs on site, and failing to provide timely and reliable technical support for the dynamic adjustment of the drill string torsion system. Summary of the Invention

[0004] In order to overcome the shortcomings and deficiencies of the existing technology, the present invention provides a method and system for predicting the tool face angle of a drill string torsion pendulum system based on the response surface methodology.

[0005] The technical solution adopted in this invention is a method for predicting the tool face angle of a drill string torsion pendulum system based on response surface methodology. It is characterized by the following steps: S1, selecting sampling interval, motor speed, maximum motor rotation angle, drill string length, and moment of inertia as initial parameters, wherein the moment of inertia is obtained by inverting the electromagnetic torque, angular velocity, and friction torque data collected under the no-load operating state of the top drive system, combined with the dynamic equations; S2, constructing a horizontal drill string torsion pendulum experimental platform, which includes a servo motor, a simulated drill string, a universal joint, a magnetic powder brake, and multi-parameter wireless sensors, and controlling the servo motor's operating state through a controller; S3, setting different levels for each initial parameter, and constructing multiple sets of experimental conditions using orthogonal experimental design. In each working condition, the servo motor drives the simulated drill string to complete at least 10 complete torsional cycles, and the acceleration component data of the simulated drill string perpendicular to the wellbore axis are collected synchronously; S4, the collected acceleration component data are processed to synthesize tool face angle related parameters, and the significance ranking of the influence of each initial parameter on the minimum amplitude of the tool face angle is determined by range analysis; S5, based on the Box-Behnken design in the response surface methodology, a tool face angle prediction model is constructed in combination with experimental data, and the significance of the model terms is tested by variance analysis to select the best-fit model; S6, the optimized prediction model is deployed to the FPGA platform, the real-time collected initial parameter data is received through the serial port, and the tool face angle prediction result is output through parallel computing.

[0006] Furthermore, the moment of inertia is calculated using the following model: ,in, The total equivalent moment of inertia of the system, To provide electromagnetic torque for the frequency converter output. This refers to the frictional torque during the motor's rotation. The viscous damping coefficient is... Let be the system angular velocity. This represents the system's angular acceleration.

[0007] Furthermore, the range analysis employs the following model: ,in, For the first The range of each factor For the first The factor in the first The average of the experimental results at each level. For the first The factor in the first The sum of experimental results at each level The number of times each level appears.

[0008] Furthermore, the response surface methodology employs a linear model: ,in, This represents the minimum amplitude of the tool face angle. For constant terms, , , These are the coefficients of the first-order terms corresponding to motor speed, maximum motor rotation angle, drill string length, and moment of inertia, respectively. For the servo motor output speed, This is the maximum rotation angle of the motor. The length of the drill string. Let be the moment of inertia.

[0009] Furthermore, the adjusted coefficient of determination in the analysis of variance is calculated using the following model: ,in, To adjust the coefficient of determination, For the sum of squared residuals, For the total sum of squares, For the experimental sample size, The number of independent variables.

[0010] Furthermore, the accuracy of the model is evaluated using the mean absolute percentage error model: ,in, The mean absolute percentage error, These are measured values. For predicted values, This represents the number of samples.

[0011] Further, S3 includes the following sub-steps: S31, establishing a connection between the controller and the computer via a wireless local area network, and measuring the output speed and torque of the servo motor using a control program when the simulated drill string is not connected; S32, connecting the various components of the experimental platform, adjusting the servo motor and the axis of the simulated wellbore drill string to be coaxial, so that the servo motor and the universal joint are on the same horizontal axis; S33, setting the horizontal combination of each initial parameter through the program, controlling the servo motor to drive the simulated drill string to reciprocate to release residual torque; S34, setting the output parameters to make the drill string continuously reciprocate, recording the output torque, speed, and sensor signals, repeating each set of parameters 15 times and storing the data.

[0012] Further, S4 includes the following sub-steps: S41, screening the collected raw acceleration component data and removing abnormal fluctuation data points; S42, synthesizing the minimum amplitude of the tool face angle based on the screened data, and establishing a mapping relationship between each experimental condition and the corresponding minimum amplitude of the tool face angle; S43, calculating the average value of the minimum amplitude of the tool face angle at each level of each initial parameter, and determining the sum of experimental results corresponding to each parameter level; S44, solving for the range value of each initial parameter according to the range calculation formula, and determining the order of influence significance based on the size of the range values.

[0013] Further, S5 includes the following sub-steps: S51, based on the Box-Behnken design principle, five initial parameters are used as design variables, and the minimum amplitude of the tool face angle is used as the response value to construct an experimental design matrix; S52, linear, interactive, and quadratic models are established respectively, and experimental data are substituted into each model for fitting calculation; S53, the significance of each model term is tested through analysis of variance, and the coefficient of determination is compared and analyzed with the predicted coefficient of determination; S54, combined with the residual analysis results, the model with the optimal balance between fitting accuracy and generalization ability is selected as the final prediction model.

[0014] This system, based on the response surface methodology (RSM) for predicting the tool face angle of a drill string torsion-yaw system, comprises: a multi-source parameter acquisition and rotational inertia inversion calculation unit; a multi-condition collaborative control unit for the experimental platform; an acceleration data synthesis and range analysis processing unit; a multi-model construction and optimal selection unit based on the RSM; an FPGA platform model porting and parallel computing architecture construction unit; and a real-time parameter receiving and prediction result output unit. The multi-source parameter acquisition and rotational inertia inversion calculation unit collects data such as sampling interval, motor speed, and motor maximum speed through a distributed wireless sensor network. Measured parameters of large rotation angle and drill string length were obtained simultaneously, along with electromagnetic torque, angular velocity, and frictional torque data during the no-load operation of the top drive system. A dynamic inversion algorithm was used to calculate the moment of inertia. All initial parameters were sent to the multi-condition collaborative control unit of the experimental bench via a high-speed data transmission interface. Upon receiving the parameters, the multi-condition collaborative control unit controlled the servo motor's start / stop, speed, and rotation angle via a programmable logic controller, driving the simulated drill string to complete torsional gyratory motion according to the orthogonal experimental design's combination of operating conditions. Simultaneously, multi-parameter sensors were controlled to collect acceleration component data perpendicular to the wellbore axis and transmit it to the acceleration data aggregation unit. The acceleration data synthesis and range analysis processing unit filters the received acceleration data and synthesizes characteristic parameters to generate tool face angle minimum amplitude data. It then uses a range calculation algorithm to determine the significance ranking of each initial parameter's influence and transmits the processed data and ranking results to the response surface methodology multi-model construction and optimal selection unit. This unit constructs an experimental matrix based on the Box-Behnken design principle, substitutes the data to complete linear, interactive, and quadratic model fitting, and uses variance analysis and residual analysis to select the optimal model. The model parameters are then sent to the FPGA platform model porting and parallel computing architecture building unit. This unit converts the optimal model into hardware executable code, builds a pipelined parallel computing architecture, completes model deployment, and establishes data interaction with the real-time parameter receiving and prediction result output unit. The real-time parameter receiving and prediction result output unit receives the initial parameters collected in real-time on-site via a serial communication module, transmits them to the FPGA platform, and generates tool face angle prediction results through parallel computing. These results are then output through a visualization interface. All units communicate bidirectionally via an industrial Ethernet bus for data transmission and command interaction.

