Ultrasonic scanning robot arm temperature drift compensation and precision calibration method

Abstract

The application discloses a kind of ultrasonic scanning mechanical arm temperature drift compensation and precision calibration method, it is related to temperature drift compensation technical field;Through multidimensional temperature field monitoring, data is collected to construct three-dimensional model using fiber grating and digital sensor.Establish the temperature-deformation mapping model of time-varying thermal resistance network, combined with finite element analysis;Adopt double time scale dynamic error compensation algorithm, and compensation instruction is transmitted through EtherCAT bus;Introduce the adaptive Kalman filter calibration of quantum particle swarm optimization, improve convergence speed and precision.The application improves the positioning accuracy of mechanical arm, temperature mutation response shortens, carbon fiber component thermal deformation reduces, self-learning calibration shortens time, provides high-precision scheme for nondestructive testing.

Description

Technical Field

[0001] This invention relates to the field of temperature drift compensation technology, and in particular to a method for temperature drift compensation and accuracy calibration of an ultrasonic scanning robotic arm. Background Technology

[0002] In the field of industrial non-destructive testing, the temperature drift problem of ultrasonic scanning robotic arms seriously affects the detection accuracy. During operation, traditional robotic arms experience thermal deformation of structural components due to joint motor heating and ambient temperature fluctuations. This causes positioning deviations in the end effector and displacement of the ultrasonic transducer, resulting in image distortion. Current temperature monitoring methods mostly employ single-point temperature measurement, which cannot capture temperature gradient changes in various components of the robotic arm. Especially in components like ultrasonic transducers where localized heat generation is significant, sudden temperature changes are often overlooked, leading to compensation lag.

[0003] Existing temperature-deformation models are mostly based on the assumption of linear thermal expansion, failing to consider the nonlinear characteristics and anisotropy of materials. The coefficients of thermal expansion of novel materials such as carbon fiber composites vary significantly across different temperature ranges, making it difficult for traditional models to accurately predict deformation, resulting in large positioning errors for robotic arms in wide-temperature environments. Furthermore, uneven temperature distribution along the ultrasonic wave propagation path leads to variations in sound velocity; traditional methods do not dynamically correct for the propagation trajectory, making it difficult to guarantee imaging resolution and defect detection rates.

[0004] In terms of dynamic error compensation, traditional algorithms have slow response speeds and cannot adapt to rapid temperature changes. When the robotic arm works continuously or the ambient temperature changes abruptly, static compensation parameters become invalid, requiring frequent shutdowns for calibration, which affects detection efficiency. Sensor data fusion accuracy is insufficient; errors from a single encoder or IMU module accumulate significantly under temperature influences, and multi-sensor collaborative calibration mechanisms lack adaptive capabilities, making it difficult to meet the requirements of high-precision detection. Summary of the Invention

[0005] The present invention proposes a method for temperature drift compensation and accuracy calibration of ultrasonic scanning robotic arms to solve the problems mentioned in the prior art.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: a method for temperature drift compensation and accuracy calibration of an ultrasonic scanning robotic arm, comprising: Real-time temperature field monitoring steps: Fiber Bragg grating sensors and digital temperature sensors are installed on the housing of the robotic arm joint drive motor, the ultrasonic transducer base, and the transmission screw nut pair, respectively. Temperature data from both types of sensors are collected simultaneously, and the data is fused using a Kalman filter algorithm. Based on the fused data, a three-dimensional temperature field model including spatial location and temporal variables is constructed to reflect the temperature distribution of each component of the robotic arm at different times in real time. When the temperature change rate at any monitoring point exceeds 0.5℃ / min, the subsequent compensation process is automatically triggered, providing accurate temperature baseline data for subsequent temperature-deformation mapping and error compensation. False trigger prevention is based on a three-layer verification principle: First, multi-sensor cross-verification (abnormalities are eliminated when the deviation exceeds ±0.3℃), combined with sliding filtering (5 sampling periods), reduces data fluctuation from ±0.5℃ to ±0.1℃, lowering the false judgment rate to below 5%; second, by calculating the average change rate over 1 second, false judgments are reduced from 30 to 1, and a 0.1℃ absolute value threshold is added to avoid 25 noise-induced false triggers; third, a second verification is performed 3 seconds after triggering, reducing invalid compensation by 20%. The temperature-deformation mapping model construction steps are as follows: Based on the three-dimensional temperature field model, a thermal-structural coupling analysis model of the robotic arm is established using finite element analysis software. By simulating the thermal effect of temperature on the structure, the correlation between temperature and deformation is established. The change in mode amplitude is measured by strain gauges attached to the surface of the connecting rod. The calculation method is to divide the difference between the high temperature amplitude and the room temperature amplitude by the room temperature amplitude and then multiply by 100%. The measured increase is 15%. The temperature field data is transformed into quantifiable deformation, which solves the problem that traditional linear models cannot reflect the nonlinear characteristics of materials and provides an accurate deformation prediction basis for dynamic error compensation. The dynamic error compensation algorithm execution steps are as follows: The programming logic controller receives the three-dimensional temperature field model data and temperature-deformation mapping model parameters, and calculates the position error of each joint caused by temperature changes in real time; for rotary joints, the angle compensation amount is converted into the pulse correction amount of the servo motor; for linear axes, the linear compensation amount is converted into the feedback correction value of the grating ruler. The purpose of these two types of conversion is to transform the abstract deformation into the control signal that the actuator can recognize; all compensation commands are synchronously transmitted to the servo driver of each axis through the EtherCAT bus to update the target position of the motion control card; a dual time scale compensation mechanism is adopted, which adapts different compensation frequencies according to the temperature change rate. When the temperature change rate is greater than 1℃ / min, 100Hz high-frequency compensation is started based on the real-time temperature field data; when the temperature change rate is less than or equal to 1℃ / min, the long short-term memory neural network is enabled to perform 1Hz low-frequency compensation.

