High-precision sensor array data interpolation fitting method and system based on time series prediction

Abstract

The application discloses a high-precision sensor array data interpolation fitting method and system based on time sequence prediction, and the method comprises the following steps: obtaining sensor time sequence data before a to-be-measured time period, in the to-be-measured time period and after the to-be-measured time period; performing prediction processing on the sensor array data before the to-be-measured time period and after the to-be-measured time period by using a forward and reverse time sequence expansion algorithm, expanding the time sequence to the to-be-measured time period, and obtaining expanded in-line sensor array data; performing interpolation processing on the expanded in-line sensor array data, obtaining interpolated in-line sensor array data; performing polynomial fitting on the interpolated in-line sensor array data, selecting a physical field function corresponding to a best polynomial fitting degree as an in-line best physical field function, and obtaining an in-line physical field change trend. The application has stable functions and good practicability, and can significantly improve fitting precision in a sensor array fitting physical field process.

Description

Technical Field

[0001] This invention belongs to the field of high-precision physical field fitting technology for sensors, and relates to a method and system for interpolating and fitting sensor array data, particularly a method and system for interpolating and fitting sensor array data based on time-series prediction. Background Technology

[0002] In recent years, with the increasing demands for data accuracy in fields such as smart agriculture, industrial production, and environmental monitoring, improving the accuracy of sensor fitting of physical fields has become a key focus. Especially in environmental monitoring, the development of advanced surveying technologies such as total stations, rangefinders, and laser ranging has provided new options for distance measurement, gradually replacing traditional measurement methods. While these advanced measuring devices significantly improve measurement accuracy, their results are also more sensitive to fluctuations in atmospheric environmental parameters. Therefore, achieving high-precision sensor array data interpolation fitting methods is crucial for further improving distance measurement accuracy in the current field.

[0003] Due to the complexity of the ranging environment, the method for obtaining atmospheric refractive index during ranging mainly relies on atmospheric environmental parameter measurement, that is, directly acquiring the physical field environmental parameters within the measurement line through high-precision sensor array equipment. This method is simple in principle and can achieve an accuracy of 10. -8 The accuracy is on the order of magnitude, theoretically meeting the ranging accuracy requirements in most situations. However, due to limitations in real-world environments such as atmospheric parameter fluctuations, uneven parameter distribution, and insufficient atmospheric parameter processing algorithms, the accuracy for long-distance measurements reaches only 10. -7 Achieving orders of magnitude remains quite challenging.

[0004] In response to this situation, in recent years many researchers have studied multi-point calibration methods based on the classic two-point method of data acquisition, which improves the accuracy of the physical field within the survey line by increasing the density of the sensor array. However, due to the influence of terrain in different ranging environments and the cost limitations of high-precision sensors and auxiliary measurement equipment, the feasibility of improving the accuracy of environmental parameter measurements by increasing the accuracy or number of sensors is limited.

[0005] Therefore, in response to the needs of current high-precision sensor array data interpolation and fitting methods and the shortcomings of existing methods, this invention proposes a high-precision sensor array data interpolation and fitting method based on time series prediction. This method expands the sensor array based on forward and reverse time series analysis and uses a hybrid surrogate model that fuses radial basis interpolation with polynomial fitting to make the physical field fitted by the sensor array more accurate. Summary of the Invention

[0006] To address the aforementioned issues, this invention provides a high-precision sensor array data interpolation and fitting method and system based on time series prediction. This sensor array data processing method uses forward and inverse time series prediction technology as its core to expand the sensor array. Simultaneously, by performing interpolation and fitting processing on the expanded sensor array data, high-precision physical field data is obtained. Practical verification has shown that this scheme is feasible and has good practicality.

[0007] The technical solution adopted in this invention is as follows:

[0008] A high-precision sensor array data interpolation and fitting method based on time-series prediction includes the following steps:

[0009] S1. Acquire sensor time series data before, during, and after the time period to be measured;

[0010] S2. The forward and reverse time series augmentation algorithm is used to predict the sensor array data before and after the time period to be measured, so that the time series is extended to the time period to be measured, and the expanded sensor array data in the measurement line is obtained.

