Visual temperature sensitive area identification method and system of numerical control machine tool

Abstract

The invention provides a visual temperature sensitive area identification method and system for a numerical control machine tool, and the method comprises the steps: carrying out the measurement of temperature field data, and employing a peak lag correlation algorithm to identify the temperature gradient change caused by the high-frequency component of a temperature signal; identifying a temperature gradient change caused by a low-frequency component of the temperature signal by adopting a self-adaptive inflection point time sequence detection algorithm; acquiring temperature field data and adjusting and identifying a data structure; and analyzing and verifying the visual temperature sensitive area by adopting hierarchical clustering-wavelet correlation, and outputting a visual result. According to the method, the arrangement position of the temperature sensor can be determined under the condition that the thermal error of the machine tool is not measured, so that the arrangement position of the temperature sensor is visualized, complex installation and debugging of multiple sensors are avoided, and the arranged sensors have high correlation coefficients while the time and the use cost of the instrument are saved; and establishing a thermal error mapping model under the condition of changing working conditions so as to carry out thermal error mapping under different operation conditions.

Description

Technical Field

[0001] The present invention belongs to the technical field of temperature-sensitive area selection. Specifically, it relates to a method and system for visually identifying temperature-sensitive areas of a numerically controlled machine tool, and in particular, an identification strategy for visually selecting temperature-sensitive areas of thermal errors of a numerically controlled machine tool. Background Art

[0002] When the working conditions of the machine tool change or the external environment changes, due to the time-varying thermal effect, the machining accuracy of the machine tool will decrease. The thermal error of the machine tool caused by the thermal effect can account for 40%-70% of the machining error, and it will also interfere with the measurement of other machine tool error items. In order to reduce the influence of thermal errors, error prevention and error compensation methods are generally used to improve the machining accuracy.

[0003] The error prevention method avoids the generation of thermal errors by improving the machine tool materials or optimizing the structural design. However, it has a boundary benefit. When the accuracy is improved to the boundary value, the cost of further improving the accuracy will exceed the benefit. The error compensation method is to model and predict the thermal error of the machine tool and reverse-compensate the predicted value to reduce the thermal error. In comparison, the error compensation method has better economy, stronger adaptability to external environment changes, and can be applied to machine tools that are already in service. The key to thermal error compensation lies in accurately modeling and predicting the thermal error of the machine tool. The change of temperature over time is the essential reason for thermal deformation. In addition, it is easy to be measured in the workshop environment and is usually used as the main physical quantity for thermal error modeling. At present, establishing a mapping relationship between the temperature measurable during machining and the thermal error is the most widely used modeling method.

[0004] The construction accuracy of the machine tool temperature field is an important prerequisite for thermal deformation prediction and compensation. The best solution is to place temperature sensors in the temperature-sensitive areas of the machine tool. Traditional redundant placement strategies are costly. If sensitive positions are not covered, the optimized sensor mapping of thermal errors will still be suboptimal. Appropriate temperature sensors can improve the accuracy and robustness of thermal error modeling and save computing resources. In order to save the number of temperature sensors arranged and the time cost, temperature sensors are also mainly deployed at the heat sources of the machine tool and then temperature-sensitive points are selected. However, the selection of the number and location of sensors is often not intuitive, and the time cost of determining the optimal location is high. If temperature-sensitive points are selected from the already arranged temperature sensors, the finely selected temperature-sensitive points have been proven to improve the modeling accuracy and model robustness. However, under the combined influence of changing internal and external factors, the thermal effects of the machine tool become more complex. Research shows that when variable working conditions and external conditions change, the temperature-sensitive points are variable. In addition, when external conditions change, such as the periodic start of active cooling, it will also bring periodic changes to the thermal error, which reduces the robustness of the temperature-sensitive points. Therefore, even if the most representative temperature sensors are selected from the already arranged temperature sensors, it may still not be able to map the changes in thermal errors well, and there is still no clear relevant research on the layout location of temperature sensors.

[0005] The patent document "Method and System for Selecting Temperature-Sensitive Points of Thermal Error Based on Comprehensive Temperature Information" (CN112307579A) discloses the selection of temperature-sensitive points using comprehensive temperature information, using multiple clustering validity indicators to judge the optimal number of clusters, and the number of temperature-sensitive points selected using comprehensive temperature information, which improves the accuracy of the thermal error model, reduces the number of temperature-sensitive points, and improves the model performance. However, due to the combined influence of changing internal and external factors such as variable working conditions and external condition changes, the temperature-sensitive points are variable. Even if the most representative measurement points are selected from the already arranged temperature sensors, it may still not be able to map the change trend of thermal errors well, and problems such as high-correlation points being misdeleted and low-sensitivity points being misselected may still occur.

[0006] For the above reasons and requirements, it is necessary to conduct further research on the initial installation location of temperature sensors under variable working conditions and changing external conditions, and propose a visual temperature-sensitive area selection strategy to guide the installation of temperature sensors. Summary of the Invention

[0007] Aiming at the defects in the prior art, the purpose of the present invention is to provide a method and system for visually identifying temperature-sensitive areas of a numerically controlled machine tool.

[0008] According to the method for visually identifying temperature-sensitive areas of a numerically controlled machine tool provided by the present invention, it includes:

[0009] High-frequency change step, temperature gradient change caused by obtaining the high-frequency component of the temperature signal using the peak lag correlation algorithm;

[0010] Low-frequency change step, temperature gradient change caused by obtaining the low-frequency component of the temperature signal using the adaptive inflection point timing detection algorithm;

[0011] Calculation step, measuring and obtaining temperature field data to obtain a temperature signal and adjusting the data structure, and performing the high-frequency change step and the low-frequency change step;

[0012] Output step, using hierarchical clustering-wavelet correlation analysis to verify the temperature-sensitive region and output the visualization result.

[0013] Preferably, the peak lag correlation algorithm includes:

[0014] Step S1.1, based on the temperature field data, obtaining the cooling start time according to the cooling signal,

[0015] where i represents the number of cooling signal starts;

[0016] represents a non-negative integer;

[0017] CS represents the cooling signal;

[0018] CST represents the cooling start time.

[0019] Step S1.2, calculating the local minimum value LMinT of the interval between two adjacent cooling starts according to the cooling start time,

[0020]

[0021] where temp represents the temperature data changing with time t.

