Method and system for compensating thermal errors of a measuring device based on time series analysis

Abstract

The present application relates to the field of data analysis, and more particularly to a measurement device thermal error compensation method and system based on time series analysis, the method comprising: obtaining an ambient temperature sequence and a device temperature sequence, differentiating the ambient temperature sequence and the device temperature sequence to obtain an ambient differential sequence and a device differential sequence, and analyzing the response efficiency of the device differential sequence relative to the ambient differential sequence; based on the response efficiency and the fluctuation degree of all local window target orders, adaptively correcting the differential order of the ARIMA model, and using the corrected ARIMA model to accurately predict the device temperature of the next local window; combining the thermal expansion coefficient of the device core material, the temperature prediction value and the reference temperature to calculate the thermal error compensation value corresponding to each time, adjusting the actual measurement result of the measurement device through the thermal error compensation value, and completing high-precision measurement of the measurement device. The present application improves the accuracy and stability of thermal error compensation.

Description

Technical Field

[0001] This invention relates to the field of data analysis, and more particularly to a method and system for thermal error compensation of measuring equipment based on time-series analysis. Background Technology

[0002] In modern industrial manufacturing and precision measurement, thermal error compensation is directly related to production efficiency and cost control. Without effective compensation, thermal errors can lead to a decrease in the pass rate of precision parts processing, resulting in a large number of scraps and rework costs, which may require additional investment in supporting facilities such as constant temperature workshops. However, through compensation technology, ineffective production losses can be reduced, dependence on extreme environmental control can be decreased, and resource utilization efficiency can be significantly improved. As the manufacturing industry upgrades towards high added value and high precision, the market's requirements for the accuracy of measurement equipment continue to increase. Traditional methods that rely on single temperature sequence analysis can no longer cope with nonlinear fluctuations such as sudden heat sources and periodic interference in complex industrial environments. The optimization of thermal error compensation technology has become the key to breaking through equipment performance bottlenecks and enhancing the core competitiveness of enterprises.

[0003] Existing thermal error compensation techniques often employ autoregressive moving average (ARMA) or autoregressive integral moving average (ARIMA) models to process temperature time-series data. However, these techniques have significant limitations: First, they rely solely on the statistical analysis of temperature sequences from a single device, failing to fully consider the interaction between ambient temperature and device temperature. Ambient temperature fluctuations can cause delays through heat conduction, leading to lag biases in time-series analysis and consequently affecting compensation accuracy. Second, they neglect the nonlinear dynamic characteristics of temperature sequences, such as sudden heat source interference and periodic fluctuations commonly found in industrial scenarios. This makes it difficult for the model to adapt to actual data patterns in complex environments, resulting in unsatisfactory compensation effects. Summary of the Invention

[0004] To address the problems of existing ARMA / ARIMA models relying on a single device temperature sequence, neglecting thermal conduction delay, and the nonlinear dynamic characteristics of the temperature sequence leading to compensation bias, this invention provides solutions in the following aspects.

[0005] In the first aspect, the time-series analysis-based thermal error compensation method for measurement equipment includes: acquiring ambient temperature sequences and equipment temperature sequences; performing differential processing on the ambient temperature sequences and equipment temperature sequences respectively to obtain ambient differential sequences and equipment differential sequences; analyzing the response efficiency of the equipment differential sequence relative to the ambient differential sequence; adaptively correcting the differential order of the ARIMA model based on the response efficiency and the fluctuation degree of the target order of all local windows; using the corrected ARIMA model to accurately predict the equipment temperature of the next local window; calculating the thermal error compensation value corresponding to each time moment based on the physical law of thermal expansion, combined with the thermal expansion coefficient of the core material of the equipment, the predicted temperature value, and the reference temperature; and adjusting the measurement equipment based on the thermal error compensation value. The actual measurement results of the equipment are used to complete high-precision measurement of the measuring equipment. The response efficiency is obtained by dividing the environmental difference sequence and the equipment difference sequence into local windows according to a preset length to obtain the corresponding environmental difference molecular sequence and equipment difference molecular sequence. Based on the temperature fluctuation of the environmental difference molecular sequence and equipment difference molecular sequence corresponding to the local window, the appropriate hysteresis order range is dynamically determined. The hysteresis correlation and target order of the equipment difference molecular sequence relative to the environmental difference molecular sequence in each local window are extracted using the cross-correlation function. The covariance of the environmental difference molecular sequence and the equipment difference molecular sequence in each local window is weighted by the change in the target order between adjacent local windows to obtain the response efficiency of the equipment difference sequence relative to the environmental difference sequence.

