Bayesian learning and piezoelectric ceramic driving numerical control machine tool thermal error compensation system and method

Abstract

The invention discloses a Bayesian learning and piezoelectric ceramic driving numerical control machine tool thermal error compensation system and method. According to the system, a distributed temperature sensor array is arranged in heat sensitive areas such as a machine tool spindle, a ball screw, a guide rail and a bearing seat, whole-field temperature information is collected in combination with a thermal infrared imager, and multi-source thermal field sensing is achieved; meanwhile, a laser interferometer and a capacitive displacement sensor are used for constructing a dynamic pose monitoring network. The intelligent decision-making unit integrates a Bayesian online learning engine, fuses a physical model and a data driving model, dynamically predicts a thermal error and generates a compensation instruction. And the piezoelectric execution mechanism carries out nonlinear pre-compensation on a driving signal through a three-section Prantl-Ishlinskii hysteresis inverse model according to the instruction, so that high-precision pose adjustment is realized. The thermal error compensation precision is remarkably improved, the adaptability of the system to complex working conditions is enhanced, the service life of equipment is prolonged, and the method is suitable for various numerical control machine tools.

Description

Technical Field

[0001] The present invention belongs to the intersection of precision manufacturing and intelligent control, and specifically relates to a dynamic compensation system and method for thermal errors of CNC machine tools based on Bayesian online learning and high-precision drive of piezoelectric ceramics. Background Art

[0002] As core processing equipment in modern manufacturing, CNC machine tools' machining accuracy directly determines product quality and corporate competitiveness. However, during actual machining, the various heat sources within CNC machine tools can cause thermal deformation of the machine tool structure. This thermal deformation can lead to thermal errors, significantly reducing machining accuracy and affecting the dimensional accuracy and surface quality of the workpiece.

[0003] Traditional thermal error compensation methods primarily rely on temperature sensors to acquire temperature data, then apply compensation using simple linear models. These methods have numerous limitations. First, they can only monitor temperature, but cannot monitor dynamic changes in posture in real time, failing to fully reflect the machine tool's actual thermal state. Second, they are poorly adaptable to complex thermal fields, and the compensation effect is poor when the heat source is unevenly distributed or when the heat source intensity varies significantly. Furthermore, traditional methods offer limited accuracy in compensating for thermal errors, making them difficult to meet the requirements of high-precision machining.

[0004] In recent years, the continuous development of sensor technology, signal processing techniques, and intelligent control algorithms has provided new ideas and methods for thermal error compensation in CNC machine tools. Multimodal sensor fusion technology can more comprehensively perceive the thermal field and posture changes of machine tools, improving the accuracy of thermal error prediction. Intelligent algorithms such as Bayesian learning can adaptively update thermal error prediction models, improving their adaptability and accuracy. Composite closed-loop control strategies can effectively compensate for thermal errors and enhance the dynamic performance and stability of compensation.

[0005] In this context, the present invention proposes an intelligent thermal error compensation method and system for CNC machine tools based on a piezoelectric ceramic micro-displacement platform, aiming to overcome the shortcomings of traditional thermal error compensation methods, realize online compensation of thermally induced posture drift, and improve the machining accuracy and stability of CNC machine tools. Summary of the Invention

[0006] The purpose of this invention is to propose a thermal error compensation system and method for CNC machine tools based on Bayesian online learning and high-precision drive of piezoelectric ceramics. Through multi-modal sensor fusion and composite control strategy, online compensation of thermally induced posture drift is realized, effectively improving the processing accuracy and stability of CNC machine tools.

[0007] To solve the above technical problems, the present invention provides an intelligent thermal error compensation method for CNC machine tools based on a piezoelectric ceramic micro-displacement platform. The method realizes online compensation of thermally induced posture drift through multimodal sensor fusion and a composite control strategy. The method includes the following steps: (1) Multi-source thermal field perception: Distributed temperature sensor arrays are arranged in heat-sensitive areas such as the machine tool spindle, ball screw, guide rail, and bearing seat. A multi-scale temperature measurement combination of infrared thermal imagers and embedded PT100 platinum resistance temperature sensors is used to synchronously collect temperature field distribution data during machine tool operation. (2) Dynamic posture monitoring: Install high-precision grating displacement sensors and capacitive micro-displacement sensors at key nodes of the machine tool kinematic pair to build a displacement-temperature coupling monitoring network to obtain thermal deformation displacement and temperature gradient data in real time; (3) Data fusion processing: The temperature-displacement heterogeneous data are temporally and spatially aligned through the improved Kalman filter algorithm, and the wavelet threshold denoising combined with the sliding window normalization method is used to eliminate environmental vibration and electromagnetic interference.

[0008] The improved federated Kalman filter is designed as follows:

[0009] Among them, the state vector Contains n temperature measurement points and displacements in three directions. The process noise covariance matrix Q adopts an adaptive adjustment mechanism:

[0010] Temperature noise variance Dynamically updated according to the sensor aging degree, displacement noise variance , , Real-time estimation is performed using wavelet packet decomposition. The data sampling interval is 5ms, and dimension differences are eliminated using sliding window normalization.