[0022] Step S1.3, calculating the local maximum value LMaxT between the local minimum values,

[0023] Step S1.4, calculating the lag time LagT(i) according to the cooling start time and the local maximum value,

[0024] where the temperature difference ΔT1 = temp(LMaxT(i)) - temp(LMinT(i));

[0025] thr. represents the set temperature change threshold, which is 10% of the maximum temperature drop of active cooling.

[0026] Preferably, the adaptive inflection point timing detection algorithm includes:

[0027] Step S2.1: Based on the temperature field data, calculate the operating condition change timestamp OCCT according to the operating condition signal. Set the points where the second-order difference exceeds the adaptively determined gradient threshold as inflection points or points with significant acceleration changes. The threshold

[0028] where OC represents the time series composed of operating conditions;

[0029] i represents the number of times the cooling signal is started;

[0030] represents a non-negative integer;

[0031] temp represents the temperature data changing with time t;

[0032] Gws represents the window size for calculating the cumulative gradient before the operating condition change, which is less than half of the duration of active cooling.

[0033] Step S2.2: Exclude the operating condition changes of CSP during the start of active cooling. Calculate the cumulative gradient change Cumgrad after the operating condition change. Cumgrad(i) = cumsum(|Δ 2 temp(OCCT(i:end))|);

[0034] where WS represents the window size, which is the duration of active cooling;

[0035] end represents the end of the cooling signal;

[0036] cumsum() represents calculating the cumulative sum of the array elements item by item and returning a vector of the same length.

[0037] Step S2.3: Find the index point where the gradient changes significantly. Scidx(i) = min{t|Cumgrad(i)[t] ≥ Gradthr(i)};

[0038] where Scidx represents the index where the gradient change significantly appears for the first time after the operating condition change.

[0039] Step S2.4: Update the lag time according to the calculated index point.

[0040] where the temperature difference ΔT2 = temp(OCCT(i + 1)) - temp(OCCT(i));

[0041] thr. represents the set temperature change threshold.

[0042] Preferably, the adjusted data structure includes expanding the dimension of the data to three dimensions [rows, cols, timeseries], and initializing the lag time as LagTime ∈ R rows×cols×Num ;

[0043] where R represents the set of real numbers;

[0044] rows, cols, and timeseries represent row pixels, column pixels, and time dimension respectively;

[0045] Num represents time.

[0046] In the calculation steps, perform the high-frequency change step, output the result and average the time dimension, perform the low-frequency change step, output the result and average the time dimension, and select the temperature-sensitive region.

[0047] The temperature-sensitive region includes the region reflecting the peak temperature rise and the region reflecting the significant temperature gradient.

[0048] Preferably, the hierarchical clustering-wavelet correlation analysis includes:

[0049] Step S4.1: Perform hierarchical clustering on the temperature time-series data in the temperature field data, observe the clustering results of the clustering clusters through the clustering tree, and combine the elbow method to judge the better number of clustering clusters. Take the sum of squared errors SSE as the cost function of the elbow method,

[0050] where, ||x i -c k || 2 represents the squared Euclidean distance between the data point x in the kth cluster i and its centroid c k ;

[0051] K represents the total number of clustering clusters.

[0052] Step S4.2: Apply the Analytic Morlet wavelet transform to the temperature and thermal error data in the temperature field data,

[0053]

[0054] where, W ψ (x)(s, τ) is the wavelet coefficient of the time signal x(t) at scale s and position τ;

[0055] ψ * represents the complex conjugate of the wavelet function;

[0056] The complex time - series signal oscillating at frequency ω0 is represented by jω0t;

[0057] σ represents the standard deviation.

[0058] Step S4.3: Perform Spearman correlation analysis on the time - frequency domain information after wavelet transform to obtain the Spearman correlation coefficient between the temperature data and the thermal error. The Spearman correlation coefficient

[0059] where, R(X i ) represents the rank of the i - th observed value of X in X i ;

[0060] R(Y i ) represents the rank of the i - th observed value of Y in Y;

[0061] n represents the number of observed values in the dataset.

[0062] According to the present invention, a visualization temperature - sensitive area identification system for a numerically controlled machine tool is provided, including:

[0063] A high - frequency change module that obtains the temperature gradient change caused by the high - frequency component of the temperature signal by using the peak - lag correlation algorithm;

[0064] A low - frequency change module that obtains the temperature gradient change caused by the low - frequency component of the temperature signal by using the adaptive inflection - point time - series detection algorithm;

[0065] A calculation module that measures and obtains temperature field data to obtain a temperature signal and adjusts the data structure, triggering the high - frequency change module and the low - frequency change module;

[0066] An output module that verifies the visualization temperature - sensitive area by using hierarchical clustering - wavelet correlation analysis and outputs the visualization result.

[0067] Preferably, the peak - lag correlation algorithm includes:

[0068] Module M1.1: Based on the temperature field data, obtain the cooling start time according to the cooling signal,

[0069] where, i represents the number of times the cooling signal starts;

[0070] represents a non - negative integer;

[0071] CS represents the cooling signal;

[0072] CST represents the cooling start time.

[0073] Module M1.2 calculates the local minimum value LMinT of the interval between two adjacent cooling starts based on the cooling start time,

[0074]

[0075] where temp represents the temperature data varying with time t.

[0076] Module M1.3 calculates the local maximum value LMaxT between the local minimum values,

[0077] Module M1.4 calculates the lag time LagT(i) based on the cooling start time and the local maximum value,

[0078] where the temperature difference ΔT1 = temp(LMaxT(i)) - temp(LMinT(i));

[0079] thr. represents the set temperature change threshold, which is 10% of the maximum temperature drop during active cooling.

[0080] Preferably, the adaptive inflection point timing detection algorithm includes:

[0081] Module M2.1 calculates the operating condition change timestamp OCCT based on the temperature field data according to the operating condition signal, Sets the points where the second-order difference exceeds the adaptively determined gradient threshold as inflection points or points with significant acceleration changes, and the threshold

[0082] where OC represents the time series composed of operating conditions;

[0083] i represents the number of times the cooling signal is started;

[0084] represents a non-negative integer;

[0085] temp represents the temperature data varying with time t;

[0086] Gws represents the window size for calculating the cumulative gradient before the operating condition change, which is less than half of the duration of active cooling.