[0006] Preferably, the step of obtaining the temperature fluctuation degree of the environmental difference molecular sequence and the device difference molecular sequence corresponding to the local window includes: Using any local window as the target window and any sampling point within the target window as the target point, calculate the ratio between the absolute value of the difference of the target point in the environmental difference molecular sequence within the target window and the standard deviation of the environmental difference molecular sequence to obtain the standard fluctuation value of the ambient temperature; calculate the ratio between the absolute value of the difference of the target point in the corresponding equipment difference molecular sequence within the target window and the standard deviation of the equipment difference molecular sequence to obtain the standard fluctuation value of the equipment temperature. The standard fluctuation values ​​of ambient temperature and equipment temperature at the target point are summed to obtain the joint fluctuation value of the target point. The average joint fluctuation value of all sampling points is accumulated and averaged to obtain the average joint fluctuation intensity within the local window. The average joint fluctuation intensity is normalized to obtain the temperature fluctuation degree of the target window.

[0007] Preferably, the step of obtaining the lag order range includes: Using any local window as the target window, the degree of temperature fluctuation corresponding to the target window is exponentially decayed using a negative exponential function. The product of the decay result and the preset hysteresis order reference value is rounded up to obtain the maximum value of the hysteresis order range of the target window. The continuous positive integer interval from 1 to the maximum value is taken as the hysteresis order range of the target window.

[0008] Preferably, the response efficiency of the device differential sequence relative to the environmental differential sequence includes the following steps: Except for the first local window, any local window is used as the target window. The absolute value of the difference of the target order of the target window is divided by the sum of the absolute values ​​of the difference of the target order of all local windows to obtain the weight coefficient of the target window. Calculate the covariance between the environmental difference numerator sequence and the equipment difference numerator sequence corresponding to the target window. Use the product of the weighting coefficient and the covariance as the weighted covariance. Accumulate the weighted covariance of all local windows to obtain the response efficiency of the equipment difference sequence relative to the environmental difference sequence.

[0009] Preferably, the step of adaptively correcting the difference order of the ARIMA model includes: The product of the response efficiency and the standard deviation of the target order of all local windows is normalized. The normalized result is multiplied by the preset hyperparameter to obtain the adjustment increment base of the difference order. The adjustment increment base is rounded down. The difference order of the ARIMA model before adjustment is added to the rounded adjustment increment base to obtain the preliminary adjusted difference order. The preliminary adjusted difference order is compared with the constant 2, and the smaller value of the two is taken as the final adjusted difference order.

[0010] Preferably, the calculation method for the thermal error compensation value includes: Calculate the difference between the device temperature and the reference temperature at each sampling point in the next local window, and multiply the difference by the coefficient of thermal expansion to obtain the thermal error compensation value for the corresponding sampling point.

[0011] Preferably, the step of obtaining the target order includes: From all lagged correlations, the cross-correlation coefficient with the largest value is selected, and the candidate lag order corresponding to the largest cross-correlation coefficient is determined as the target order of the local window.

[0012] Secondly, a time-series analysis-based thermal error compensation system for measurement equipment includes a processor and a memory, wherein the memory stores computer program instructions, and when the computer program instructions are executed by the processor, the aforementioned time-series analysis-based thermal error compensation method for measurement equipment is implemented.