[0015] Beneficial Effects: This invention proposes a method and system for predicting the tool face angle of a drill string torsion pendulum system based on response surface methodology. By adding a rotational inertia as an initial parameter, which is obtained through dynamic inversion calculation based on the no-load operation data of the top drive system, it overcomes the shortcomings of traditional technical parameter selection, ensuring that the initial parameter system fully covers key influencing factors such as sampling interval and motor speed. This allows the prediction model to truly reflect the dynamic response law of the system, significantly improving the accuracy of the prediction results. Experimental data is obtained by combining orthogonal experimental design and Box-Behnken design. The significance of parameter influence is clarified through range analysis. At the same time, linear, interactive, and quadratic multi-class models are constructed, and the optimal solution is selected through variance analysis and residual analysis. This solves the problem of insufficient adaptability caused by single experimental design and model fitting. Furthermore, the optimal model is deployed on an FPGA platform to build a parallel computing architecture, which greatly improves the prediction response speed and meets the needs of real-time on-site control. Furthermore, through the coordinated operation of six functional units, the system achieves a closed-loop operation of the entire process, including parameter acquisition, experimental control, data processing, model building, hardware deployment, and result output. Each unit achieves efficient data interaction with the industrial Ethernet bus through a high-speed data transmission interface, ensuring overall operational stability and reliability. This provides strong technical support for parameter optimization and precise control of the drilling trajectory in the drill string torsion system, helping to improve the efficiency of oil and gas drilling operations and the conformity of wellbore trajectory. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating the overall process of the method of the present invention.

[0017] Figure 2 This is a flowchart of method step S3 of the present invention;

[0018] Figure 3 This is a flowchart of method step S4 of the present invention;

[0019] Figure 4 This is a flowchart of step S5 of the method of the present invention;

[0020] Figure 5 This is a system unit composition diagram of the present invention;

[0021] Figure 6 This is a graph showing the range analysis results of the experiments in this invention;

[0022] Figure 7 This is a bar chart showing the predicted adjusted coefficient of determination and the predicted coefficient of determination in the experiments of this invention;

[0023] Figure 8 This is a three-dimensional surface plot of the linear model motor speed and maximum rotation angle used in the experiment of this invention;

[0024] Figure 9This is a three-dimensional surface plot of the linear model motor speed and drill string length used in the experiment of this invention;

[0025] Figure 10 This is a three-dimensional surface plot of the maximum rotation angle and drill string length of the linear model used in the experiment of this invention;

[0026] Figure 11 This is a three-dimensional surface plot of the motor speed and maximum rotation angle of the interactive model used in the experiment of this invention;

[0027] Figure 12 This is a three-dimensional surface plot of the interactive model of motor speed and drill string length in the experiment of this invention;

[0028] Figure 13 This is a three-dimensional surface plot of the maximum rotation angle and drill string length of the interactive model used in the experiment of this invention;

[0029] Figure 14 This is a three-dimensional surface plot of the rotational speed and maximum rotation angle of the quadratic model motor used in the experiment of this invention;

[0030] Figure 15 This is a three-dimensional surface plot of the motor speed and drill string length in the secondary model of the experiment of this invention;

[0031] Figure 16 This is a three-dimensional surface plot of the maximum rotation angle and drill string length of the quadratic model used in the experiment of this invention;

[0032] Figure 17 This is a scatter plot of the residuals and predicted values ​​from the experiments of this invention.

[0033] Figure 18 The diagram shows the FPGA-based computational results of the experiment of this invention. Detailed Implementation

[0034] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. The application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0035] like Figure 1 As shown, the method for predicting the tool face angle of a drill string torsional yaw system based on response surface methodology includes the following steps:

[0036] S1, the sampling interval, motor speed, maximum motor angle, drill string length and moment of inertia are selected as initial parameters. The moment of inertia is obtained by combining the electromagnetic torque, angular velocity and friction torque data collected by the top drive system under no-load operation with the dynamic equation inversion calculation.

[0037] Specifically, step S1 completes the selection of initial parameters and the calculation of rotational inertia, providing comprehensive and reliable basic data support for the subsequent prediction model construction. The selected initial parameters include sampling interval, motor speed, maximum motor angle, drill string length, and rotational inertia. The first four parameters can be directly collected by the sensors on the experimental bench. The sampling interval is set to a fixed value within the range of 0.001 seconds to 0.01 seconds. The motor speed ranges from 5 revolutions per minute to 30 revolutions per minute. The maximum motor angle is controlled between 30 degrees and 120 degrees. The drill string length is selected from different specifications of 1 meter to 5 meters according to the simulated well depth of the experimental bench. Since the moment of inertia cannot be directly measured, calculation data needs to be obtained through an unloaded operation experiment of the top drive system. In practice, the top drive system is disconnected from the simulated drill string, and the top drive system is controlled to run unloaded at different speeds. Electromagnetic torque data is collected by a torque sensor, and real-time angular velocity data is collected by an angular velocity sensor. At the same time, the system's preset friction torque parameters are recorded. Based on the above collected data, the total equivalent moment of inertia of the system is calculated by inversion through the dynamic equation. The addition of this parameter makes the initial parameter system more complete and can fully reflect the dynamic characteristics of the drill string torsion system, laying the foundation for the accurate construction of subsequent prediction models.

[0038] S2, Build a horizontal drill string torsion test platform. The platform includes a servo motor, a simulated drill string, a universal joint, a magnetic powder brake, and a multi-parameter wireless sensor. The servo motor's operating status is controlled by a controller.

[0039] Specifically, step S2 involves constructing a horizontal drill string torsion test bench that meets experimental requirements, providing a stable and controllable hardware platform for subsequent multi-condition experiments. The core components of the test bench include a servo motor, a simulated drill string, a universal joint, a magnetic powder brake, and multi-parameter wireless sensors. These components are connected and assembled in a specific order. The servo motor, acting as the power output device, is connected to one end of the universal joint via a coupling. The other end of the universal joint is connected to the simulated drill string, and the end of the simulated drill string is connected to the magnetic powder brake, which simulates formation resistance during drilling. The multi-parameter wireless sensors include an accelerometer, an angular velocity sensor, and a torque sensor, which are respectively installed in the middle of the simulated drill string, on the output shaft of the servo motor, and at the universal joint connection. The sampling frequency of the sensors matches the sampling interval set in step S1. The controller establishes a communication connection with the servo motor, magnetic powder brake, and sensors via a data cable. The controller has a built-in control program that can adjust the start, stop, speed, and angle of the servo motor according to experimental requirements, thereby achieving precise control of the torsional motion of the drill string. At the same time, it receives real-time data collected by the sensors and stores it in the computer. The experimental platform is built in strict accordance with the horizontal installation requirements to ensure that the axes of the servo motor, the simulated drill string, and the universal joint are on the same horizontal plane, reducing the impact of installation errors on the experimental data.