[0087] Module M2.2 excludes the operating condition changes of CSP during the start of active cooling, Calculates the cumulative gradient change Cumgrad after the operating condition change, Cumgrad(i) = cumsum(|Δ 2 temp(OCCT(i:end))|);

[0088] Among them, WS represents the window size, and its size is the active cooling duration;

[0089] end represents the end of the cooling signal;

[0090] cumsum() represents calculating the cumulative sum of array elements item by item and returning a vector of the same length.

[0091] Module M2.3, find the index points where the gradient changes significantly, Scidx(i) = min{t| Cumgrad(i)[t] ≥ Gradthr(i)};

[0092] Among them, Scidx represents the index where the gradient first changes significantly after the working condition changes.

[0093] Module M2.4, update the lag time according to the calculated index points

[0094] Among them, the temperature difference ΔT2 = temp(OCCT(i + 1)) - temp(OCCT(i));

[0095] thr. represents the set temperature change threshold.

[0096] Preferably, the adjusted data structure includes expanding the dimension of the data to three - dimensional [rows, cols, timeseries], and initializing the lag time as LagTime ∈ R rows×cols×Num ;

[0097] Among them, R represents the set of real numbers;

[0098] rows, cols, and timeseries represent row pixels, column pixels, and time dimension respectively;

[0099] Num represents time.

[0100] In the calculation module, trigger the high - frequency change module, output the result and average the time dimension, trigger the low - frequency change module, output the result and average the time dimension, and select the temperature - sensitive area.

[0101] The temperature - sensitive area includes the area reflecting the peak value of temperature rise and the area reflecting the significant temperature gradient.

[0102] Preferably, the hierarchical clustering - wavelet correlation analysis includes:

[0103] Module M4.1, perform hierarchical clustering on the temperature time - series data in the temperature field data, observe the division result of the clustering clusters through the clustering tree, and combine the elbow method to judge the better number of clustering clusters. Use the sum of squared errors as the cost function of the elbow method, and the sum of squared errors

[0104] Among them, ||x i -c k || 2 represents the squared Euclidean distance between the data point x in the k-th cluster i and its centroid c k ;

[0105] K represents the total number of clustering clusters.

[0106] Module M4.2 uses the Analytic Morlet wavelet transform for the temperature and thermal error data in the temperature field data,

[0107]

[0108] Among them, W ψ (x)(s, τ) is the wavelet coefficient of the time signal x(t) at scale s and position τ;

[0109] ψ * represents the complex conjugate of the wavelet function;

[0110] jω0t represents a complex time series signal oscillating at frequency ω0;

[0111] σ represents the standard deviation.

[0112] Module M4.3 uses Spearman correlation analysis for the time-frequency domain information after wavelet transform to obtain the Spearman correlation coefficient between temperature data and thermal error. The Spearman correlation coefficient

[0113] Among them, R(X i ) represents the rank of the i-th observation value of X i in X;

[0114] R(Y i ) represents the rank of the i-th observation value of Y

[0115] in Y; n represents the number of observation values in the dataset.

[0116] Compared with the prior art, the present invention has the following beneficial effects:

[0117] 1. Compared with the traditional clustering-related analysis method for selecting temperature-sensitive points, the present invention can determine the layout positions of temperature sensors without measuring the thermal error of the machine tool, saving time and the usage cost of instruments, and the sensors arranged have a relatively high correlation coefficient.

[0118] 2. The present invention proposes a criterion for determining the temperature-sensitive region, identifies the temperature-sensitive region under the influence of internal and external factors of the machine tool, and establishes a thermal error mapping model under variable operating conditions of the machine tool based on the variable operating conditions of the machine tool, so as to perform thermal error mapping under different operating conditions.

[0119] 3. By visualizing the lag time from "operating condition change" to "temperature change", the present invention visualizes the arrangement position of the temperature sensor, avoids the complex installation and debugging of multiple sensors, and does not need to rely on expert experience, providing visual guidance for the installation of the temperature sensor. BRIEF DESCRIPTION OF THE DRAWINGS

[0120] Other features, objects, and advantages of the present invention will become more apparent by reading the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0121] Figure 1 Schematic diagram of the measurement and acquisition equipment for the visual temperature-sensitive region identification system of a numerically controlled machine tool;

[0122] Figure 2 Schematic diagram of the spindle speed spectrum of the thermal test;

[0123] Figure 3 Schematic diagram of the thermal imaging results of the milling spindle and the turning spindle;

[0124] Figure 4 Schematic diagram of the spindle thermal error change under the influence of operating condition change and active cooling signal;

[0125] Figure 5 Schematic diagram of the visual temperature-sensitive region under the influence of the high-frequency component of temperature;

[0126] Figure 6 Schematic diagram of the visual temperature-sensitive region under the influence of the low-frequency component of temperature;

[0127] Figure 7(a) is a schematic diagram of the analysis result of the clustering dendrogram of the milling spindle.

[0128] Figure 7(b) is a schematic diagram of the result of the elbow method of the milling spindle.

[0129] Figure 7(c) is a schematic diagram of the analysis result of the clustering dendrogram of the milling spindle.

[0130] Figure 7(d) is a schematic diagram of the clustering result and the correlation coefficient of the turning spindle.

[0131] Figure 7(e) is a schematic diagram of the result of the elbow method of the turning spindle.

[0132] Figure 7(f) is a schematic diagram of the clustering result and the correlation coefficient of the turning spindle. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0133] The present invention will be described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but do not limit the present invention in any form. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several changes and improvements can still be made. These all belong to the protection scope of the present invention.

[0134] The installation of temperature sensors and the selection of temperature-sensitive points are one of the most important steps before thermal error modeling and compensation. The traditional installation of temperature sensors is random and depends on expert experience. Selecting the best sensitive points not only requires installing and screening a large number of temperature sensors, but also highly depends on the random positions of the sensors.

[0135] In order to study the temperature change characteristics of machine tools and find the best temperature measurement area, according to the present invention, a visualization method for identifying temperature-sensitive areas of CNC machine tools is provided to guide the installation of temperature sensors. Visualize the temperature-sensitive areas, and the temperature sensors arranged in the temperature-sensitive areas can better reflect the thermal error changes when the working conditions and external conditions change, including the following steps:

[0136] Step 1: Measure the temperature field data, and propose and use the peak lag correlation algorithm to identify the temperature gradient changes caused by the high-frequency components of the temperature signal.