[0013] The present invention has the following effects: 1. This invention solves the problem that traditional single-sequence models cannot capture the impact of environmental fluctuation delays by introducing dual-sequence interactive analysis of ambient temperature and equipment temperature, combined with the quantitative calculation of heat conduction delay effect. In scenarios such as sudden heat sources and sudden changes in ambient temperature, it can accurately avoid prediction bias and significantly improve the accuracy of compensation.

[0014] 2. This invention enables the model to effectively adapt to the nonlinear dynamic characteristics of temperature sequences through local window fluctuation analysis, dynamic lag order range adjustment, and adaptive correction of ARIMA difference order. It can maintain a stable compensation effect even under complex environments such as periodic disturbances and sudden fluctuations. At the same time, it reduces the dependence on extreme environmental control facilities such as constant temperature workshops, thereby improving resource utilization efficiency and production economy. Attached Figure Description

[0015] Figure 1 This is a flowchart of steps S1-S3 in the thermal error compensation method for measurement equipment based on time-series analysis according to an embodiment of the present invention.

[0016] Figure 2 This is a structural block diagram of a measurement equipment thermal error compensation system based on time-series analysis according to an embodiment of the present invention. Detailed Implementation

[0017] 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 some embodiments of the present invention, but not all embodiments.

[0018] The specific implementation scenario of this invention focuses on thermal error compensation for precision measuring equipment in the industrial manufacturing field, with typical equipment including high-precision devices such as CNC machine tools and coordinate measuring machines. In the actual production process in the workshop, the core thermal error of such equipment originates from the structural thermal deformation caused by temperature changes. These temperature changes come from both the heat generated during the operation of the equipment itself and the dynamic fluctuations in the external ambient temperature.

[0019] Taking the start-up and shutdown of related equipment in the workshop as an example, the start-up of surrounding equipment creates a sudden heat source, causing a rapid increase in the ambient temperature 5-10 meters outside the equipment within a short period. Due to the thermal resistance of structural components such as the equipment shell and bed, this temperature change cannot be instantaneously transmitted to core working components such as the spindle. There is an inherent time delay related to the equipment structure and material thermal conductivity, resulting in a lag and non-stationarity in the temperature sequence of the core equipment components relative to the ambient temperature sequence. Traditional thermal error compensation methods do not consider this lag effect and cannot compensate for thermal expansion deformation in a timely manner, ultimately leading to measurement deviations, directly reducing the pass rate of precision parts processing, and affecting production quality and efficiency. This invention addresses the technical pain points under this actual working condition by proposing a compensation scheme based on dual temperature sequence analysis and dynamic lag order adjustment.

[0020] Reference Figure 1 The time-series analysis-based thermal error compensation method for measurement equipment includes steps S1-S3, as detailed below: S1: Obtain the ambient temperature sequence and the equipment temperature sequence, perform differential processing on the ambient temperature sequence and the equipment temperature sequence respectively to obtain the ambient differential sequence and the equipment differential sequence, and analyze the response efficiency of the equipment differential sequence relative to the ambient differential sequence.

[0021] Install an ambient temperature sensor 5-10 meters outside the device. This placement effectively avoids interference from the device's own heat generation on the ambient temperature measurement, ensuring that the collected ambient temperature data accurately reflects the temperature fluctuations of the external environment where the device is located.

[0022] Install temperature sensors on the equipment and deploy them in the core and critical parts of the equipment (such as the spindle, bed, and other structural components that directly affect the measurement accuracy). Since the thermal deformation of these parts is directly related to the measurement reference of the measuring equipment, collecting their temperature data can accurately reflect the temperature changes of the equipment related to thermal errors.

[0023] The preset acquisition frequency is 1Hz. This frequency can capture dynamic temperature changes in real time (including sudden fluctuations, periodic fluctuations, and other nonlinear characteristics) while avoiding data redundancy and increased computational costs caused by excessively high frequencies, thus achieving a balance between real-time performance and economy. Through the above sensor deployment and acquisition parameter settings, continuous ambient temperature sequences and equipment temperature sequences are acquired simultaneously.