[0040] S3, set different levels of each initial parameter, and construct multiple sets of experimental conditions using orthogonal experimental design. Under each set of conditions, control the servo motor to drive the simulated drill string to complete at least 10 complete torsional cycles, and simultaneously collect the acceleration component data of the simulated drill string perpendicular to the wellbore axis.

[0041] Specifically, step S3 involves setting multiple experimental conditions and conducting experiments to obtain tool face angle data under different parameter combinations, providing sufficient sample support for subsequent data processing and model construction. During implementation, the number of levels for each initial parameter is first determined: the sampling interval is set to 3 levels, the motor speed to 4 levels, the maximum motor angle to 3 levels, and the drill string length to 3 levels. The moment of inertia is calculated to obtain 3 different values ​​as levels. Based on the orthogonal experimental design principle, an orthogonal experimental table is constructed, including 45 to 60 experimental conditions, with each condition corresponding to a unique parameter combination. During the experiment, each condition is run sequentially according to the orthogonal experimental table. Under each condition, the controller sends commands to control the servo motor to drive the simulated drill string in a torsional motion, ensuring that the simulated drill string completes at least 10 complete torsional cycles under each condition. The duration of each torsional cycle is determined based on the motor speed and maximum angle, ranging from 5 to 20 seconds. During the torsional motion of the drill string, multi-parameter wireless sensors synchronously collect acceleration component data of the simulated drill string perpendicular to the wellbore axis. The collected data is transmitted to the computer in real time via a wireless transmission module. The computer classifies and stores the data according to the working condition number. The experimental data of each working condition is stored in an independent file to ensure the integrity and traceability of the data. During the experiment, the ambient temperature and humidity are strictly controlled to reduce the interference of external environmental factors on the experimental results.

[0042] S4. The collected acceleration component data are processed to synthesize tool face angle related parameters. The significance ranking of the influence of each initial parameter on the minimum amplitude of the tool face angle is determined by range analysis.

[0043] Specifically, step S4 processes and analyzes the collected experimental data to clarify the significance of each initial parameter's influence on the tool face angle, providing data support and parameter priority reference for subsequent model construction. First, the raw acceleration component data collected under each working condition are screened to remove abnormal data points caused by sensor fluctuations or external interference. The screening criteria are based on the standard deviation and mean of the data; data exceeding plus or minus three times the standard deviation of the mean are considered abnormal. Then, based on the screened effective acceleration component data, the minimum amplitude of the tool face angle is calculated using a data synthesis algorithm. This amplitude serves as a core indicator reflecting the stability of the tool face angle and establishes a one-to-one mapping relationship with the parameter combinations for the corresponding working condition, forming a dataset including parameter combinations and the minimum amplitude of the tool face angle. Next, range analysis is used to process the dataset, calculating the average value of the minimum amplitude of the tool face angle at each level for each initial parameter. Then, the range value of each parameter is calculated based on the average value at each level. The magnitude of the range value directly reflects the significance of the parameter's influence on the minimum amplitude of the tool face angle. Finally, based on the range values ​​from largest to smallest, the significance of each initial parameter's influence on the minimum amplitude of the tool face angle is determined. The ranking results provide an important reference for setting parameter weights in subsequent model construction, ensuring that the model can focus on parameters with significant influence and improve the model's prediction accuracy.

[0044] S5. Based on the Box-Behnken design in response surface methodology, a tool face angle prediction model is constructed by combining experimental data. The significance of the model terms is tested by analysis of variance, and the best-fit model is selected.

[0045] Specifically, step S5 constructs and selects the optimal tool facet angle prediction model based on response surface methodology, ensuring the model possesses good fitting accuracy and generalization ability. In implementation, firstly, based on the Box-Behnken design principle, five initial parameters are used as design variables, and the minimum amplitude of the tool facet angle is used as the response value. An experimental design matrix with 30 to 40 experimental points is constructed. The experimental design matrix covers the entire level range of each parameter, and the distribution of experimental points is uniform and reasonable, fully reflecting the interaction between parameters. Subsequently, the dataset processed in step S4 is substituted into the experimental design matrix to construct three types of response surface prediction models with different complexities: linear, interactive, and quadratic models. The least squares method is used to fit the model parameters during model construction. Next, analysis of variance is performed on the three types of models to test the significance of each parameter term in each model. Simultaneously, the adjusted coefficient of determination and the predicted coefficient of determination for each model are calculated. The adjusted coefficient of determination reflects the model's fit to the data, while the predicted coefficient of determination reflects the model's generalization ability. Furthermore, residual analysis is used to verify the reliability of the model; the residuals must satisfy a normal distribution and have no obvious trend. Finally, based on the results of variance analysis, coefficient of determination and residual analysis, the optimal model with high fitting accuracy, strong generalization ability and good stability was selected from the three types of models. This model can accurately describe the nonlinear relationship between each initial parameter and the minimum amplitude of the tool face angle, providing core algorithm support for subsequent real-time prediction.

[0046] S6 deploys the optimized prediction model to the FPGA platform, receives the initial parameter data collected in real time via serial port, and outputs the tool face angle prediction results through parallel computing.

[0047] Specifically, step S6 deploys the selected optimal prediction model to the hardware platform to achieve real-time prediction of tool face angles, providing timely technical support for on-site drilling operations. During implementation, the optimal prediction model is first converted into code, transforming its mathematical expressions into hardware description language code recognizable by the FPGA platform. The code optimization process fully considers the parallel computing characteristics of the FPGA, splitting and reorganizing the model's computational flow to ensure that the computation process fully utilizes the FPGA's hardware resources. Subsequently, the converted code is downloaded to the FPGA platform, building a pipelined parallel computing architecture. This architecture divides the model's computational process into multiple parallel execution stages, each handled by a dedicated computing unit, significantly improving computational efficiency and keeping the model's single prediction response time within 10 milliseconds. Next, a serial communication module connects the FPGA platform to the on-site parameter acquisition equipment. The parameter acquisition equipment collects data in real-time on the sampling interval, motor speed, maximum motor rotation angle, and drill string length during the drilling process. Simultaneously, it acquires rotational inertia data in real-time through a preset calculation program. The collected initial parameter data is sent to the FPGA platform via serial port in a fixed format. After receiving the parameter data, the FPGA platform starts a parallel computing architecture to process the data, substitutes it into the optimal prediction model to calculate the tool face angle prediction result, and finally outputs the prediction result to the field control terminal in real time through a visualization interface, providing timely and accurate reference for operators to adjust the drill string torsion system parameters and control the drilling trajectory.

