Rice yield prediction method and system based on drone images
Through drone image acquisition and gray correlation analysis, a mapping matrix of vegetation index and influencing factors was constructed, which solved the problem of poor accuracy in rice yield prediction in the existing technology, and achieved more accurate yield prediction.
Patent Information
- Application Number
- CN202410425525.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-04-10
- Publication Date
- 2025-01-14
- Estimated Expiration
- 2044-04-10
AI Technical Summary
The existing rice yield prediction methods fail to effectively comprehensively consider the environmental parameters and fertilizer application parameters during the rice growth period, resulting in a large deviation between the prediction results and the actual yield measurement value and poor accuracy.
采用基于无人机图像的水稻产量预测方法,通过采集生育期内的无人机遥感影像及影响因素数据,计算植被指数与产量值的相关系数,进行灰色关联分析,构建植被指数及影响因素的映射矩阵,计算匹配度以确定预测产量阈值。
The accuracy of rice yield prediction is improved, and the yield situation is more accurately reflected by comprehensively considering vegetation index, growth environment characteristics and fertilizer application parameters.
Smart Images

Figure CN118246602B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of rice yield prediction, and in particular to a rice yield prediction method and system based on unmanned aerial vehicle images. Background Art
[0002] The phenotypic information of field crops is a direct reflection of the growth status and health status of crops, and is an important factor affecting crop production management decisions. As an emerging technical means, UAV low-altitude remote sensing is gradually becoming one of the most important means of large-scale non-destructive testing of crops, with its advantages of high temporal and spatial resolution, low cost, flexibility, and strong adaptability to complex farmland environments. It plays a huge role in precision agriculture applications. At present, the vegetation index composed of spectral information in various bands by UAV remote sensing has been confirmed by many research results to have a significant correlation with yield, and is therefore widely used in crop yield estimation.
[0003] In the existing technology, the most commonly used rice yield prediction is based on the regression model of vegetation index and yield data, which only considers the linear relationship between vegetation index and rice yield, and does not comprehensively consider the environmental parameters and fertilizer application parameters during the rice growth period, resulting in a large deviation between the prediction results and the actual yield measurement values, and the prediction accuracy is poor. To this end, we propose a rice yield prediction method and system based on drone images. Summary of the invention
[0004] The main purpose of the present invention is to provide a rice yield prediction method and system based on drone images, which can effectively solve the problems in the background technology.
[0005] In order to achieve the above object, the technical solution adopted by the present invention is:
[0006] The rice yield prediction method based on drone images includes:
[0007] Collect UAV remote sensing images and influencing factor data of rice in various growth stages in the experimental area, including growth environment characteristics and fertilizer application parameter characteristics, interpret remote sensing images, and obtain common vegetation index characteristic data;
[0008] Furthermore, the growth environment characteristic data may be one or more of the ambient temperature, ambient humidity, moisture content, average sunshine, etc., and the fertilizer application parameter characteristic data may be one or more of the application type, application amount and application time of fertilizers and pesticides, etc.
[0009] The ground measurement method is used to sample and weigh the rice at maturity to obtain the measured data of rice yield;
[0010] Calculating the correlation coefficient between each of the commonly used vegetation index values and the rice yield value in each growth period, and selecting the commonly used vegetation index whose correlation coefficient is within the correlation threshold range as the evaluative time-domain vegetation index;
[0011] Conduct grey correlation analysis on the acquired growth environment characteristic data, fertilizer application parameter characteristic data and rice yield value, and determine the weight of the influencing factors on rice yield based on the analysis results;
[0012] Constructing a mapping matrix table V→P of the evaluative temporal vegetation index and the influencing factors to rice yield values;
[0013] The evaluative temporal vegetation index of rice in the test area and the influencing factor value are obtained as the value to be evaluated, and the matching degree between the value to be evaluated and the basis of the number set V in the mapping matrix table is calculated, wherein the calculation formula of the matching degree is:
[0014]
[0015] Where Md is the matching value; α, β are constant coefficients, and α∈(0,1), β∈(0,1), α+β=1; a i b' is the evaluative temporal vegetation index value of the i-th item of rice in the tested area; lj It is expressed as the measured value of the influencing factor of the jth item in the lth experimental area; b j is the jth influencing factor value of rice in the tested area; is the weight of the jth influencing factor on rice yield; and the predicted yield threshold of rice in the tested area is determined by the matching degree.
[0016] A rice yield prediction system based on unmanned aerial vehicle images comprises a remote sensing image acquisition module, a vegetation index acquisition module, an influencing factor data acquisition module, a yield measurement module, a yield correlation analysis module, a yield association analysis module, a model building module and a yield prediction module.
