A high-speed numerical control machine tool thermal error real-time compensation control system

Abstract

The application discloses a high-speed numerical control machine tool thermal error real-time compensation control system, which is applied to the technical field of numerical control machine tool thermal error control and comprises a preprocessing module, a learning module, a main real-time control module and a compensation module. The learning module constructs a fourth-order thermal state tensor according to a second sampling period, solves an orthogonal factor matrix based on random block Krilov iteration and truncated singular value decomposition, and constructs a low-rank evolution space; the main real-time control module extracts a three-dimensional physical observation slice according to a first sampling period and projects to obtain a low-dimensional thermal state coordinate vector, recursively predicts by using a local linear state space model, reconstructs a high-dimensional predicted physical thermal field tensor by an orthogonal projection operator and maps out a tool tip thermal error vector, and injects a servo drive unit to execute feedforward compensation. The application solves the problems of time-consuming high-dimensional calculation, dimension conflict and control divergence caused by basis vector flip, and improves control stability and machining precision.

Description

Technical Field

[0001] This invention relates to the field of thermal error control technology for CNC machine tools, and particularly to a real-time thermal error compensation control system for high-speed CNC machine tools. Background Technology

[0002] As core equipment in high-end manufacturing, high-speed CNC machine tools directly determine the quality of high-precision components through their machining accuracy. During the high cutting speeds and high feed dynamic response of machine tools, spindle bearing friction, heat generation from the lead screw motors of each motion axis, and ambient temperature fluctuations induce complex non-uniform thermal field distributions, leading to thermal expansion and bending deformation of structural components. Studies show that thermal errors account for 40% to 70% of the total machining errors of machine tools. Without significantly increasing the cost of mechanical hardware, using real-time feedforward compensation technology to dynamically correct the thermal error at the machine tool tip is the most effective way to improve the machining accuracy of machine tools.

[0003] However, traditional CNC machine tool thermal error compensation methods mostly rely on empirical models such as multiple linear regression or neural networks for a few specific temperature measurement points, which have serious technical defects: First, the spatial temperature sensor placement is limited and is easily affected by high-frequency cutting heat and environmental noise, resulting in poor model generalization and robustness; Second, establishing a high-dimensional dynamic physical thermal field model requires matrix tensor calculations of massive amounts of data, which cannot meet the hard real-time requirement of millisecond-level (1ms) interpolation control cycle of CNC systems; Third, there is a conflict in dimensional definition between the time characteristics including historical sliding windows and the recursive prediction of the real-time state space model; Fourth, during the online update of the orthogonal subspace, the orthogonal basis vectors of singular value decomposition are prone to 180-degree sign flipping, which in turn leads to the inverse superposition of compensation control quantities and divergence of the control system. Summary of the Invention

[0004] The purpose of this application is to at least solve one of the above-mentioned technical defects, in particular the technical defects in the prior art such as loss of high-dimensional thermal field features, high computational complexity of tensor decomposition which cannot meet the requirements of real-time control cycle, recursive conflict of core tensor time dimension, and control divergence caused by factor matrix sign flipping.

[0005] In a first aspect, this application provides a real-time thermal error compensation control system for a high-speed CNC machine tool, comprising: The preprocessing module is used to acquire the control signals of the CNC machine tool according to the first sampling period, perform multi-rate time synchronization on the control signals, and obtain the thermal state observation sequence through standardization; The learning module is used to read the thermal state observation sequence according to the second sampling period, construct a fourth-order thermal state tensor, and use a Gaussian random sampling matrix to perform modular-n matrix transformation and dimension reduction sketching on the fourth-order thermal state tensor. Based on random block Krylov iteration, column-pivot orthogonal triangular decomposition and small-scale truncated singular value decomposition, the spatial modular orthogonal factor matrix, the temporal modular orthogonal factor matrix, the operating condition modular orthogonal factor matrix, the topological modular orthogonal factor matrix and the core tensor are solved to construct the low-rank evolution space of the thermal state. The main real-time control module is used to extract the three-dimensional physical observation slice at the current moment in each first sampling period, and project the three-dimensional physical observation slice onto the thermal state low-rank evolution space using the orthogonal factor matrix of each mode to obtain the current thermal state coordinate vector. The current thermal state coordinate vector is recursively derived using a local linear state-space model to obtain the predicted thermal state coordinate vector. The high-dimensional predicted physical thermal field tensor is reconstructed using an orthogonal projection operator, and the tip thermal error vector is calculated using a physical topology mapping matrix based on regularization. The compensation module is used to subtract the tool tip thermal error vector from the original motion command position vector of the CNC system, calculate the corrected control position vector, and inject it into the servo drive unit to perform compensation.

[0006] As an optional implementation, the preprocessing module specifically includes: The first sampling period is 0.001 seconds; The control signals include spatial measurement point temperature signals, operating condition signals, and structural topology position signals; The calculation process for obtaining the thermal state observation sequence includes: Extract the physical sampling mean and physical sampling standard deviation of each control signal within the set historical sliding window. Subtract the physical sampling mean from the original physical sampling value at the current moment and then divide by the physical sampling standard deviation to obtain the normalized physical thermal state observation value. Then, concatenate the normalized physical thermal state observation values ​​of the signals included in the sliding window into a thermal state observation sequence.

[0007] As an optional implementation, the learning module specifically includes: Connected to the preprocessing module, the thermal state observation sequence within the sliding time window is extracted according to the second sampling period, which is 1.0 second; The fourth-order thermal state tensor includes: Spatial measurement point dimension represents the number of temperature sensors arranged in the space; The sliding time window dimension represents the number of historical sampling points included; In terms of operating conditions, this represents the number of heat source parameters such as spindle speed, spindle drive current, and cutting load rate. The fourth dimension is the structural topology dimension, which represents the number of topological nodes of the machine tool motion axes and bed components.

[0008] As an optional implementation, the learning module utilizes a Gaussian random sampling matrix to perform a modular-n matrix expansion and dimensionality reduction sketching of the fourth-order thermal state tensor, which includes: The expansion matrix is ​​obtained by performing a modular-n matrix expansion along the four dimensions of the fourth-order thermal state tensor. The expansion matrix is ​​then multiplied by the fixed Gaussian random sampling matrix generated during the system startup phase to obtain the dimension-reduced sketch matrix. Based on the expansion matrix and the dimensionality reduction sketch matrix, a modular-n block Krylov extended subspace matrix is ​​constructed by performing right-multiplication associative chain decomposition calculation through matrix multiplication.