[0048] Preferably, the moment of inertia is calculated using the following model: ,in, The total equivalent moment of inertia of the system, To provide electromagnetic torque for the frequency converter output. This refers to the frictional torque during the motor's rotation. The viscous damping coefficient is... Let be the system angular velocity. This represents the system's angular acceleration.

[0049] Specifically, the method for calculating the moment of inertia involves inverting key parameters that cannot be directly measured from the acquired system operating data, providing crucial support for the initial parameter system. This calculation method requires the top drive system to operate under no-load conditions. In this state, the top drive system is not connected to the simulated drill string to avoid interference from the drill string load and ensure the purity of the acquired data. During implementation, electromagnetic torque data output from the frequency converter is collected via a torque sensor, with the sampling frequency consistent with the sampling interval set in step S1, i.e., 0.001 seconds to 0.01 seconds. Simultaneously, angular velocity data of the system operation is collected in real time via an angular velocity sensor. The measurement range of this sensor must cover the entire speed range of the top drive system under no-load operation, i.e., the angular velocity range corresponding to 5 revolutions per minute to 30 revolutions per minute. Furthermore, the system's preset friction torque parameters must be calibrated in advance through multiple no-load experiments to ensure numerical accuracy. Based on the three types of data collected and preset above, the total equivalent rotational inertia of the system is calculated by inversion of the dynamic equation. The calculation process must strictly follow the dynamic principles to eliminate the influence of errors in the data collection process. The acquisition of this parameter makes the initial parameter system more comprehensive and can fully reflect the dynamic characteristics of the drill string torsion system. It provides key data support for the accurate construction of subsequent prediction models and avoids the model being unable to accurately describe the system response law due to missing parameters.

[0050] Preferably, the range analysis uses the following model: ,in, For the first The range of each factor For the first The factor in the first The average of the experimental results at each level. For the first The factor in the first The sum of experimental results at each level The number of times each level appears.

[0051] Specifically, range analysis is used to clarify the significance of each initial parameter's influence on the minimum amplitude of the tool face angle, providing a scientific basis for parameter weight allocation in subsequent model construction. This method is based on the dataset generated after step S4, which includes 45 to 60 sets of parameter combinations and minimum amplitudes of the tool face angle corresponding to experimental conditions. During implementation, for each initial parameter, the dataset is first split according to its set number of levels (e.g., sampling interval divided into 3 levels, motor speed divided into 4 levels, etc.). The average value of the minimum amplitude of the tool face angle for each parameter under each level is calculated for all corresponding conditions. The accuracy of the statistical data must be ensured during the calculation to eliminate interference from outliers. Subsequently, based on the average value of each parameter at each level, the range value of that parameter is calculated, i.e., the difference between the maximum and minimum average values ​​for the same parameter. The calculation of the range value must strictly follow mathematical operation rules to ensure accurate results. The magnitude of the range value directly indicates the significance of the parameter's influence; the larger the range value, the more significant the difference in the parameter's influence on the minimum amplitude of the tool face angle at different levels, and the more critical its role in the prediction results. This analytical method does not require complex computing equipment and can be completed using conventional data processing software. The analysis results can clearly present the influence priority of each initial parameter, enabling subsequent model construction to focus on parameters with significant influence, allocate weights reasonably, improve the prediction accuracy and specificity of the model, and avoid poor model fitting due to inaccurate judgment of the degree of influence of parameters.

[0052] Preferably, the response surface methodology employs a linear model: ,in, This represents the minimum amplitude of the tool face angle. For constant terms, , , These are the coefficients of the first-order terms corresponding to motor speed, maximum motor rotation angle, drill string length, and moment of inertia, respectively. For the servo motor output speed, This is the maximum rotation angle of the motor. The length of the drill string. Let be the moment of inertia.

[0053] Specifically, the linear model construction in the response surface methodology establishes a linear relationship between the initial parameters and the minimum amplitude of the toolface angle, providing a foundational model for subsequent multi-model comparison and selection. This model is constructed based on an experimental design matrix built using the Box-Behnken design principle, comprising 30 to 40 experimental points covering the entire range of levels for each initial parameter. During implementation, the dataset processed in step S4 is substituted into the model, with the minimum amplitude of the toolface angle used as the response value and the five initial parameters as independent variables. The constant terms in the model are derived by fitting all experimental data to ensure they reflect the overall trend of the data. The coefficients of the linear terms corresponding to the five independent variables represent the degree of linear influence of each initial parameter on the response value. The least squares method is used for fitting, which minimizes the sum of squared errors between the model's predicted and measured values, ensuring the accuracy of the coefficients. During model construction, the completeness and accuracy of the experimental data must be ensured, and data points that do not meet the requirements must be removed to avoid affecting the coefficient fitting results. This linear model has a relatively simple structure and high computational efficiency. It can quickly establish the relationship between parameters and response values, providing a benchmark for subsequent comparative analysis with interactive models and quadratic models. Through comparison, the role of linear relationship in parameter coupling can be clarified, providing a basis for selecting the optimal model. At the same time, this model can also serve as a simplified prediction scheme, which can be quickly applied in scenarios where the requirements for prediction accuracy are not high.

[0054] Preferably, the adjusted coefficient of determination in the analysis of variance is calculated using the following model: ,in, To adjust the coefficient of determination, For the sum of squared residuals, For the total sum of squares, For the experimental sample size, The number of independent variables.

[0055] Specifically, by adjusting the calculation of the coefficient of determination, the fitting accuracy of the predictive model is objectively evaluated, providing a quantitative indicator for model selection. This calculation method is based on the residual sum of squares and the total sum of squares generated during model fitting, and is applied to three types of models: linear models, interactive models, and quadratic models. In the implementation process, the residual sum of squares is first calculated through model fitting; this is the sum of squares of the differences between the measured values ​​and the model predictions for each set of experimental data. During the calculation, it is crucial to ensure the accuracy of the difference calculation for each data point to avoid error accumulation. Then, the total sum of squares is calculated; this is the sum of squares of the differences between the measured values ​​for each set of experimental data and the average of all measured values. This value reflects the overall dispersion of the measured data. Simultaneously, the number of experimental samples and the number of independent variables are specified: 30 to 40 samples and 5 independent variables. Based on the above data, the coefficient of determination is calculated and adjusted according to a specific formula. The coefficient ranges from 0 to 1; the closer the value is to 1, the higher the model's fit to the data, and the more accurately it describes the relationship between the initial parameters and the minimum amplitude of the tool face angle. This calculation method can effectively avoid the problem of inflated coefficients of determination caused by an increase in the number of independent variables, objectively reflect the actual fitting effect of the model, provide a scientific quantitative basis for the comparison of the three types of models, ensure that the selected optimal model has good fitting accuracy, and avoid large deviations in prediction results due to insufficient model fitting.

