CN116739133A - Regional reed NDVI pattern simulation prediction method based on natural-social dual-drive analysis - Google Patents
Regional reed NDVI pattern simulation prediction method based on natural-social dual-drive analysis Download PDFInfo
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Abstract
The application relates to the technical field of simulated regulation of vegetation patterns, in particular to a simulated prediction method of a regional reed NDVI pattern based on natural-social dual-drive analysis, which considers the influence of social elements such as policy planning, social development, land evolution and the like on the distribution of a macroscopic pattern of reed and also considers the influence of natural conditions on the distribution of a microscopic pattern of reed, and simultaneously realizes the simulation of a multi-scenario scheme by combining the driving actions of natural factors and social factors, thereby overcoming the limitation that the traditional method only considers the natural driving action and the limited simulation scheme.
Description
Technical Field
The application relates to the technical field of vegetation pattern simulation and regulation, in particular to a natural-society double-drive analysis-based regional reed NDVI pattern simulation and prediction method.
Background
Vegetation is an important component of the ecosystem, plays an important role in maintaining its ecological balance and environmental quality, and for ecosystems with serious damage to the ecological environment, vegetation pattern regulation is an effective way to repair its impaired structure and function. However, due to the double interference of climate change and artificial activities, the vegetation growth condition is damaged, the distribution pattern is encroached, and the vegetation survival is endangered, so that the ecological environment health is more threatened.
Reed has long growth time, wide distribution range and strong water purifying capacity, and is the main object for regulating and controlling vegetation pattern. The normalized vegetation index (NDVI) can eliminate the interference of external factors, enhance the response capability to vegetation changes, and is often used to reflect the growth and distribution of regional vegetation. Therefore, the influence of natural and social factors on the reed NDVI pattern is accurately identified, the distribution situation of the reed NDVI pattern under the environment of simulated and predicted change is simulated, and the method has important significance for vegetation pattern regulation and ecological environment restoration.
Currently, the conventional reed NDVI pattern simulation methods in the prior art at home and abroad include a mathematical statistical analysis method and a spatial analysis model method:
based on the relation between NDVI and natural driving factors of temperature and precipitation, the mathematical statistical analysis method predicts the NDVI change by using a multiple linear regression method. Although the driving mechanism is involved, only the driving effect of natural factors is considered, and the influence of social and economic development and utilization activity artificial factors is not involved; the method is only suitable for researching small sample size data of a certain point location and limited situations, and if the NDVI of all the point locations in the regional space is subjected to multi-scenario simulation, a large amount of time is required, so that the efficiency is low.
The spatial analysis model method predicts the change of the NDVI pattern of the region based on the NDVI spatial transfer matrix, but only predicts based on the NDVI historical spatial change rule, and does not relate to a driving mechanism, so that the evolution of the NDVI in a changing environment is difficult to predict.
In summary, the simulation prediction method of the reed NDVI pattern in the current area has the following limitations:
1. the driving mechanism of the NDVI change is not involved, or the driving mechanism only considers natural factors, and the driving effect of the socioeconomic factors is not involved.
2. The calculation efficiency is low, and the reed NDVI pattern in the whole area cannot be comprehensively simulated and predicted quickly and efficiently.
3. Because of imperfect consideration of driving mechanism and low calculation efficiency, the current simulation method has limited changeable environment and policy situations, and cannot simulate multiple compound changeable situations combining social economic development and natural environment change.
Therefore, in order to solve the problems, the application provides a natural-social dual-drive analysis-based regional reed NDVI pattern simulation prediction method, fills the blank in the field, considers the influence of policy planning on the distribution of the macroscopic patterns of the reed and the influence of natural conditions on the distribution of the microscopic patterns of the reed, and realizes the simulation of the multi-situation regional reed NDVI pattern under the dual influence of social and economic development and natural climate change.