[0024] Traditional thermal error compensation techniques using the ARIMA (Autoregressive Integrated Moving Average Model) model have a core flaw: they cannot quantify the contribution of external environmental heat sources to equipment temperature. They rely solely on a single equipment temperature sequence for data processing and error prediction, failing to consider the dynamic interaction between ambient and equipment temperatures, and particularly ignoring the delay caused by heat conduction. From the perspective of heat conduction, when ambient temperature fluctuations are transmitted to the equipment, they are subject to thermal resistance from the equipment structure and media. Heat transfer has an inherent time delay; changes in ambient temperature cannot be instantaneously transmitted to the core working components of the equipment (such as the spindle and bed). This results in a lag correlation between the equipment temperature sequence and the ambient temperature sequence, meaning that after an ambient temperature change, a certain amount of time is required for a corresponding trend to appear in the equipment temperature.

[0025] Therefore, the dynamic interaction between environmental and equipment temperatures and the heat conduction delay effect are quantified through in-depth analysis of dual temperature sequences. The specific steps are as follows: Starting from the second sampling point, the ambient temperature sequence and the equipment temperature sequence are subtracted from the previous sampling point to obtain the ambient difference sequence (reflecting the rate of change of ambient temperature) and the equipment difference sequence (reflecting the rate of change of equipment temperature). A local window of preset length 100 is used to divide the ambient difference sequence and the equipment difference sequence, resulting in... Each local window contains a corresponding environmental difference molecular sequence and a device difference molecular sequence, enabling segmented capture of dynamic temperature changes.

[0026] Using any local window as the target window and any sampling point within the target window as the target point, the temperature fluctuation of the target window is calculated. The specific operation steps include: The ratio of the absolute value of the difference of the target point in the molecular sequence of environmental differences within the target window to the standard deviation of the molecular sequence of environmental differences within the target window is used as the standard fluctuation value of the ambient temperature at the target point. This operation can eliminate the dimensional influence of ambient temperature fluctuations and achieve standardization of fluctuation intensity. The ratio of the absolute value of the difference of the target point in the molecular sequence of equipment differences within the target window to the standard deviation of the molecular sequence of equipment differences in the local window is used as the standard fluctuation value of the equipment temperature at the target point, ensuring that the intensity of equipment temperature fluctuations is comparable to the intensity of ambient temperature fluctuations.

[0027] The standard fluctuation values ​​of ambient temperature and equipment temperature at the target point are summed to obtain the joint fluctuation value of the target point, which characterizes the coordinated fluctuation level of ambient and equipment temperatures at a single sampling point. The joint fluctuation values ​​of all sampling points within the target window are accumulated, and the result is divided by the number of valid sampling points within the window (i.e., window length minus 1) to obtain the average joint fluctuation intensity within the target window, which stably reflects the overall fluctuation characteristics within the target window. The average joint fluctuation intensity is then normalized and mapped to... This allows us to obtain the degree of temperature fluctuation in the target window.

[0028] Specifically, the degree of temperature fluctuation satisfies the following relationship: ; In the formula, Indicates the first The degree of temperature fluctuation in a local window; Indicates the first The length of each local window; Indicates the ordinal number of the sampling point in the local window; Indicates the first In the poor environmental molecular sequence within the local window, the first... The difference value of each sampling point; Indicates the first In the device difference molecule sequence within a local window, the first... The difference value of each sampling point; Indicates the first The standard deviation of molecular sequences in poor environments within a local window; Indicates the first The standard deviation of the molecular sequence of the device difference in a local window; This represents the standard normalization function.

[0029] From the perspective of the physical characteristics of heat conduction, the impact of ambient temperature fluctuations on equipment temperature has an inherent time delay; the changes of the two do not occur synchronously. Based on this, this invention needs to combine the relative change characteristics of the ambient temperature sequence and the equipment temperature sequence to calculate the lag correlation between sequences at different lag orders. In the calculation of lag correlation, a range of lag orders needs to be pre-defined, and then the lag correlation corresponding to any lag order within that range is solved. Traditional techniques use a fixed range of lag orders, which has the drawback of difficulty in balancing computational accuracy and efficiency: if the lag order range is too small, although computational efficiency can be improved, long-period change trends in the temperature sequence are easily missed; if the lag order range is too large, although various change characteristics can be comprehensively captured, computational costs will be significantly increased, and the real-time performance of the algorithm will be reduced.