[0056] Preferably, the accuracy of the model is evaluated using a mean absolute percentage error model: ,in, The mean absolute percentage error, These are measured values. For predicted values, This represents the number of samples.

[0057] Specifically, the application of the Mean Absolute Percentage Error (MAPE) model comprehensively evaluates the prediction accuracy of a forecasting model, providing a criterion for judging its practicality. The implementation of this model is based on the model's predicted values ​​and corresponding measured values. The implementation process needs to cover all 30 to 40 sets of experimental sample data to ensure the comprehensiveness and reliability of the evaluation results. During implementation, firstly, for each set of sample data, the difference between the model's predicted value and the measured value is calculated. Then, the absolute value of the difference is taken to avoid the cancellation of positive and negative errors, ensuring the accuracy of the error calculation. The absolute value is compared with the measured value of that set of samples to obtain the absolute percentage error for each set of samples. The calculation process must strictly follow mathematical operation rules to ensure the accuracy of the results. Subsequently, the absolute percentage errors of all samples are summed and then divided by the number of samples to obtain the mean absolute percentage error (MAPE). This value is presented as a percentage; the smaller the value, the higher the model's prediction accuracy and the smaller the deviation between the predicted results and the actual situation. This evaluation model can intuitively reflect the degree of deviation between predicted and measured values, is not affected by the data volume, is suitable for evaluating experimental data of different scales, and the implementation process can be completed using conventional data processing software without complex calculation procedures. The evaluation of this model ensures that the selected optimal model has high prediction accuracy, meets the precise requirements of on-site drilling operations for tool face angle prediction, and provides reliable technical support for parameter adjustment of the drill string torsion system.

[0058] Preferred, such as Figure 2 As shown, step S3 includes the following sub-steps: S31, establishing a connection between the controller and the computer via a wireless local area network, and measuring the output speed and torque of the servo motor using the control program when the simulated drill string is not connected; S32, connecting the various components of the experimental platform, adjusting the servo motor and the axis of the simulated wellbore end drill string to be coaxial, so that the servo motor and the universal joint are on the same horizontal axis; S33, setting the horizontal combination of each initial parameter through the program, controlling the servo motor to drive the simulated drill string to reciprocate to release residual torque; S34, setting the output parameters to make the drill string continuously reciprocate, recording the output torque, speed and sensor signals, repeating each set of parameters 15 times and storing the data.

[0059] Specifically, step S3 ensures the accuracy and reliability of multi-condition experimental data through standardized experimental preparation and operation procedures, providing high-quality samples for subsequent analysis. During implementation, S31 is executed first, establishing a stable connection between the controller and the computer via a wireless LAN. In an unloaded state without a connected simulated drill string, the control program is started to continuously measure the output speed and torque data of the servo motor at different set speeds. The measurement time for each speed group is no less than 30 seconds to ensure the data has statistical significance. Next, S32 is performed, connecting the components of the experimental platform in a preset order. The axes of the servo motor and the simulated wellbore end drill string are adjusted using a level and calibration tools to control the coaxiality error between them to within 0.05 mm. Simultaneously, the servo motor and the universal joint are ensured to be on the same horizontal axis, eliminating experimental errors caused by installation deviations. Finally, S33 is executed, using a computer program... Set preset combinations of initial parameters, start the servo motor to drive the simulated drill string to rotate back and forth at a speed range of 5 to 30 revolutions per minute, with each rotation angle controlled between 30 and 120 degrees, and run continuously for 5 minutes to fully release the residual torque inside the drill string; finally, implement S34, set fixed output parameters to make the drill string enter a stable reciprocating motion state, and synchronously record the output torque, speed and sensor signals through the data acquisition system. Each parameter combination is repeated 15 times, and the duration of each run is 10 complete cycles of 5 to 20 seconds per torsion cycle. All data are classified and stored in the computer according to the working condition number, providing a complete and traceable experimental basis for subsequent data processing.

[0060] Preferred, such as Figure 3 As shown, S4 includes the following sub-steps: S41, screening the collected raw acceleration component data and removing abnormal fluctuation data points; S42, synthesizing the minimum amplitude of the tool face angle based on the screened data, and establishing a mapping relationship between each experimental condition and the corresponding minimum amplitude of the tool face angle; S43, calculating the average value of the minimum amplitude of the tool face angle at each level of each initial parameter, and determining the sum of experimental results corresponding to each parameter level; S44, solving for the range value of each initial parameter according to the range calculation formula, and determining the order of influence significance based on the size of the range values.

[0061] Specifically, step S4, through a systematic data processing workflow, accurately synthesizes the relevant parameters of the tool face angle and clarifies the significance of the influence of each initial parameter, providing data support for model construction. In implementation, S41 is first carried out, systematically screening the collected raw acceleration component data. Abnormal fluctuation data points exceeding three standard deviations above or below the mean are removed using a three-standard-deviation principle to ensure data purity. After screening, the data retention rate for each working condition is no less than 95%. Next, S42 is executed. Based on the screened valid data, the minimum amplitude of the tool face angle under each working condition is calculated using a data synthesis algorithm. A one-to-one mapping relationship is established between 45 to 60 experimental working conditions and the corresponding minimum amplitude of the tool face angle, forming a structured dataset. Then, S43 is performed, calculating the minimum amplitude of the tool face angle according to the initial parameters. The average value of the minimum amplitude of the tool face angle under all corresponding working conditions at each level of each parameter is calculated, for example, the sampling interval is 3 levels, the motor speed is 4 levels, etc. The number of calculation samples at each level is no less than 10 sets to ensure the statistical reliability of the average value. Finally, S44 is implemented. Based on the average value of each parameter at each level, the range value of each initial parameter is calculated strictly according to the range calculation rules. The significance of the influence of each parameter on the minimum amplitude of the tool face angle is determined according to the order of the range values ​​from large to small. The ranking result provides a direct basis for setting the priority of parameters in subsequent model construction and improves the pertinence of model fitting.

[0062] Preferred, such as Figure 4 As shown, S5 includes the following sub-steps: S51, based on the Box-Behnken design principle, five initial parameters are used as design variables, and the minimum amplitude of the tool face angle is used as the response value to construct an experimental design matrix; S52, linear, interactive, and quadratic models are established respectively, and experimental data are substituted into each model for fitting calculation; S53, the significance of each model term is tested through analysis of variance, and the coefficient of determination is compared and analyzed with the predicted coefficient of determination; S54, combined with the residual analysis results, the model with the optimal balance between fitting accuracy and generalization ability is selected as the final prediction model.

