A numerical control machine tool temperature key point screening method combined with causality analysis

Abstract

The present application relates to the field of numerical control machine tool error compensation, especially to a numerical control machine tool temperature key point screening method combined with causality analysis, first collecting temperature data of key positions of the machine tool; using self-organizing mapping clustering to classify the measuring points with similar thermal behaviors into the same cluster; performing stationarity test on the temperature time series data in each cluster, and constructing a directed causal adjacency matrix between the temperature measuring points based on Toda-Yamamoto Granger causality test; through Pareto multi-objective optimization, taking maximizing out-degree and minimizing in-degree as the criteria, screening out the temperature measuring points which play the role of equivalent heat source in time series as the final temperature key points of the cluster. The present application introduces causality analysis into the temperature key point screening process, and uses the time series direction information to eliminate downstream passive measuring points in each cluster formed by clustering; provides input variables with clear physical meaning and low redundancy for thermal error modeling and compensation, and provides technical support for the arrangement of temperature sensors.

Description

Technical Field

[0001] This invention relates to the field of error compensation for CNC machine tools, and in particular to a method for screening key temperature points of CNC machine tools by combining causal analysis. Background Technology

[0002] As a key piece of equipment in modern industrial systems, the machining accuracy of CNC machine tools directly determines the quality and performance of the final product. Among the various factors affecting the accuracy of CNC machine tools, thermal error is one of the main sources of error affecting machining accuracy and long-term stability. Implementing thermal error compensation is an effective technical approach to suppress thermally induced errors and improve machining accuracy. Establishing an accurate and reliable thermal error model is a prerequisite for achieving high-performance compensation, and the selection of key temperature points directly determines the input quality and generalization ability of the model.

[0003] Existing methods for screening key temperature points are mostly based on correlation analysis, which measures the strength of the statistical correlation between temperature measurement points and thermal errors. These methods, relying on the statistical correlation between variables, have inherent limitations when processing time-series temperature data. Firstly, the correlation coefficient only reflects whether the temperature time-series data and thermal error data change synchronously, without addressing the causal relationships between different measurement points, and thus cannot reveal the order of heat conduction within the temperature field. Secondly, these methods do not explicitly consider the time lag of heat conduction. Under non-steady-state conditions such as variable speed or start-stop cycles, the static correlation may fluctuate with the lag time, leading to a decrease in the stability of the correlation between the selected key points and the thermal error. Summary of the Invention

[0004] The purpose of this invention is to provide a method for screening key temperature points in CNC machine tools that combines causal analysis. This method introduces causal analysis to determine the direction of heat conduction and time lag between measuring points from temperature time series data, thus solving the technical problems of existing methods that are difficult to distinguish the direction of heat conduction and time lag and are prone to misjudging passive measuring points as key variables.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: A method for screening key temperature points in CNC machine tools by combining causal analysis includes the following steps: Step 1: Collect time-series temperature data from multiple temperature measurement points on the machine tool; Step 2: Cluster the temperature measurement points based on the self-organizing map algorithm, and group the temperature measurement points with similar thermal behavior into the same cluster; Step 3: Use the augmented Dickey-Fuller test to check the stationarity of the time series temperature data at each temperature measurement point, determine the integration order of each time series temperature data, and take the maximum integration order of all measurement points as the additional lag order. Step 4: Based on the additional lag order, perform pairwise Toda-Yamamoto Granger causality tests on all temperature measurement points within the cluster, and construct a directed causal adjacency matrix that reflects the Granger causal relationship between temperature measurement points within the cluster. Step 5: Based on the directed causal adjacency matrix, calculate the out-degree and in-degree of each temperature measurement point; the out-degree is the number of other measurement points in the cluster caused by the measurement point as a Granger cause, and the in-degree is the number of other measurement points in the cluster caused by the measurement point as a Granger result. With the dual objectives of maximizing out-degree and minimizing in-degree, Pareto optimality is used to select Pareto optimal measurement points within each cluster, and all Pareto optimal measurement points constitute the temperature key point set of the cluster.

[0006] Furthermore, in step 2, the temperature measurement points are clustered based on the self-organizing map algorithm, including: taking the time-series temperature data of each temperature measurement point as input; mapping the input to a low-dimensional neuron grid, and determining the best matching unit for each input by iteratively updating the weight vector of each neuron; and grouping the temperature measurement points with the same or adjacent best matching units into the same cluster.

[0007] Furthermore, the optimal matching unit is established by calculating temperature data. With weight vector The minimum Euclidean distance is obtained; Weight vector update: ,in, The number of iterations. The learning rate decays over time. For neighborhood functions, and Neuron and Coordinates on the output grid, is the neighborhood radius that decays over time.