[0137] Specifically, for the high-frequency components of the temperature signal, the peak lag correlation algorithm is applied to the temperature gradient changes caused by active cooling. The peak lag correlation algorithm also includes calculation steps:

[0138] Step S1.1: Based on the temperature field data obtained from the temperature field measurement, identify the time stamp of the start of cooling, i.e., the cooling start time (CST), according to the cooling signal (CS). The principle is as follows:

[0139]

[0140] where i represents the number of times the cooling signal is started, represents a non-negative integer.

[0141] Step S1.2: Calculate the time stamp of the local minimum (LMinT) of the interval between two adjacent cooling starts according to the obtained cooling start time (CST):

[0142]

[0143] where temp represents the temperature data changing with time t.

[0144] Step S1.3: Calculate the time stamp of the local maximum (LMaxT) between the start of cooling and the adjacent local minimum (LMinT) according to the calculation results of the above formula:

[0145]

[0146] Step S1.4. Calculate the lag time (LagT(i)) based on the calculation results of the above two formulas, that is, the cooling start time and the local maximum timestamp:

[0147]

[0148] Among them, the temperature difference ΔT1 = temp(LMaxT(i)) - temp(LMinT(i)). Due to the influence of the ambient temperature and the noise signal on the sensor, a temperature change threshold (thr.) is set to filter out the above interference. Therefore, when the difference between two adjacent local maxima and minima does not exceed this threshold, the lag time is set to ∞. The threshold is set to 10% of the maximum temperature drop of active cooling.

[0149] In more preferred examples, taking the dual spindles of a turning-milling compound machine tool with two different structural types of spindles as the research object, the temperature field and thermal error of the dual spindles under different working conditions are measured by a thermal imager and an eddy current displacement sensor. The equipment used is as Figure 1 shown. When determining the thermal effect of the rotating spindle, the spindle speed is designed as a variable speed spectrum. Each speed is maintained for 15 minutes to simulate typical machining conditions. According to the thermal test guidelines recommended by ISO 230-3, the duration of the preheating test is 4 hours, and the variable speed spectrum changes with time as Figure 2 shown.

[0150] Step two. Propose and use an adaptive inflection point timing detection algorithm to identify the temperature gradient change caused by the low-frequency component of the temperature signal.

[0151] Specifically, for the low-frequency component of the temperature signal, an adaptive inflection point timing detection algorithm is applied to the temperature gradient change caused by the operating conditions. The adaptive inflection point timing detection algorithm includes the following calculation steps:

[0152] Step S2.1. Based on the original measured temperature data, identify the operating condition change timestamp (OCCT) according to the operating condition signal:

[0153]

[0154] Among them, OC is a time series composed of operating conditions (rotational speeds). After the active cooling control is started, the temperature of the component to be cooled will drop rapidly, and the high-frequency information brings interference. Therefore, the second-order difference is used to identify the inflection point of the temperature or its acceleration change. When the second-order difference exceeds the adaptively determined gradient threshold (Gradthr), it is considered that an inflection point or a significant acceleration change occurs. The threshold is set as follows:

[0155]

[0156] Among them, Gws is the window size for calculating the cumulative gradient before the working condition change, and is set to be less than half of the active cooling duration.

[0157] Step S2.2: Since the temperature change in the long-period mode will be disturbed by the active cooling process, additional rules are added to avoid possible interference. That is, the working condition change during the active cooling start period (CSP) is no longer involved in the calculation:

[0158]

[0159] Among them, WS represents the window size, and its size is the active cooling duration. After meeting the above rules, the cumulative gradient change (Cumgrad) after the working condition change is calculated from the result obtained by the above formula:

[0160] Cumgrad(i) = cumsum(|Δ 2 temp(OCCT(i:end))|)

[0161] Among them, the cumsum function calculates the cumulative sum of the array elements item by item and returns a vector of the same length.

[0162] Step S2.3: Subsequently, according to the calculation results of the above two formulas, find the index points where the gradient changes significantly:

[0163] Scidx(i) = min{t|Cumgrad(i)[t] ≥ Gradthr(i)}

[0164] Among them, Scidx represents the index where the gradient change first appears significantly after the working condition change.

[0165] Step S2.4: Finally, update the lag time according to the calculated index points:

[0166]

[0167] Among them, the temperature difference ΔT2 = temp(OCCT(i + 1)) - temp(OCCT(i)).

[0168] In more preferred examples, experiments are carried out on the turning spindle and the milling spindle respectively. The maximum speed of the turning spindle is 2500 RPM, and the maximum speed of the milling spindle is 8000 RPM. During the experiment, a thermal imager is used to continuously photograph the turning spindle and the milling spindle. The five-point eddy current sensor is used to measure the thermal displacement during the preheating cycle in real time.

[0169] During the thermal test, the thermal images of the turning spindle and the milling spindle are captured respectively, asFigure 3 As shown. The changes in the operating conditions of the machine tool during the complete thermal test and the active cooling start data are also recorded. Under the combined action of the active cooling control and the changes in the operating conditions, the thermal errors of the turning spindle and the milling spindle in the X, Y, and Z directions are recorded. As Figure 4 shown, after the active cooling signal appears, the thermal error fluctuates within a short period. Although the changes in temperature and the amplitude of the thermal error are very small, the high-frequency components will affect the surface finish quality. In contrast, the changes in the operating conditions will cause larger changes in the amplitude of temperature and thermal error, but the low-frequency and long periods will affect the overall accuracy of machining. The above experimental results indicate that it is necessary to consider the influence of the two temperature frequency components in the temperature-sensitive area selection strategy.

[0170] The lag time identification algorithm based on the high-frequency and low-frequency components of the temperature signal can be used to identify the temperature-sensitive areas affected by internal and external factors of the machine tool.

[0171] Step 3: Algorithm application and visualization based on parallel computing, obtaining the machine tool temperature field data, and adjusting the data structure to be identified by the algorithm;

[0172] Specifically, taking the turning-milling compound machine tool as a preferred example for experiments, and applying this algorithm to identify and visually display the temperature-sensitive areas.

[0173] Adjust the data structure to achieve the visualization of the temperature-sensitive area, expand the dimension of the data to three dimensions [rows, cols, timeseries], that is, row pixels, column pixels, and time dimension. Initialize the lag time as:

[0174] LagTime∈R rows×cols×Num

[0175] where R represents the set of real numbers. Subsequently, apply all the algorithms in Step 1 and Step 2, aiming to find the area where the temperature gradient first starts to respond after the thermal equilibrium is disrupted.