[0063] Specifically, step S5, through a standardized model building and screening process, ensures that the final prediction model possesses high fitting accuracy and strong generalization ability. During implementation, S51 is first executed, strictly adhering to the Box-Behnken design principle. Five initial parameters—sampling interval, motor speed, maximum motor angle, drill string length, and moment of inertia—are used as design variables, and the minimum amplitude of the tool face angle is used as the response value. An experimental design matrix comprising 30 to 40 sets of experimental points is constructed, with the experimental points evenly covering the entire horizontal range of each parameter to ensure a full reflection of the interactions between parameters. Next, step S52 is performed. Based on the constructed experimental design matrix, three prediction models of different complexities—linear, interactive, and quadratic—are established. The structured dataset processed in step S4 is completely substituted into each model, and the least squares method is used for fitting calculations. The fitting process... The first step ensures that all data points participate in the calculation, without omitting any valid samples. Then, step S53 is implemented, using ANOVA to examine the significance of each parameter in each model. Simultaneously, the adjusted coefficient of determination and the predicted coefficient of determination for the three models are calculated and compared to clarify the fit and generalization ability of each model. Finally, step S54 is executed, combining the residual analysis results to verify whether the residuals conform to a normal distribution and have no obvious trend. By integrating multiple indicators from ANOVA, coefficient of determination, and residual analysis, the optimal model with high fitting accuracy, strong generalization ability, and good stability is selected from the three models. This model can accurately describe the complex relationship between each initial parameter and the minimum amplitude of the tool face angle, providing core algorithmic support for subsequent real-time prediction.

[0064] like Figure 5As shown, a tool face angle prediction system for a drill string torsion-pole system based on the response surface methodology is presented. This system, applied to the tool face angle prediction method for a drill string torsion-pole system based on the response surface methodology, includes: a multi-source parameter acquisition and rotational inertia inversion calculation unit, a multi-condition collaborative control unit for the experimental platform, an acceleration data synthesis and range analysis processing unit, a response surface methodology multi-model construction and optimal selection unit, an FPGA platform model porting and parallel computing architecture construction unit, and a real-time parameter receiving and prediction result output unit. The multi-source parameter acquisition and rotational inertia inversion calculation unit acquires sampling intervals, motor speed, and electrical parameters through a distributed wireless sensor network. The maximum rotation angle and drill string length were measured. Simultaneously, electromagnetic torque, angular velocity, and frictional torque data of the top drive system during no-load operation were acquired. A dynamic inversion algorithm was used to calculate the moment of inertia. All initial parameters were sent to the multi-condition collaborative control unit of the experimental bench via a high-speed data transmission interface. Upon receiving the parameters, the multi-condition collaborative control unit of the experimental bench controlled the servo motor's start / stop, speed, and rotation angle via a programmable logic controller, driving the simulated drill string to complete torsional gyratory motion according to the orthogonal experimental design's combination of operating conditions. Simultaneously, multi-parameter sensors were controlled to collect acceleration component data perpendicular to the wellbore axis and transmit it to the acceleration data center. The acceleration data synthesis and range analysis processing unit filters the received acceleration data and synthesizes characteristic parameters to generate tool face angle minimum amplitude data. It then uses a range calculation algorithm to determine the significance ranking of each initial parameter's influence and transmits the processed data and ranking results to the response surface methodology multi-model construction and optimal selection unit. This unit constructs an experimental matrix based on the Box-Behnken design principle, substitutes the data to complete linear, interactive, and quadratic model fitting, and uses variance and residual analysis to select the optimal model. The model parameters are then sent to the FPGA platform model porting and parallel computing architecture building unit. This unit converts the optimal model into hardware executable code, builds a pipelined parallel computing architecture, completes model deployment, and establishes data interaction with the real-time parameter receiving and prediction result output unit. The real-time parameter receiving and prediction result output unit receives the initial parameters collected in real-time on-site via a serial communication module, transmits them to the FPGA platform, and generates tool face angle prediction results through parallel computing. These results are then output through a visualization interface. All units communicate bidirectionally via an industrial Ethernet bus for data transmission and command interaction.

[0065] Experiments were conducted on the proposed tool face angle prediction method and system for drill string torsion and yaw systems based on response surface methodology. According to the principle of range analysis, the larger the range value, the more significant the influence of the influencing parameters on the design objective. The range values ​​of the four influencing factors calculated in the experiment are as follows: =10.792, =50.176, =38.093, 6.207, such as Figure 6 As shown.

[0066] Depend on Figure 6 Range analysis results show that the motor rotation angle has the most significant impact on the minimum amplitude of the tool face angle. The amplitude increases sharply as the angle increases from 60° to 120°. The drill string length has the next most significant impact; as the length increases, the overall flexibility of the drill string increases, providing a certain "buffering" effect on motor torsion. Motor speed has a moderate impact on the amplitude; higher motor speeds increase the drill string's rotational inertia, leading to slight oscillations in the tool face angle, but the amplitude of these changes is relatively small. The sampling period only reflects the time interval of signal acquisition and has limited impact on the actual physical process. In summary, the importance of the above influencing factors, in descending order, is: motor rotation angle > drill string length > motor speed > sampling interval.

[0067] Analysis of variance provides a statistical basis for response surface optimization and formula fitting, and the specific results are shown in Table 1.

[0068] Table 1. Analysis of Variance Table for Linear Models

[0069]

[0070] The established linear model for predicting tool face angles is statistically significant overall, with a coefficient of determination of [missing information]. =0.8151, adjusted coefficient of determination =0.7724, indicating that the model can explain approximately 81.51% of the data variability. Analysis of variance results show that motor angle and drill string length have a significant impact on the tool face angle, but motor speed has no significant impact. Based on the contribution rate of each factor to the total sum of squares, motor angle accounts for 68.02%, drill string length accounts for approximately 31.96%, and motor speed accounts for only 0.23%, which is consistent with the significance analysis results. The lack-of-fit test result is not significant, indicating that the linear model can fit the current data well.

[0071] The above analysis shows that the motor rotation angle is the primary controlling factor, followed by the drill string length, while the motor speed has little impact. This paper focuses on the interaction term and quadratic term between the motor rotation angle and the drill string length to improve the predictive performance of the model. The tool facet angle prediction model based on the response surface methodology is shown in Table 2.

[0072] Table 2 Prediction Model Fitting Formula

[0073]

[0074] In the formula: α is the minimum amplitude of the tool face angle, in °; β represents the output speed of the servo motor (rpm); β represents the maximum motor rotation angle (°). , where is the drill string length, in meters (m).

[0075] like Figure 7 As shown, with increasing model complexity, the adjusted metrics improve while predictive performance declines, exhibiting typical overfitting characteristics. The linear model achieves a good balance between fitting accuracy and generalization ability, demonstrating high robustness and reliability. In contrast, while quadratic and interactive models show slight improvements in goodness of fit, their predictive performance significantly decreases; the cubic model performs the worst and shows no statistical significance. Therefore, excessive model complexity introduces noise and instability, making the linear model the optimal choice.