[0009] As an optional implementation, the process of solving the orthogonal factor matrix and the core tensor in the learning module includes: The orthogonal projection basis matrix is ​​extracted by column-pivoting orthogonal triangular decomposition of the modular-n block Krylov extended subspace matrix; The expanded matrix is ​​projected onto a low-dimensional subspace constructed by orthogonal projection basis matrices to obtain a small-scale projection matrix. The small-scale projection matrix is ​​then truncated and singular value decomposition is performed to extract singular vectors. The orthogonal projection basis matrix is ​​right-multiplied by a small-scale left singular matrix to obtain the orthogonal factor matrix, which includes the spatial model orthogonal factor matrix, the temporal model orthogonal factor matrix, the working condition model orthogonal factor matrix, and the topological model orthogonal factor matrix. The core tensor is calculated by performing modular-n multiplications on the transpose of the corresponding orthogonal factor matrix along the four dimensions of the fourth-order thermal state tensor.

[0010] As an optional implementation, the main real-time control module is connected to both the preprocessing module and the learning module, wherein the process of extracting the transient low-dimensional current thermal state coordinate vector includes: At the current time t, the latest sampling point section is extracted from the fourth-order thermal state tensor along the time axis to obtain a three-dimensional physical observation slice, which includes spatial measurement point dimension, operating condition dimension and structural topology dimension. The three-dimensional physical observation slice is multiplied along each of the three dimensions by the transpose of the spatial mode orthogonal factor matrix, the transpose of the working condition mode orthogonal factor matrix, and the transpose of the topological mode orthogonal factor matrix, and the product results are vectorized to generate the current thermal state coordinate vector.

[0011] As an optional implementation method, the state recursion to obtain the predicted thermal state coordinate vector specifically includes: The normalized spindle speed and cutting load rate at the current moment are spliced ​​together to form a feedforward input column vector. Based on the feedforward input column vector and the current thermal state coordinate vector, a state transition matrix and an input matrix are introduced. A single-step prior prediction is performed on the current moment in the low-rank thermal state evolution space to obtain the first predicted thermal state coordinate vector. The weighted recursive least squares algorithm is used to update the state transition matrix and input matrix online. The current feedforward input column vector and the current thermal state coordinate vector are input, and the second predicted thermal state coordinate vector after the total control response delay of the system is calculated.

[0012] As an optional implementation method, reconstructing the high-dimensional predictive physical thermal field tensor specifically includes: By using the tensor inverse vectorization operator, the second predicted thermal state coordinate vector is reconstructed and restored into a three-dimensional third thermal state prediction tensor according to the index inverse mapping rule from one-dimensional index to three-dimensional index. The third thermal state prediction tensor is multiplied along the three dimensions by the spatial mode orthogonality factor matrix, the working condition mode orthogonality factor matrix, and the topological mode orthogonality factor matrix to reconstruct the high-dimensional prediction physical thermal field tensor. Among them, the orthogonal projection operator formed by multiplying the orthogonal factor matrix and its transpose matrix has the property of sign invariance.

[0013] As an optional implementation method, the specific process of calculating the thermal error vector at the tool tip includes: The high-dimensional predicted physical thermal field tensor is vectorized and expanded, then multiplied by a physical topology mapping matrix obtained in advance through calibration of the machine tool's thermoelastic physical properties, to output a tool tip thermal error vector containing the three-dimensional spatial translation and rotation directions.

[0014] As an optional implementation, the compensation module is connected to the main real-time control module, and the process of calculating the corrected control position vector includes: The tool tip thermal error vector is subtracted from the original motion command position vector of the CNC system to generate a corrected control position vector, which is then injected into the servo drive unit through the tool tip follower interface or servo bias register.

[0015] As can be seen from the above technical solutions, the embodiments of this application have the following advantages: This invention decouples the low-speed tensor low-rank space learning with a 1.0-second cycle in the background from the ultra-fast 1.0-millisecond control loop in the foreground by lock-free pointer asynchronous decoupling. The main control loop only needs to perform a very small number of (less than 2800 FLOPs) low-dimensional matrix projections and vector multiplications, with a computation time of only microseconds. This completely solves the hard real-time contradiction between high-dimensional thermal field feature extraction and the millisecond-level interpolation cycle of the CNC system.

[0016] The learning module constructs a dimensionality reduction sketch by multiplying the Gaussian random sampling matrix by the flattening matrix on the right, and performs block Krylov chain iterative decomposition based on the right multiplication associative law of matrix multiplication. This explicitly avoids the direct calculation of the high-dimensional covariance matrix, greatly suppressing tail singular values ​​and high-frequency noise interference. While ensuring the energy accuracy of the principal components in space, the computational complexity of dimensionality reduction is reduced by several orders of magnitude.

[0017] The main real-time control module extracts a three-dimensional physical observation slice from the fourth-order thermal state tensor, which is the latest discrete moment without the historical sliding window, and projects it to obtain the current transient low-dimensional thermal state coordinate vector. This completely eliminates the conflict between the dimension definition of the sliding time window and the single-step recursive prediction of the state space model, and ensures the physical and mathematical consistency of the state recursion.

[0018] By chain-expanding the transient coordinate extraction formula and the high-dimensional physical thermal field reconstruction formula, it is proved that the orthogonal projection reconstruction operator has the invariance of quadratic multiplication negative sign cancellation when the orthogonal factor matrix undergoes U→-U sign flip, thus completely avoiding the risk of control quantity inverse superposition and servo control divergence caused by background truncation singular value decomposition orthogonal basis flip.

[0019] A ridge regression algorithm with L2 regularization is introduced to construct a physical topology mapping matrix, which effectively overcomes the problem of spatial multicollinearity among high-dimensional thermal field features. It realizes a stable mapping from a 640-dimensional high-dimensional thermal field to the thermal error of the tool tip point, which includes 5 degrees of freedom (3 translations and 2 rotations), and significantly improves the accuracy of thermal error compensation in the entire machining space of the machine tool. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0021] Figure 1 The flowchart illustrates a real-time thermal error compensation control system for a high-speed CNC machine tool, as provided in an embodiment of the present invention. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0023] Furthermore, the technical features in the various embodiments or individual embodiments provided in this application can be arbitrarily combined with each other to form a feasible technical solution. Such combination is not constrained by the order of steps and / or the structural composition mode, but must be based on the ability of those skilled in the art to implement it. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed in this application.

[0024] In the embodiments provided in this application, it should be understood that the disclosed methods and systems can be implemented in other ways. The system embodiments described below are merely illustrative. For example, the division of units and modules is only a logical functional division, and in actual implementation, there may be other division methods, such as: multiple units or modules can be combined, or integrated into another system, or some features can be ignored or not executed. In addition, the coupling or direct coupling communication connection between the various components shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or modules, and can be electrical, mechanical or other forms.