[0008] Furthermore, in step 4, the Toda-Yamamoto Granger causality test includes: For any two temperature measurement points within the cluster and The optimal lag order can be determined using the AIC or BIC criterion. Combined with the additional lag order obtained in step 3 The lag order is constructed as Vector autoregression model; , in, , The first The and the first At time 1, temperature measuring points Observed values; For constant terms; The coefficient for the trend term; , These are the coefficients of the lagged dependent variable and the lagged explanatory variables, respectively. This is the random error term; For the variables in the vector autoregressive model The former The lag coefficients are subjected to a Wald test; if the test statistic exceeds the critical value, then the result is determined to be... yes The Granger causality; by performing pairwise checks on all measure points within the cluster, a directed causal adjacency matrix can be constructed. , , The number of temperature measurement points within the cluster. .

[0009] Furthermore, in step 5, Pareto optimality screening is employed, including: For any two temperature measurement points within the cluster and If both conditions are met and If at least one inequality holds strictly, then the temperature measuring point is called a temperature measuring point. Pareto-dominated temperature measurement points If there are no other measuring points within the cluster, the Pareto-dominated measuring points are... Then the measuring point This is the Pareto optimal measurement point.

[0010] The present invention also provides a thermal error prediction method, which includes using the above-mentioned CNC machine tool temperature key point screening method combined with causal analysis to screen temperature key point set and collect temperature data, and predicting spindle thermal error based on a thermal error prediction model that integrates gated loop unit and self-attention mechanism.

[0011] Compared with the prior art, the present invention has the following beneficial effects: (1) Introducing causal analysis, constructing a vector autoregression model through the Granger causality test method, and directly performing causal analysis on non-stationary temperature sequences, can clearly identify the direction of heat conduction and time lag between each measuring point from the time series data, fundamentally solving the technical problem that traditional methods cannot distinguish between equivalent heat source measuring points and passive response measuring points.

[0012] (2) The screening of temperature key points is transformed into a bi-objective optimization problem of "maximizing out-degree and minimizing in-degree". The Pareto front is used to solve the non-dominated solution set as the temperature key points, which can identify the equivalent heat source measurement points that play a dominant role in the time sequence, while eliminating redundant measurement points with passive response.

[0013] (3) The selected temperature key points have clear engineering guidance significance, namely, the measuring points that play the role of equivalent heat source in the time sequence, which can be directly used to guide the optimization of the temperature sensor layout scheme of CNC machine tool, reduce the number of sensors while ensuring the thermal error compensation effect, and reduce the system hardware cost and engineering implementation difficulty. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of the process of the present invention.

[0015] Figure 2 A comparison chart of thermal error predictions for the SOM-GC, FCM-PC, and FCM-SC methods.

[0016] Figure 3 A comparison chart of the prediction residuals for the SOM-GC, FCM-PC, and FCM-SC methods.

[0017] Figure 4 The chart shows the comparison of MAE and RMSE for the SOM-GC, FCM-PC, and FCM-SC methods. Detailed Implementation

[0018] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0019] This embodiment discloses a method for screening key temperature points in CNC machine tools based on causal analysis, comprising the following steps: Step 1: Acquisition of temperature data and thermal error data; Several PT100 temperature sensors are arranged at key locations on the machine tool to collect a set of time-series temperature data for each temperature measurement point every minute. At the same time, eddy current displacement sensors are used to measure the spindle thermal error data, providing data support for subsequent screening of key temperature points and verification of thermal error modeling.

[0020] The key locations of the machine tool include, but are not limited to, the spindle, spindle box, column, and key heat-sensitive parts such as the spindle coolant inlet and outlet.

[0021] Step 2: Self-organizing mapping clustering of temperature measurement points; The self-organizing map algorithm is used to cluster the temperature measurement points, and the measurement points with similar thermal behavior are grouped into the same cluster, so as to identify the equivalent heat source measurement points and downstream passive measurement points when performing causal analysis within the cluster.

[0022] Temperature measurement point dataset ,in, For the first Temperature data from each temperature measuring point This represents the total number of temperature measurement points. The temperature measurement point dataset is a high-dimensional temperature time-series feature. In this embodiment, it is mapped onto a low-dimensional neural network using a self-organizing map algorithm, with temperature data as its input. The output layer contains 1 neuron, each neuron Corresponding to a weight vector , By calculating temperature data With weight vector The Euclidean distance between the two elements is used to determine the optimal matching unit; the optimal matching unit is determined by the minimum distance between the two elements. In the formula, It is the Euclidean norm.