[0011] (4) Thermal error modeling: Establish a dynamic thermal error prediction model based on Bayesian learning to generate XYZ three-axis thermal error displacement prediction values; (5) Piezoelectric drive command generation: The predicted thermal error displacement is converted into a driving voltage signal for the piezoelectric ceramic actuator, and the three-stage Prandtl-Ishlinskii hysteresis inverse model is used to perform nonlinear pre-compensation on the driving signal; (6) Composite closed-loop control: Execute the feedforward-feedback composite control strategy. The feedforward channel outputs the open-loop compensation command according to the thermal error model. The feedback channel monitors the platform posture deviation in real time through the capacitive displacement sensor and uses the sliding mode variable structure algorithm for dynamic error correction. The sliding mode controller is designed as:

[0012] The switching function , boundary layer thickness Adaptive adjustment based on error amplitude:

[0013] (7) Multi-axis collaborative compensation: Based on the kinematic inverse model of the piezoelectric micro-displacement platform, the three-dimensional thermal error compensation is decomposed into the axial expansion and contraction of each piezoelectric actuator, and multi-degree-of-freedom collaborative compensation is achieved through distributed piezoelectric drives.

[0014] Preferably, the dynamic thermal error prediction model of Bayesian learning in step S4 includes the following steps: (1) Prior knowledge embedding: A prior distribution model is constructed based on the thermodynamic characteristics of the machine tool, and physical parameters such as the thermal expansion coefficient of the spindle and the frictional heat generation rate of the guide rail are used as prior inputs of the Gaussian process; (2) Likelihood function design: Considering the coupling effect of heat conduction and structural deformation, a parameterized likelihood function is established: ; (3) Online posterior update: The stochastic variational inference algorithm is used to perform incremental learning on the temperature-displacement observation data, and the posterior probability distribution is updated in real time through the natural gradient descent method:

[0015] Where θ is the thermal-mechanical coupling parameter, is the temperature-displacement data pair collected in real time, is the historical training dataset; (4) Multi-scale feature fusion: A dual-channel Bayesian network is designed. The first channel processes the spatiotemporal distribution characteristics of the temperature field (spindle temperature rise rate, heat source spatial gradient), and the second channel analyzes the structural thermal resistance network (heat conduction path discretized by the finite element method). The outputs of the two channels are averaged by the Bayesian model at the evidence layer. (5) Uncertainty quantification: Output the predicted value of the XYZ three-axis thermal error displacement and its confidence interval. When the confidence interval exceeds the preset threshold, the active learning mechanism of the piezoelectric compensation system is triggered, and additional sensor data is collected for model retraining.

[0016] Preferably, the hierarchical Bayesian model in step S4 comprises a three-level structure: First level (physical layer): Establish a parameterized likelihood function based on the thermoelasticity equation:

[0017] in is the contribution coefficient of each heat source to the displacement, which obeys the semi-Cauchy prior distribution.

[0018] Second level (data layer): Gaussian process regression is used to construct a non-parametric mapping relationship between temperature and displacement, and the kernel function uses the thermodynamically modified Matern 5 / 2 kernel:

[0019] where r is the temperature field distance metric weighted by the heat conduction rate.

[0020] Level 3 (decision-making layer): The prediction results of the physical-driven model and the data-driven model are integrated through Bayesian model blending (BMA), and the weight coefficients are dynamically optimized according to the WAIC criterion. .

[0021] Preferably, the active learning mechanism in step S4 adopts a Bayesian experimental design method: (1) Define information entropy gain as the sampling criterion: ; (2) Select the temperature measurement point combination that maximizes H_new through Monte Carlo tree search; (3) Drive the CNC machine tool to execute a specific detection path to collect the temperature-displacement data with the maximum amount of information.

[0022] Preferably, the three-segment PI hysteresis inverse model in step S5 includes: a linear segment adopts a polynomial to fit the voltage-displacement relationship, a saturation segment adopts an inverse tangent function to describe the nonlinear characteristics, a dead zone segment introduces a dynamic threshold compensation mechanism, and the parameters of each segment are optimized by a genetic algorithm.

[0023] Preferably, the sliding mode variable structure algorithm in step S6 designs an adaptive reaching law: ; in To switch the gain, is the convergence coefficient, is the external disturbance observation value, and the global stability of the control system is guaranteed by the Lyapunov function.

[0024] Furthermore, in order to implement the above-mentioned CNC machine tool thermal error compensation method based on Bayesian online learning, a CNC machine tool thermal error compensation system based on Bayesian online learning and piezoelectric ceramic high-precision drive is also provided, which specifically includes the following core modules: (1) Multi-physics field perception module Distributed temperature sensing array: including miniature K-type thermocouples (range 0-200°C) and FBG fiber optic sensors (accuracy ±0.1°C); Displacement detection unit: laser interferometer (resolution 1 nm) and differential capacitance sensor (range ±20 μm, nonlinearity 0.01%).