[0025] In addition, each functional unit in the various embodiments of this application can be integrated into a single processor, or each unit can be a separate device, or two or more units can be integrated into a single device; each functional unit in the various embodiments of this application can be implemented in hardware or in the form of hardware plus software functional units.

[0026] Those skilled in the art will understand that all or part of the steps of the following method embodiments can be implemented by program instructions and related hardware. The aforementioned program instructions can be stored in a computer-readable storage medium. When executed, the program instructions perform the steps of the following method embodiments. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, read-only memory (ROM), magnetic disks, or optical disks. It should be understood that the use of terms such as "system," "device," "unit," and / or "module" in this application is merely to distinguish different components, elements, parts, sections, or assemblies at different levels. However, if other terms can achieve the same purpose, they can be replaced by other expressions.

[0027] 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 technical features indicated. Therefore, a feature marked "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this application, "multiple" or "several" means two or more, unless otherwise explicitly specified. It should be understood that the structures, proportions, sizes, etc., depicted in the accompanying drawings are only for illustrative purposes and to aid those skilled in the art, and are not intended to limit the implementation conditions of this application. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in proportions, or adjustments to size, without affecting the effects and objectives of this application, should still fall within the scope of the technical content disclosed in this application.

[0028] If a flowchart is used in this application, it is used to illustrate the operations performed by the system according to embodiments of this application. It should be understood that the preceding or following operations are not necessarily performed in exact order. Instead, the steps can be processed in reverse order or simultaneously. Furthermore, other operations can be added to these processes, or one or more steps can be removed from them.

[0029] It should also be noted that, in this document, terms such as “comprising,” “including,” or any other variations thereof are intended to cover non-exclusive inclusion, such that an article or device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such an article or device. Without further limitation, an element defined by the phrase “comprising one…” does not exclude the presence of other identical elements in the article or device that includes the aforementioned element.

[0030] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0031] The following are explanations of technical terms used in this specification that are not commonly understood by those skilled in the art: Cubic spline interpolation: A mathematical method that uses piecewise cubic polynomials to fit discrete sampled data into a continuous curve with continuous second derivatives in order to obtain equally spaced high-resolution sampled data.

[0032] Modular-n matrix transformation: Expanding a multidimensional tensor along a specific nth dimension and merging the indices of the remaining dimensions into column indices, thereby transforming the tensor into tensor algebra operations of a two-dimensional matrix.

[0033] Tensor inverse vectorization operator: The inverse operation that refolds a one-dimensional array that has been vectorized and expanded back into a multi-dimensional tensor according to a preset dimensional structure.

[0034] Column permutation matrix: An orthogonal square matrix composed of 0s and 1s. When multiplied by the target matrix on the right, it can change the order of the columns of the matrix. This is used to ensure the numerical stability of the decomposition and to arrange the diagonal elements in descending order of energy.

[0035] Recursive least squares algorithm: An adaptive estimation method that updates model parameters recursively using newly input observation data and parameter estimates from the previous time step within each sampling period.

[0036] Ridge regression algorithm: an estimation method specifically designed for collinear data analysis. It improves the stability of inverting ill-conditioned matrices by introducing an L2 norm regularization penalty term into the least squares method.

[0037] Core tensor: In tensor Tucker decomposition, it represents a low-dimensional tensor that connects the various modular orthogonal factor matrices, reflecting the energy distribution law of high-dimensional tensors in low-rank space.

[0038] like Figure 1 As shown, a real-time thermal error compensation control system for a high-speed CNC machine tool includes: The preprocessing module is used to acquire the control signals of the CNC machine tool according to the first sampling period, perform multi-rate time synchronization on the control signals, and obtain the thermal state observation sequence through standardization; The learning module is used to read the thermal state observation sequence according to the second sampling period, construct a fourth-order thermal state tensor, use a Gaussian random sampling matrix to perform modular-n matrix transformation and dimension reduction sketching on the fourth-order thermal state tensor, and solve the spatial modular orthogonal factor matrix, temporal modular orthogonal factor matrix, operating condition modular orthogonal factor matrix, topological modular orthogonal factor matrix and core tensor based on random block Krylov iteration, column principal component orthogonal triangular decomposition and small-scale truncated singular value decomposition to construct the low-rank evolution space of thermal state. The main real-time control module is used to extract the three-dimensional physical observation slice at the current moment in each first sampling period, and project the three-dimensional physical observation slice onto the thermal state low-rank evolution space using the orthogonal factor matrix of each mode to obtain the current thermal state coordinate vector. The current thermal state coordinate vector is recursively derived using a local linear state-space model to obtain the predicted thermal state coordinate vector. The high-dimensional predicted physical thermal field tensor is reconstructed using an orthogonal projection operator, and the tip thermal error vector is calculated using a physical topology mapping matrix based on regularization. The compensation module is used to subtract the tool tip thermal error vector from the original motion command position vector of the CNC system, calculate the corrected control position vector, and inject it into the servo drive unit to perform compensation.

[0039] The core innovation of this invention lies in constructing a closed-loop real-time control system based on dual-rate asynchronous decoupling, random block Krylov tensor dimensionality reduction, state space recursion, and sign-invariant reconstruction. The dual-rate asynchronous decoupling architecture breaks down the hard real-time barrier between high-dimensional tensor computation and millisecond-level interpolation control. Random block Krylov chain decomposition explicitly avoids high-dimensional covariance matrix operations. The innovative extraction of three-dimensional physical slices without sliding windows resolves dimensionality conflicts in recursive prediction. Furthermore, through the quadratic multiplication sign-invariant mechanism of the orthogonal projection reconstruction operator, the theoretically sound control divergence risk caused by the flipping of orthogonal basis vectors in singular value decomposition is completely eliminated, achieving extremely fast, stable, and high-precision feedforward compensation for full-degree-of-freedom thermal errors in high-speed CNC machine tools.

[0040] The preprocessing module specifically includes: The first sampling period is 0.001 seconds; Control signals include temperature signals from spatial measuring points, operating condition signals, and structural topology position signals; Specifically, the operating condition signals include spindle speed, spindle drive current, cutting load rate, and ambient temperature signals. The spatial measurement point temperature signals include 32 temperature sensor signals arranged at the spindle bearing, lead screw nuts of each motion axis, motor base, and bed. The structural topology position signals include position and angle sensor signals of the X-axis, Y-axis, Z-axis, A-axis, and C-axis.

[0041] The calculation process for obtaining the thermal state observation sequence includes: Extract the physical sampling mean and physical sampling standard deviation of each control signal within the set historical sliding window. Subtract the physical sampling mean from the original physical sampling value at the current moment and then divide by the physical sampling standard deviation to obtain the normalized physical thermal state observation value. Then, concatenate the normalized physical thermal state observation values ​​of the signals included in the sliding window into a thermal state observation sequence.