[0011] S3. Interpolate the expanded sensor array data within the survey line to obtain the interpolated sensor array data within the survey line;

[0012] S4. Perform polynomial fitting on the interpolated sensor array data within the measurement line, select the physical field function corresponding to the best polynomial fitting degree as the best physical field function within the measurement line, and obtain the trend of physical field change within the measurement line.

[0013] Furthermore, step S1 specifically involves collecting time series data of the sensors within the measurement line during three time periods: before the measurement period, during the measurement period, and after the measurement period, with the sensors located at different points within the measurement line during the three time periods.

[0014] Furthermore, step S2 specifically involves: using a forward time series augmentation algorithm to predict and process the sensor time series data before the time period to be measured, thereby augmenting the time series to the time period to be measured; using a reverse time series augmentation algorithm to transpose and predict the sensor time series data after the time period to be measured, and transposing the processed time series again to augment it to the time period to be measured, so that data from different locations can be augmented to the same time dimension through time series prediction, thereby increasing the number of sensor observation points at the same time within the measurement line to three times the original number.

[0015] Furthermore, in step S3, the radial basis function interpolation method is used to interpolate the sensor array data within the expanded measurement line, making the data within the measurement line denser and facilitating subsequent polynomial fitting of the physical field.

[0016] Further, step S4 specifically involves: performing polynomial fitting on the interpolated sensor array data within the measurement line to determine the changes and trends of the physical field function on the measurement line; comparing the fitted physical field with the actual sensor time series data to obtain the root mean square error under different polynomial fitting orders; comparing the root mean square error values ​​under different polynomial fitting orders; selecting the physical field function corresponding to the polynomial fitting order that minimizes the root mean square error as the optimal physical field function within the measurement line; and obtaining the trend of physical field changes within the measurement line.

[0017] A high-precision sensor array data interpolation and fitting system based on time-series prediction includes:

[0018] Data acquisition module: used to acquire sensor time series data before, during, and after the time period to be measured;

[0019] Data augmentation module: Used to predict sensor array data before and after the time period to be measured using forward and reverse time series augmentation algorithms, so that the time series is expanded to the time period to be measured, and the expanded sensor array data within the measurement line is obtained.

[0020] Data interpolation module: used to interpolate the expanded sensor array data within the survey line to obtain the interpolated sensor array data within the survey line;

[0021] Polynomial optimization fitting module: used to perform polynomial fitting on the interpolated sensor array data within the measurement line, select the physical field function corresponding to the best polynomial fitting degree as the best physical field function within the measurement line, and obtain the trend of physical field change within the measurement line.

[0022] A computer device, the computer device comprising:

[0023] One or more processors;

[0024] Memory, used to store one or more programs;

[0025] When the one or more programs are executed by the one or more processors, the one or more processors implement the above-described high-precision sensor array data interpolation fitting method based on time-series prediction.

[0026] A computer-readable storage medium storing computer instructions that, when executed by one or more processors, cause the one or more processors to perform the steps in the above-described method.

[0027] The beneficial effects of this invention are as follows:

[0028] 1) An algorithm for expanding the density of sensor arrays based on forward and reverse time series. The sensor array performs detection within the required test time period. Before and after the test time period, the sensor array is placed at different locations. The data is expanded to the required time period through forward and reverse time series expansion, respectively. This deep learning strategy improves the density of observation points of the sensor array without increasing the number of sensors.

[0029] 2) Physical field fitting based on radial basis interpolation fusion polynomial. Based on the sensor array expanded by forward and reverse time series, the sensor data in the measurement line is further expanded by radial basis interpolation to facilitate subsequent polynomial fitting of the physical field.