[0007] Furthermore, it also includes: Adaptive Kalman filter calibration steps: A laser displacement sensor is installed on the end effector of the robotic arm to measure the deviation between the actual and theoretical positions of the end effector in real time; the joint position after dynamic error compensation is used as the state vector, including the three-dimensional spatial coordinates of the end effector and the attitude angles in three rotational directions, to construct the system state equation and observation equation. The state equation describes the natural change of the joint position over time, and the observation equation correlates the state vector with the sensor's measured data. Together, they form the mathematical basis for calibration; a quantum particle swarm optimization algorithm is introduced to optimize the noise covariance matrix of the Kalman filter. A specific population size and number of iterations are set, and the filtering accuracy is improved by minimizing the mean square value of the position prediction error. The Kalman filter algorithm's data fusion process involves establishing a state equation describing the dynamic changes in temperature. The current temperature estimate is the superposition of the previous temperature estimate and process noise. The observation equation represents the observation vector, which is the superposition of measurements from two types of sensors and observation noise. Dynamic correction is achieved through iterative updates of the error covariance matrix. The current error covariance matrix is ​​equal to the identity matrix minus the product of the gain matrix and the observation matrix, and then multiplied by the error covariance matrix from the previous time step to quantify the change in estimation error. The gain matrix is ​​calculated from the error covariance matrix from the previous time step, the transpose of the observation matrix, and the observation noise covariance matrix, balancing the weights of the predicted and observed values.

[0008] Furthermore, the modal analysis operation in the construction of the temperature-deformation mapping model involves attaching foil strain gauges to the surface of the aluminum alloy connecting rod of the robotic arm, collecting vibration signals at different temperatures using a dynamic signal analyzer, converting the mechanical vibration into electrical signals, and extracting the frequency characteristics. The nonlinear correction parameters are obtained by fitting nine sets of temperature-deformation data. The deformation of the connecting rod is measured after each set of data has been stable for 30 minutes. The fitted mapping relationship reflects the nonlinear deformation characteristics in the range of 20℃ to 60℃, providing a deformation prediction basis for dynamic error compensation.

[0009] Furthermore, the dual-timescale compensation mechanism is implemented as follows: In high-frequency compensation mode, the temperature change in the next 300ms is predicted based on the Kalman filter algorithm, and instructions are issued through the EtherCAT bus to offset the system's delayed response to temperature abrupt changes using the prediction lead; In low-frequency compensation mode, the input layer of the long short-term memory neural network includes 17-dimensional features, the current temperature value, the rate of temperature change, and 15 temperature data points collected at 2-minute intervals within the past 30 minutes. The hidden layer consists of 3 layers with 64 neurons each, and the tanh activation function is used to capture the time-dependent features of temperature changes. The output layer is a 6-dimensional vector corresponding to the compensation coefficients of 6 joints. Prediction is achieved by mining patterns in historical data through deep learning, providing stable compensation when the temperature changes slowly.

[0010] Furthermore, in the adaptive Kalman filter calibration, the three-dimensional spatial coordinates of the state vector correspond to the positions of the robotic arm's end effector along the x-axis from the base to the end effector extension direction, the y-axis (horizontal direction perpendicular to the x-axis), and the z-axis (vertical direction). The three rotation angles correspond to the attitude deflections around the x-axis, y-axis, and z-axis, respectively, describing the pose state of the end effector. The state transition matrix is ​​determined based on the forward kinematics of the robotic arm. The control input matrix correlates the conversion relationship between servo motor pulses and joint movements, linking control commands with pose changes. In the quantum particle swarm optimization algorithm, the contraction and expansion coefficients are linearly reduced from 0.7 to 0.4. Particle position updates are combined with quantum probability distributions to achieve global optimization. The optimal parameters are found through the swarm algorithm, improving the adaptability of the noise covariance matrix. After calibration, the optimized parameters are fed back to the temperature-deformation mapping model to achieve dynamic optimization and compensation accuracy of the model.

[0011] Furthermore, it also includes: Sensor data fusion calibration steps: An inertial measurement unit (IMU) consisting of a gyroscope, accelerometer, and encoder is deployed at each joint of the robotic arm. The gyroscope measures the angular velocity of the joint around the x, y, and z axes, and the angle value is obtained by integration. The encoder directly measures the joint angle. The role of the two types of sensors is to obtain angle information from different dimensions. A complementary filtering algorithm is used to fuse the two types of angle data, taking advantage of the dynamic response of the gyroscope and the static accuracy of the encoder to improve the overall accuracy of angle measurement. When the IMU detects a vibration frequency exceeding 50Hz and an amplitude greater than 0.1g, it is determined to be abnormal vibration and the proportional, integral, and derivative parameters of the servo driver are automatically adjusted to suppress resonance.

[0012] The ultrasonic propagation path temperature correction steps are as follows: An array of temperature sensors is arranged in the scanning area to collect the temperature distribution along the ultrasonic propagation path in real time, obtaining temperature gradient information along the path; based on the relationship between sound speed and temperature, the sound speed at 20℃ (343 m / s) is used as a reference. The actual sound speed is calculated by multiplying the square root of the ratio of the current absolute temperature to the reference absolute temperature by the reference sound speed, thus calculating the sound speed at different temperatures; the echo time correction is the difference between the propagation time corresponding to the actual sound speed and the propagation time corresponding to the reference sound speed at the same propagation distance, quantifying the influence of temperature on propagation time; the ray difference method is used to iteratively solve the acoustic ray equation until the change in propagation time is less than 0.1 microseconds, at which point the iteration stops, and the propagation trajectory of the sound wave in the non-uniform medium is solved numerically.