[0042] In this embodiment, the temperature signal is acquired at a frequency of 100Hz, and the position signal and operating condition signal are acquired at a frequency of 1000Hz. The preprocessing module uses a cubic spline interpolation algorithm to interpolate and align the temperature signal to a time base of 0.001 seconds.

[0043] The window length of the historical sliding window is set to 1000 discrete sampling points.

[0044] The learning modules specifically include: Connected to the preprocessing module, the thermal state observation sequence within the sliding time window is extracted according to the second sampling period, which is 1.0 second; The fourth-order thermal state tensor includes: Spatial measurement point dimension represents the number of temperature sensors arranged in the space; The sliding time window dimension represents the number of historical sampling points included; In terms of operating conditions, this represents the number of heat source parameters such as spindle speed, spindle drive current, and cutting load rate. The fourth dimension is the structural topology dimension, which represents the number of topological nodes of the machine tool motion axes and bed components.

[0045] Specifically, the thermal state observation sequence of the past 1000 sampling points within the sliding time window is extracted to construct a fourth-order thermal state tensor. Among them, the spatial measurement point dimension =32, corresponding to the real-time normalized observations of 32 space temperature sensors; Sliding time window dimension =1000 represents the number of historical discrete sampling points included; Operating condition dimension =4, corresponding to four types of heat source characteristics: real-time spindle speed, spindle drive current, cutting load rate, and ambient temperature signal; Structural topology dimension =5, corresponding to 5 topological nodes: spindle, X-axis, Y-axis, Z-axis, and bed; Represents the space of real numbers.

[0046] The learning module utilizes a Gaussian random sampling matrix to perform a modular-n matrix expansion and dimensionality reduction sketching of the fourth-order thermal state tensor. This process includes: The expansion matrix is ​​obtained by performing a modular-n matrix expansion along the four dimensions of the fourth-order thermal state tensor. The expansion matrix is ​​then multiplied by the fixed Gaussian random sampling matrix generated during the system startup phase to obtain the dimension-reduced sketch matrix. Specifically, during the system initialization and startup phase, the target cutoff ranks from modulo-1 to modulo-4 are set as follows: =4, =10, =2, =2; Sketch sampling dimension set to =8, =14, =6, =6, which satisfies the condition. ,in Let n be the original dimension. When the original dimension is small, the Gaussian random sampling matrix acts as a full-rank preservation or dimension reduction projection operator. When the system starts up, it uses a standard normal distribution random number generator to generate four Gaussian random sampling matrices and locks them in memory. These matrices remain fixed during online operation. The reduced-dimensional sketch matrix of each module is calculated by multiplying the expanded matrix by the Gaussian random sampling matrix. Based on the expanded matrix and the reduced-dimensional sketch matrix, a modular-n block Krylov extended subspace matrix is ​​constructed by performing right-multiplication associative chain decomposition calculation through matrix multiplication.

[0047] Specifically, to reduce high-frequency sensor noise interference and suppress tail singularities, the Krylov iteration order is set to q=2. For each modulus n∈{1,2,3,4}, a modulus-n block Krylov extended subspace matrix K(n) is constructed: To avoid directly calculating the high-dimensional covariance matrix The resulting massive computational complexity is addressed by strictly adhering to the associative law of right-multiplication in matrix multiplication, which involves chain decomposition. First, the 0th-order term matrix is ​​defined as a reduced-dimensional sketch matrix. This 0th-order term matrix is ​​then used as the right-hand matrix in the matrix multiplication. Multiplying it on the left by the transpose of the expansion matrix yields the 1st-order intermediate term matrix. Multiplying this matrix on the left by the expansion matrix yields the 1st-order extended term matrix. Multiplying this matrix on the left by the transpose of the expansion matrix yields the 2nd-order intermediate term matrix. Multiplying this matrix on the left by the expansion matrix yields the 2nd-order extended term matrix. Finally, the 0th-order term matrix, the 1st-order extended term matrix, and the 2nd-order extended term matrix are concatenated along the column direction to generate a modular-n-block Krylov extended subspace matrix K(n).

[0048] In the learning module, the process of solving for the orthogonal factor matrix and the core tensor includes: The orthogonal projection basis matrix is ​​extracted by column-pivoting orthogonal triangular decomposition of the modular-n block Krylov extended subspace matrix; Specifically, perform column pivoting orthogonal triangular decomposition on the modular-n Krylov extended subspace matrix K(n), multiply by the column permutation matrix operator on the right, and expand to obtain the orthogonal projection basis matrix multiplied by the upper triangular matrix on the right. The expanded matrix is ​​projected onto a low-dimensional subspace constructed by orthogonal projection basis matrices to obtain a small-scale projection matrix. The small-scale projection matrix is ​​then truncated and singular value decomposition is performed to extract singular vectors. Specifically, the expansion matrix is ​​multiplied by the transpose of the orthogonal projection basis matrix to generate a small-scale projection matrix Z(n), which represents the projection onto a low-dimensional subspace. Perform truncated singular value decomposition on the small-scale projection matrix Z(n) to obtain the matrix multiplication expansion of the small-scale left singular matrix, singular value diagonal matrix, and right singular matrix, and extract the first... Small-scale left singular matrix of order; Multiplying the orthogonal projection basis matrix by a small-scale left singular matrix yields the orthogonal factor matrix, which includes the spatial module orthogonal factor matrix, the temporal module orthogonal factor matrix, the working condition module orthogonal factor matrix, and the topological module orthogonal factor matrix. Specifically, when n is 1, matrix multiplication yields the spatial modulus orthogonal factor matrix, which represents the orthogonal projection basis of the spatial measurement point dimension; When n is 2, matrix multiplication yields the time modulus orthogonality factor matrix; When n is 3, matrix multiplication yields the orthogonal factor matrix of the operating condition module, which represents the orthogonal projection basis of the operating condition dimension; When n is 4, matrix multiplication yields the orthogonal factor matrix of the topological modulus, which represents the orthogonal projection basis of the topological dimension of the structure. The core tensor is calculated by performing modular-n multiplications on the transpose of the corresponding orthogonal factor matrix along the four dimensions of the fourth-order thermal state tensor.

[0049] Specifically, the core tensor is calculated by performing a modular-n multiplication folding with the transpose of the four obtained orthogonal factor matrices and the fourth-order thermal state tensor. Its mathematical expression is: ; in, For dimension size The core tensor represents the low-rank principal components of the machine tool thermal state energy distribution within the current historical sliding window. It is a fourth-order thermal state tensor. , , and These represent the spatial model orthogonality factor matrix, the temporal model orthogonality factor matrix, the operating condition model orthogonality factor matrix, and the topological model orthogonality factor matrix, respectively. This represents the tensor modulus-n multiplication operator. This represents the transpose matrix, and the calculated factor matrix is ​​latched and written to shared memory.