[0176] Regarding the characteristics of the component temperature changing with time, the clustering-correlation analysis screening process is transformed into two methods for identifying temperature-sensitive areas based on the minimum temperature lag time. Through the lag time identification algorithm based on the high / low-frequency components of the temperature signal change, it is used to identify the temperature-sensitive areas under the combined influence of internal and external factors of the machine tool.

[0177] In more preferred examples, the format of the thermal imaging temperature data is (row, column, time), i.e., [480×640×14400]. The analysis process of the visualization result of the temperature-sensitive region of the high-frequency component of the temperature change is as follows: The time series of the start and stop of the milling spindle active cooling system was recorded and analyzed 51 times. The set cooling amplitude of the active cooling device is 1°C, so the threshold of the algorithm is set to 0.1°C. After performing step one, the dimension of the final output result is [480×640×51]. Then, the time dimension is averaged, and the obtained visualization result is as shown in Figure 5 the left figure. The visualization distribution area of the lag time can be directly observed, that is, the darker area can better reflect the high-frequency temperature fluctuation changes. Similarly, during the thermal test of the turning spindle, the active cooling system started and stopped 54 times. That is to say, the dimension of the final output after performing step one is [480×640×54]. The final visualization is as shown in Figure 5 the right figure. Visualize and display the lag time from the change of working conditions / external conditions to the temperature change, and realize the visual identification of the temperature sensor layout position.

[0178] The analysis process of the visualization result of the temperature-sensitive region of the low-frequency component of the temperature change is as follows: During the 4-hour thermal test of the milling spindle, there were 15 changes in operating conditions. Search for the active cooling system start signal before and after the time stamp of the change in operating conditions. After excluding the influence of the active cooling control, a total of 10 changes in operating conditions were involved in the calculation. After performing step two, the dimension of the final output result is [480×640×10]. The final visualization after averaging the time dimension is as shown in Figure 6 the left figure. Figure 5 The comparison between the left figure and Figure 6 the left figure shows that the temperature change of the front bearing of the milling spindle can better reflect the low-frequency component. This is because the milling spindle motor is covered by the cooling system circuit, so the change in operating conditions is not better reflected near the motor. During the thermal test of the turning spindle, after excluding the influence of the active cooling control, a total of 12 changes in working conditions were involved in the calculation. After performing step two, the dimension of the final output result is [480×640×12]. The final visualization is as shown in Figure 6 the right figure. Figure 6 The dark area in the right figure shows the heat sink of the hydraulic oil. The visualization result shows that the heat sink can better reflect the change of operating conditions. In contrast, the motor and bearing of the turning spindle are covered by the protective cover, and the temperature change caused by the change of operating conditions cannot be better reflected.

[0179] A determination criterion for temperature-sensitive regions is proposed, including regions that can reflect the peak temperature rise and regions that can reflect significant temperature gradients as temperature-sensitive regions. By visualizing the lag time from "operating condition change" to "temperature change", the identification results of temperature-sensitive regions and the installation positions of temperature sensors are visualized, providing visual guidance for the installation of temperature sensors, avoiding the installation of a large number of temperature sensors on the machine tool and screening them, saving time, avoiding waste of sensors, and not relying on expert experience, which is more conducive to implementation in an industrial (workshop) environment and is especially suitable for the temperature point layout of large machine tools.

[0180] Step 4: Use hierarchical clustering-wavelet correlation analysis to compare and verify the correctness of the visualized temperature-sensitive regions. This step is used for the display and explanation of the visualization effect

[0181] Specifically, to verify the effectiveness of the algorithm, traditional hierarchical clustering-wavelet correlation analysis is used to screen temperature-sensitive points and compare them with the identified temperature-sensitive regions.

[0182] Mechanism analysis shows that the fundamental cause of machine tool thermal deformation is the change of temperature over time. The hierarchical clustering-elbow method-wavelet correlation analysis algorithm, that is, hierarchical clustering-wavelet correlation analysis, is adopted to verify the temperature sensors arranged in the visualized temperature-sensitive region:

[0183] Step S4.1: First, perform hierarchical clustering on the temperature time series data obtained from the temperature field. Hierarchical clustering does not require pre-specifying the number of clustering clusters k, and the division results of the clustering clusters can be observed through the clustering tree. And the elbow method is combined to determine a better number of clustering clusters. The sum of squared errors (SSE) is used as the cost function of the elbow method, and its calculation process is as follows:

[0184]

[0185] where, ||x i -c k || 2 represents the squared Euclidean distance between the data point x in the k-th cluster i and its centroid c k

[0186] Step S4.2: Subsequently, perform wavelet transform on the temperature and thermal error data. The Analytic Morlet wavelet transform is adopted, and its form is as follows:

[0187]

[0188] where, W ψ (x)(s,τ) is the wavelet coefficient of the time signal x(t) at scale s and position τ. ψ * ​Represents the complex conjugate of the wavelet function. \(j\omega_0t\) represents a complex time-series signal oscillating at frequency \(\omega_0\), and \(\sigma\) represents the standard deviation.

[0189] Step S4.3: Using the variable-speed spectrum, the relationship between temperature and thermal error is highly non-linear. In the correlation analysis, Spearman correlation analysis is used for the time-frequency domain information after wavelet transform. The calculation method of the Spearman correlation coefficient \(\rho\) is as follows:

[0190]

[0191] where \(R(X\) i ) represents the rank of the \(i\)-th observation value of \(X\) in \(X\). \(R(Y\) i ) represents the rank of the \(i\)-th observation value in \(Y\). \(n\) represents the number of observation values in the dataset, that is, the size of the sample. The correlation coefficient between the temperature data and the thermal error is obtained in the above manner. i

[0192] The effectiveness and advantages of the proposed algorithm are verified through comparative experiments.

[0193] In more preferred examples, in order to verify the effectiveness and correctness of the proposed visualization strategy for selecting temperature-sensitive regions, it is necessary to conduct a comparative verification with the traditional strategy. The equipment used for the verification experiment still uses the same configuration, and a contact temperature sensor for obtaining temperature information is added. A four-wire PT-100 RTD is used as the temperature sensor, with a measurement accuracy of ±0.1 °C. The temperature sensor is used together with the NI-9216 integrated temperature acquisition module. LabVIEW is used as the acquisition software and the acquisition frequency is set to 5 Hz. The collected temperature data is averaged and filtered.