Disclosure of Invention
The application aims to overcome the defects of the prior art, and provides a natural-society dual-drive analysis-based regional reed NDVI pattern simulation prediction method, which fills the blank in the field, and considers the influence of policy planning on the distribution of the macroscopic pattern of the reed and the influence of natural conditions on the distribution of the microscopic pattern of the reed, thereby realizing the simulation of the reed NDVI pattern in a multi-scene region under the dual influence of social and economic development and natural climate change. In order to achieve the above purpose, the application provides a natural-society double-drive analysis-based regional reed NDVI pattern simulation prediction method, which comprises the following steps:
s1, collecting land utilization pattern data in a historical period of an area, and identifying land utilization types and areas of various land types; collecting social, economic, hydrological, climate and environmental data of the same historical period;
s2, dividing the whole socioeconomic-ecological environment composite system into four modules of socioeconomic development, water demand, water quality and land area demand, qualitatively analyzing interaction relations of variables inside each module and among the modules, and drawing different land area change causal feedback loop diagrams;
s3, quantitatively analyzing an action relation equation among variables, determining the parameter values of the variables, establishing a regional land area demand system dynamics model, and reflecting the double driving action of natural factors and social factors on land area change, especially reed area change through action mechanisms and feedback relations between a social economic system and an ecological environment system;
s4, parameter calibration is carried out on the system dynamics model constructed in the step S3 by utilizing historical data, and validity of a model prediction result is checked;
s5, different change scenes are designed according to future policy planning and climate change characteristics, the area requirements of each land class in different future scenes of a system dynamics model prediction area are used, and multi-scene prediction analysis is carried out based on the influence of different social development and natural change scenes on land class area change;
s6, collecting regional land utilization pattern change driving factor data, wherein the factor data comprise terrain elements, meteorological elements, soil conditions and zone bit positions;
s7, determining the total probability of each land type in a specific plaque unit based on historical land utilization pattern and pattern change driving factor data, combining related research and expert advice, comprehensively considering a driving mechanism of the natural condition and the social condition on the land type space pattern change, and simultaneously combining the space change rule of the land utilization pattern;
s8, constructing a regional land utilization space pattern distribution simulation model by using the FLUS model based on the space change rule of the land utilization pattern explored in the S7;
s9, performing simulation precision test on the FLUS model constructed in the step S8 by using historical data, analyzing the difference between the simulation pattern and the actual pattern, and testing the effectiveness of the simulation result of the FLUS model;
s10, simulating the land utilization space pattern distribution of the areas under different scenes by using an FLUS model and combining the area requirements of the areas under different scenes obtained in the S5, and further extracting the reed space pattern distribution condition under each scene on the basis;
s11, collecting historical NDVI and NDVI change driving factor data;
s12, dividing the effective data set into a training data set, a test data set and other data sets after eliminating abnormal values in the data;
s13, analyzing the correlation between the historical NDVI data and the NDVI change driving factor data, and determining a driving mechanism of the NDVI change of the area;
s14, based on historical NDVI data and NDVI change driving factor data, constructing an NDVI prediction model by using a random forest algorithm, determining an optimal parameter value of the model, and training the model by using a training data set to obtain a regional reed NDVI simulation random forest model;
s15, testing the simulation performance of the NDVI simulation random forest model constructed in the S14 by using a test data set and other data sets, and evaluating whether the prediction precision of the model meets the requirement;
s16, based on reed space pattern distribution under different scenes obtained from S10, based on future temperature, precipitation and groundwater burial depth parameters designed in S5, simulating and predicting the future reed NDVI pattern distribution conditions of areas under different scenes by using a random forest model, combining the effects of policy planning, social development and land evolution social elements on the basis of a traditional natural driving mechanism, and reflecting the double driving effect of natural-society on reed NDVI pattern change.
In S9, if the Kappa coefficient between the simulation pattern and the actual pattern is greater than 0.6, the model simulation effect is remarkable, and the calculation formula of the Kappa coefficient is:
equation one:
formula II:
p 0 for the overall classification accuracy, the ratio of the accurately classified land sample size to the total sample size is pointed out; a, a i The area of the i-th land in the actual pattern; b i The area of the i-th land in the simulation pattern; n is the total sample size.
S15, selecting a determination coefficient R 2 As an evaluation index of the model simulation accuracy, if R 2 If the prediction accuracy of the model is more than 0.5, the prediction accuracy of the model is considered to meet the requirement, and the coefficient R is determined through validity test 2 The calculation formula of (2) is as follows:
and (3) a formula III:
X i and Y i The actual value and the analog value of the i-th sample, respectively, n being the number of samples,is the average of the actual values. Compared with the prior art, the application has the following beneficial effects:
1. the system dynamics model can clearly reflect complex, nonlinear and dynamic action mechanisms and feedback loops between the socioeconomic system and the ecological environment system, the FLUS model can combine the space change rule of the vegetation pattern on the basis of the simulation result of the system dynamics model, simulate different natural changes and the distribution condition of the regional reed space pattern under the social development scene, successfully combine the driving actions of natural factors and social factors, simultaneously realize the simulation of a multi-scenario scheme, and overcome the limitation that the traditional method only considers the natural driving action and the limited simulation scheme.