[0050] Using core tensor The energy proportion is used to evaluate the fitting quality of the low-rank space and dynamically update the truncated rank. It should be noted that the learning module will calculate the spatial modulus orthogonal factor matrix. Orthogonal factor matrix of working condition model orthogonal factor matrix of topological modulus Write to the ping-pong double buffer register. After writing, update the shared memory pointer without locking using an atomic pointer swap instruction.

[0051] When the main real-time control module detects an update to the orthogonal factor matrix pointer, it calculates the basis transformation matrix based on the new and old orthogonal factor matrices and performs orthogonal coordinate transformation on the covariance matrix of the state-space model, or it reinitializes the parameter matrix of the recursive least squares algorithm, resetting the covariance matrix to the initial diagonal matrix and resetting the state transition matrix and input matrix to their initial values.

[0052] The main real-time control module is connected to both the preprocessing module and the learning module. The process of extracting the transient low-dimensional current thermal state coordinate vector includes: At the current time t, the latest sampling point section is extracted from the fourth-order thermal state tensor along the time axis to obtain a three-dimensional physical observation slice, which includes the spatial measurement point dimension, the operating condition dimension and the structural topology dimension. Specifically, at the current time t of each first sampling period, the latest sampling point section is extracted along the second-dimensional sliding time window dimension of the fourth-order thermal state tensor T, i.e., the discrete-time index is locked. = =1000, generates a 3D physical observation slice without the historical time dimension. ; Within the first 0.00001 seconds of the first sampling period, the ping-pong double buffer register in shared memory is accessed through atomic pointers to read the spatial modulus orthogonal factor matrix, the working condition modulus orthogonal factor matrix, and the topology modulus orthogonal factor matrix, which are latest updated and latched by the learning module. The main real-time control module temporarily latches the above three orthogonal factor matrices in the local high-speed cache of the current control period to ensure that the orthogonal basis data remains absolutely constant during subsequent matrix operations within the current 0.001-second period, thus avoiding data competition caused by asynchronous updates from the background module. The three-dimensional physical observation slice is multiplied along each of the three dimensions by the transpose of the spatial mode orthogonal factor matrix, the transpose of the working condition mode orthogonal factor matrix, and the transpose of the topological mode orthogonal factor matrix, and the product results are vectorized to generate the current thermal state coordinate vector.

[0053] Specifically, 3D physical observation slices Multiplying the transpose of the spatial modulus orthogonal factor matrix along the spatial measurement point dimension generates the first intermediate tensor. Its mathematical expression is: ; First intermediate tensor The expression for calculating the scalar element is: ; in, , , This is the low-rank target dimension index for the low-rank evolution space of the thermal state. This is the original spatial measurement point index. This is the original operating condition index. This is the original structure topology index.

[0054] Similarly, following the calculation logic of the first intermediate tensor, the first intermediate tensor is multiplied along the operating condition dimension by the transpose of the orthogonal factor matrix of the operating condition module to generate the second intermediate tensor. Similarly, the second intermediate tensor is multiplied along the structural topology dimension by the transpose of the topological modulus orthogonality factor matrix to generate a three-dimensional current thermal state tensor. The main real-time control module uses the column-major order vectorization operator to expand the three-dimensional current thermal state tensor into a one-dimensional column vector according to the column priority rule, generating a transient low-dimensional current thermal state coordinate vector, which accurately expresses the coordinate position of the machine tool's transient thermal state in the low-rank evolution space at the current time t.

[0055] It should be noted that, in one embodiment of the present invention, a first intermediate tensor is generated during the entire extraction process of the current thermal state coordinate vector. The number of multiplication operations is The number of multiplication operations required to generate the second intermediate tensor is [number]. The number of multiplication operations required to generate the three-dimensional current thermal state tensor is [number]. The number of memory addressing and expansion operations is 16, and the total number of floating-point operations is only 2560+160+80=2800. The actual calculation time on the general-purpose industrial control computer embedded processor (2.0GHz) is less than 0.000002 seconds (2 microseconds), which only occupies 0.2% of the 1000 microsecond time quota of the first sampling period. The architecture ensures the extremely high hard real-time performance and control response speed of the main real-time control module.

[0056] The state recursion yields the predicted thermal state coordinate vector, specifically including: The normalized spindle speed and cutting load rate at the current moment are spliced ​​together to form a feedforward input column vector. Based on the feedforward input column vector and the current thermal state coordinate vector, a state transition matrix and an input matrix are introduced. A single-step prior prediction is performed on the current moment in the low-rank thermal state evolution space to obtain the first predicted thermal state coordinate vector. Specifically, at the current moment, the discrete sampling step number k of the first sampling period is used to extract the real-time controllable spindle speed and cutting load rate from the 4-dimensional operating condition features, and then normalize them and splice them to form a feedforward input column vector. The 4-dimensional operating condition features are the 4th order thermal state tensor expanded in the modulus-3 (i.e., n=3) direction, which is used to construct the operating condition signal of the modulus-3 block Krylov extended subspace K(3). Ambient temperature and spindle drive current are preserved as slowly varying background features within a low-rank subspace spanned by orthogonal factor matrices; The augmented parameter matrix based on the previous discrete sampling step number k-1 A single-step priori prediction is performed at the current moment to calculate the first predicted thermal state coordinate vector, whose mathematical expression is: ; in, Let be the coordinate vector of the current thermal state at step k-1. This is the first predicted thermal state coordinate vector. Let be the state transition matrix for the (k-1)th step. The input matrix for the (k-1)th step. Let be the feedforward input column vector at step k-1. Let be the augmented parameter matrix of the previous discrete sampling step number k-1. To augment the data vector; The weighted recursive least squares algorithm is used to update the state transition matrix and input matrix online. The current feedforward input column vector and the current thermal state coordinate vector are input, and the second predicted thermal state coordinate vector after the total control response delay of the system is calculated.

[0057] Specifically, the overall system control response delay , For the first sampling period, the number of discrete recursion steps ; The calculation process of updating the state transition matrix and the input matrix online using the weighted recursive least squares algorithm within each first sampling period includes: The state transition matrix and input matrix The augmented parameter matrix is ​​obtained by splicing. The current thermal state coordinate vector Subtract the first predicted thermal state coordinate vector The prior prediction error vector of the current state is calculated. Its mathematical expression is: ; Calculate the gain vector And updating the covariance matrix Its mathematical expression is: ; ; in, The weighted forgetting factor is set to a fixed value of [value missing]. =0.98, Let be the covariance matrix of the previous discrete sampling step number k-1.