[0013] Thermal balance control steps: A semiconductor cooling chip is built into the base of the robotic arm. It automatically starts when the joint motor temperature exceeds 50℃. The cooling power is calculated based on the difference between the current temperature and the set temperature of 40℃, with a proportionality coefficient of 2 watts / ℃. For every 1℃ increase in temperature above the set temperature, the cooling power increases by 2 watts. The ultrasonic transducer base is designed with a circulating water cooling channel. The coolant flow rate is proportional to the temperature change rate. When the change rate is 1℃ / min, the flow rate is 10mL / min, and when the change rate is 2℃ / min, the flow rate increases to 20mL / min. At the same time, the phase change material absorbs heat, and the heat dissipation capacity is dynamically adjusted to adapt to temperature changes and stabilize the transducer temperature. The temperature fluctuation of each component of the robotic arm is controlled within ±1℃. When the ambient temperature is below 5℃, the system automatically switches to heating mode to provide a stable temperature reference for the temperature-deformation mapping model and reduce model errors caused by drastic temperature fluctuations.

[0014] Furthermore, it also includes: Dynamic reference point calibration steps: Three optical positioning markers distributed in a triangle are set at the edge of the scanning area. After the robotic arm completes 10 scanning cycles, it automatically moves to the marker position. The industrial camera on the end effector captures the marker image, identifies the pixel coordinates of the marker center and converts them into actual spatial coordinates to obtain the actual position of the reference point. The deviation between the actual coordinates and the theoretical coordinates of the marker in the x, y, and z directions is calculated. The least squares method is used to fit the deviation and the corresponding temperature data into a calibration function in the form of a quadratic polynomial. The correlation between the deviation and temperature is established through mathematical fitting to quantify the influence of temperature on the position of the reference point.

[0015] Material nonlinear thermal property compensation steps: For carbon fiber composite connecting rods, a segmented thermal expansion model is established, using a 0.5×10⁻⁻⁶ thermal expansion coefficient in the temperature range of -20℃ to 20℃. 6 The coefficient of thermal expansion is 1.2 × 10⁻⁻⁶ °C in the range of 20 °C to 60 °C. 6 The coefficient of thermal expansion at / ℃ is used to calculate deformation by real-time temperature detection using a temperature sensor and automatically switching the corresponding coefficient. The temperature dependence of carbon fiber's thermal expansion characteristics predicts deformation in different temperature ranges. By uniformly doping 1% carbon nanotubes into the carbon fiber resin matrix, the thermal conductivity and structural reinforcement properties are utilized to reduce the overall coefficient of thermal expansion of the composite material to 0.1×10⁻⁻⁶. 6 Below / ℃, the results are fed back to the temperature-deformation mapping model to optimize the nonlinear correction parameters, which, together with the temperature-deformation mapping model construction steps, improves the compensation accuracy of carbon fiber components.

[0016] Compared with existing technologies, the beneficial effects of this invention are: Multi-sensor fusion monitoring enables sub-micron level thermal strain capture, and the three-dimensional temperature field model updates compensation parameters in real time, significantly reducing end-point positioning error and providing a practical improvement over traditional methods. The dynamic error compensation algorithm, combined with Kalman filtering and quantum optimization, shortens the response time to 45 seconds during temperature abrupt changes, ensuring stable accuracy in high-speed scanning.

[0017] Material nonlinearity compensation and phase change heat dissipation structure design reduce thermal deformation of carbon fiber components by 90% and cooling energy consumption by 40%. A sound ray tracking algorithm for ultrasonic propagation paths corrects the sound velocity distribution, improving imaging resolution from 0.5mm to 0.3mm and achieving a defect detection rate of 95%. Information entropy-based scanning trajectory optimization improves scanning efficiency under complex temperature fields by 40%, with a false negative rate of less than 1% in critical areas.

[0018] Self-learning calibration and a meta-learning framework enable intelligent parameter optimization, reducing initial calibration time by 70% and maintaining long-term operational accuracy at ±0.05mm. Microwave interferometry online verification technology allows for real-time calibration without downtime, reducing annual downtime losses in industrial applications. This proposed method comprehensively addresses the technical bottlenecks of traditional robotic arms in temperature drift compensation and accuracy calibration, providing reliable hardware support for high-end nondestructive testing. Attached Figure Description

[0019] Figure 1 This is a schematic block diagram of the temperature drift compensation and accuracy calibration method for the ultrasonic scanning robotic arm proposed in this invention. Figure 2 This is a schematic diagram of the temperature field prediction model error for the temperature drift compensation and accuracy calibration method of the ultrasonic scanning robotic arm proposed in this invention. Figure 3 This is a schematic diagram illustrating the material thermal property compensation effect of the temperature drift compensation and accuracy calibration method for the ultrasonic scanning robotic arm proposed in this invention. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," and "counterclockwise," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0022] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first" and "second" may explicitly or implicitly include one or more of the stated features. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified. Furthermore, the terms "installed," "connected," and "linked" should be interpreted broadly; for example, they may refer to a fixed connection, a detachable connection, or an integral connection; they may refer to a mechanical connection or an electrical connection; they may refer to a direct connection or an indirect connection through an intermediate medium; and they may refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances. The invention will now be described in further detail with reference to the accompanying drawings.

[0023] Reference Figures 1 to 3 Detailed Implementation of a Temperature Drift Compensation and Accuracy Calibration Method for an Ultrasonic Scanning Robotic Arm I. Specific Implementation of Real-time Temperature Field Monitoring Procedures Inside the heat sink fins of the robotic arm joint drive motor housing, a digital temperature sensor is fixed using thermally conductive silicone. The sensor is embedded 0.5 mm into the heat sink fins to ensure close contact with the motor housing and obtain accurate temperature readings. A miniature digital temperature sensor is attached 5 mm below the ultrasonic transducer base using thermally conductive silver adhesive to reduce thermal resistance. A 4 mm blind hole is made on the outer side of the ball bearing circulation channel of the transmission screw nut pair, filled with thermally conductive epoxy resin, and then a digital temperature sensor is installed to avoid interference from ball bearing movement. Simultaneously, a miniature fiber Bragg grating sensor is integrated inside the transducer base. Utilizing the characteristic that light wavelength changes with temperature, thermal strain monitoring is achieved, and the optical signal is converted into temperature data using a wavelength demodulator.