2. Because the random forest model has the advantage of efficiently processing large sample size data, the NDVI value of each point location of a region can be accurately simulated by combining a natural driving mechanism of NDVI change on the basis of reed space pattern simulation, the distribution situation of the reed NDVI patterns of the region under different natural and policy situations is obtained, and the limitations that the traditional method has long calculation time, low simulation efficiency and incapability of simulating the whole region are overcome.
Drawings
FIG. 1 is a schematic flow chart of a simulation prediction method of the present application.
FIG. 2 is a schematic diagram of a socioeconomic development module of a causal feedback loop for different areas of white lakes according to an embodiment of the present application.
FIG. 3 is a schematic diagram of a water demand module for a causal feedback loop for different areas of a white lake according to an embodiment of the present application.
FIG. 4 is a schematic diagram of a water quality module of a causal feedback loop for different areas of white lakes according to an embodiment of the present application.
FIG. 5 is a schematic diagram of a model of the area-like demand module of the causal feedback loop for different area-like changes of white lakes according to an embodiment of the present application.
FIG. 6 is a schematic diagram of the overall structure of a causal feedback loop model for different areas of white lakes according to an embodiment of the present application.
Fig. 7 is a schematic diagram of an actual layout and a simulated layout of a 2015 land use of a white lake according to an embodiment of the present application.
Fig. 8 is a schematic diagram of an actual layout and a simulated layout of a land use in 2020 of a white lake according to an embodiment of the present application.
Fig. 9 is a schematic diagram of land utilization layout in 2025 years old in white lake according to an embodiment of the present application.
Fig. 10 is a schematic diagram showing the distribution of reed NDVI patterns in 2025 years old white lake according to the embodiment of the present application.
Detailed Description
The application will now be further described with reference to the accompanying drawings.
Referring to fig. 1 to 6, the application provides a natural-society dual-drive analysis-based regional reed NDVI pattern simulation prediction method, which takes the white lake wetland reed NDVI pattern simulation as an implementation case to show the operation flow and implementation effect of the application:
the white lake is located in the middle of the Hebei province, is the shallow lake wetland with the largest North China plain, and the ravines distributed in the lake divide the whole lake into a plurality of different-size and interrelated lakes, so that the special land utilization pattern of the combination of reed terraces, garden terraces, village buildings and open water areas is formed. Reed is a typical vegetation of the white lake wetland and is a main regulation object for repairing vegetation patterns, so that the change and distribution conditions of the white lake reed NDVI patterns under different development scenes need to be simulated.
As shown in fig. 1, the simulation of the present application applied to the reed NDVI pattern of the white lake wetland needs to follow 16 operation steps in total, which are specifically as follows:
1. simulation of ground area requirements in a multi-scene of white lakes:
(1) Collecting land utilization office data of the white lakes 2010, 2015 and 2020, wherein the data type is 30m grid data, knowing that the main land utilization types of the white lakes are divided into four types of construction land, cultivated land, reed terraces and water areas, and counting the area of each land type in each period; social (population number, population birth rate, population reduction rate, average grain demand, average water consumption), economic (total GDP, industrial GDP, every ten thousand yuan industrial GDP water consumption), hydrologic (lake water consumption, lake water intake, lake water output, leakage, return water consumption, water supplement, ecological water consumption), climate (air temperature, precipitation), environmental (lake water intake pollution amount, reed pollution removal amount) data of the white lakes 2010 to 2015 are collected.
(2) Dividing the whole white lake system into four modules of social and economic development, water demand, water quality and land area demand according to the characteristics of the white lake, qualitatively analyzing the interaction relation of variables inside each module and among the modules, and drawing causal feedback loop diagrams of different land area changes, as shown in figures 2-6;
(3) Quantitative analysis of the equation of action relationship between the variables and determination of the parameter values of the variables are shown in table 1:
TABLE 1 dynamic model relationship and parameter settings for white lake-area demand systems
(4) With 2010 as the beginning year and 2010 mating data as the initial data, other parameter settings are shown in table 1, the model time step is set to 1 year, the area requirements of various places in 2015 and 2020 are simulated, and meanwhile, the area requirements are compared with actual values, and the results are shown in table 2. The validity test result shows that the relative error range of the prediction of the system dynamics model constructed by the application is 0.03% -5.59%, and the relative error ranges are all within the acceptable error range of 10%, so that the model has good prediction performance.