[0025] (2) Intelligent decision-making unit Equipped with the Xilinx Zynq UltraScale+ MPSoC chip, it integrates a Bayesian online learning engine and motion control algorithms, including the following modules: Bayesian Accelerator: Parallelizes the variational inference algorithm within the FPGA, completing 1,200 posterior updates per second. Uncertainty management module: When the prediction confidence interval exceeds 3σ, the closed-loop control gain of the piezoelectric compensation system is automatically increased; Self-diagnosis module: evaluates the contribution of each sensor based on the Shapley value and triggers the abnormal sensor replacement mechanism; Digital twin module.

[0026] (3) Piezoelectric actuator The three-degree-of-freedom parallel micro-motion stage is equipped with a PZT-8 piezoelectric actuator on each axis (stroke ±15μm, stiffness 50N / μm); it integrates a pre-tightened flexible hinge guide mechanism and has a radial parasitic motion of <0.5%.

[0027] It adopts a three-dimensional stacked structure. The bottom layer is a macro-dynamic servo motor to achieve millimeter-level coarse positioning, the middle layer is a piezoelectric ceramic actuator to complete micron-level fine adjustment, and the top layer is a diamond-turned hemispherical contact head, forming a macro-micro composite drive system.

[0028] The flexible hinge mechanism adopts a topological optimization design, a titanium alloy thin-wall structure formed by electric spark wire cutting (thickness 0.2mm, axial stiffness ≥30N / μm), and a diamond-like coating on the surface (friction coefficient <0.01).

[0029] (4) Drive and feedback module High-voltage linear amplifier: output voltage 0-150V, bandwidth DC-20kHz, ripple <1mVrms; Pre-amplifier: low noise instrumentation amplifier (AD8421, gain 1-1000 adjustable); Post-stage driver: power operational amplifier (PA94, slew rate 200V / μs); Adaptive bias compensation circuit: Dynamically adjusts the bias voltage to suppress piezoelectric creep. The formula is:

[0030] in α 、 β is the material characteristic coefficient, is the real-time leakage current value.

[0031] Capacitive sensor detection circuit: Contains AD9833 sinusoidal excitation source, AD630 synchronous demodulator and 24-bit Σ-Δ ADC.

[0032] (5) Human-computer interaction terminal Three-dimensional thermal error visualization interface, real-time display of temperature field cloud displacement compensation trajectory; Provide Bayesian model parameter debugging interface and compensation effect evaluation tools; Provides digital twin modules, which are implemented in the following ways: Real-time thermal-mechanical coupled simulation: Based on the ANSYS Mechanical APDL kernel, thermal boundary conditions are updated every 5 seconds; Online calibration of model parameters: Simultaneously optimize the simulation model and physical sensor data through particle swarm optimization.

[0033] Beneficial effects of the present invention: By integrating Bayesian online learning with piezoelectric ceramic micro-displacement technology, high-precision real-time compensation of thermal errors in CNC machine tools is achieved. The displacement compensation accuracy can reach sub-micron level (<0.5μm), significantly improving the machining accuracy of machine tools.

[0034] The three-level hierarchical Bayesian model combines physical-driven and data-driven methods to overcome the shortcomings of traditional thermal error models that are highly dependent on specific working conditions, giving the system excellent adaptability and generalization performance.

[0035] The active learning mechanism can automatically trigger additional data collection based on prediction uncertainty, select the optimal measurement points through the information entropy gain maximization strategy, enable the model to continuously self-optimize, and reduce the need for manual intervention.

[0036] The three-stage PI hysteresis inverse model effectively eliminates the nonlinear characteristics of the piezoelectric ceramic actuator, with a hysteresis elimination rate of >95%, achieving high linearity (>98%) and fast response (adjustment time <5ms) of the compensation system.

[0037] The multi-physics field perception module uses a multi-scale temperature measurement combination of an infrared thermal imager and an embedded PT100 platinum resistance sensor, combined with a grating displacement sensor and a capacitive micro-displacement sensor to build a comprehensive thermal-displacement coupling monitoring network.

[0038] The feedforward-feedback composite control strategy realizes dual protection of the system. The feedforward channel provides fast response, the feedback channel ensures accuracy and stability, and the sliding mode variable structure control algorithm has the ability to resist external disturbances.

[0039] The digital twin module realizes real-time synchronization of the machine tool's thermal-mechanical coupling simulation and the physical system, provides data support for fault diagnosis and predictive maintenance, and extends the service life of the equipment.