[0024] All sensors are connected to the programmable logic controller via the Modbus RTU protocol, synchronously acquiring data every 50 milliseconds. A Kalman filter algorithm is used to fuse data from the fiber Bragg grating sensor and the digital temperature sensor. The specific process is as follows: establishing the state equation T...k =T k ₋1+w k T k Let T be the estimated temperature at time k. k ₋1 represents the estimated temperature at time k-1, w k For process noise; observation equation Z k =[TFBG;TDS18B20]+v k Z k Here, TFBG represents the temperature measurement from the fiber Bragg grating sensor, and TDS18B20 represents the measurement from the digital temperature sensor. k For observation noise, the process noise variance is set to Q = 0.01 (Q is the process noise covariance), the observation noise variance matrix is ​​set to R = [[0.02,0],[0,0.5]] (R is the observation noise covariance, 0.02 corresponds to the fiber Bragg grating sensor noise, and 0.5 corresponds to the digital temperature sensor noise), and the observation matrix is ​​set to H = [1;1] (H is the observation matrix). The gain matrix K is then used to determine the noise level. k =P k ₋1Hᵀ(HP k ₋1Hᵀ+R)⁻¹Recursively update the temperature estimate, where P k Let P be the error covariance matrix, and P be the error covariance matrix. k =(IK k H)P k ₋1 (I is the identity matrix). The accuracy of the fused data reaches ±0.03℃, which is used to construct a three-dimensional temperature field model T(x,y,z,t), where x is the horizontal coordinate of the robotic arm base to the end effector, y is the horizontal coordinate perpendicular to x, z is the vertical coordinate, and t is the time variable. This model can reflect the temperature distribution of each component at different spatial locations and times in real time. When the temperature change rate at any monitoring point exceeds 0.5℃ / min, the system automatically triggers the compensation mechanism, providing accurate temperature baseline data for subsequent temperature-deformation mapping and error compensation. This step is the "sensing layer" of the entire compensation system, which solves the limitations of single-point temperature measurement through multi-sensor fusion, ensuring the comprehensiveness and accuracy of temperature data.

[0025] To avoid false triggering, one approach is to verify the validity of sensor data. Cross-validation is performed using a fiber Bragg grating sensor and a digital temperature sensor, with a deviation threshold of ±0.3℃. When the deviation exceeds the threshold, abnormal data is discarded (e.g., all 15 instances of FBG vibration interference in 100 operating conditions were corrected). Simultaneously, a sliding window filter with 5 sampling periods (50ms / period) is used to compress data fluctuations from ±0.5℃ to ±0.1℃, effectively filtering instantaneous pulse interference and reducing the false positive rate to below 5%.

[0026] Second, the calculation of temperature change rate was optimized. The instantaneous change rate was changed to the average change rate of 20 samples within 1 second. In a 1-hour monitoring experiment, the number of misjudgments was reduced from 30 times in the traditional method to 1 time. At the same time, a threshold of 0.1℃ absolute value of temperature change was set, and the noise interference of "high change rate but small temperature difference" in 25 out of 100 data sets did not trigger compensation.

[0027] Third, secondary verification after triggering. After the first trigger, a 3-second trend confirmation is performed. In 100 simulation experiments, 20 cases of temperature trend reversal or stabilization were judged as false triggers and compensation was terminated, reducing invalid operations by 20%.

[0028] Through the coordinated efforts of three layers, timely response to real temperature changes is ensured, while data filtering and trend verification prevent false triggering caused by various interferences.

[0029] II. Specific Implementation of the Temperature-Deformation Mapping Model Construction Steps Based on the three-dimensional temperature field model T(x,y,z,t), a thermo-structural coupling model of the robotic arm was established using ANSYS. For the aluminum alloy connecting rod, mesh generation was first performed using tetrahedral elements, with mesh refinement at joint connections and stress concentration areas to ensure computational accuracy. A reference temperature of 20℃ was set, and nine temperature gradients (20℃, 25℃, 30℃, 35℃, 40℃, 45℃, 50℃, 55℃, 60℃) were set at 5℃ intervals within the range of 20℃ to 60℃. Static thermal analysis was performed under each temperature gradient: a convective heat transfer coefficient (valued at 10W / (m²・℃)) was applied to the surface of the joint motor to simulate natural heat dissipation; a heat generation rate (valued at 5W / m³) was applied to the surface of the ultrasonic transducer to simulate operational heat generation. The thermal stress distribution at each node of the connecting rod was obtained through thermal analysis.

[0030] Modal analysis was performed simultaneously, using the Lanczos method to extract the first 10 natural frequencies and mode shapes. Foil strain gauges (sensitivity coefficient 2.0, resistance 120Ω) were attached to the connecting rod surface. Vibration signals at different temperatures were collected using a dynamic signal analyzer to determine the effect of temperature on natural frequencies and mode shapes. Experimental results showed that when the temperature increased from 20℃ to 60℃, the first natural frequency decreased from 125Hz to 110Hz. The change in mode shape amplitude was calculated using the formula (high temperature amplitude - room temperature amplitude) / room temperature amplitude × 100%, yielding a result of 15%. Combining nine sets of temperature-deformation experimental data (each set of data was obtained by measuring the connecting rod deformation using a laser micrometer after 30 minutes of temperature stabilization), the least squares method was used to fit the nonlinear mapping relationship ΔL = α・L0・(T-T0) + β・L0・(T-T0)², where ΔL is the deformation and α is the linear thermal expansion coefficient (value 23.6 × 10⁻⁻⁻⁴). 6 / ℃), L0 is the initial length of the connecting rod, T is the current temperature, T0 is the reference temperature (value is 20℃), β is the nonlinear correction coefficient (value is 0.02×10⁻ 6 / ℃²). The role of this model is to transform temperature field data into quantifiable deformation, solving the problem that traditional linear models cannot reflect the nonlinear characteristics of materials, and providing accurate deformation prediction basis for dynamic error compensation. Its logical connection with the real-time temperature field monitoring step is that only based on accurate temperature distribution data can a temperature-deformation relationship that fits the reality be established, ensuring the accuracy of subsequent compensation.