[0030] Therefore, based on the temperature fluctuation level of any local window, the maximum value of the hysteresis order range corresponding to that local window is dynamically calculated, thereby achieving accurate quantification of the hysteresis order range. This allows the hysteresis order range to adaptively adjust with the fluctuation characteristics of the temperature sequence, effectively balancing computational accuracy and efficiency. The specific steps are as follows: Using any local window as the target window, the degree of temperature fluctuation corresponding to the target window is exponentially decayed using a negative exponential function. The product of the decay result and the preset hysteresis order reference value is rounded up to obtain the maximum value of the hysteresis order range of the target window.

[0031] Specifically, the maximum value of the lag order range satisfies the following relationship: ； In the formula, Indicates the first The maximum value of the hysteresis order range for each local window; This indicates the preset lag order reference value, for example... ; Indicates the first The degree of temperature fluctuation in a local window; Represented by natural constant An exponential function with base 1; This represents the function for rounding up.

[0032] The maximum value of the lag order range directly limits the upper limit of the search for lag correlation within the local window. The range of consecutive positive integers from 1 to the maximum value is taken as the lag order range of the target window, and the search interval is... The existence of this boundary allows subsequent calculations of the cross-correlation function to focus on the effective lag order range that matches the fluctuation characteristics of the current window, ensuring both the accuracy of lag correlation capture and controlling computational costs.

[0033] To further explain, when the temperature fluctuation is large, it indicates that there are sudden and drastic fluctuations in the ambient and equipment temperatures within the local window. These fluctuations are mostly caused by short-term heat sources (such as the start-up and shutdown of surrounding equipment). The heat conduction delay time is short and the hysteresis characteristics are stable. It is not necessary to traverse a large range of hysteresis orders. The maximum value of a smaller range of hysteresis orders is sufficient to accurately capture effective hysteresis correlations. When the temperature fluctuation is small, it indicates that the temperature within the local window is in a stable change state. These changes are more likely to imply long-period hysteresis characteristics (such as the diurnal periodic fluctuations of ambient temperature). The maximum value of the range of hysteresis orders is needed to cover the long time lag range to avoid missing key hysteresis correlation information.

[0034] The range of hysteresis order in each local window Within this model, the hysteresis correlation between the device temperature series and the ambient temperature series is calculated using a cross-correlation function. The hysteresis order corresponding to the maximum hysteresis correlation is extracted as the target order of the local window, quantifying the delay time of heat conduction within the local window. It should be noted that the calculation method of the cross-correlation function is a technique well-known to those skilled in the art and will not be described in detail here.

[0035] Considering the dynamic changes in heat conduction processes in industrial environments, such as sudden changes in heat sources and fluctuations in equipment load leading to gradual or abrupt changes in hysteresis order, except for the first local window, the difference between the target order and the previous local window is calculated. The covariance of the ambient temperature series and the equipment temperature series is then weighted based on the difference in the target order. The specific steps are as follows: Using any local window as the target window, the absolute value of the difference in the target order of the target window is divided by the sum of the absolute values ​​of the differences in the target order of all local windows to obtain the weight coefficient of the target window.

[0036] The covariance between the environmental difference molecular sequence and the equipment difference molecular sequence corresponding to the target window is calculated to characterize the linear correlation strength between the environmental difference molecular sequence and the equipment difference molecular sequence within the local window. The product of the weighting coefficient and the covariance is used as the weighted covariance. The weighted covariances of all local windows are accumulated to obtain the response efficiency of the equipment difference sequence relative to the environmental difference sequence.