[0058] Using gain vector With the state prior prediction error vector Recursively update the augmented parameter matrix Its mathematical expression is: ; in, Gain vector The transpose of ; From the updated augmented parameter matrix Extract the state transition matrix of the current discrete sampling step k from the middle. and input matrix .

[0059] During the state recursion process over d consecutive steps, it is assumed that the future control input satisfies the zeroth-order preservation assumption within the prediction window, i.e. ; The main real-time control module utilizes the updated state transition matrix and input matrix Perform d-step continuous state recursive calculations to obtain the coordinate vector of the second predicted thermal state. Its mathematical expression is: ; in, and These represent the state transition matrices after state evolution and propagation through d and j cycles, respectively.

[0060] Since the learning module runs in the second sampling period (1.0 second) and the main real-time control module runs in the first sampling period (0.001 seconds), both use ping-pong double-buffered registers for lock-free data exchange. When the main real-time control module detects an update to the pointer of the orthogonal factor matrix at offline step k, the basis of the projected low-dimensional coordinates changes from the old orthogonal factor matrix to the new orthogonal factor matrix. To prevent the state transition matrix and covariance matrix under the old basis from directly acting on the new basis space, causing the state prediction values ​​to diverge, the following parameter reset mechanism is adopted in this embodiment: when a pointer update is detected, the main real-time control module resets the covariance matrix of the recursive least squares algorithm to a diagonal matrix. ,in express The identity matrix of dimension is used to reset the augmented parameter matrix, formed by concatenating the state transition matrix and the input matrix, to its initial structure. ,in This represents an all-zero matrix. This reset mechanism avoids state recursion distortion caused by switching of spatial orthogonal basis, ensuring the operational stability of the control system.

[0061] Reconstructing the high-dimensional predictive physical thermal field tensor specifically includes: By using the tensor inverse vectorization operator, the second predicted thermal state coordinate vector is reconstructed and restored into a three-dimensional third thermal state prediction tensor according to the index inverse mapping rule from one-dimensional index to three-dimensional index. Specifically, the calculation rules for the index inverse mapping rule are as follows: Fill the m-th element of the second predicted thermal state coordinate vector into the three-dimensional third thermal state prediction tensor. The corresponding position , Its mathematical expression is: , ; , ; , ; Where m represents the index of an element in the second predicted thermal state coordinate vector. For low-rank spatial dimension index, This is a low-rank dimension index for operating conditions. For topological low-rank dimension index, Truncating the rank of the spatial model target Cut the rank of the target for the working condition model. This indicates the floor function. This represents the modulo operation.

[0062] The third thermal state prediction tensor is multiplied along the three dimensions by the spatial mode orthogonality factor matrix, the working condition mode orthogonality factor matrix, and the topological mode orthogonality factor matrix to reconstruct the high-dimensional prediction physical thermal field tensor. Among them, the orthogonal projection operator formed by multiplying the orthogonal factor matrix and its transpose matrix has the property of sign invariance.

[0063] Specifically, the main real-time control module performs modular multiplication on the three-dimensional low-dimensional thermal state prediction tensor along the three dimensions with the spatial modulus orthogonal factor matrix, the operating condition modulus orthogonal factor matrix, and the topological modulus orthogonal factor matrix, respectively, to reconstruct the high-dimensional predicted physical thermal field tensor. Its mathematical expression is: ; in, , and These are tensor modular multiplication operators modulo-1, modulo-2, and modulo-3, respectively; Reconstructed high-dimensional predictive physical thermal field tensor The mathematical expression for the scalar element in the formula is: ; in, Represents the high-dimensional predictive physics thermal field tensor The spatial measurement point dimension index is The operating condition dimension index is The structural topology dimension index is scalar element at the location, For spatial measurement point dimension index, For indexing the operating condition dimension, For structural topology dimension indexing, The first element in the spatial modulus orthogonal factor matrix Line 1 Column matrix elements, The first element in the orthogonal factor matrix of the working condition model Line 1 Column matrix elements, The first element in the topological modulus orthogonal factor matrix Line 1 Columns of matrix elements.

[0064] The proof logic for the invariance of positive and negative signs includes: In the chain expansion mapping relationship of projecting three-dimensional physical observation slices onto a low-dimensional subspace and then reconstructing them into a high-dimensional predicted physical thermal field tensor, the reconstructed predicted physical thermal field satisfies: ; in, The orthogonal projection operator is defined as follows: (This refers to a 3D physical observation slice at prediction time k+d.) Spatial Module Orthogonal Projection Operator ; orthogonal projection operator of working condition model ; Topological orthogonal projection operator .

[0065] When the learning module encounters a 180-degree sign flip of the orthogonal basis vectors during the truncated singular value decomposition process, i.e., the orthogonal factor matrix changes... The transformation, among which When the orthogonal projection operator is used, the calculation result is: ; Meanwhile, the chain mapping formula for predicting recursion and reconstruction is as follows: ; in, Represents the discrete state transition matrix. Generally refers to orthogonal factor matrices, where the superscript d indicates the recursion step number and the superscript T indicates matrix transpose. The positive and negative signs cancel each other out in coordinate projection and spatial reconstruction, keeping the calculation results of the orthogonal projection operator constant, thus ensuring the reconstructed high-dimensional predicted physical thermal field tensor. The magnitude and direction of the value are not affected by the sign flipping of the orthogonal basis in the background singular value decomposition, thus ensuring the stability of the control system.

[0066] The specific process of calculating the thermal error vector at the tool tip includes: The high-dimensional predicted physical thermal field tensor is vectorized and expanded, then multiplied by the physical topology mapping matrix obtained in advance through the calibration of the machine tool's thermoelastic physical properties, and the output is a tool tip thermal error vector containing the translation and rotation directions in three-dimensional space.