[0040] The macro-micro composite drive system adopts a three-dimensional stacked structure, organically combining millimeter-level coarse positioning with micron-level fine adjustment, greatly expanding the system's working range and making the compensation system suitable for CNC machine tools of different specifications. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 This is a technical flow chart of a Bayesian learning and piezoelectric ceramic driven CNC machine tool thermal error compensation system and method according to an embodiment of the present invention.

[0042] Figure 2 A top view of a three-degree-of-freedom parallel micro-motion platform of a Bayesian learning and piezoelectric ceramic driven CNC machine tool thermal error compensation system and method according to an embodiment of the present invention.

[0043] Figure 3 This is a piezoelectric brake installation diagram of a Bayesian learning and piezoelectric ceramic driven CNC machine tool thermal error compensation system and method according to an embodiment of the present invention.

[0044] Figure 4 This is a three-dimensional stacked structure diagram of a macro-micro composite drive system of a Bayesian learning and piezoelectric ceramic driven CNC machine tool thermal error compensation system and method according to an embodiment of the present invention.

[0045] Figure 5 This is a signal flow diagram of a feedforward-feedback composite control strategy for a thermal error compensation system and method for a CNC machine tool using Bayesian learning and piezoelectric ceramic drive according to an embodiment of the present invention. DETAILED DESCRIPTION

[0046] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be implemented in a variety of forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that the present disclosure will be more comprehensive and complete and will fully convey the concepts of the example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. In the following description, many specific details are provided to provide a full understanding of the embodiments of the present disclosure. However, those skilled in the art will appreciate that the technical solutions of the present disclosure may be practiced while omitting one or more of the specific details, or that other methods, components, devices, steps, etc. may be employed. In other cases, well-known technical solutions are not shown or described in detail to avoid obscuring various aspects of the present disclosure.

[0047] In addition, the accompanying drawings are merely schematic illustrations of the present disclosure and are not necessarily drawn to scale. Identical reference numerals in the figures denote identical or similar parts, and thus repetitive descriptions thereof will be omitted. Some of the block diagrams shown in the accompanying drawings are functional entities that do not necessarily correspond to physically or logically separate entities. These functional entities may be implemented in software, in one or more hardware modules or integrated circuits, or in different networks and / or processor devices and / or microcontroller devices.

[0048] Figure 1 The technical flow chart of a Bayesian learning and piezoelectric ceramic driven CNC machine tool thermal error compensation system and method according to the embodiment of the present invention is shown below. Figure 1 The application process of the present invention is described in detail.

[0049] 1. Implementation Scenario This embodiment is applied to a VH800 vertical machining center used by a precision machining company. When machining complex, high-precision parts, the long machining process causes internal components like the spindle and column to heat up, leading to accumulated thermal errors and affecting machining accuracy. Traditional compensation methods struggle to meet the required ±0.01mm machining accuracy.

[0050] 2. System Deployment (1) Installation of the Multi-Physical Field Perception Module (1) Temperature sensor layout A K-type thermocouple (range 0-200°C) is placed at the front, middle and rear ends of the machine tool spindle to monitor the temperature changes at different positions of the spindle in real time and reflect the temperature rise of the spindle caused by cutting heat, etc.

[0051] A K-type thermocouple is installed at the top, middle and bottom of the spindle box to obtain the overall temperature distribution of the spindle box in order to analyze the influence of its thermal deformation on the machining accuracy.

[0052] A K-type thermocouple is set on the front and back sides of the column to monitor the heating condition of the column during the processing. Considering that the column mainly bears the vertical cutting force, the temperature difference between the front and back may cause the column to bend and deform, thereby affecting the position accuracy of the tool.

[0053] For the feed system in the X, Y, and Z directions, one K-type thermocouple is arranged at the starting and end of the screw in each direction, for a total of six, to measure the temperature changes of the feed system. This is because the feed screw generates frictional heat during movement, causing it to elongate or shorten, resulting in positioning errors.

[0054] (2) Infrared thermal imager configuration An infrared thermal imager is installed at a suitable position on the outer protective cover of the machine tool. It has a wide field of view and high thermal sensitivity, can cover the entire working area of ​​the machine tool, and collect full-field temperature distribution information in real time when the machine tool is running, to supplement the measurement data of the point temperature sensor and provide more comprehensive thermal field information for thermal error modeling.

[0055] (3) Installation of displacement monitoring equipment Two laser interferometers (with a resolution of 1nm) are installed beneath the machine tool worktable at key locations along the X, Y, and Z axes to measure the worktable's displacement in each direction. The transmitter end of the laser interferometer is fixed to a stable position on the machine tool bed, while the receiver end is mounted on a measurement target in the corresponding direction of the worktable. Using the principle of interference, these interferometers precisely measure displacement, providing highly accurate displacement feedback data for thermal error compensation.

[0056] (2) Intelligent decision-making unit configuration The Xilinx Zynq UltraScale+ MPSoC chip was selected as the core processor, and its FPGA part was pre-programmed to implement a parallel variational inference algorithm. A hierarchical Bayesian online learning engine was built, and a physical-driven model based on thermoelastic mechanics equations and a data-driven model built with Gaussian process regression were embedded for thermal error prediction.