[0037] Specifically, the response efficiency of the device differential sequence relative to the environment differential sequence satisfies the following relationship: ; In the formula, This indicates the response efficiency of the device differential sequence relative to the environmental differential sequence; Indicates the total number of local windows; Indicates the first The difference in the target order of each local window; Indicates the first The difference in the target order of each local window; Indicates the first Molecular sequences with varying environmental conditions within a local window; Indicates the first The device difference molecular sequence in a local window; Indicates the first The covariance between the environmental difference molecular sequence and the device difference molecular sequence in a local window.

[0038] in, Used to quantify the The linear correlation strength between the environmental difference molecular sequence and the equipment difference molecular sequence within a local window. The larger the value, the higher the correlation between the environmental temperature change and the equipment temperature change, the higher the corresponding heat transfer efficiency, and the better the response efficiency of the equipment difference sequence relative to the environmental difference sequence. Characterizing the first The magnitude of the change in the target order of each local window relative to the previous local window, i.e. the activity of the heat conduction delay characteristics within the local window, indicates that the larger the value, the more drastic the change in hysteresis characteristics between consecutive windows, and the higher the weight of the influence of the heat conduction dynamic characteristics reflected by the local window on the overall response efficiency.

[0039] Specifically, when heat transfer efficiency is high, the equipment temperature responds more rapidly to changes in ambient temperature, a process often accompanied by significant changes in hysteresis characteristics. For example, in the event of a sudden heat source disturbance in an industrial setting, the equipment temperature's delayed response will adjust rapidly, corresponding to... The numerical value increases. At this point, by increasing the weight of the local window covariance, the final calculated response efficiency can more accurately reflect the dynamic interaction characteristics between the environment and equipment temperature, ensuring that the quantitative result of the response efficiency is highly consistent with the actual heat conduction law.

[0040] S2: Based on the response efficiency and the fluctuation of the target order of all local windows, the difference order of the ARIMA model is adaptively corrected, and the corrected ARIMA model is used to accurately predict the device temperature of the next local window.

[0041] The fixed difference order of traditional ARIMA models can easily lead to non-stationary residuals or excessive information loss. This step optimizes the parameters based on response efficiency. The product of the response efficiency and the standard deviation of the target order of all local windows is normalized. Specifically, in this embodiment, the hyperbolic tangent function is used for normalization. The normalization result is multiplied by the preset hyperparameter to obtain the adjustment increment base of the difference order. The adjustment increment base is rounded down, and the difference order of the ARIMA model before adjustment is added to the rounded adjustment increment base to obtain the preliminary adjusted difference order. The initially adjusted difference order is compared with the constant 2, and the smaller of the two is taken as the final adjusted difference order; it should be noted that the constant 2 represents the upper limit of the preset difference order.

[0042] Specifically, the adjusted difference order satisfies the following relationship: ; In the formula, This indicates the adjusted difference order; This represents the minimum function, and the difference order is kept too large in this invention; This indicates the difference order before adjustment (a value obtained by traditional methods, where the minimum difference order is determined by a stationarity test of the sequence, and the stationarity test can be calculated from the standard deviation of the temperature sequence). For hyperparameters, preset , indicating the adjustment range of the difference order; This indicates the response efficiency of the device differential sequence relative to the environmental differential sequence; The standard deviation of the target order for all local windows; Represents the hyperbolic tangent function; This represents the floor function.

[0043] The core function of the difference order is to eliminate the non-stationarity of the temperature series. Different orders correspond to clear physical meanings and only need to cover all non-stationary types in the thermal error compensation scenario: when the thermal interaction between the adapted device and the ambient temperature is stable and the temperature series has no significant non-stationary trend, no difference operation is performed; when the adapted temperature series has linear temperature changes caused by slow fluctuations in ambient temperature or continuous heating of the device, the non-stationarity can be eliminated by the first-order difference; when the adapted temperature series has temperature acceleration changes caused by sudden heat sources or abrupt changes in heat conduction delay, the higher-order non-stationarity can be eliminated by the second-order difference.