[0031] III. Specific Implementation of the Dynamic Error Compensation Algorithm Execution Steps The programmable logic controller (PLC) receives real-time data from the three-dimensional temperature field model and parameters from the temperature-deformation mapping model, and calculates the position error of each joint in real time. For rotary joints, the angle compensation amount Δθ is converted into the number of servo motor pulses using the formula ΔP=Δθ・P0 / (2π), where P0 is the number of pulses per motor revolution (taken as 10000). For example, when Δθ=0.01rad, ΔP=0.01×10000 / (2π)≈1.59. The system rounds this to 2 pulses to ensure accurate correction of the motor rotation angle. For linear axes, the linear compensation amount ΔL is directly converted into the feedback correction value of the grating ruler. The grating ruler has a resolution of 0.001mm and can provide real-time feedback on the deviation between the actual position and the target position of the linear axis.

[0032] All compensation commands are transmitted to the servo drives of each axis via an EtherCAT bus with a transmission rate of 100Mbps to ensure command synchronization and a delay of ≤10ms. After receiving the command, the drive updates the target position register of the motion control card to achieve real-time compensation. A dual-timescale compensation mechanism is employed: when the temperature change rate is >1℃ / min, high-frequency compensation (100Hz) based on Kalman filtering is activated. This works by predicting the temperature change 300ms later (e.g., when the current temperature is 25℃ and the change rate is 1.5℃ / min, the predicted temperature is 25.075℃), calculating the compensation amount in advance to avoid error accumulation caused by sudden temperature changes. When the temperature change rate is ≤1℃ / min, a 1Hz low-frequency compensation is performed using an LSTM neural network. The input layer of this network includes 17-dimensional features (current temperature, temperature...). The dataset consists of 15 temperature data points sampled at 2-minute intervals over the past 30 minutes, with a rate of change and 3 hidden layers (each with 64 neurons and an activation function of tanh). The output layer predicts the compensation coefficients for 6 joints over the next 5 minutes. The training dataset includes 1000 temperature-deformation samples (each containing a 30-minute temperature sequence and the corresponding measured deformation value). The mean squared error is used as the loss function, and the Adam optimizer (initial learning rate 0.001, decaying by 0.95 every 50 epochs) is used for 200 epochs of training. The validation set has a mean squared error <0.005 mm².

[0033] The dual-timescale mechanism balances response speed and system load: high-frequency compensation quickly responds to temperature abrupt changes, while low-frequency compensation learns and optimizes parameters through historical data. Together, they ensure compensation accuracy under different temperature change scenarios. This step is logically related to the previous two steps as follows: based on real-time data from temperature field monitoring and the prediction results of the temperature-deformation model, abstract temperature changes are transformed into specific actuator control commands, representing a crucial link from "perception-modeling" to "execution."

[0034] To verify the compensation effect, positioning accuracy tests were conducted at different temperature ranges, and the data are shown in the table below: The data in the table shows that the positioning accuracy of this invention is significantly better than that of traditional methods across different temperature ranges, especially with a 60% improvement over a wide temperature range (-20-60℃). This is because the dynamic compensation algorithm can track temperature changes in real time and combine them with nonlinear model corrections, while traditional static compensation cannot adapt to dynamic temperature changes, and the uncompensated state results in excessive errors due to the accumulation of thermal deformation. This data directly demonstrates the core role of the dynamic error compensation step in improving the positioning accuracy of the robotic arm.

[0035] IV. Specific Implementation of Adaptive Kalman Filter Calibration Steps A laser displacement sensor (0.001 mm resolution) is installed on the end effector of the robotic arm to measure the distance deviation between the end effector and a standard plane, which serves as the calibration observation data. The state vector X = [x, y, z, θx, θy, θz] is constructed using the joint position after dynamic error compensation as the state vector, where x, y, and z are the Cartesian coordinate positions of the end effector, and θx, θy, and θz are the rotation angles about the x, y, and z axes, respectively. k =A・X k ₋1+B・W k , where X k Let X be the state vector at time k. k ₋1 is the state vector at time k-1, A is the state transition matrix (determined based on the forward kinematics of the robotic arm, including velocity parameters for uniform motion), B is the control input matrix (corresponding to motor pulses and joint motion), and W is the state transition matrix. k For process noise (reflecting interference such as transmission backlash); observation equation Z k =H・X k +V k Z k Let X be the observation vector of the laser sensor, H be the observation matrix (extracting the position parameters from X), and V be the observation vector. k This refers to observation noise (sensor measurement error).

[0036] A quantum particle swarm optimization algorithm is introduced to adjust the noise covariance matrices Q and R. With a population size of 20 and 50 iterations, the shrinkage / expansion coefficient linearly decreases from 0.7 to 0.4. The optimization objective is the mean squared error MSE = E[(X̂ k -X k )²](X̂ k X is the state estimate. k (where Q is the true value), where Q = α・I (α is the thermal diffusivity, with a value of 0.02; I is the identity matrix), and R = 0.01・I. When the error variance of 5 consecutive iterations is <0.01mm², the calibration is considered complete, and the optimized parameters (such as the corrected α and β) are fed back to the temperature-deformation mapping model to achieve model iteration.

[0037] The principle behind this step is to reduce pose error through the "prediction-correction" mechanism of Kalman filtering, and to improve the adaptability of filter parameters by combining quantum particle swarm optimization. Its function is to perform a secondary calibration of the dynamic error compensation results, ensuring long-term operational accuracy. Its logical connection with the dynamic error compensation step is as follows: model errors may still exist after dynamic compensation; by optimizing model parameters through calibration feedback, a closed loop of "compensation-calibration-recompensation" is formed, improving system robustness.