[0023] Through iterative updates, the weight vector gradually fits the distribution of the input data. (Weight update) ,in, The number of iterations. The learning rate decays over time. For neighborhood functions, , and Neuron and Coordinates on the output grid, is the neighborhood radius that decays over time.

[0024] After iterative convergence, measurement points with the same or adjacent best-matching units (BMUs) are grouped into the same cluster, thereby achieving effective clustering of measurement points with similar thermal behavior and providing a reasonable grouping basis for subsequent intra-cluster causal analysis.

[0025] Step 3: Temperature series stationarity test; During machine tool operation, the time-series data of temperature measurement points are often non-stationary due to the influence of the environment, operating conditions, and heat conduction processes. To meet the requirement of the order of integration of the sequence for the subsequent Toda-Yamamoto Granger causality test, this embodiment uses the augmented Dickey-Fuller test to determine the order of integration of the temperature sequence.

[0026] The regression model with augmented Dickie-Fuller test: , in, This is a constant term (drift term). For time trend items, The coefficients to be estimated; These are differential lag terms used to eliminate autocorrelation in the series. The lag order is... , These are the coefficients of the difference lag term; This represents the random error term.

[0027] Null hypothesis Coefficients to be estimated This indicates the existence of a unit root and that the sequence is non-stationary. The augmented Dickey-Fuller test statistic is defined as follows: , The least squares estimate of γ. yes The standard error is calculated. If the test statistic is less than the critical value, the null hypothesis is rejected, and the temperature series is considered stationary. Otherwise, the null hypothesis is not rejected, and the temperature series is considered non-stationary. Differentiation is required until the series becomes stationary, and its order of integration is recorded.

[0028] In practical engineering applications, all temperature measuring points on a machine tool are under the same heat source excitation and heat conduction environment, and the non-stationary order of their temperature sequences has inherent consistency. Therefore, after determining the integrated order by performing an augmented Dickey-Fuller test on each measuring point, the maximum value of the integrated order among all measuring points is taken as the additional lag order for the Toda-Yamamoto Granger causality test between any pair of temperature measuring points within any cluster. This utilizes the Granger test's inclusiveness towards additional lag terms and reduces the risk of underestimating the order of individual measuring points in small samples, simplifying the preprocessing procedure while ensuring the reliability of the test.

[0029] Step 4: Toda-Yamamoto Granger causality test; To identify the direction and time lag of heat conduction among temperature measurement points within the same cluster, and to distinguish between the equivalent heat source measurement points that play a dominant role in time sequence and the downstream measurement points that passively respond, each temperature measurement point cluster obtained by the self-organizing map algorithm is analyzed. Within it, paired Toda-Yamamoto Granger causality tests are performed.

[0030] Cluster Contains For each temperature measurement point, and for two temperature measurement points to be tested, the optimal lag order of the temperature sequence is determined using the AIC or BIC criterion. And based on the additional lag order Construct a lag order of Vector Autoregression (VAR) model: ,in , The first The and the first At time 1, temperature measuring points Observed values; For constant terms; The coefficient for the trend term; , These are the coefficients of the lagged dependent variable and the lagged explanatory variables, respectively. This is the random error term.

[0031] The Toda-Yamamoto Granger causality test only applies to the preceding... The first lag coefficient is constrained for testing; after ignoring it... The coefficients of the first lag term are used to avoid spurious regression problems caused by the non-stationarity of the temperature series.

[0032] Null hypothesis ,Right now no The Granger causation was investigated. The Wald statistic was used for the test. , For the constraint matrix, This is the coefficient estimation vector for the vector autoregressive model. for Estimation of the covariance matrix.

[0033] If the Wald statistic exceeds the critical value, the null hypothesis is rejected, and it is considered that... yes The Granger causality is determined. By performing pairwise tests on all measurement points within the cluster, a directed causal adjacency matrix can be constructed, providing a basis for subsequent screening of equivalent heat source measurement points based on the Pareto front.

[0034] Step 5: Screening of key temperature points within the cluster based on the Pareto front;

[0035] According to the Toda-Yamamoto Granger causality test, the cluster Granger causality is established between any two measurement points within the range. If yes Granger's cause indicates Leading in time sequence Changes, at this time the measuring point It can be considered relative to the measuring point The equivalent heat source measurement point. To obtain the equivalent heat source measurement point from the cluster. The equivalent heat source measurement points that play a dominant role in the time series and are not passively responded to are selected. The Pareto multi-objective optimization framework is introduced to eliminate passive measurement points caused by the Granger effect of most other measurement points, and retain equivalent heat source measurement points that have Granger causation effect or are located upstream in the time series.