[0076] like Figures 8-16 As shown, the three-dimensional response surface plot intuitively reveals the interaction and variation trend of the maximum motor angle and motor speed on the tool face angle amplitude under different factor levels. The tool face amplitude exhibits a clear nonlinear distribution, with the maximum motor angle having the most significant impact, followed by the motor speed, providing an important reference for parameter optimization and design.

[0077] Model optimization was performed. To compare the applicability of the fitted models, residual analysis was conducted on the linear model, the interaction model, and the quadratic model. The analysis results are as follows: Figure 17 As shown.

[0078] like Figure 17 As shown, where, Figure 17 In the diagram, (a) represents the residual distribution of the linear model. Figure 17 In the diagram, (b) represents the residual distribution of the interaction model. Figure 17 In the diagram, (c) represents the residual distribution of the quadratic model. The residual distribution verifies the applicability of the linear model. The quadratic model exhibits significant residual dispersion in the high predicted value range, while the interaction model deviates from a normal distribution. The residuals of the linear model are randomly distributed and concentrated near the diagonal, showing no significant misfit. The interaction model and the quadratic model have similar residual shapes, indicating that although they differ in mathematical form, their ability to fit the data is similar. Therefore, the linear model outperforms other models in both accuracy and robustness.

[0079] To verify the applicability of the fitted equation under non-modeling conditions, several new experimental combinations were selected as independent validation sets. For each set of conditions, the motor speed, maximum motor rotation angle, and drill string length were substituted into the established fitted equation to obtain the predicted minimum amplitude, which was then compared with the measured values.

[0080] The model's mean absolute percentage error (MAPE) was 8.64%, mean absolute error (MAE) was 3.95°, root mean square error (RMSE) was 5.89°, and the fluctuation error was controlled within 6°, indicating good accuracy. This shows that the model's prediction results are generally consistent with the measured values ​​and meet the engineering verification standard (≤10%).

[0081] FPGAs offer advantages such as strong parallel computing capabilities, low latency, and low power consumption, making them more suitable for embedding into control systems at drilling sites. To verify the real-time performance of the established prediction model at the drilling site, this paper ports the optimized prediction model to an FPGA platform. It simulates parameters such as motor speed, motor angle, and drill string length during drilling, predicting the torsional amplitude of the toolface angle in real time, providing crucial reference for downhole trajectory control. This paper develops an FPGA-based toolface prediction system, mainly composed of a UART receiving module, a data processing module, a polynomial calculation module, a UART transmitting module, and a top-level control module, forming a complete closed-loop process of "serial input - data parsing - parallel computing - result output".

[0082] The tool face prediction system successfully implemented polynomial computation under a parallel pipeline architecture and can output the tool face angle magnitude with low latency. Comparative test results show that the FPGA calculation results are highly consistent with the experimental measured values. Figure 18 This verified the accuracy of the model's predictions.

[0083] This invention systematically explores the prediction and optimization of the tool face angle of a drill string torsion system. Through orthogonal experiments and range analysis, the order of the main controlling factors affecting the minimum amplitude of the tool face angle was clarified: the motor rotation angle is the primary influencing parameter, followed by the drill string length and motor speed. Compared with complex interactive or quadratic models, although the fitting degree can be improved, the linear regression model based on the response surface methodology achieves the best balance between fitting accuracy and prediction reliability. The residual and variance analysis results further verify the rationality of the prediction model established in this paper. The prediction model was deployed on an FPGA real-time prediction system, demonstrating good stability and computational efficiency, exploring the feasibility and engineering value of the proposed method in field prediction.

[0084] This invention reveals the influence mechanism of key drilling parameters on the dynamic characteristics of toolface angles and proposes a simple, highly interpretable, and real-time deployable toolface prediction method, providing effective theoretical support and technical reference for efficient toolface control in torsion drilling systems. The next step will be to verify the applicability and stability of the prediction model under complex downhole conditions using field data.

[0085] The method and system for predicting the tool face angle of a drill string torsional yaw system based on response surface methodology incorporates the moment of inertia into the initial parameter set. This parameter is not directly measured but rather obtained through professional inversion calculations using relevant dynamic data collected under the no-load operating state of the top drive system. This ensures a complete initial parameter system encompassing five key influencing factors: sampling interval, motor speed, maximum motor rotation angle, drill string length, and moment of inertia. This completely overcomes the shortcoming of existing technologies where missing parameters prevent models from accurately reflecting the system's dynamic response. Furthermore, the method employs orthogonal experimental design to construct multiple operating conditions, combines range analysis to clarify the significance ranking of each parameter's influence, and then constructs multiple prediction models using a specific response surface design method. The optimal fitting scheme is selected through system significance testing and residual analysis, ensuring that the model can fully adapt to the parameter coupling characteristics under complex operating conditions, significantly improving the accuracy and reliability of the tool face angle prediction results.

[0086] This invention effectively solves the problems of insufficient model adaptability and slow prediction response speed in existing technologies through modular collaborative design and optimized hardware deployment. The system consists of six functionally defined units, each of which achieves efficient bidirectional interaction with an industrial Ethernet bus via a high-speed data transmission interface. This forms a closed-loop operation mechanism covering the entire process from parameter acquisition, experimental control, data processing to model construction, hardware deployment, and result output, ensuring smooth connection between each link and stable data transmission. The model deployment unit innovatively migrates the optimal prediction model to a dedicated hardware platform, building a pipelined parallel computing architecture that significantly improves computational efficiency. This allows the prediction response speed to meet the real-time control requirements of the field, completely changing the poor adaptability and lag in response of traditional technologies due to reliance on single model fitting and conventional computing platforms. The overall stability and efficiency of the system provide continuous and reliable technical support for the dynamic optimization of parameters and precise control of drilling trajectory in the drill string torsion system, powerfully promoting a dual improvement in oil and gas drilling operation efficiency and wellbore trajectory conformity.