[0067] Specifically, the main real-time control module uses the column-major order vectorization operator to transform the three-dimensional high-dimensional predictive physical thermal field tensor according to the column priority rule. Expanded into a one-dimensional column vector of the predicted physical thermal field, its dimension is ; Physical topology mapping matrix Multiply the one-dimensional predicted physical thermal field column vector on the right to calculate the predicted time. The thermal error vector at the blade tip; Physical topology mapping matrix The equations were obtained by solving the overdetermined ill-conditioned system of equations using a ridge regression algorithm with L2 regularization during the offline initialization phase of the machine tool. The calculation expression is as follows: ; in, The physical topology mapping matrix, This is a matrix composed of column vectors of the high-dimensional predicted physical thermal field from historical sampling, with its dimension being the number of samples. , This is the matrix of measured values ​​for the thermal error at the blade tip, with the dimension being the number of samples. , The regularization coefficient is . for The identity matrix; In the standard thermal calibration experiment, a laser interferometer and a five-axis thermal error measuring instrument were used to simultaneously acquire three translational displacements and two rotational angles of the tool tip under different thermal conditions. A linear thermo-elastic compliance equation system was established from the 640-dimensional high-dimensional thermal field to the 5-dimensional tool tip thermal error, and the physical topological mapping matrix was solved. The physical topology mapping matrix has a dimension of 5×640; Referring to Table 1, the physical topology mapping matrix is ​​shown. Parameter values ​​table (units: translation is in mm / normalized units, rotation is in rad / normalized units)

[0068] Physical topology mapping matrix matrix elements ,in , respectively representing the translation coefficients Translation coefficient Translation coefficient Rotation coefficient Rotation coefficient ,and , represents the element index in the column vector of the one-dimensional predicted physical thermal field, matrix element The numerical distribution patterns include: exist , representing spatial measurement points Operating conditions Structural topology At this location, the matrix elements are ,and ,exist , representing spatial measurement points Operating conditions Structural topology At this location, the matrix elements are ,and ;exist , representing spatial measurement points Operating conditions Structural topology At this location, the matrix elements are ;exist , representing spatial measurement points Operating conditions Structural topology At this location, the matrix elements are ; The translation transfer coefficients in rows 1 to 3 have numerical values ​​distributed on the order of magnitude of... ~ Thermal error of spindle components (e.g., N=1, 2, 33) in the Z-axis direction within the range of mm. The transfer coefficient is significantly greater than that in the X and Y axis directions, reflecting the physical characteristic that the thermal deformation of the main shaft is concentrated in the axial elongation. The motion axis lead screw components (such as N=129,257,385) generate the maximum mapping coefficient for their main motion direction (e.g., X-axis lead screw nut measuring point pair). mapping coefficients Y-axis lead screw nut measuring point pair mapping coefficients Z-axis lead screw nut measuring point pair mapping coefficients This aligns with the physical laws governing thermal expansion of each feed axis of the machine tool.

[0069] The angular deformation transfer coefficients in rows 4 and 5 have numerical values ​​distributed in the range of... Within the range, the bending deformation of the Z-axis column and spindle box mainly induces the A-axis rotational thermal tilt angle error. Asymmetrical heating of the X-axis / Y-axis bed mainly induces C-axis rotational thermal deviation error. .

[0070] Multiply the physical topology mapping matrix by the one-dimensional predicted physical thermal field column vector to obtain the tip thermal error vector at the predicted time. The tip thermal error vector includes the tip thermal error in the X-axis translation direction at the prediction time, the tip thermal error in the Y-axis translation direction at the prediction time, the tip thermal error in the Z-axis translation direction at the prediction time, the tip thermal tilt angle error in the A-axis rotation direction at the prediction time, and the tip thermal deflection angle error in the C-axis rotation direction at the prediction time. The output tool tip thermal error vector is transmitted to the feedforward compensation execution module to generate the corrected control position vector of the servo drive unit in real time.

[0071] The compensation module is connected to the main real-time control module, and the process of calculating the corrected control position vector includes: The tool tip thermal error vector is subtracted from the original motion command position vector of the CNC system to generate a corrected control position vector, which is then injected into the servo drive unit through the tool tip follower interface or servo bias register.

[0072] This invention decouples the low-speed tensor low-rank space learning with a 1.0-second cycle in the background from the ultra-fast 1.0-millisecond control loop in the foreground by lock-free pointer asynchronous decoupling. The main control loop only needs to perform a very small number of (less than 2800 FLOPs) low-dimensional matrix projections and vector multiplications, with a computation time of only microseconds. This completely solves the hard real-time contradiction between high-dimensional thermal field feature extraction and the millisecond-level interpolation cycle of the CNC system.

[0073] The learning module constructs a dimensionality reduction sketch by multiplying the Gaussian random sampling matrix by the flattening matrix on the right, and performs block Krylov chain iterative decomposition based on the right multiplication associative law of matrix multiplication. This explicitly avoids the direct calculation of the high-dimensional covariance matrix, greatly suppressing tail singular values ​​and high-frequency noise interference. While ensuring the energy accuracy of the principal components in space, the computational complexity of dimensionality reduction is reduced by several orders of magnitude.

[0074] The main real-time control module extracts a three-dimensional physical observation slice from the fourth-order thermal state tensor, which is the latest discrete moment without the historical sliding window, and projects it to obtain the current transient low-dimensional thermal state coordinate vector. This completely eliminates the conflict between the dimension definition of the sliding time window and the single-step recursive prediction of the state space model, and ensures the physical and mathematical consistency of the state recursion.

[0075] By chain-expanding the transient coordinate extraction formula and the high-dimensional physical thermal field reconstruction formula, it is proved that the orthogonal projection reconstruction operator has the invariance of quadratic multiplication negative sign cancellation when the orthogonal factor matrix undergoes U→-U sign flip, thus completely avoiding the risk of control quantity inverse superposition and servo control divergence caused by background truncation singular value decomposition orthogonal basis flip.

[0076] A ridge regression algorithm with L2 regularization is introduced to construct a physical topology mapping matrix, which effectively overcomes the problem of spatial multicollinearity among high-dimensional thermal field features. It realizes a stable mapping from a 640-dimensional high-dimensional thermal field to the thermal error of the tool tip point, which includes 5 degrees of freedom (3 translations and 2 rotations), and significantly improves the accuracy of thermal error compensation in the entire machining space of the machine tool.

[0077] The sequence numbers of the embodiments in this application are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0078] In the above embodiments of this application, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0079] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A real-time thermal error compensation control system for high-speed CNC machine tools, characterized in that, include: The preprocessing module is used to acquire the control signals of the CNC machine tool according to the first sampling period, perform multi-rate time synchronization on the control signals, and obtain the thermal state observation sequence through standardization; The learning module is used to read the thermal state observation sequence according to the second sampling period, construct a fourth-order thermal state tensor, and use a Gaussian random sampling matrix to perform modular-n matrix transformation and dimension reduction sketching on the fourth-order thermal state tensor. Based on random block Krylov iteration, column-pivot orthogonal triangular decomposition and small-scale truncated singular value decomposition, the spatial modular orthogonal factor matrix, the temporal modular orthogonal factor matrix, the operating condition modular orthogonal factor matrix, the topological modular orthogonal factor matrix and the core tensor are solved to construct the low-rank evolution space of the thermal state. The main real-time control module is used to extract the three-dimensional physical observation slice at the current moment in each first sampling period, and project the three-dimensional physical observation slice onto the thermal state low-rank evolution space using the orthogonal factor matrix of each mode to obtain the current thermal state coordinate vector. The current thermal state coordinate vector is recursively derived using a local linear state-space model to obtain the predicted thermal state coordinate vector. The high-dimensional predicted physical thermal field tensor is reconstructed using an orthogonal projection operator, and the tip thermal error vector is calculated using a physical topology mapping matrix based on regularization. The compensation module is used to subtract the tool tip thermal error vector from the original motion command position vector of the CNC system, calculate the corrected control position vector, and inject it into the servo drive unit to perform compensation.