[0057] The hierarchical Bayesian model contains a three-level structure: First level (physical layer): Establish a parameterized likelihood function based on the thermoelasticity equation:

[0058] in is the contribution coefficient of each heat source to the displacement, which obeys the semi-Cauchy prior distribution.

[0059] Second level (data layer): Gaussian process regression is used to construct a non-parametric mapping relationship between temperature and displacement, and the kernel function uses the thermodynamically modified Matern 5 / 2 kernel:

[0060] where r is the temperature field distance metric weighted by the heat conduction rate.

[0061] The third level (decision-making level): The prediction results of the physical-driven model and the data-driven model are integrated through Bayesian model blending (BMA), and the weight coefficients are dynamically optimized according to the WAIC criterion.

[0062] At the same time, the built-in digital twin module is connected to the machine tool thermal-mechanical coupling simulation model. The model is built based on the ANSYS Mechanical APDL kernel. The initial parameters are set according to the machine tool design drawings and material properties, and are calibrated online through the particle swarm algorithm and physical sensor data.

[0063] (3) Piezoelectric actuator assembly Figure 2 A top view of a three-degree-of-freedom parallel micro-motion platform according to an embodiment of the present invention is shown; Figure 3 A diagram showing the installation of a piezoelectric brake according to an embodiment of the present invention is shown; Figure 4This is a three-dimensional stacking structure diagram of the macro-micro composite drive system according to an embodiment of the present invention. Figure 2 、 Figure 3 、 Figure 4 As shown, a three-degree-of-freedom parallel micro-motion platform is installed beneath the machine tool worktable. Each axis is equipped with a PZT-8 piezoelectric actuator (±15μm travel, 50N / μm stiffness). The platform and worktable are connected by a preloaded flexible hinge guide mechanism. This hinge is a topologically optimized thin-walled titanium alloy structure (0.2mm thickness, axial stiffness ≥30N / μm), formed by wire electro-discharge cutting, and coated with a diamond-like carbon coating (friction coefficient <0.01) to reduce friction. The piezoelectric actuator's drive line is connected to a high-voltage linear amplifier.

[0064] (IV) Construction of drive and feedback modules The high-voltage linear amplifier uses a low-noise instrumentation amplifier (AD8421, adjustable gain 1-1000) in the front stage, paired with a power operational amplifier (PA94, slew rate 200V / μs) in the back stage. An adaptive bias compensation circuit is designed to set the α and β parameters based on the piezoelectric material's characteristics, dynamically adjusting the bias voltage to suppress piezoelectric creep. The capacitive sensor detection circuit includes an AD9833 sinusoidal excitation source, an AD630 synchronous demodulator, and a 24-bit Σ-Δ ADC for real-time monitoring of the piezoelectric actuator's actual displacement feedback.

[0065] (V) Human-computer interaction terminal settings An industrial computer is installed at the machine tool console as a human-computer interaction terminal. Its screen displays a 3D thermal error visualization interface, showing real-time temperature field cloud maps at each temperature measurement point on the machine tool and the worktable displacement compensation trajectory. A Bayesian model parameter debugging interface is also available, allowing technicians to adjust prior distributions and kernel function parameters based on actual conditions. A compensation effect evaluation tool is also integrated to compare machining accuracy data before and after compensation.

[0066] 3. Operation process (1) System startup and initialization After powering on, the intelligent decision-making unit performs a self-check on each sensor, confirming that the temperature and displacement sensors are communicating properly and have appropriate ranges. Simultaneously, the digital twin module loads the initial simulation model, resets the piezoelectric actuator to zero, and performs gain calibration on the drive and feedback modules to ensure the system is in standby mode.

[0067] (2) Processing task execution and data collection When a precision component machining command is issued, the machine tool begins operation, with the spindle rotating and the feed system driving the worktable. At this point, a distributed temperature sensor array collects real-time temperature data from heat-sensitive areas of the machine tool. An infrared thermal imager simultaneously captures global temperature distribution information. A displacement detection unit monitors the position and posture of key areas, such as the worktable. Both transmit this data to the intelligent decision-making unit at a sampling interval of 5ms.