[0194] ​The temperature sensors of the turning spindle and the milling spindle device are screened separately. The number of clusters and the clustering results are determined by hierarchical clustering and the elbow method. Then, the temperature-sensitive points are obtained through wavelet transform and correlation analysis. The dendrograms of clustering, the discriminant results of the elbow method, and the calculation results of the correlation coefficients of the milling spindle and the turning spindle are shown in Fig. 7. The left two figures in Fig. 7 show the dendrograms of clustering of the milling spindle and the turning spindle respectively. By drawing a horizontal line from the bottom to view the dendrogram of clustering, the number of vertical lines crossed represents the number of clusters. As the horizontal line continues to rise, the number of vertical lines passing through it decreases, that is, the number of clusters decreases. The purpose of clustering is to reduce the collinearity of temperature data and map the thermal error data with the fewest variables. The optimal number of clusters is to find a balance between the within-cluster sum of squares and the between-cluster sum of squares. The middle two figures in Fig. 7 show the results of the elbow method for the milling spindle and the turning spindle respectively, showing the elbow inflection points that appear when the number of clusters is 5, that is, the optimal number of clusters is 5. Similarly, the optimal number of clusters for the turning spindle is 6. According to the clustering results and correlation coefficients in the right two figures of Fig. 7, Table 1 shows the screening results of the temperature-sensitive points. The temperature points of the milling spindle are T2, T4, T10, and T12, and the group with the lowest correlation coefficient is discarded. The temperature points of the turning spindle are T2, T3, T5, T7, and T9, and the group with the lowest correlation coefficient is discarded again.

[0195] Table 1. Matching between sensitive points and visualization areas:

[0196]

[0197]

[0198] Compared with the traditional clustering correlation analysis strategy, the visualization method can separately identify the temperature-sensitive areas affected by internal and external factors of the machine tool. The selection of the temperature-sensitive area is based on the variable working conditions of the machine tool. Therefore, it is possible to model the temperature sensors arranged in the selected thermosensitive area and establish a thermal error mapping model under changing working conditions and different operating conditions. This is very helpful for optimizing the sensor layout and target thermal error modeling. Since the milling spindle motor is surrounded by a cooling water jacket, the temperature sensors on the motor cannot fully capture the changes in operating conditions. However, the temperature sensors can effectively detect the temperature fluctuations caused by active cooling control. The temperature sensors T5 to T7 arranged on the spindle correspond to Figure 5A relatively small rear bearing cooling area in the right figure. Although the distance between sensors T5 and T6 is less than 10 cm, the temperature trends and correlation coefficients of the two are very different. However, the method proposed by the present invention can determine the positions of temperature sensors without measuring the thermal error of the machine tool. All selected sensor positions are located in the visualization sensitive area, and the temperature sensors arranged in the visualization sensitive area have a high correlation coefficient. By observing the gradient color area, key positions are well identified, and the temperature sensitive areas of different components are visualized.

[0199] In more preferred examples, the data collected by the thermal imager is applied to form a visualization of the temperature sensitive area selection strategy.

[0200] The present invention also provides a visualization temperature sensitive area identification system for a numerically controlled machine tool. The visualization temperature sensitive area identification system for the numerically controlled machine tool can be implemented by executing the process steps of the visualization temperature sensitive area identification method for the numerically controlled machine tool. That is, those skilled in the art can understand the visualization temperature sensitive area identification method for the numerically controlled machine tool as a preferred implementation manner of the visualization temperature sensitive area identification system for the numerically controlled machine tool.

[0201] According to the present invention, there is provided a visualization temperature sensitive area identification system for a numerically controlled machine tool, including:

[0202] A high-frequency change module, which obtains the temperature gradient change caused by the high-frequency component of the temperature signal by using the peak lag correlation algorithm;

[0203] A low-frequency change module, which obtains the temperature gradient change caused by the low-frequency component of the temperature signal by using the adaptive inflection point time series detection algorithm;

[0204] A calculation module, which measures and obtains temperature field data to obtain a temperature signal and adjusts the data structure, triggering the high-frequency change module and the low-frequency change module;

[0205] An output module, which uses hierarchical clustering-wavelet correlation analysis to verify the visualization temperature sensitive area and outputs the visualization result.

[0206] In more preferred examples, the peak lag correlation algorithm includes:

[0207] Module M1.1, based on the temperature field data, obtains the cooling start time according to the cooling signal,

[0208] where i represents the number of cooling signal starts;

[0209] represents a non-negative integer;

[0210] CS represents the cooling signal;

[0211] CST represents the cooling start time.

[0212] Module M1.2 calculates the local minimum value LMinT of the interval between two adjacent cooling starts based on the cooling start time,

[0213] where temp represents the temperature data that changes with time t.

[0214] Module M1.3 calculates the local maximum value LMaxT between the local minimum values,

[0215] Module M1.4 calculates the lag time LagT(i) based on the cooling start time and the local maximum value,

[0216] where the temperature difference ΔT1 = temp(LMaxT(i)) - temp(LMinT(i));

[0217] thr. represents the set temperature change threshold, which is 10% of the maximum temperature drop during active cooling.

[0218] In more preferred examples, the adaptive inflection point timing detection algorithm includes:

[0219] Module M2.1 calculates the operating condition change timestamp OCCT based on the temperature field data according to the operating condition signal, Sets the points with a second-order difference exceeding the adaptively determined gradient threshold as inflection points or points with a significant acceleration change, and the threshold

[0220] where OC represents the time series composed of operating conditions;

[0221] i represents the number of times the cooling signal is started;

[0222] represents a non-negative integer;

[0223] temp represents the temperature data that changes with time t;

[0224] Gws represents the window size for calculating the cumulative gradient before the operating condition change, which is less than half of the duration of active cooling. <000**********]]

[0225] Module M2.2 excludes the operating condition changes of CSP during the start of active cooling, calculates the cumulative gradient change Cumgrad after the operating condition change, Cumgrad(i) = cumsum(|Δ 2temp(OCCT(i:end))|);

[0226] Among them, WS represents the window size, and the size is the active cooling duration;

[0227] end represents the end of the cooling signal;

[0228] cumsum() represents calculating the cumulative sum of array elements item by item and returning a vector of the same length.

[0229] Module M2.3, find the index points where the gradient changes significantly, Scidx(i) = min{t|Cumgrad(i)[t]≥Gradthr(i)};

[0230] Among them, Scidx represents the index where the gradient first changes significantly after the working condition changes.