[0030] 3) Optimization strategy for polynomial fitting of sensor array data. Based on the expansion of observation data points through radial basis interpolation of sensor array data, the root mean square error data of the physical field are fitted according to different polynomial degrees. The optimal polynomial fitting parameters are selected through optimization algorithm to obtain a more accurate physical field fitting result.

[0031] This invention addresses the need for high-precision sensor array data interpolation and fitting methods based on time-series prediction, and designs a practical sensor array data processing method. After implementing this sensor array data processing method, functional tests were conducted. The tests show that the high-precision sensor array data interpolation and fitting method based on time-series prediction of this invention is feasible and has good practicality, capable of excellently completing the task of high-precision sensor array data processing in a baseline field. Attached Figure Description

[0032] Figure 1 This is a hardware block diagram of the high-precision sensor array data interpolation and fitting method based on time-series prediction in an embodiment of the present invention.

[0033] Figure 2 This is a software functional block diagram of a high-precision sensor array data interpolation and fitting method based on time-series prediction in an embodiment of the present invention.

[0034] Figure 3 This is a model diagram of a forward and reverse time series augmented sensor array in an embodiment of the present invention.

[0035] Figure 4 This is a schematic diagram of the sensor array layout in an embodiment of the present invention.

[0036] Figure 5 This is a schematic diagram illustrating the expansion of the sensor array observation points in an embodiment of the present invention.

[0037] Figure 6 This is a flowchart of the interpolation fitting optimization module algorithm in an embodiment of the present invention.

[0038] Figure 7 This is a schematic diagram of the reverse time series partitioning of the dataset in an embodiment of the present invention.

[0039] Figure 8 This is a flowchart of the reverse time series partitioning algorithm in an embodiment of the present invention.

[0040] Figure 9 This is a hardware test diagram of the sensor array compensation system in an embodiment of the present invention. Detailed Implementation

[0041] The technical solution of the present invention will be further described clearly and in detail below with reference to the accompanying drawings and specific examples.

[0042] A high-precision sensor array data interpolation and fitting method based on time-series prediction is proposed for applications requiring high accuracy in physical field fitting, such as smart agriculture, industrial production, and environmental monitoring. The method includes the following steps:

[0043] S1. Acquire sensor time series data before, during, and after the time period to be measured;

[0044] S2. The forward and reverse time series augmentation algorithm is used to predict the sensor array data before and after the time period to be measured, so that the time series is extended to the time period to be measured, and the expanded sensor array data in the measurement line is obtained.

[0045] S3. Interpolate the expanded sensor array data within the survey line to obtain the interpolated sensor array data within the survey line;

[0046] S4. Perform polynomial fitting on the interpolated sensor array data within the measurement line, select the physical field function corresponding to the best polynomial fitting degree as the best physical field function within the measurement line, and obtain the trend of physical field change within the measurement line.

[0047] Step S1 specifically involves collecting time series data from the sensors within the measurement line during three time periods: before, during, and after the measurement period, with the sensors located at different points within the measurement line during these three time periods.

[0048] Step S2 specifically involves: using a forward time series augmentation algorithm to predict and process the sensor time series data before the time period to be measured, thus augmenting the time series to the time period to be measured; using a reverse time series augmentation algorithm to transpose and predict the sensor time series data after the time period to be measured, then transposing the processed time series again to augment it to the time period to be measured, thereby augmenting the data at different locations to the same time dimension through time series prediction, thus increasing the number of sensor observation points at the same time within the measurement line to three times the original number.

[0049] In step S3, the radial basis function interpolation method is used to interpolate the sensor array data within the expanded measurement line, making the data within the measurement line denser and facilitating subsequent polynomial fitting of the physical field.

[0050] Step S4 specifically involves: performing polynomial fitting on the interpolated sensor array data within the measurement line to determine the changes and trends of the physical field function on the measurement line; comparing the fitted physical field with the actual sensor time series data to obtain the root mean square error under different polynomial fitting orders; comparing the root mean square error values ​​under different polynomial fitting orders; selecting the physical field function corresponding to the polynomial fitting order that minimizes the root mean square error as the optimal physical field function within the measurement line; and obtaining the trend of physical field changes within the measurement line.