[0068] (3) Data fusion and thermal error modeling and prediction In the intelligent decision-making unit, the improved Kalman filter algorithm first performs spatiotemporal registration of the temperature-displacement heterogeneous data, and uses wavelet threshold denoising and sliding window normalization to eliminate interference. Subsequently, the Bayesian online learning engine is activated, and the prior knowledge embedding module constructs a prior distribution based on the thermodynamic parameters of the machine tool, and the thermal expansion coefficient of the spindle (for example, set to 12×10 -6 The online posterior update module uses a stochastic variational inference algorithm to collect temperature-displacement data pairs and historical training datasets in real time. It updates the posterior probability distribution 1200 times per second via natural gradient descent to dynamically adjust the thermo-mechanical coupling parameter θ. In the multi-scale feature fusion module, a dual-channel Bayesian network processes the spatiotemporal distribution characteristics of the temperature field (e.g., the spindle temperature rise rate of 0.8°C / min and the heat source spatial gradient of 3.2°C / m) and the structural thermal resistance network (based on the heat conduction path matrix discretized using the finite element method). After averaging through the evidence-level Bayesian model, a hierarchical Bayesian model integrates information from the physical and data layers to ultimately output predicted X, Y, and Z-axis thermal error displacements and their confidence intervals. For example, at a certain point in the machining process, the predicted worktable thermal error displacements are 18.7μm in the X direction, 14.2μm in the Y direction, and 9.6μm in the Z direction, with confidence intervals of ±1.2μm.

[0069] (IV) Piezoelectric drive command generation and compensation execution The predicted thermal error displacement is transmitted to the piezoelectric actuator module. A three-segment Prandtl-Ishlinskii hysteresis inverse model, based on parameters optimized using a genetic algorithm (polynomial coefficients for the linear segment, amplitude and phase of the inverse tangent function for the saturation segment, and dynamic threshold for the dead zone segment), converts the thermal error displacement in the X, Y, and Z directions into driving voltage signals for the piezoelectric ceramic actuator. A high-voltage linear amplifier receives the signal and outputs a 0-150V voltage to drive the piezoelectric actuator, achieving fine-tuning and compensation of the worktable's posture. Based on the predicted thermal error displacement, the corresponding driving voltage for each piezoelectric actuator is generated, correcting the worktable's three-dimensional posture.

[0070] (V) Composite closed-loop control and multi-axis coordinated compensation Figure 5The signal flow diagram of the feedforward-feedback composite control strategy of the thermal error compensation method according to the embodiment of the present invention is shown. Figure 5 As shown, the feedforward channel outputs open-loop compensation instructions based on the thermal error model. The feedback channel uses a capacitive displacement sensor to monitor the worktable's actual position deviation in real time. The sliding mode variable structure algorithm dynamically adjusts the control variable according to the adaptive reaching law to correct the residual error after feedforward compensation. Simultaneously, based on the inverse kinematic model of the piezoelectric micro-displacement platform, the three-dimensional thermal error compensation is decomposed into the axial expansion and contraction of each piezoelectric actuator. The distributed piezoelectric actuators work in coordination to ensure precise compensation of the worktable within multiple degrees of freedom.

[0071] (6) Active Learning and Uncertainty Management During the compensation process, if the uncertainty quantification module detects that the confidence interval for the X, Y, and Z axis thermal error displacement prediction exceeds a preset 3σ threshold (for example, the Z-axis confidence interval reaches ±2.5μm at a certain moment), an active learning mechanism is triggered. A Bayesian experimental design method uses information entropy gain as a sampling criterion. A Monte Carlo tree search is used to determine the optimal combination of temperature measurement points. The machine tool is then controlled to execute a specific probing path, collecting high-information temperature-displacement data for model retraining and optimization of the thermal error prediction model. Simultaneously, the uncertainty management module automatically increases the closed-loop control gain of the piezoelectric compensation system to improve compensation stability.

[0072] (VII) Self-diagnosis and maintenance tips The self-diagnostic module continuously evaluates the contribution of each sensor based on Shapley values. If a temperature sensor (such as the thermocouple at the front end of the spindle) experiences a sudden drop in contribution, indicating a possible failure, it immediately triggers the abnormal sensor replacement mechanism, prompting the operator to perform inspection and maintenance. The system then maintains basic compensation capabilities based on data from the remaining normal sensors.

[0073] IV. Experimental Verification 1. Experimental design A batch of high-precision aviation parts requiring machining, with a dimensional accuracy of ±0.01 mm, was selected. Multiple batches of 10 parts were processed, both without and with the proposed thermal error compensation system. The actual measured deviations of key dimensions (such as hole spacing and profile) of each part were recorded after machining.

[0074] (2) Comparison of results When compensation is not enabled, due to the influence of the thermal error of the machine tool, the maximum dimensional deviation of the part reaches ±0.043mm, and the deviation rate reaches 35%. After the compensation system of the present invention is enabled, the dimensional deviation is controlled within ±0.008mm, and the deviation rate is reduced to 0%, which effectively verifies the significant effect of the system and method on the thermal error compensation of the vertical machining center and meets the machining accuracy requirements of precision parts.