[0038] V. Specific Implementation of Sensor Data Fusion Calibration Steps An IMU module (including a gyroscope, accelerometer, and encoder) is deployed at each joint of the robotic arm. The gyroscope measures the angular velocity ω=[ωx,ωy,ωz] (ωx, ωy, ωz are the three-axis angular velocities), and calculates the angle θg=∫ωdt by integration. The encoder directly measures the joint angle θe. A complementary filtering algorithm is used to fuse the angle θf=α・θg+(1-α)・θe, where α is the filtering coefficient (value 0.98). This leverages the fast dynamic response of the gyroscope and the high static accuracy of the encoder to improve the angle measurement accuracy. When the IMU detects a vibration frequency >50Hz and an amplitude >0.1g, the system determines it as abnormal vibration and automatically adjusts the servo driver PID parameters (proportional gain reduced by 30%, integral time increased by 50%) to suppress resonance.

[0039] The principle of this step is to complement data from multiple sensors to compensate for the cumulative error of a single sensor under the influence of temperature. Its function is to provide a more accurate angle input for dynamic error compensation. It works in conjunction with the temperature field monitoring step: temperature changes may cause encoder drift, which can be corrected by IMU fusion to ensure the reliability of angle data.

[0040] VI. Specific Implementation of Ultrasonic Propagation Path Temperature Correction Steps A 3×3 array of miniature temperature sensors (50 mm spacing) was arranged in the scanning area to measure the temperature distribution Tpath along the ultrasonic wave propagation path. Based on the sound speed-temperature relationship v = v0・√(T / T0), where v is the current sound speed, v0 is the reference sound speed (valued at 343 m / s), T is the absolute temperature, and T0 is the reference absolute temperature (valued at 293.15 K), the echo time correction Δt = (L / vL / v0) (where L is the propagation distance) was calculated. The ray difference method was used to iteratively solve the ray equation d²r / ds² = (1 / v)・∇v (where r is the ray position vector, s is the ray length, and ∇v is the sound speed gradient) until the propagation time change was <0.1 μs.

[0041] The principle behind this step is the physical property of sound speed varying with temperature. Its function is to correct the effect of temperature on ultrasonic wave propagation, improving imaging accuracy. The logical connection with the temperature field monitoring step is that it uses temperature field data to calculate the sound speed distribution, ensuring the accuracy of the propagation path correction. Test data shows that in an environment with a temperature gradient of 5℃ / cm, the corrected imaging resolution improved from 0.5mm to 0.3mm, verifying the effectiveness of this step.

[0042] VII. Specific Implementation of Thermal Balance Control Steps A semiconductor cooling chip is built into the base of the robotic arm. It starts when the joint motor temperature is >50℃, and the cooling power is P=2W / ℃・(T-40℃) (T is the current temperature). For example, P=20W when the temperature is 50℃. The transducer base is designed with a circulating water cooling channel. The flow rate of the coolant is proportional to the rate of temperature change (the flow rate is 10mL / min when the rate of change is 1℃ / min). Combined with phase change material (paraffin, phase change temperature 40℃) to absorb heat, the temperature fluctuation of the components is ≤±1℃. When the ambient temperature is <5℃, it automatically heats up to maintain the working temperature at 20±2℃.

[0043] The principle of this step is active temperature control combined with phase change thermal storage. Its function is to provide a stable reference temperature for the temperature-deformation model, reduce model errors caused by drastic temperature fluctuations, and work in conjunction with the temperature field monitoring step to maintain a stable temperature environment. Tests show that the cooling energy consumption is reduced by 40% compared with traditional methods.

[0044] VIII. Specific Implementation of Dynamic Reference Point Calibration Procedures Three optical markers (distributed in a triangle) are set at the edge of the scanning area. After every 10 scanning cycles, the industrial camera identifies the center of the markers, converts them into spatial coordinates, and calculates the deviations Δx, Δy, and Δz from the theoretical coordinates. The least squares method is used to fit the calibration function f(T) = a0 + a1・T + a2・T² (where a0, a1, and a2 are fitting coefficients), and the motion control algorithm is integrated to correct the target position in real time. Each calibration takes less than 1.5 minutes, ensuring a long-term positioning accuracy of ±0.03mm.

[0045] The principle behind this step is to dynamically correct system errors using a reference point. This compensates for the accuracy degradation caused by long-term operation of the robotic arm and, together with adaptive Kalman filter calibration, forms a dual calibration mechanism to improve system stability.

[0046] IX. Specific Implementation of Material Nonlinear Thermal Property Compensation Steps For carbon fiber connecting rods, a segmented thermal expansion model is established: α1 = 0.5 × 10⁻ at -20 to -20℃. 6 / ℃, α2=1.2×10⁻ at 20-60℃ 6 / ℃, switching coefficient via temperature sensor; considering anisotropy, correction coefficient of 0.8 in the x-direction (fiber direction) and 1.2 in the y-direction; doping with 1% carbon nanotubes to achieve a thermal expansion coefficient ≤0.1×10⁻ 6 At 60℃, the deformation decreased from 0.12mm to 0.01mm, and the result was fed back to the temperature-deformation model to optimize the β value.

[0047] The principle behind this step is the temperature dependence and modification enhancement of material properties. Its function is to improve the compensation accuracy of carbon fiber components and, in conjunction with the temperature-deformation mapping model, solve the nonlinear problem of new materials. Tests show that thermal deformation is reduced by 90%.

[0048] All the above steps are closely related: temperature field monitoring provides basic data, mapping models establish the relationship between temperature and deformation, dynamic compensation converts deformation into control commands, and calibration and temperature control ensure the long-term reliability of the model and execution. Together, they achieve high-precision temperature drift compensation and calibration of the ultrasonic scanning robotic arm, providing technical support for industrial non-destructive testing.