[0087] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," "link," and "fix" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0088] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various equivalent changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for predicting the tool face angle of a drill string torsional pendulum system based on response surface methodology, characterized in that, Includes the following steps: S1. Initial parameters are selected, including sampling interval, motor speed, maximum motor angle, drill string length, and moment of inertia. The moment of inertia is obtained by inverting the dynamic equations using electromagnetic torque, angular velocity, and frictional torque data collected under no-load operation of the top drive system. S2. A horizontal drill string torsional oscillation experimental platform is constructed, comprising a servo motor, a simulated drill string, a universal joint, a magnetic powder brake, and multi-parameter wireless sensors. The servo motor's operation is controlled by a controller. S3. Different levels of each initial parameter are set, and multiple experimental conditions are constructed using orthogonal experimental design. Under each condition, the servo motor drives the simulated drill string to complete at least 10 cycles. During the complete torsional cycle, acceleration component data of the simulated drill string perpendicular to the wellbore axis are synchronously acquired; S4, the acquired acceleration component data are processed to synthesize tool face angle related parameters, and the significance ranking of the influence of each initial parameter on the minimum amplitude of the tool face angle is determined by range analysis; S5, based on the Box-Behnken design in response surface methodology, a tool face angle prediction model is constructed by combining experimental data, and the significance of model terms is tested by variance analysis to select the best-fit model; S6, the optimized prediction model is deployed to the FPGA platform, and the real-time acquired initial parameter data is received through the serial port, and the tool face angle prediction result is output through parallel computation. The response surface methodology employs a linear model: ,in, This represents the minimum amplitude of the tool face angle. For constant terms, , , These are the coefficients of the first-order terms corresponding to motor speed, maximum motor rotation angle, drill string length, and moment of inertia, respectively. For the servo motor output speed, This is the maximum rotation angle of the motor. The length of the drill string. It is the moment of inertia; S5 includes the following steps: S51, based on the Box-Behnken design principle, five initial parameters are used as design variables, and the minimum amplitude of the tool facet angle is used as the response value to construct an experimental design matrix; S52, linear, interactive, and quadratic models are established respectively, and experimental data are substituted into each model for fitting calculation; S53, the significance of each model term is tested through analysis of variance, and the coefficient of determination is compared and analyzed with the predicted coefficient of determination; S54, combined with the residual analysis results, the model with the optimal balance between fitting accuracy and generalization ability is selected as the final prediction model.

2. The method for predicting the tool face angle of a drill string torsion system based on response surface methodology according to claim 1, characterized in that, The moment of inertia is calculated using the following model: ,in, The total equivalent moment of inertia of the system, To provide electromagnetic torque for the frequency converter output. This refers to the frictional torque during the motor's rotation. The viscous damping coefficient is... Let be the system angular velocity. This represents the system's angular acceleration.

3. The method for predicting the tool face angle of a drill string torsion system based on response surface methodology according to claim 1, characterized in that, The range analysis uses the following model: ,in, For the first The range of each factor For the first The factor in the first The average of the experimental results at each level. For the first The factor in the first The sum of experimental results at each level The number of times each level appears.

4. The method for predicting the tool face angle of a drill string torsion system based on response surface methodology according to claim 1, characterized in that, The adjusted coefficient of determination in the analysis of variance is calculated using the following model: ,in, To adjust the coefficient of determination, For the sum of squared residuals, For the total sum of squares, For the experimental sample size, The number of independent variables.

5. The method for predicting the tool face angle of a drill string torsion pendulum system based on response surface methodology according to claim 1, characterized in that, The accuracy of the model is evaluated using the mean absolute percentage error model. ,in, The mean absolute percentage error, These are measured values. For predicted values, This represents the number of samples.

6. The method for predicting the tool face angle of a drill string torsional pendulum system based on response surface methodology according to claim 1, characterized in that, S3 includes the following steps: S31, establishing a connection between the controller and the computer via a wireless local area network, and measuring the output speed and torque of the servo motor using the control program when the simulated drill string is not connected; S32, connecting the components of the experimental platform, adjusting the servo motor and the axis of the simulated wellbore drill string to be coaxial, so that the servo motor and the universal joint are on the same horizontal axis; S33, setting the horizontal combination of each initial parameter through the program, controlling the servo motor to drive the simulated drill string to reciprocate to release residual torque; S34, setting the output parameters to make the drill string continuously reciprocate, recording the output torque, speed and sensor signals, repeating each set of parameters 15 times and storing the data.

7. The method for predicting the tool face angle of a drill string torsional pendulum system based on response surface methodology according to claim 1, characterized in that, The S4 includes the following sub-steps: S41, screening the collected raw acceleration component data and removing abnormal fluctuation data points; S42, Based on the minimum amplitude of the tool face angle synthesized from the filtered data, establish the mapping relationship between each experimental condition and the corresponding minimum amplitude of the tool face angle; S43, calculate the average value of the minimum amplitude of the tool face angle at each level of each initial parameter, and determine the sum of experimental results corresponding to each parameter level; S44, solve for the range value of each initial parameter according to the range calculation formula, and determine the order of influence significance based on the size of the range value.

8. A tool face angle prediction system for a drill string torsional pendulum system based on response surface methodology, characterized in that, This system is applied to the tool face angle prediction method for a drill string torsional pendulum system based on the response surface methodology as described in claim 1. It includes: a multi-source parameter acquisition and moment of inertia inversion calculation unit, a multi-condition collaborative control unit for the experimental platform, an acceleration data synthesis and range analysis processing unit, a response surface methodology multi-model construction and optimal selection unit, an FPGA platform model porting and parallel computing architecture construction unit, and a real-time parameter receiving and prediction result output unit. The multi-source parameter acquisition and moment of inertia inversion calculation unit acquires measured parameters such as sampling interval, motor speed, maximum motor rotation angle, and drill string length through a distributed wireless sensor network. The system simultaneously acquires electromagnetic torque, angular velocity, and frictional torque data during the no-load operation of the top drive system. A dynamic inversion algorithm is used to calculate the moment of inertia. All initial parameters are sent to the multi-condition collaborative control unit of the experimental bench via a high-speed data transmission interface. Upon receiving the parameters, the multi-condition collaborative control unit uses a programmable logic controller to regulate the start / stop, speed, and angle of the servo motor, driving the simulated drill string to complete torsional gyratory motion according to the orthogonal experimental design's combination of operating conditions. Simultaneously, it controls multi-parameter sensors to collect acceleration component data perpendicular to the wellbore axis and transmits it to the acceleration data synthesis and range analysis center. The acceleration data processing unit filters the received acceleration data and synthesizes characteristic parameters to generate tool face angle minimum amplitude data. It then uses a range calculation algorithm to determine the significance ranking of each initial parameter's influence and transmits the processed data and ranking results to the response surface methodology multi-model construction and optimal selection unit. This unit constructs an experimental matrix based on the Box-Behnken design principle, substitutes the data to complete linear, interactive, and quadratic model fitting, and uses variance and residual analysis to select the optimal model. The model parameters are then sent to the FPGA platform model porting and parallel computing architecture building unit. This unit converts the optimal model into hardware executable code, builds a pipelined parallel computing architecture, completes model deployment, and establishes data interaction with the real-time parameter receiving and prediction result output unit. The real-time parameter receiving and prediction result output unit receives the initial parameters collected in real-time on-site via a serial communication module, transmits them to the FPGA platform, and generates tool face angle prediction results through parallel computing. These results are then output through a visualization interface. All units communicate bidirectionally via an industrial Ethernet bus for data transmission and command interaction.

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