[0075] The present invention discloses a thermal error compensation system and method for CNC machine tools based on Bayesian online learning and high-precision drive of piezoelectric ceramics. By integrating Bayesian online learning with piezoelectric ceramic micro-displacement technology, high-precision real-time compensation of thermal errors of CNC machine tools is achieved, significantly improving the processing accuracy to the sub-micron level. The three-level hierarchical Bayesian model combines physical and data-driven methods to enhance the adaptability and generalization performance of the system. The active learning mechanism optimizes the model to reduce manual intervention. The linearity and response speed of the compensation system are improved through the three-stage PI hysteresis inverse model, and a full-dimensional multi-physical field monitoring network is constructed to ensure monitoring accuracy. The feedforward-feedback composite control strategy ensures system stability, and the digital twin module supports fault diagnosis and predictive maintenance, extending the life of the equipment. The macro-micro composite drive system expands the working range of the system, making the compensation system suitable for machine tools of different specifications.

[0076] References in this specification to "an embodiment" mean that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, the phrases "one embodiment" or "an embodiment" appearing in various places throughout this specification do not necessarily refer to the same embodiment.

[0077] Although the embodiments disclosed above are for facilitating understanding of the present invention, the contents described are merely embodiments adopted for facilitating understanding of the present invention and are not intended to limit the present invention. Any person skilled in the art of the present invention may make any modifications and changes in the form and details of the implementation without departing from the spirit and scope of the present invention. However, the scope of patent protection of the present invention shall still be subject to the scope defined by the appended claims.

Claims

1. A Bayesian learning and piezoelectric ceramic driven CNC machine tool thermal error compensation system and method, characterized by: Online compensation of thermally induced posture drift is achieved through multimodal sensor fusion and composite control strategy, which includes the following steps: S1 Multi-source Thermal Field Perception: Distributed temperature sensor arrays are placed in heat-sensitive areas such as the machine tool spindle, ball screw, guide rail, and bearing seat. A multi-scale temperature measurement combination of infrared thermal imagers and embedded PT100 platinum resistance temperature sensors is used to synchronously collect temperature field distribution data during machine tool operation. S2 dynamic posture monitoring: High-precision grating displacement sensors and capacitive micro-displacement sensors are installed at key nodes of the machine tool kinematic joint to build a displacement-temperature coupling monitoring network to obtain thermal deformation displacement and temperature gradient data in real time; S3 data fusion processing: The improved Kalman filter algorithm is used to perform spatiotemporal registration of temperature-displacement heterogeneous data, and wavelet threshold denoising combined with sliding window normalization is used to eliminate environmental vibration and electromagnetic interference; S4 Thermal Error Modeling: Establish a dynamic thermal error prediction model based on Bayesian learning to generate XYZ three-axis thermal error displacement prediction values; S5 piezoelectric drive command generation: Converts the predicted thermal error displacement into a driving voltage signal for the piezoelectric ceramic actuator and uses a three-stage Prandtl-Ishlinskii hysteresis inverse model to perform nonlinear pre-compensation on the driving signal. S6 composite closed-loop control: Executes a feedforward-feedback composite control strategy. The feedforward channel outputs open-loop compensation instructions based on the thermal error model. The feedback channel monitors the platform posture deviation in real time through a capacitive displacement sensor and uses a sliding mode variable structure algorithm for dynamic error correction. S7 multi-axis collaborative compensation: Based on the kinematic inverse model of the piezoelectric micro-displacement platform, the three-dimensional thermal error compensation is decomposed into the axial expansion and contraction of each piezoelectric actuator, and multi-degree-of-freedom collaborative compensation is achieved through distributed piezoelectric drives.

2. The method according to claim 1, wherein: The dynamic thermal error prediction model of Bayesian learning in step S4 includes the following steps: S4.1 Prior knowledge embedding: Build a prior distribution model based on the thermodynamic characteristics of the machine tool, using physical parameters such as the thermal expansion coefficient of the spindle and the frictional heat generation rate of the guide rail as prior inputs to the Gaussian process; S4.2 Online Posterior Update: The stochastic variational inference algorithm is used to perform incremental learning on the temperature-displacement observation data, and the posterior probability distribution is updated in real time through the natural gradient descent method: ； in θ is the thermal-mechanical coupling parameter, is the temperature-displacement data pair collected in real time, is the historical training dataset; S4.3 Multi-scale feature fusion: Design a dual-channel Bayesian network. The first channel processes the spatiotemporal distribution characteristics of the temperature field (spindle temperature rise rate, heat source spatial gradient), and the second channel analyzes the structural thermal resistance network (heat conduction path discretized by finite element method). The outputs of the two channels are Bayesian model averaged at the evidence layer. S4.4 Uncertainty quantification: Output the predicted value of the XYZ three-axis thermal error displacement and its confidence interval. When the confidence interval exceeds the preset threshold, the active learning mechanism of the piezoelectric compensation system is triggered, and additional sensor data is collected for model retraining.