[0049] The above are merely preferred embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for temperature drift compensation and accuracy calibration of an ultrasonic scanning robotic arm, characterized in that, include: Real-time temperature field monitoring steps: Fiber Bragg grating sensors and digital temperature sensors are installed on the housing of the robotic arm joint drive motor, the ultrasonic transducer base, and the transmission screw nut pair, respectively. Temperature data from both types of sensors are collected simultaneously, and the data is fused using a Kalman filter algorithm. Based on the fused data, a three-dimensional temperature field model including spatial location and temporal variables is constructed to reflect the temperature distribution of each component of the robotic arm at different times in real time. When the temperature change rate at any monitoring point exceeds a threshold, the subsequent compensation process is automatically triggered, providing basic temperature data for subsequent temperature-deformation mapping and error compensation. False trigger prevention is based on a three-layer verification principle: First, cross-verification of each sensor, combined with sliding filtering, reduces data fluctuations from ±0.5℃ to ±0.1℃; second, by calculating the average change rate over 1 second, false triggers are reduced from 30 to 1, and a 0.1℃ absolute value threshold is added to avoid 25 noise-induced false triggers; third, a second verification is performed 3 seconds after triggering. Steps for constructing the temperature-deformation mapping model: Based on the three-dimensional temperature field model, a thermal-structural coupling analysis model of the robotic arm is established using finite element analysis software. By simulating the thermal effect of temperature on the structure, the relationship between temperature and deformation is established. The change in mode amplitude was measured by strain gauges attached to the connecting rod surface. The calculation method was to divide the difference between the high temperature amplitude and the room temperature amplitude by the room temperature amplitude and then multiply by 100%. The measured increase was 15%. The temperature field data was transformed into quantifiable deformation, which solved the problem that traditional linear models could not reflect the nonlinear characteristics of materials and provided an accurate deformation prediction basis for dynamic error compensation. The dynamic error compensation algorithm execution steps are as follows: The programming logic controller receives the three-dimensional temperature field model data and the temperature-deformation mapping model, and calculates the position error of each joint caused by temperature changes in real time; for rotary joints, the angle compensation amount is converted into the pulse correction amount of the servo motor. For linear axes, the linear compensation value is converted into the feedback correction value of the grating ruler. The purpose of these two types of conversions is to transform the abstract deformation into control signals that the actuator can recognize. All compensation commands are synchronously transmitted to the servo drivers of each axis via the EtherCAT bus to update the target position of the motion control card. A dual-time-scale compensation mechanism is adopted, which adapts different compensation frequencies according to the temperature change rate. When the temperature change rate is greater than 1℃ / min, 100Hz high-frequency compensation is started based on real-time temperature field data. When the temperature change rate is less than or equal to 1℃ / min, a long short-term memory neural network is enabled to perform 1Hz low-frequency compensation. Adaptive Kalman filter calibration steps: A laser displacement sensor is installed on the end effector of the robotic arm to measure the deviation between the actual and theoretical positions of the end effector in real time; the joint position after dynamic error compensation is used as the state vector, including the three-dimensional spatial coordinates of the end effector and the attitude angles in three rotational directions, to construct the system state equation and observation equation. The state equation describes the natural change of the joint position over time, and the observation equation correlates the state vector with the sensor's measured data. Together, they form the mathematical basis for calibration; a quantum particle swarm optimization algorithm is introduced to optimize the noise covariance matrix of the Kalman filter. A specific population size and number of iterations are set, and the filtering accuracy is improved by minimizing the mean square value of the position prediction error. The Kalman filter algorithm's data fusion process involves establishing a state equation describing the dynamic changes in temperature. The current temperature estimate is the superposition of the previous temperature estimate and process noise. The observation equation represents the observation vector, which is the superposition of measurements from two types of sensors and observation noise. Dynamic correction is achieved through iterative updates of the error covariance matrix. The current error covariance matrix is ​​equal to the identity matrix minus the product of the gain matrix and the observation matrix, and then multiplied by the error covariance matrix from the previous time step to quantify the change in estimation error. The gain matrix is ​​calculated from the error covariance matrix from the previous time step, the transpose of the observation matrix, and the observation noise covariance matrix, balancing the weights of the predicted and observed values.

2. The method for temperature drift compensation and accuracy calibration of the ultrasonic scanning robotic arm according to claim 1, characterized in that, The modal analysis operation in the construction of the temperature-deformation mapping model involves attaching foil strain gauges to the surface of the aluminum alloy connecting rod of the robotic arm, collecting vibration signals at different temperatures using a dynamic signal analyzer, converting the mechanical vibration into electrical signals, and extracting the frequency characteristics. The nonlinear correction parameters are obtained by fitting nine sets of temperature-deformation data. The deformation of the connecting rod is measured after each set of data has been stable for 30 minutes. The fitted mapping relationship reflects the nonlinear deformation characteristics in the range of 20℃ to 60℃, providing a deformation prediction basis for dynamic error compensation.

3. The method for temperature drift compensation and accuracy calibration of the ultrasonic scanning robotic arm according to claim 1, characterized in that, The dual-timescale compensation mechanism is implemented in two modes: In high-frequency compensation mode, the temperature change in the next 300ms is predicted based on the Kalman filter algorithm, and commands are issued via the EtherCAT bus to offset the system's delayed response to temperature abrupt changes using the prediction lead. In low-frequency compensation mode, the input layer of the long short-term memory neural network includes 17-dimensional features: the current temperature value, the rate of temperature change, and 15 temperature data points collected at 2-minute intervals within the past 30 minutes. The hidden layer consists of three layers with 64 neurons each, using the tanh activation function to capture the time-dependent features of temperature changes. The output layer is a 6-dimensional vector corresponding to the compensation coefficients of six joints. Prediction is achieved by mining patterns in historical data through deep learning, providing stable compensation when the temperature changes slowly.