[0051] Example

[0052] The high-precision sensor array data interpolation and fitting method based on time-series prediction in this embodiment has been applied to a baseline field atmospheric compensation and correction system at a university microsatellite center.

[0053] like Figure 1 As shown, the hardware of the high-precision sensor array data interpolation fitting method based on time-series prediction of the present invention includes: a high-precision sensor unit for measuring sensor data at different points on the survey line; and a data communication module for communication between the host computer and the high-precision sensor unit.

[0054] like Figure 2 As shown, the main algorithms for processing sensor array data in the host computer include: forward and reverse time series expansion and interpolation fitting algorithms. First, sensor array data for three scenarios—before, during, and after the measurement period—are processed separately. Data before the measurement period is expanded to the measurement period using a forward time series expansion algorithm, and data after the measurement period is expanded to the measurement period using a reverse time series expansion algorithm. This forward and reverse time series expansion algorithm expands the actual sensor array observation points within the measurement line to three times the original size. After completing the forward and reverse time series expansion, a suitable radial basis function and polynomial degree fitting range are selected. The physical field changes within the measurement line are then fitted using an interpolation fitting surrogate model. Simultaneously, since different interpolation fitting surrogate models have different interpolation functions and polynomial degrees, the root mean square error between the corresponding observation points and the fitting function varies. Based on the trend of the root mean square error, an optimization algorithm is used to finally select a suitable physical field function.

[0055] like Figure 3As shown, the sensor array data processing method of this invention employs forward and reverse time series expansion of the sensor array model. Its neural network architecture is built using Python. Taking a three-point sensor as an example, the data in the time period t2–t3 is the expanded dataset, the time period t1–t2 is the leading data, and the time period t3–t4 is the lagging data. The time series of sensors 1–3 are expanded at times t1–t2, and the time series of sensors 1'–3' are expanded at times t3–t4. Both of these time series are learned and expanded to the time period t2–t3 through the neural network model. This achieves the goal of expanding the sensor array data in the time period t2–t3 by collecting data from the sensors during the time periods t1–t2 and t3–t4, which would otherwise not require data collection.

[0056] like Figure 4 As shown, the sensor array data processing method of this invention requires changing the sampling points of the sensor array in three time periods: t1~t2, t2~t3, and t3~t4. When changing the sensor array points, it is necessary to ensure that the expanded sensor arrangement is uniform, and the sensor relocation time should be minimized as much as possible. The data measured in the t1~t2 time period is the first data measured in the entire time dimension. After this period, the sensor is relocated. The data measured in t2~t3 is the time period data to be processed based on the high-precision sensor array data interpolation fitting method of time series prediction. After completing the measurement in this period, the sensor is relocated again. The data measured in the t3~t4 time period after this period is the last data measured by the sensor array, i.e., the reverse time series data segment in the entire method. This data is used to invert the data in the t2~t3 time period at this point.

[0057] like Figure 5 As shown, the sensor array data processing method of this invention can ultimately expand sensor array data from three different dimensions to the same time dimension through forward and reverse time series expansion, making the observation points of the physical field within the survey line more dense. Specifically, data from sensors 1 to 3 are used for forward time series processing, while time series data from sensors I to III are temporarily stored, awaiting the completion of forward and reverse time series data processing for the remaining sensor locations. Data from sensors 1' to 3' are used for reverse time series processing. After processing, the sensor array data from these three locations is expanded to the same time dimension, achieving an increase in the number of sensor array observation points while maintaining the same number of sensors and accuracy.