[0231] Module M2.4, update the lag time according to the calculated index points

[0232] Among them, the temperature difference ΔT2 = temp(OCCT(i + 1)) - temp(OCCT(i));

[0233] thr. represents the set temperature change threshold.

[0234] In more preferred examples, the adjusted data structure includes expanding the dimension of the data to three dimensions [rows, cols, timeseries], and initializing the lag time as LagTime ∈ R rows×cols×Num ;

[0235] Among them, R represents the set of real numbers;

[0236] rows, cols, and timeseries represent the row pixels, column pixels, and time dimension respectively;

[0237] Num represents time.

[0238] In the calculation module, trigger the high-frequency change module, output the result and average the time dimension, trigger the low-frequency change module, output the result and average the time dimension, and select the temperature-sensitive area.

[0239] The temperature-sensitive area includes the area reflecting the peak value of temperature rise and the area reflecting the significant temperature gradient.

[0240] In more preferred examples, the hierarchical clustering-wavelet correlation analysis includes:

[0241] Module M4.1: Perform hierarchical clustering on the temperature time series data in the temperature field data. Observe the clustering results of the clusters through the clustering tree, and combine the elbow method to determine a better number of clusters. Use the sum of squared errors as the cost function of the elbow method, and the sum of squared errors

[0242] where, ||x i -c k || 2 represents the square of the Euclidean distance between the data point x in the k-th cluster i and its centroid c k ;

[0243] K represents the total number of clusters.

[0244] Module M4.2: Apply the Analytic Morlet wavelet transform to the temperature and thermal error data in the temperature field data

[0245] where, W ψ (x)(s,τ) is the wavelet coefficient of the time signal x(t) at scale s and position τ;

[0246] ψ * represents the complex conjugate of the wavelet function;

[0247] jω0t represents a complex time series signal oscillating at frequency ω0;

[0248] σ represents the standard deviation.

[0249] Module M4.3: Perform Spearman correlation analysis on the time-frequency domain information after wavelet transform to obtain the Spearman correlation coefficient between the temperature data and the thermal error, and the Spearman correlation coefficient

[0250] where, R(X i ) represents the rank of the i-th observation in X i in X;

[0251] R(Y i ) represents the rank of the i-th observation in Y;

[0252] n represents the number of observations in the dataset.

[0253] Those skilled in the art know that in addition to implementing the system and its various devices, modules, and units provided by the present invention in the form of pure computer-readable program code, the method steps can be logically programmed to enable the system and its various devices, modules, and units provided by the present invention to be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers, etc. to achieve the same functions. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered as a kind of hardware component, and the devices, modules, and units included therein for implementing various functions can also be regarded as the structures within the hardware component; the devices, modules, and units for implementing various functions can also be regarded as both software modules for implementing the method and the structures within the hardware component.

[0254] The specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Without conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A method for identifying visual temperature-sensitive areas of a numerically controlled machine tool, characterized in that, Including: High-frequency change step, temperature gradient change caused by obtaining the high-frequency component of the temperature signal using the peak lag correlation algorithm; Low-frequency change step, temperature gradient change caused by obtaining the low-frequency component of the temperature signal using the adaptive inflection point timing detection algorithm; Calculation step, measuring and obtaining temperature field data to obtain the temperature signal and adjusting the data structure, and executing the high-frequency change step and the low-frequency change step; Output step, using hierarchical clustering-wavelet correlation analysis to verify the visual temperature-sensitive area and output the visualization result.

2. The method for identifying the visual temperature-sensitive area of a numerically controlled machine tool according to claim 1, characterized in that, The peak lag correlation algorithm includes: Step S1.

1. Based on the temperature field data, obtain the cooling start time according to the cooling signal. Where, i represents the number of cooling signal startups; represents a non - negative integer; CS represents the cooling signal; CST represents the cooling start time; Step S1.2, calculating the local minimum value LMinT of the interval between two adjacent cooling starts according to the cooling start time, Where, temp represents the temperature data changing with time t; Step S1.3, calculate the local maximum value LMaxT between local minima, Step S1.4: Calculate the lag time LagT(i) based on the cooling start time and the local maximum value. Where, the temperature difference ΔT1 = temp(LMaxT(i)) - temp(LMinT(i)); thr. represents the set temperature change threshold, which is 10% of the maximum temperature drop of active cooling.

3. The method for identifying the visual temperature-sensitive area of a numerically controlled machine tool according to claim 1, characterized in that, The adaptive inflection point timing detection algorithm includes: Step S2.

1. Calculate the timestamp of the operating condition change based on the temperature field data according to the operating condition signal Set the points where the second-order difference exceeds the gradient threshold adaptively determined as inflection points or points with significant acceleration changes, and the threshold Where, OC represents the time series composed of working conditions; i represents the number of cooling signal startups; represents a non - negative integer; temp represents the temperature data changing with time t; Gws represents the window size for calculating the cumulative gradient before the working condition change, which is less than half of the duration of active cooling; Step S2.

2. Exclude the operating condition changes of the CSP during the start-up of active cooling, calculate the cumulative gradient change Cumgrad after the operating condition change, Cumgrad(i) = cumsum(|Δ 2 temp(OCCT(i:end))|); Where, WS represents the window size, and its size is the duration of active cooling; end represents the end of the cooling signal; cumsum() represents calculating the cumulative sum of array elements item by item and returning a vector of the same length; Step S2.3, finding the index point where the gradient changes significantly, Scidx(i) = min{t|Cumgrad(i)[t]≥Gradthr(i)}; Where, Scidx represents the index of the first occurrence of a significant gradient change after the working condition change; Step S2.4: Update the lag time according to the calculated index points Where, the temperature difference ΔT2 = temp(OCCT(i + 1)) - temp(OCCT(i)); thr. represents the set temperature change threshold.

4. The method for identifying the visual temperature-sensitive area of a numerically controlled machine tool according to claim 1, characterized in that The adjusted data structure includes expanding the dimension of the data to three dimensions [rows, cols, timeseries], and initializing the lag time as LagTime ∈ R rows×cols×Num ; Where, R represents the set of real numbers; rows, cols, timeseries represent the row pixels, column pixels, and time dimension respectively; Num represents time; In the calculation step, execute the high-frequency change step, output the result and average the time dimension, execute the low-frequency change step, output the result and average the time dimension, and select the temperature-sensitive area; The temperature-sensitive area includes the area reflecting the peak value of temperature rise and the area reflecting the significant temperature gradient.