[0036] Building clusters Directed causal adjacency matrix Its elements , This adjacency matrix characterizes the directed causal relationships between measurement points within a cluster.

[0037] For clusters Any internal measuring point Define two metrics: out-degree and in-degree . out degree The measure of a measuring point's ability to function as an equivalent heat source, i.e., the number of other measuring points within the cluster whose Granger causation results in; in-degree. The degree of passive response of a measurement point is measured by the number of Granger induced by other measurement points within the cluster.

[0038] For cluster In the selection of equivalent heat source measurement points with significant Granger causality, the measurement point selection problem is formalized into a bi-objective decision problem: Objective 1 is to maximize the out-degree. Objective 2 is to minimize the in-degree. We use the concept of Pareto optimality to seek the non-dominated solution set: The decision variable is the cluster indices of the measurement points. .

[0039] For intra-cluster measurement points and , referred to as measuring point Pareto Dominant Measurement Points (recorded as) ), if and only if: and And at least one of the inequalities is strictly true.

[0040] In cluster In the middle, if there are no other measuring points, Pareto dominates the measuring point. Then it is called These are Pareto optimal measurement points. All Pareto optimal measurement points constitute the Pareto front set of this cluster. . The measurement points in the cluster are the equivalent heat source measurement points selected by the cluster. They represent the optimal balance measurement points that are ahead in time and Granger cause multiple other measurement points, while being less affected by Granger causes of other measurement points. These measurement points are used as the final temperature key points for subsequent thermal error modeling and verification.

[0041] Step 6: Predict thermal errors based on the GRU-SA model; A set of key temperature measurement points was obtained through self-organizing map clustering, temperature series stationarity test, Toda-Yamamoto Granger causality test, and Pareto front screening. K represents the final number of retained temperature key points, i.e., the number of equivalent heat source measurement points. This is based on the set of temperature key measurement points. Based on thermal error data, the hyperparameters of the GRU-SA neural network model, which integrates classic gated recurrent units and a self-attention mechanism, are optimized using a Bayesian optimization algorithm. The optimized GRU-SA model is then used to predict spindle thermal error.

[0042] Set sampling time Key temperature vector To capture the dynamic dependence of thermal errors on historical temperature field information, a sliding window approach is used to construct the input sequence. Taking a window length of τ, then... Model input sequence at time step .

[0043] Input sequence The dynamic evolution features of the temperature sequence are extracted step-by-step through a gated recurrent unit (GRU). Let the... The input vector at each time step is The GRU unit adaptively retains long-term dependency information through a gating mechanism, and its calculation process is as follows: , , , , in, , This refers to the hidden state of the previous time step and the current time step. This is the candidate hidden state; To reset the door, The update gate is used to control the degree of forgetting and updating of information; It is the sigmoid activation function. It is the hyperbolic tangent activation function; This represents the Hadamard product operation; , This is the weight matrix. This is the bias vector.

[0044] After τ time steps, the hidden state sequence is obtained. To capture the global dependencies between different time steps within a time window, a self-attention mechanism is introduced to process the hidden state sequence. Perform projection and calculate the query matrix. Key matrix Sum matrix , This is a trainable weight matrix.

[0045] Calculate the attention weights and sum the value vectors using weighted methods to obtain the self-attention context sequence. Softmax is the weight calculation function. Let this be the dimension of the attention space. The context vector of the last time step is taken as the global temporal representation, i.e. .

[0046] global feature vectors The input is fed to the fully connected output layer to calculate the predicted value of the spindle thermal error. , This is the output layer weight matrix; This is a bias term.

[0047] To verify the effectiveness and superiority of the temperature key point screening method combining causal analysis SOM-GC proposed in this embodiment, classic fuzzy C-means clustering (FCM) combined with Pearson correlation analysis (FCM-PC) and FCM combined with Spearman correlation analysis (FCM-SC) were used as comparative point selection methods. To ensure the comparability of the methods, the network model used in all cases was the GRU-SA model. Figure 2 As shown, the GRU-SA model constructed using the SOM-GC screening method proposed in this embodiment exhibits the best predictive performance and is closer to the experimental values. Figure 3 As shown, the prediction residuals of the SOM-GC screening method range from -9.97 μm to 5.50 μm, while the prediction residuals of FCM-PC and FCM-SC range from -16.25 μm to 4.13 μm and -14.91 μm to 4.96 μm, respectively. Figure 4 As shown, the mean absolute error (MAE) and root mean square error (RMSE) of each model are as follows: MAE of SOM-GC, FCM-PC, and FCM-SC are 3.60 μm, 4.59 μm, and 4.23 μm, respectively, and RMSE are 4.27 μm, 6.36 μm, and 5.77 μm, respectively. Compared with the classic FCM-PC and FCM-SC screening methods, the MAE of the model corresponding to the SOM-GC screening method proposed in this embodiment is reduced by 22% and 15%, respectively, and the RMSE is reduced by 33% and 26%, respectively.