[0058] like Figure 6As shown, the interpolation fitting algorithm of the sensor array data processing method of this invention requires an optimization module to select a suitable physical field for fitting. The core of this optimization is to use the root mean square error of different functions after interpolation fitting for selection. Before interpolation fitting, the sensor array data expanded by forward and reverse time series is first imported into the radial basis function to generate a mapping function. Discrete observation points after interpolation expansion are generated according to the physical field dimension. After completing the radial basis interpolation, let the variable polynomial fitting degree be i, and define loss(i-1) = inf. The interpolated discrete points are imported into the i-th degree polynomial for fitting, and the loss value of the polynomial fitting function and the discrete points is calculated. Based on the loss values ​​of different polynomial degrees, the optimal physical field fitting polynomial is obtained. The steps of the overall method implementation after combining the interpolation fitting algorithm with the forward and reverse time series algorithm are detailed below:

[0059] 1) This sensor array time series prediction method requires that the sensors be placed at other locations before and after the time period to be measured, and the time series data of the three segments before the time period to be measured, during the time period to be measured, and after the time period to be measured be transmitted to the host computer through the data communication module.

[0060] 2) Using sensor data before the time to be measured, the host computer analyzes and predicts the data using a forward time series augmentation algorithm to augment it to the time to be measured; after the sensor data after the time to be measured is transposed, the host computer analyzes and predicts the data using a reverse time series augmentation algorithm to augment it to the time to be measured.

[0061] 3) After the sensor array data is processed through forward and reverse time series processing, the sensor array data within the survey line is expanded, so that the number of sensor observation points within the survey line at the same time is increased to three times the original number.

[0062] 4) Interpolate the sensor array after forward and reverse time series processing to make the data within the measurement line denser, which facilitates the subsequent polynomial fitting of the physical field.

[0063] 5) Perform polynomial fitting on the interpolated sensor array data, and compare the fitted physical field with the actual measurement point data to obtain the root mean square error under different polynomial fitting orders.

[0064] 6) Compare the changes in root mean square error values ​​under different polynomial fitting orders, select the polynomial fitting order with the lowest root mean square error, and obtain the optimal physical field function within the survey line under this condition.

[0065] like Figure 7 As shown, the core of the reverse time series augmentation algorithm of this invention lies in reverse-engineering data based on the reverse time series. Let t... s As the dividing point, t sSubsequent observations are used as the training set, while earlier observations are used as the test set. The trained and tested deep learning model can then be applied to real-world time series prediction experiments.

[0066] like Figure 8 As shown, the biggest difference between the reverse time series augmentation algorithm of this invention and the forward time series augmentation algorithm is that the original time series needs to be transposed before further processing. First, the input forward time series X and the serialization ratio γ are determined. Then, the partitioning time t is initialized according to the forward time series and the serialization ratio. s =floor(γ*X), and reverse the time series X = reverse(X), based on the time division t s The time series is divided into training and test sets. A sliding window N is set according to the range of the training and test sets, resulting in the inverse time series test set and training set after sliding window processing. After processing by the inverse time series transpose algorithm, the inverse time series can be expanded to the specified test period, just like the forward time series.

[0067] like Figure 9 The diagram shows the hardware test results of the sensor array compensation system according to this invention. To test the functionality and performance of the high-precision sensor array data interpolation fitting method based on time-series prediction, the hardware includes a ranging system primarily composed of transmitting and receiving antennas, a high-precision sensor unit, and a data communication module. This invention utilizes the communication technology of the data communication module to transmit sensor data from all time periods to a host computer, and uses Python to implement the software functionality of the high-precision sensor array data interpolation fitting method based on time-series prediction on the host computer. The high-precision sensor array data interpolation fitting method based on time-series prediction of this invention expands the sensor array in the same time dimension to three times its original size without changing the number and accuracy of sensors by using forward and reverse time series analysis. Furthermore, it improves the accuracy and stability of the physical field fitting during ranging by using radial basis interpolation fused with polynomial fitting. To verify the feasibility and performance of this invention, the effect of the high-precision sensor array data interpolation fitting method based on time-series prediction was observed through multiple simulations using the Monte Carlo method. After verification, taking the temperature field in meteorological parameters as an example, the simulation results show that the high-precision sensor array data interpolation fitting method based on time-series prediction improves the accuracy of environmental parameters by 71.8% and reduces the standard deviation by 73.1%. The Monte Carlo simulation analysis results further prove that this method has stronger stability than the traditional multi-point method.