2. The high-speed CNC machine tool thermal error real-time compensation control system according to claim 1, characterized in that, The preprocessing module specifically includes: The first sampling period is 0.001 seconds; The control signals include spatial measurement point temperature signals, operating condition signals, and structural topology position signals; The calculation process for obtaining the thermal state observation sequence includes: Extract the physical sampling mean and physical sampling standard deviation of each control signal within the set historical sliding window. Subtract the physical sampling mean from the original physical sampling value at the current moment and then divide by the physical sampling standard deviation to obtain the normalized physical thermal state observation value. Then, concatenate the normalized physical thermal state observation values ​​of the signals included in the sliding window into a thermal state observation sequence.

3. The real-time thermal error compensation control system for high-speed CNC machine tools according to claim 1, characterized in that, The learning module specifically includes: Connected to the preprocessing module, the thermal state observation sequence within the sliding time window is extracted according to the second sampling period, which is 1.0 second; The fourth-order thermal state tensor includes: Spatial measurement point dimension represents the number of temperature sensors arranged in the space; The sliding time window dimension represents the number of historical sampling points included; In terms of operating conditions, this represents the number of heat source parameters such as spindle speed, spindle drive current, and cutting load rate. The fourth dimension is the structural topology dimension, which represents the number of topological nodes of the machine tool motion axes and bed components.

4. The high-speed CNC machine tool thermal error real-time compensation control system according to claim 3, characterized in that, The learning module utilizes a Gaussian random sampling matrix to perform modular-n matrix expansion and dimension reduction sketching on the fourth-order thermal state tensor, including the following process: The expansion matrix is ​​obtained by performing a modular-n matrix expansion along the four dimensions of the fourth-order thermal state tensor. The expansion matrix is ​​then multiplied by the fixed Gaussian random sampling matrix generated during the system startup phase to obtain the dimension-reduced sketch matrix. Based on the expansion matrix and the dimensionality reduction sketch matrix, a modular-n block Krylov extended subspace matrix is ​​constructed by performing right-multiplication associative chain decomposition calculation through matrix multiplication.

5. The high-speed CNC machine tool thermal error real-time compensation control system according to claim 4, characterized in that: In the learning module, the process of solving for the orthogonal factor matrix and the core tensor includes: The orthogonal projection basis matrix is ​​extracted by column-pivoting orthogonal triangular decomposition of the modular-n block Krylov extended subspace matrix; The expanded matrix is ​​projected onto a low-dimensional subspace constructed by orthogonal projection basis matrices to obtain a small-scale projection matrix. The small-scale projection matrix is ​​then truncated and singular value decomposition is performed to extract singular vectors. The orthogonal projection basis matrix is ​​right-multiplied by a small-scale left singular matrix to obtain the orthogonal factor matrix, which includes the spatial model orthogonal factor matrix, the temporal model orthogonal factor matrix, the working condition model orthogonal factor matrix, and the topological model orthogonal factor matrix. The core tensor is calculated by performing modular-n multiplications on the transpose of the corresponding orthogonal factor matrix along the four dimensions of the fourth-order thermal state tensor.

6. The real-time thermal error compensation control system for high-speed CNC machine tools according to claim 1, characterized in that: The main real-time control module is connected to both the preprocessing module and the learning module. The process of extracting the transient low-dimensional current thermal state coordinate vector includes: At the current time t, the latest sampling point section is extracted from the fourth-order thermal state tensor along the time axis to obtain a three-dimensional physical observation slice, which includes spatial measurement point dimension, operating condition dimension and structural topology dimension. The three-dimensional physical observation slice is multiplied along each of the three dimensions by the transpose of the spatial mode orthogonal factor matrix, the transpose of the working condition mode orthogonal factor matrix, and the transpose of the topological mode orthogonal factor matrix, and the product results are vectorized to generate the current thermal state coordinate vector.

7. The real-time thermal error compensation control system for high-speed CNC machine tools according to claim 6, characterized in that: The state recursion yields the predicted thermal state coordinate vector, specifically including: The normalized spindle speed and cutting load rate at the current moment are spliced ​​together to form a feedforward input column vector. Based on the feedforward input column vector and the current thermal state coordinate vector, a state transition matrix and an input matrix are introduced. A single-step prior prediction is performed on the current moment in the low-rank thermal state evolution space to obtain the first predicted thermal state coordinate vector. The weighted recursive least squares algorithm is used to update the state transition matrix and input matrix online. The current feedforward input column vector and the current thermal state coordinate vector are input, and the second predicted thermal state coordinate vector after the total control response delay of the system is calculated.

8. The real-time thermal error compensation control system for high-speed CNC machine tools according to claim 7, characterized in that: Reconstructing the high-dimensional predictive physical thermal field tensor specifically includes: By using the tensor inverse vectorization operator, the second predicted thermal state coordinate vector is reconstructed and restored into a three-dimensional third thermal state prediction tensor according to the index inverse mapping rule from one-dimensional index to three-dimensional index. The third thermal state prediction tensor is multiplied along the three dimensions by the spatial mode orthogonality factor matrix, the working condition mode orthogonality factor matrix, and the topological mode orthogonality factor matrix to reconstruct the high-dimensional prediction physical thermal field tensor. Among them, the orthogonal projection operator formed by multiplying the orthogonal factor matrix and its transpose matrix has the property of sign invariance.

9. The real-time thermal error compensation control system for high-speed CNC machine tools according to claim 8, characterized in that: The specific process of calculating the thermal error vector at the tool tip includes: The high-dimensional predicted physical thermal field tensor is vectorized and expanded, then multiplied by a physical topology mapping matrix obtained in advance through calibration of the machine tool's thermoelastic physical properties, to output a tool tip thermal error vector containing the three-dimensional spatial translation and rotation directions.

10. The real-time thermal error compensation control system for high-speed CNC machine tools according to claim 1, characterized in that: The compensation module is connected to the main real-time control module, and the process of calculating the corrected control position vector includes: The tool tip thermal error vector is subtracted from the original motion command position vector of the CNC system to generate a corrected control position vector, which is then injected into the servo drive unit through the tool tip follower interface or servo bias register.

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