[0044] A higher response efficiency indicates better heat transfer efficiency from ambient temperature changes to equipment temperature, resulting in a faster and more direct impact of ambient temperature fluctuations on equipment temperature, and thus increased sensitivity to the thermal interaction process. A larger standard deviation of the target order indicates more significant differences in hysteresis characteristics between different local windows, reflecting a higher degree of dynamic fluctuation in heat transfer delay characteristics. In this case, the temperature sequence is more prone to non-stationary trends due to sudden events such as sudden heat source interference. Increasing the difference order can effectively eliminate such non-stationary characteristics, ensuring the prediction accuracy of the ARIMA model.

[0045] Adjusted difference order The model is updated to ARIMA and trained using historical temperature sequences (ambient temperature sequence and equipment temperature sequence) to predict the equipment temperature at each sampling point in the next local window. The difference order is updated every 100 seconds (i.e., one local window period) to ensure that the model adapts to dynamic temperature changes in real time.

[0046] S3: Based on the physical laws of thermal expansion, combined with the thermal expansion coefficient of the core material of the equipment, the predicted temperature and the reference temperature, calculate the corresponding thermal error compensation value at each moment, and adjust the actual measurement results of the measuring equipment through the thermal error compensation value to complete the high-precision measurement of the measuring equipment.

[0047] Thermal error is essentially the thermal expansion and deformation of equipment caused by temperature changes. Compensation values ​​are calculated based on physical laws; specifically, the compensation values ​​satisfy the following relationship: ; In the formula, Indicates the first The compensation value of the sampling point corresponding to the given time; The coefficient of thermal expansion (laboratory measurement results; at the same temperature, the coefficient of thermal expansion of the same material is a constant value; the average value of the coefficient of thermal expansion of the same material at different temperatures can be used). Indicates the first The predicted value of the sampling point corresponding to the given time; This indicates the reference temperature, which is the calibration temperature used in industrial precision measurement, specifically 20°C.

[0048] compensation value The system inputs data into the measuring equipment's control system, adjusts the actual measured values, and compensates for deformation deviations caused by temperature changes, thereby achieving precise measurement.

[0049] This invention also provides a thermal error compensation system for measurement equipment based on time-series analysis. For example... Figure 2As shown, the system includes a processor and a memory. The memory stores computer program instructions, which, when executed by the processor, implement the thermal error compensation method for a measuring device based on time-series analysis according to the first aspect of the present invention. The system also includes other components well known to those skilled in the art, such as a communication bus and a communication interface, the setup and functions of which are known in the art and will not be described further here.

[0050] It should be noted that those skilled in the art can make various modifications and improvements without departing from the inventive concept, and these all fall within the scope of protection of this invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A method for compensating thermal errors in measuring equipment based on time-series analysis, characterized in that, include: Obtain the ambient temperature sequence and the equipment temperature sequence, perform differential processing on the ambient temperature sequence and the equipment temperature sequence respectively to obtain the ambient differential sequence and the equipment differential sequence, and analyze the response efficiency of the equipment differential sequence relative to the ambient differential sequence. Based on the response efficiency and the fluctuation of the target order of all local windows, the difference order of the ARIMA model is adaptively corrected, and the corrected ARIMA model is used to accurately predict the device temperature of the next local window. Based on the physical laws of thermal expansion, and combined with the thermal expansion coefficient of the core material of the equipment, the predicted temperature and the reference temperature, the thermal error compensation value corresponding to each moment is calculated. The actual measurement results of the measuring equipment are adjusted by the thermal error compensation value to complete the high-precision measurement of the measuring equipment. The response efficiency is obtained as follows: the environmental difference sequence and the device difference sequence are divided into local windows of a preset length to obtain the corresponding environmental difference molecular sequence and device difference molecular sequence. The appropriate hysteresis order range is dynamically determined based on the temperature fluctuation of the environmental difference molecular sequence and device difference molecular sequence corresponding to the local window. The hysteresis correlation and target order of the device difference molecular sequence relative to the environmental difference molecular sequence in each local window are extracted using the cross-correlation function. The covariance of the environmental difference molecular sequence and device difference molecular sequence in each local window is weighted by the change in the target order between adjacent local windows to obtain the response efficiency of the device difference sequence relative to the environmental difference sequence.