3. The method according to claim 1, wherein: The hierarchical Bayesian model described in step S4 comprises a three-level structure: First level (physical layer): Establish a parameterized likelihood function based on the thermoelasticity equation: ； in is the contribution coefficient of each heat source to the displacement, which obeys the semi-Cauchy prior distribution; Second level (data layer): Gaussian process regression is used to construct a non-parametric mapping relationship between temperature and displacement, and the kernel function uses the thermodynamically modified Matern 5 / 2 kernel: ； Where r is the temperature field distance metric weighted by the heat conduction rate; The third level (decision-making level): The prediction results of the physical-driven model and the data-driven model are integrated through Bayesian model blending (BMA), and the weight coefficients are dynamically optimized according to the WAIC criterion.

4. The method according to claim 1, wherein: The active learning mechanism described in step S4 adopts the Bayesian experimental design method: (1) Define information entropy gain as the sampling criterion: ； (2) Select using Monte Carlo tree search H new Maximized combination of temperature measurement points; (3) Drive the CNC machine tool to execute a specific detection path to collect the temperature-displacement data with the maximum amount of information.

5. The method according to claim 1, wherein: The three-segment PI hysteresis inverse model in step S5 includes: a linear segment uses a polynomial to fit the voltage-displacement relationship, a saturation segment uses an inverse tangent function to describe the nonlinear characteristics, a dead zone segment introduces a dynamic threshold compensation mechanism, and the parameters of each segment are optimized by a genetic algorithm.

6. The method according to claim 1, wherein: The sliding mode variable structure algorithm in step S6 designs an adaptive reaching law: ； in To switch the gain, is the convergence coefficient, is the external disturbance observation value, and the global stability of the control system is guaranteed by the Lyapunov function.

7. A thermal error compensation system for a CNC machine tool implementing the method according to any one of claims 1 to 6, characterized in that: Contains the following core modules: (1) Multi-physics field perception module Distributed temperature sensing array: including miniature K-type thermocouples (range 0-200°C) and FBG fiber optic sensors (accuracy ±0.1°C); Displacement detection unit: laser interferometer (resolution 1nm) and differential capacitance sensor (range ±20μm, nonlinearity 0.01%); (2) Intelligent decision-making unit Equipped with Xilinx Zynq UltraScale+ MPSoC chip, it integrates Bayesian online learning engine and motion control algorithm; Built-in digital twin module to synchronize machine tool thermal-mechanical coupling simulation data in real time; (3) Piezoelectric actuator Three-degree-of-freedom parallel micro-motion stage, each axis is equipped with a PZT-8 piezoelectric actuator (stroke ±15μm, stiffness 50N / μm); Integrated pre-tightened flexible hinge guide mechanism, radial parasitic motion <0.5%; (4) Drive and feedback module High-voltage linear amplifier: output voltage 0-150V, bandwidth DC-20kHz, ripple <1mVrms; Capacitive sensor detection circuit: including AD9833 sinusoidal excitation source, AD630 synchronous demodulator and 24-bit Σ-Δ ADC; (5) Human-computer interaction terminal Three-dimensional thermal error visualization interface, real-time display of temperature field cloud map and displacement compensation trajectory; Provides Bayesian model parameter debugging interface and compensation effect evaluation tools.

8. The system according to claim 7, characterized in that: The intelligent decision-making unit comprises: (1) Bayesian acceleration module: implements a parallel variational inference algorithm within the FPGA, completing 1200 posterior updates per second; (2) Uncertainty Management Module: When the prediction confidence interval exceeds 3 σ When , the closed-loop control gain of the piezoelectric compensation system is automatically enhanced; (3) Self-diagnosis module: Evaluates the contribution of each sensor based on the Shapley value and triggers the abnormal sensor replacement mechanism.

9. The system according to claim 7, characterized in that: The piezoelectric actuator adopts a three-dimensional stacked structure: the bottom layer is a macro-motion servo motor to achieve millimeter-level coarse positioning, the middle layer is a piezoelectric ceramic actuator to complete micron-level fine adjustment, and the top layer is a diamond-turned hemispherical contact head, forming a macro-micro composite drive system.

10. The system according to claim 7, wherein: The high voltage linear amplifier design includes: (1) Pre-amplifier: low-noise instrumentation amplifier (AD8421, gain adjustable from 1 to 1000); (2) Post-stage driver: power operational amplifier (PA94, slew rate 200V / μs); (3) Adaptive bias compensation circuit: Dynamically adjust the bias voltage to suppress piezoelectric creep. The formula is: ； in α 、 β is the material characteristic coefficient, is the real-time leakage current value.

11. The system according to claim 7, wherein: The flexible hinge mechanism adopts: (1) Topology optimization design: parametric finite element model based on variable density method; (2) Thin-walled titanium alloy structures formed by wire-cut electrospark cutting (thickness 0.2 mm, axial stiffness ≥ 30 N / μm); (3) Surface diamond-like coating (friction coefficient < 0.01).

12. The system according to claim 7, wherein: The digital twin module implements: (1) Real-time thermal-mechanical coupling simulation: based on ANSYS Mechanical APDL kernel; (2) Online calibration of model parameters: The simulation model and physical sensor data are optimized synchronously through the particle swarm algorithm.

Images