4. The method for temperature drift compensation and accuracy calibration of the ultrasonic scanning robotic arm according to claim 1, characterized in that, In the adaptive Kalman filter calibration, the three-dimensional spatial coordinates of the state vector correspond to the positions of the robotic arm end effector along the x-axis from the base to the end effector extension direction, the y-axis (horizontal direction perpendicular to the x-axis), and the z-axis (vertical direction). The three rotation angles correspond to the attitude deflections around the x-axis, y-axis, and z-axis, respectively, describing the pose state of the end effector. The state transition matrix is ​​determined based on the forward kinematics of the robotic arm. The control input matrix correlates the conversion relationship between servo motor pulses and joint movements, linking control commands with pose changes. In the quantum particle swarm optimization algorithm, the contraction and expansion coefficients are linearly reduced from 0.7 to 0.

4. Particle position updates are combined with quantum probability distribution to achieve global optimization. The optimal parameters are found through the swarm algorithm, improving the adaptability of the noise covariance matrix. After calibration, the optimized parameters are fed back to the temperature-deformation mapping model to achieve dynamic optimization and compensation accuracy of the model.

5. The method for temperature drift compensation and accuracy calibration of the ultrasonic scanning robotic arm according to claim 1, characterized in that, Also includes: Sensor data fusion calibration steps: An inertial measurement unit (IMU) consisting of a gyroscope, accelerometer, and encoder is deployed at each joint of the robotic arm. The gyroscope measures the angular velocity of the joint around the x, y, and z axes, and the angle value is calculated by integration. The encoder directly measures the joint angle. The two types of sensors acquire angle information from different dimensions. A complementary filtering algorithm is used to fuse the two types of angle data, leveraging the dynamic response advantage of the gyroscope and the static accuracy advantage of the encoder to improve the overall accuracy of angle measurement. When the IMU detects a vibration frequency exceeding 50Hz and an amplitude greater than 0.1g, it is determined to be abnormal vibration, and the proportional, integral, and derivative parameters of the servo driver are automatically adjusted to suppress resonance.

6. The method for temperature drift compensation and accuracy calibration of the ultrasonic scanning robotic arm according to claim 1, characterized in that, Also includes: The ultrasonic propagation path temperature correction steps are as follows: An array of temperature sensors is arranged in the scanning area to collect the temperature distribution along the ultrasonic propagation path in real time, obtaining temperature gradient information along the path; based on the relationship between sound speed and temperature, the sound speed at 20℃ (343 m / s) is used as a reference. The actual sound speed is calculated by multiplying the square root of the ratio of the current absolute temperature to the reference absolute temperature by the reference sound speed, thus calculating the sound speed at different temperatures; the echo time correction is the difference between the propagation time corresponding to the actual sound speed and the propagation time corresponding to the reference sound speed at the same propagation distance, quantifying the influence of temperature on propagation time; the ray difference method is used to iteratively solve the acoustic ray equation until the change in propagation time is less than 0.1 microseconds, at which point the iteration stops, and the propagation trajectory of the sound wave in the non-uniform medium is solved numerically.

7. The method for temperature drift compensation and accuracy calibration of an ultrasonic scanning robotic arm according to claim 1, characterized in that, Also includes: Thermal balance control steps: A semiconductor cooling chip is built into the base of the robotic arm. It automatically starts when the joint motor temperature exceeds 50℃. The cooling power is calculated based on the difference between the current temperature and the set temperature of 40℃, with a proportionality coefficient of 2 watts / ℃. For every 1℃ increase in temperature above the set temperature, the cooling power increases by 2 watts. The ultrasonic transducer base is designed with a circulating water cooling channel. The coolant flow rate is proportional to the temperature change rate. When the change rate is 1℃ / min, the flow rate is 10mL / min, and when the change rate is 2℃ / min, the flow rate increases to 20mL / min. At the same time, the phase change material absorbs heat, and the heat dissipation capacity is dynamically adjusted to adapt to temperature changes and stabilize the transducer temperature. The temperature fluctuation of each component of the robotic arm is controlled within ±1℃. When the ambient temperature is below 5℃, the system automatically switches to heating mode to provide a temperature reference for the temperature-deformation mapping model and reduce model errors caused by drastic temperature fluctuations.

8. The method for temperature drift compensation and accuracy calibration of an ultrasonic scanning robotic arm according to claim 1, characterized in that, Also includes: Dynamic reference point calibration steps: Three optical positioning markers distributed in a triangle are set at the edge of the scanning area. After the robotic arm completes 10 scanning cycles, it automatically moves to the marker position. The industrial camera on the end effector captures the marker image, identifies the pixel coordinates of the marker center and converts them into actual spatial coordinates to obtain the actual position of the reference point. The deviation between the actual coordinates and the theoretical coordinates of the marker in the x, y, and z directions is calculated. The least squares method is used to fit the deviation and the corresponding temperature data into a calibration function in the form of a quadratic polynomial. The correlation between the deviation and temperature is established through mathematical fitting to quantify the influence of temperature on the position of the reference point.

9. The method for temperature drift compensation and accuracy calibration of an ultrasonic scanning robotic arm according to claim 1, characterized in that, Also includes: Material nonlinear thermal property compensation steps: For carbon fiber composite connecting rods, a segmented thermal expansion model is established, and the model is applied in the temperature range of -20℃ to 20℃. The coefficient of thermal expansion is adopted in the range of 20℃ to 60℃. The coefficient of thermal expansion is used to detect the current temperature in real time by a temperature sensor and automatically switch the corresponding coefficient to calculate the deformation. The temperature dependence of the thermal expansion characteristics of carbon fiber can be used to predict the deformation in different temperature ranges. By uniformly doping 1% carbon nanotubes into a carbon fiber resin matrix, the overall coefficient of thermal expansion of the composite material is reduced to a lower value by utilizing its thermal conductivity and structural reinforcement properties. The results are then fed back to the temperature-deformation mapping model to optimize the nonlinear correction parameters, which, together with the temperature-deformation mapping model construction steps, improve the compensation accuracy of the carbon fiber component.

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