TABLE 2 simulation results and inspection of the dynamics model of the white lake area demand system
(5) In the aspect of socioeconomic development, two situations of current development and ecological migration are set, wherein socioeconomic parameters in the current development situation are maintained at 2010-2020, and 60% of the in-lake population is migrated annually by the white lake in the ecological migration situation. In terms of climate change, referring to a CMIP6 climate change mode, selecting two modes of SSP1-2.6 (sustainable development) and SSP5-8.5 (fossil fuel driven development), wherein the annual air temperature in the SSP1-2.6 mode is increased by 0.01 ℃ and the rainfall is increased by 0.3mm; in SSP5-8.5 mode, the annual temperature rises by 0.06 deg.C and rainfall increases by 2.3mm. In the aspect of ecological environment protection, referring to the white lake ecological environment management and protection planning, two water level modes of 7.3m (ecological water level) and 7.5m (flood control safety water level) are set. Based on the above scene changes, the changes in the regional demand of the white lake 2025 were simulated, and the results are shown in tables 3 and 4.
TABLE 3 area requirements of each of the different climate and water level scenarios in 2025 years in the current development context (×10) 7 m 2 )
TABLE 4 area requirement of each of the different types of places in 2025 years in different climates and water level scenarios in ecological immigration context (×10) 7 m 2 )
2. Reed space pattern distribution simulation under multi-scene of white lake:
(6) Collecting driving factor data of land utilization pattern changes in the white lakes 2010-2020, including DEM data, extracting gradient, slope distribution, air temperature and rainfall data, sand, silt, clay and organic carbon content data of the soil surface layer, setting a road network vector diagram in Xin county, calculating a road distance diagram, setting a white lake river network water system diagram, and calculating a river distance diagram; all the data are processed into 30m raster data, the unified geographic coordinate system is GCS_WGS_1984, and the projection coordinate system is WGS_1984_UTM_zone_50N.
(7) Based on historical land utilization patterns and pattern change driving factor data, setting the sampling rate to be 30/1000, hiding the layer number to be 30 by using an artificial neural network module in an FLUS model, and calculating the occurrence probability of each type of land in each specific plaque unit in the space; and simultaneously combining related researches and expert suggestions, determining neighborhood factor parameters of the white lake land class conversion and a land class conversion cost matrix, as shown in tables 5 and 6 respectively.
TABLE 5 local variation of FLUS model neighborhood factor parameters for white lake land utilization
TABLE 6 white lake place class conversion cost matrix
(8) Taking the 2010 land utilization pattern as basic period data, using the land occurrence probability and the neighborhood factor parameters calculated in the step (7), setting the maximum iteration number, the acceleration factor and the parallel running line number of the model to be 300, 0.1 and 1 respectively, and simulating the space distribution condition of the land utilization patterns in the white lakes 2015 and 2020 by using a cellular automaton module in the FLUS model, wherein the result is shown in fig. 7 and 8.
(9) Calculating Kappa coefficients based on the actual land utilization patterns of the white lakes 2015 and 2020 and the land utilization patterns simulated in the step (8) to verify the simulation accuracy of the FLUS model, wherein the result shows that the Kappa coefficients of the overall simulation results of the land utilization patterns in the year 2015 are 0.6338, and the Kappa coefficients of the simulation results of the reed and the water area are 0.7260 and 0.6844 respectively; the Kappa coefficient of the overall simulation result in 2020 was 0.7163, wherein the Kappa coefficients of the reed and water simulation results were 0.7856 and 0.7009, respectively. The overall Kappa coefficients of the land utilization bureau are all larger than 0.6, and the Kappa coefficients of the reed are all larger than 0.7, which shows that the FLUS model simulation result is obvious.