[0048] The above results demonstrate that the method described in this embodiment can identify equivalent heat source measurement points and eliminate downstream measurement points with passive responses through causal analysis. The prediction accuracy and robustness of the established model are significantly improved compared to traditional correlation screening methods. The selected key temperature points are highly interpretable and can effectively enhance the model's predictive ability, providing core technical support for subsequent sensor placement and thermal error compensation.

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

Claims

1. A method for screening key temperature points in CNC machine tools based on causal analysis, characterized in that, Includes the following steps: Step 1: Collect time-series temperature data from multiple temperature measurement points on the machine tool; Step 2: Cluster the temperature measurement points based on the self-organizing map algorithm, and group the temperature measurement points with similar thermal behavior into the same cluster; Step 3: Use the augmented Dickey-Fuller test to check the stationarity of the time series temperature data at each temperature measurement point, determine the integration order of each time series temperature data, and take the maximum integration order of all measurement points as the additional lag order. Step 4: Based on the additional lag order, perform pairwise Toda-Yamamoto Granger causality tests on all temperature measurement points within the cluster, and construct a directed causal adjacency matrix that reflects the Granger causal relationship between temperature measurement points within the cluster. Step 5: Based on the directed causal adjacency matrix, calculate the out-degree and in-degree of each temperature measurement point; the out-degree is the number of other measurement points in the cluster caused by the measurement point as a Granger cause, and the in-degree is the number of other measurement points in the cluster caused by the measurement point as a Granger result. With the dual objectives of maximizing out-degree and minimizing in-degree, Pareto optimality is used to select Pareto optimal measurement points within each cluster, and all Pareto optimal measurement points constitute the temperature key point set of the cluster.

2. The method for screening key temperature points in CNC machine tools based on causal analysis according to claim 1, characterized in that, In step 2, the temperature measurement points are clustered based on the self-organizing map algorithm, including: taking the time-series temperature data of each temperature measurement point as input; mapping the input to a low-dimensional neuron grid, and determining the best matching unit for each input by iteratively updating the weight vector of each neuron; and grouping the temperature measurement points with the same or adjacent best matching units into the same cluster.

3. The method for screening key temperature points in CNC machine tools based on causal analysis according to claim 2, characterized in that, The optimal matching unit calculates temperature data. With weight vector The minimum Euclidean distance is obtained; Weight vector update: ,in, The number of iterations. The learning rate decays over time. For neighborhood functions, and Neuron and Coordinates on the output grid, is the neighborhood radius that decays over time.

4. The method for screening key temperature points in CNC machine tools based on causal analysis according to claim 1, characterized in that, In step 4, the Toda-Yamamoto Granger causality test includes: For any two temperature measurement points within the cluster and The optimal lag order can be determined using the AIC or BIC criterion. Combined with the additional lag order obtained in step 3 The lag order is constructed as Vector autoregression model; ， in, , The first The and the first At time 1, temperature measuring points Observed values; For constant terms; The coefficient for the trend term; , These are the coefficients of the lagged dependent variable and the lagged explanatory variables, respectively. This is the random error term; For the variables in the vector autoregressive model The former The lag coefficients are subjected to a Wald test; if the test statistic exceeds the critical value, then the result is determined to be... yes The Granger causality; by performing pairwise checks on all measure points within the cluster, a directed causal adjacency matrix can be constructed. , , The number of temperature measurement points within the cluster. .

5. The method for screening key temperature points in CNC machine tools based on causal analysis according to claim 1, characterized in that, Step 5 employs Pareto optimality screening, including: For any two temperature measurement points within the cluster and If both conditions are met and If at least one inequality holds strictly, then the temperature measuring point is called a temperature measuring point. Pareto-dominated temperature measurement points If there are no other measuring points within the cluster, the Pareto-dominated measuring points are... Then the measuring point This is the Pareto optimal measurement point.

6. A method for predicting thermal errors, characterized in that, This includes using a CNC machine tool temperature key point screening method combining causal analysis as described in any one of claims 1 to 5 to screen temperature data collected from temperature key points, and predicting spindle thermal error based on a thermal error prediction model that integrates a gated loop unit and a self-attention mechanism.

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