2. The method for thermal error compensation of measuring equipment based on time series analysis according to claim 1, characterized in that, The steps for obtaining the temperature fluctuation levels of the environmental difference molecular sequence and the device difference molecular sequence corresponding to the local window include: Using any local window as the target window and any sampling point within the target window as the target point, calculate the ratio between the absolute value of the difference value of the target point in the environmental difference subsequence within the target window and the standard deviation of the environmental difference subsequence to obtain the standard fluctuation value of the ambient temperature; calculate the ratio between the absolute value of the difference value of the target point in the corresponding equipment difference numerator sequence within the target window and the standard deviation of the equipment difference numerator sequence to obtain the standard fluctuation value of the equipment temperature. The standard fluctuation values ​​of ambient temperature and equipment temperature at the target point are summed to obtain the joint fluctuation value of the target point. The average joint fluctuation value of all sampling points is accumulated and averaged to obtain the average joint fluctuation intensity within the local window. The average joint fluctuation intensity is normalized to obtain the temperature fluctuation degree of the target window.

3. The method for thermal error compensation of measuring equipment based on time series analysis according to claim 1, characterized in that, The steps for obtaining the lag order range include: Using any local window as the target window, the degree of temperature fluctuation corresponding to the target window is exponentially decayed using a negative exponential function. The product of the decay result and the preset hysteresis order reference value is rounded up to obtain the maximum value of the hysteresis order range of the target window. The continuous positive integer interval from 1 to the maximum value is taken as the hysteresis order range of the target window.

4. The method for thermal error compensation of measuring equipment based on time series analysis according to claim 1, characterized in that, The response efficiency of the device differential sequence relative to the environmental differential sequence includes the following steps: Except for the first local window, any local window is used as the target window. The absolute value of the difference of the target order of the target window is divided by the sum of the absolute values ​​of the difference of the target order of all local windows to obtain the weight coefficient of the target window. Calculate the covariance between the environmental difference numerator sequence and the equipment difference numerator sequence corresponding to the target window. Use the product of the weighting coefficient and the covariance as the weighted covariance. Accumulate the weighted covariance of all local windows to obtain the response efficiency of the equipment difference sequence relative to the environmental difference sequence.

5. The method for thermal error compensation of measuring equipment based on time series analysis according to claim 1, characterized in that, The step of adaptively correcting the difference order of the ARIMA model includes: The product of the response efficiency and the standard deviation of the target order of all local windows is normalized. The normalized result is multiplied by the preset hyperparameter to obtain the adjustment increment base of the difference order. The adjustment increment base is rounded down. The difference order of the ARIMA model before adjustment is added to the rounded adjustment increment base to obtain the preliminary adjusted difference order. The preliminary adjusted difference order is compared with the constant 2, and the smaller value of the two is taken as the final adjusted difference order.

6. The method for thermal error compensation of measuring equipment based on time series analysis according to claim 1, characterized in that, The calculation method for the thermal error compensation value includes: Calculate the difference between the device temperature and the reference temperature at each sampling point in the next local window, and multiply the difference by the coefficient of thermal expansion to obtain the thermal error compensation value for the corresponding sampling point.

7. The method for thermal error compensation of measuring equipment based on time series analysis according to claim 1, characterized in that, The steps for obtaining the target order include: From all lagged correlations, the cross-correlation coefficient with the largest value is selected, and the candidate lag order corresponding to the largest cross-correlation coefficient is determined as the target order of the local window.

8. A thermal error compensation system for measurement equipment based on time-series analysis, characterized in that, include: A processor and a memory, the memory storing computer program instructions that, when executed by the processor, implement the thermal error compensation method for a measurement device based on time-series analysis according to any one of claims 1-7.

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