(10) Using the FLUS model constructed in the step (8), taking the actual land utilization pattern in 2020 as basic period data, taking the area requirement of each land class of 2025 white lake in multiple scenes simulated in the step (5) as a simulation target, simulating the distribution situation of the land utilization pattern of 2025 white lake in each scene, and further extracting the space pattern distribution of reed in each scene on the basis of the result as shown in fig. 9.
3. Reed NDVI pattern distribution simulation under multi-scene of white lake:
(11) Collecting the NDVI data of the white lake reed every 5 months in 2010-2019; meanwhile, NDVI change driving factor data in 2010-2019, namely average air temperature data in 1-4 months, accumulated rainfall data in 1-4 months and underground water burial depth data are collected, wherein the underground water burial depth is calculated by the following formula:
GWD＝H L -H W
wherein, GWD is the land water burial depth (m) of reed; h L Is land elevation (m), i.e., DEM data; h W Is the mean water level (m) of the white lake.
(12) And (3) unifying the data of the NDVI, the air temperature, the precipitation and the underground water burial depth of 10 stages from 2010 to 2019 into a comprehensive data set, removing abnormal values generated in the original data and in the interpolation calculation process, and extracting 3% of data pairs from the effective data pairs by adopting a random sampling mode to form a modeling data set, wherein other data pairs which are not extracted into the data pairs form other data sets. For the modeling dataset, 70% of the data is randomly extracted to form the training dataset, and the remaining 30% of the data forms the test dataset for construction and testing of the machine learning model.
(13) Based on the effective data set pretreated in the step (12), the correlation between reed NDVI data and air temperature, precipitation and underground water burial depth data is analyzed, the driving effect of each driving factor on the change of the reed NDVI is verified, and the result shows that for the white lake reed, the air temperature, the precipitation and the underground water burial depth are key driving factors for influencing the change of the reed NDVI.
(14) Based on the training data set obtained by preprocessing in the step (12), a simulation model of the NDVI change of the white lake reed is built by using a random forest algorithm, the parameter value of the optimal algorithm is searched by using a tuneRF traversal function, and the result shows that when the mtry value is 7, the prediction precision of the model is highest, namely the mtry parameter is set to be 7, the model is trained again by using the training data set, and the optimal simulation model of the NDVI of the white lake reed is obtained.
(15) Testing the simulation performance of the NDVI simulation random forest model constructed in step (14) using the test dataset and the other datasets, and calculating the decision coefficients (R 2 ) Results show R in training, testing and other centralized models 2 0.9008, 0.5233 and 0.5164 are respectively greater than 0.5, which shows that the model has good prediction performance and effective simulation result.
(16) On the basis of the spatial pattern distribution of the reed under different scenes obtained in the step (10), the optimal white lake reed NDVI simulation model constructed in the step (14) is used for predicting the distribution situation of the white lake 2025-year reed NDVI pattern under each scene, and the result is shown in fig. 10.
The embodiment can be seen that the simulation and prediction method for the regional reed NDVI pattern based on the natural-social dual-drive analysis provided by the application mainly considers the drive effect of social and economic elements on reed space pattern distribution in the construction process of a system dynamics model and an FLUS model, and simultaneously considers the drive effect of natural elements; the modeling of the random forest model inherits the consideration of the traditional method to the natural driving mechanism, thereby not only absorbing the advantages of the traditional technology, but also expanding the traditional technology. Meanwhile, as the system dynamics model has good multi-scenario simulation advantages and the random forest model has good big data processing capacity, the method provided by the application can simulate and predict the NDVI value in each plaque unit on the basis of reed space pattern distribution, thereby realizing the simulation of the full-area reed NDVI pattern and breaking through the limitation that the traditional method can only simulate the NDVI values of a plurality of specific point units.
The above is only a preferred embodiment of the present application, only for helping to understand the method and the core idea of the present application, and the scope of the present application is not limited to the above examples, and all technical solutions belonging to the concept of the present application belong to the scope of the present application. It should be noted that modifications and adaptations to the present application may occur to one skilled in the art without departing from the principles of the present application and are intended to be within the scope of the present application.
The application solves the problems that the prior art does not relate to a driving mechanism, the evolution of the NDVI under a variable environment is difficult to predict, the consideration factors are few, the calculation efficiency is low, and the research on all points in a target area is impossible.