[0068] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0069] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0070] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0071] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0072] The above specific embodiments are used to explain and illustrate the present invention, but not to limit the present invention. Any modifications and changes made to the present invention within the spirit and scope of the claims shall fall within the protection scope of the present invention.

Claims

1. A high-precision sensor array data interpolation and fitting method based on time-series prediction, characterized in that, Includes the following steps: S1. Acquire sensor time series data before, during, and after the time period to be measured; S2. The forward and reverse time series augmentation algorithm is used to predict the sensor array data before and after the time period to be measured, so that the time series is extended to the time period to be measured, and the expanded sensor array data in the measurement line is obtained. S3. Interpolate the expanded sensor array data within the survey line to obtain the interpolated sensor array data within the survey line; S4. Perform polynomial fitting on the interpolated sensor array data within the measurement line, select the physical field function corresponding to the best polynomial fitting degree as the best physical field function within the measurement line, and obtain the trend of physical field change within the measurement line.

2. The high-precision sensor array data interpolation and fitting method based on time-series prediction according to claim 1, characterized in that, Step S1 specifically involves collecting time series data from the sensors within the measurement line during three time periods: before, during, and after the measurement period, with the sensors located at different points within the measurement line during these three time periods.

3. The high-precision sensor array data interpolation and fitting method based on time-series prediction according to claim 1, characterized in that, Step S2 specifically involves: using a forward time series augmentation algorithm to predict and expand the sensor time series data before the time period to be measured into the time period; using a reverse time series augmentation algorithm to transpose and predict the sensor time series data after the time period to be measured, and transposing the processed time series again into the time period to be measured.

4. The high-precision sensor array data interpolation and fitting method based on time-series prediction according to claim 1, characterized in that, In step S3, the radial basis function interpolation method is used to interpolate the sensor array data within the expanded survey line.

5. The high-precision sensor array data interpolation and fitting method based on time-series prediction according to claim 1, characterized in that, Step S4 specifically involves: performing polynomial fitting on the interpolated sensor array data within the measurement line, comparing the fitted physical field with the actual sensor time series data, obtaining the root mean square error under different polynomial fitting orders, comparing the root mean square error values ​​under different polynomial fitting orders, selecting the physical field function corresponding to the polynomial fitting order that minimizes the root mean square error as the optimal physical field function within the measurement line, and obtaining the trend of physical field changes within the measurement line.

6. A high-precision sensor array data interpolation and fitting system based on time-series prediction, characterized in that, include: Data acquisition module: used to acquire sensor time series data before, during, and after the time period to be measured; Data augmentation module: Used to predict sensor array data before and after the time period to be measured using forward and reverse time series augmentation algorithms, so that the time series is expanded to the time period to be measured, and the expanded sensor array data within the measurement line is obtained. Data interpolation module: used to interpolate the expanded sensor array data within the survey line to obtain the interpolated sensor array data within the survey line; Polynomial optimization fitting module: used to perform polynomial fitting on the interpolated sensor array data within the measurement line, select the physical field function corresponding to the best polynomial fitting degree as the best physical field function within the measurement line, and obtain the trend of physical field change within the measurement line.

7. A computer device, characterized in that, The computer device includes: One or more processors; Memory, used to store one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the high-precision sensor array data interpolation fitting method based on time-series prediction as described in any one of claims 1-5.

8. A computer-readable storage medium storing computer instructions, characterized in that, When the computer instructions are executed by one or more processors, the one or more processors cause the processors to perform the steps of the method according to any one of claims 1-5.

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