5. The method for identifying the visual temperature-sensitive area of the numerically controlled machine tool according to claim 1, characterized in that, The hierarchical clustering-wavelet correlation analysis includes: Step S4.1: Perform hierarchical clustering on the temperature time series data in the temperature field data, observe the division results of the clustering clusters through the clustering tree, and combine the elbow method to determine a better number of clustering clusters. Use the sum of squared errors SSE as the cost function of the elbow method. Among them, ‖x i -c k ‖ 2 represents the square of the Euclidean distance between the data point x in the k-th cluster i and its centroid c k ; K represents the total number of clustering clusters; Step S4.2, performing Analytic Morlet wavelet transform on the temperature and thermal error data in the temperature field data, Among them, W ψ (x)(s, τ) is the wavelet coefficient of the time signal x(t) at scale s and position τ; ψ * represents the complex conjugate of the wavelet function; jω0t represents the complex time series signal oscillating at the frequency ω0; σ represents the standard deviation; Step S4.3: Perform Spearman correlation analysis on the time-frequency domain information after wavelet transform to obtain the Spearman correlation coefficient between the temperature data and the thermal error. The Spearman correlation coefficient where, R(X i ) represents the rank of the i ith observation in X; R(Y i ) represents the rank of the i-th observation in Y; n represents the number of observed values in the dataset.

6. A visualization temperature-sensitive area identification system for a numerical control machine tool, characterized in that, Including: High-frequency change module, temperature gradient change caused by obtaining the high-frequency component of the temperature signal using the peak lag correlation algorithm; Low-frequency change module, temperature gradient change caused by obtaining the low-frequency component of the temperature signal using the adaptive inflection point timing detection algorithm; Calculation module, measuring and obtaining temperature field data to obtain temperature signals and adjusting the data structure, triggering the high-frequency change module and the low-frequency change module; Output module, using hierarchical clustering-wavelet correlation analysis to verify the visually temperature-sensitive area and output the visualization result.

7. The visualization temperature-sensitive area identification system for a numerically controlled machine tool according to claim 6, wherein The peak lag correlation algorithm includes: Module M1.1, based on the temperature field data, obtains the cooling start time according to the cooling signal. Among them, i represents the number of cooling signal startups; represents a non - negative integer; CS represents the cooling signal; CST represents the cooling start time; Module M1.2, calculating the local minimum value LMinT of the interval between two adjacent cooling starts according to the cooling start time, Among them, temp represents the temperature data that changes with time t; Module M1.3 calculates the local maximum LMaxT between local minima. Module M1.4 calculates the lag time LagT(i) based on the cooling start time and local maximum value. Among them, the temperature difference ΔT1 = temp(LMaxT(i)) - temp(LMinT(i)); thr. represents the set temperature change threshold, which is 10% of the maximum temperature drop of active cooling.

8. The visualization temperature-sensitive area identification system for a numerically controlled machine tool according to claim 6, wherein The adaptive inflection point timing detection algorithm includes: Module M2.1 calculates the operating condition change timestamp OCCT based on the temperature field data according to the operating condition signal. Points with a second-order difference exceeding an adaptively determined gradient threshold are set as inflection points or points with a significant acceleration change, and the threshold Among them, OC represents the time series composed of working conditions; i represents the number of cooling signal startups; represents a non-negative integer; temp represents the temperature data that changes with time t; Gws represents the window size used to calculate the cumulative gradient before the working condition change, which is less than half of the duration of active cooling; Module M2.2 excludes the operating condition changes of the CSP during the start of active cooling. Calculate the cumulative gradient change Cumgrad after the operating condition change, Cumgrad(i) = cumsum(|Δ 2 temp(OCCT(i:end))|); Among them, WS represents the window size, and its size is the duration of active cooling; end represents the end of the cooling signal; cumsum() represents calculating the cumulative sum of array elements item by item and returning a vector of the same length; Module M2.3, finding the index point where the gradient changes significantly, Scidx(i) = min{t|Cumgrad(i)[t]≥Gradthr(i)}; Among them, Scidx represents the index where the gradient first changes significantly after the working condition change; Module M2.4, update the lag time according to the calculated index point where the temperature difference ΔT2 = temp(OCCT(i + 1)) - temp(OCCT(i)); thr. represents the set temperature change threshold.

9. The visualization temperature-sensitive area identification system of the numerical control machine tool according to claim 6, wherein The adjusted data structure includes expanding the dimension of the data to three dimensions [rows, cols, timeseries], and initializing the lag time as LagTime ∈ R rows×cols×Num ; Among them, R represents the set of real numbers; rows, cols, timeseries represent the number of row pixels, the number of column pixels, and the time dimension respectively; Num represents time; In the calculation module, the high-frequency change module is triggered, the result is output and averaged over the time dimension, the low-frequency change module is triggered, the result is output and averaged over the time dimension, and the temperature-sensitive area is selected; The temperature-sensitive area includes the area reflecting the peak value of temperature rise and the area reflecting the significant temperature gradient.

10. The visual temperature-sensitive area identification system for a numerically controlled machine tool according to claim 6, characterized in that, The hierarchical clustering-wavelet correlation analysis includes: Module M4.1 performs hierarchical clustering on the temperature time series data in the temperature field data, observes the division results of the clustering clusters through the clustering tree, and combines the elbow method to determine the better number of clustering clusters. The sum of squared errors is used as the cost function of the elbow method, and the sum of squared errors where, ||x i - c k || 2 represents the squared Euclidean distance between the data point x in the k-th cluster i and its centroid c k ; K represents the total number of clustering clusters; Module M4.2, performing Analytic Morlet wavelet transform on the temperature and thermal error data in the temperature field data, where W ψ (x)(s,τ) is the wavelet coefficient of the time signal x(t) at scale s and position τ; ψ * represents the complex conjugate of the wavelet function; jω0t represents a complex time series signal oscillating at frequency ω0; σ represents the standard deviation; Module M4.3 performs Spearman correlation analysis on the time-frequency domain information after wavelet transform to obtain the Spearman correlation coefficient between the temperature data and the thermal error. The Spearman correlation coefficient where R)X i ) represents the rank of the i-th observation in X i ; R(Y i ) represents the rank of the i-th observation in Y; n represents the number of observed values in the dataset.

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