Claims (3)
1. The regional reed NDVI pattern simulation prediction method based on natural-social dual-drive analysis is characterized by comprising the following steps of:
s1, collecting land utilization pattern data in a historical period of an area, and identifying land utilization types and areas of various land types; collecting social, economic, hydrological, climate and environmental data of the same historical period;
s2, dividing the whole socioeconomic-ecological environment composite system into four modules of socioeconomic development, water demand, water quality and land area demand, qualitatively analyzing interaction relations of variables inside each module and among the modules, and drawing different land area change causal feedback loop diagrams;
s3, quantitatively analyzing an action relation equation among the variables, determining the parameter values of the variables, establishing a regional land area demand system dynamics model, and reflecting the double driving action of natural factors and social factors on land area change, especially reed area change through action mechanisms and feedback relations between a social economic system and an ecological environment system;
s4, parameter calibration is carried out on the system dynamics model constructed in the S3 by utilizing historical data, and validity of a model prediction result is checked;
s5, different change scenes are designed according to future policy planning and climate change characteristics, the system dynamics model is used for predicting the area requirements of each type of land under different future scenes, and multi-scene prediction analysis is carried out based on the influence of different social development and natural change scenes on the area change of the land;
s6, collecting regional land utilization pattern change driving factor data, wherein the factor data comprise terrain elements, meteorological elements, soil conditions and location positions;
s7, determining the total probability of each land type in a specific plaque unit based on historical land utilization pattern and pattern change driving factor data, combining related research and expert advice, comprehensively considering a driving mechanism of the natural condition and the social condition on the land type space pattern change, and simultaneously combining the space change rule of the land utilization pattern;
s8, constructing a regional land utilization space pattern distribution simulation model by using an FLUS model based on the land utilization pattern space change rule explored in the S7;
s9, performing simulation precision test on the FLUS model constructed in the step S8 by using historical data, analyzing the difference between a simulation pattern and an actual pattern, and testing the effectiveness of a simulation result of the FLUS model;
s10, simulating land utilization space pattern distribution of areas under different scenes by using an FLUS model and combining the area requirements of each scene under the different scenes obtained in the S5, and further extracting reed space pattern distribution conditions under each scene on the basis;
s11, collecting historical NDVI and NDVI change driving factor data;
s12, dividing the effective data set into a training data set, a test data set and other data sets after eliminating abnormal values in the data;
s13, analyzing the correlation between the historical NDVI data and the NDVI change driving factor data, and determining a driving mechanism of the NDVI change of the area;
s14, based on the historical NDVI data and the NDVI change driving factor data, constructing an NDVI prediction model by using a random forest algorithm, determining an optimal parameter value of the model, and training the model by using a training data set to obtain a regional reed NDVI simulation random forest model;
s15, testing the simulation performance of the NDVI simulation random forest model constructed in the S14 by using the test data set and other data sets, and evaluating whether the prediction precision of the model meets the requirement;
s16, based on reed space pattern distribution under different scenes obtained from the S10, based on future temperature, precipitation and underground water burial depth parameters designed in the S5, simulating and predicting future reed NDVI pattern distribution conditions of areas under different scenes by using the random forest model, combining the effects of policy planning, social development and land evolution social elements on the basis of a traditional natural driving mechanism, and reflecting the double driving effect of natural-society on reed NDVI pattern change.
2. The method for simulating and predicting the natural-society double-drive analysis-based area reed NDVI pattern according to claim 1, wherein in S9, if the Kappa coefficient between the simulated pattern and the actual pattern is greater than 0.6, the model simulation effect is significant, and the validity test is passed, and the calculation formula of the Kappa coefficient is:
equation one:
formula II:
the p is 0 For the overall classification accuracy, the ratio of the accurately classified land sample size to the total sample size is pointed out; the a i The area of the i-th land in the actual pattern; said b i The area of the i-th land in the simulation pattern; and n is the total sample size.
3. The method for simulating and predicting the NDVI pattern of a regional reed based on natural-society dual drive analysis as claimed in claim 1, wherein in S15, a decision coefficient R is selected 2 As an evaluation index of the model simulation accuracy, if R 2 If the prediction accuracy of the model is greater than 0.5, the prediction accuracy of the model is considered to meet the requirement, and the validity test is passed, and the decision coefficient R is determined 2 The calculation formula of (2) is as follows:
and (3) a formula III:
the X is i And Y i The actual value and the analog value of the ith sample are respectively, n is the number of samples, andis the average of the actual values.
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