[0017] The remote sensing image acquisition module is used to collect UAV remote sensing images of rice in the experimental area and the area to be tested at various growth stages;
[0018] The vegetation index acquisition module is used to interpret the acquired remote sensing images and obtain common vegetation index feature data;
[0019] The influencing factor data acquisition module is used to collect the growth environment characteristics and fertilizer application parameter characteristic data of rice in the experimental area and the area to be tested;
[0020] The yield measurement module uses a ground measurement method to sample and weigh the mature rice in the experimental area to obtain measured data of rice yield;
[0021] The yield correlation analysis module is connected to the vegetation index acquisition module, and is used to calculate the correlation coefficient between the common vegetation index value and the rice yield value in each growth period of rice in the experimental area, and screen out the common vegetation index whose correlation coefficient is within the correlation threshold [0.7,1] as the evaluation time domain vegetation index;
[0022] The yield correlation analysis module is connected to the influencing factor data acquisition module, and is used to perform grey correlation analysis on the acquired growth environment characteristic data and fertilizer application parameter characteristic data and rice yield value, and determine the weight of each influencing factor on rice yield according to the analysis result;
[0023] The model building module is connected with the yield measurement module, the yield correlation analysis module and the yield association analysis module, and is used to build the mapping matrix table V→P of the evaluative temporal vegetation index and the influencing factors to the rice yield value according to the acquired data;
[0024] The yield prediction module is connected to the model building module, and is used to calculate the matching degree between the growth environment characteristics and fertilizer application parameter characteristic data of the rice in the test area and the basis of the data set in the mapping matrix table, and determine the predicted yield threshold of the rice in the test area according to the matching degree;
[0025] The system further includes a memory, a processor, and an electronic program stored in the memory and capable of running on the processor.
[0026] The present invention has the following beneficial effects:
[0027] Compared with the prior art, the technical solution of the present invention collects UAV remote sensing images and influencing factor data of rice in various growth stages in the experimental area, wherein the influencing factors include growth environment characteristics and fertilizer application parameter characteristics, interprets the remote sensing images, obtains common vegetation index characteristic data, adopts ground measurement method to sample and weigh the rice in the mature stage, obtains the measured data of rice yield, calculates the correlation coefficient between each of the common vegetation index values in each growth stage and the rice yield value, selects the common vegetation index whose correlation coefficient is within the correlation threshold range as the evaluative time-domain vegetation index, performs grey correlation analysis on the acquired growth environment characteristic data and fertilizer application parameter characteristic data and the rice yield value, The weights of the influencing factors on rice yield are determined according to the analysis results, a mapping matrix table of the evaluative temporal vegetation index and the influencing factors to the rice yield value is constructed, the evaluative temporal vegetation index and the influencing factor value of the rice in the test area are obtained as the value to be evaluated, the matching degree between the value to be evaluated and the basis of the number set in the mapping matrix table is calculated, and the predicted yield threshold of the rice in the test area is determined by the matching degree, and the vegetation index type that can best reflect the yield and the influence of the growth environment characteristics and fertilizer application parameter characteristics on the rice yield during the rice growth period are comprehensively considered, so that the prediction result is more in line with the actual situation, thereby effectively improving the accuracy of rice yield prediction. BRIEF DESCRIPTION OF THE DRAWINGS
[0028] Figure 1 The present invention is a flow chart of a rice yield prediction method based on drone images;
[0029] Figure 2 The figure is a block diagram of the overall structure of the rice yield prediction system based on drone images of the present invention. DETAILED DESCRIPTION
[0030] The present invention will be further described below in conjunction with specific implementation methods, wherein the accompanying drawings are only used for exemplary descriptions and represent only schematic diagrams rather than actual drawings, and should not be understood as limiting the present invention. In order to better illustrate the specific implementation methods of the present invention, some parts of the accompanying drawings may be omitted, enlarged or reduced, and do not represent the size of the actual product.
[0031] Example 1
[0032] like Figure 1 The flowchart of the rice yield prediction method based on drone images is shown in Figure 2 The overall structural block diagram of the rice yield prediction system based on drone images is shown.
[0033] The specific implementation process of the technical solution of the inventor includes the following steps:
[0034] Step 1: Collect rice data from the experimental area to build a prediction model
[0035] The specific steps are:
[0036] Step 1), collect UAV remote sensing images of rice in the experimental area and the test area in various growth stages through the remote sensing image acquisition module. In this embodiment, the UAV is equipped with an RGB camera and a RedEdge-M multispectral camera for remote sensing image acquisition. The flight altitude, heading overlap, lateral overlap, and flight speed data of the UAV are set, and the RGB camera is adjusted to select the automatic photo mode, and the shooting time interval of the multispectral camera is set. It should be noted that before the UAV enters the route and after the flight, it is necessary to shoot the radiation calibration plate for the calibration of the multispectral image reflectivity. The UAV data collection selects a clear and cloudless time period with good lighting to obtain high-quality remote sensing image data.
[0037] Step 2), remote sensing image interpretation is performed based on visible light orthophotos and radiation-corrected multispectral orthoreflectance maps through a vegetation index acquisition module to obtain common vegetation indices, wherein the common vegetation indices include spectral parameters of surface vegetation coverage summarized based on spectral characteristics such as vegetation chlorophyll, normalized vegetation index NDVI, green normalized vegetation index GNDVI, renormalized vegetation index RDVI, ratio vegetation index RVI1 / RVI2 that can effectively reflect rice coverage and growth conditions, terrestrial chlorophyll index MTCI that can effectively reflect rice growth conditions, vegetation extraction color index CIVE, overgreen vegetation index ExG, green leaf vegetation index GLA, plant pigment ratio PPR, red-green-blue vegetation index RGBVI, moisture index WI, improved red edge ratio vegetation index MSR, vegetation attenuation index PSRI at least one of the following, and the calculation formula thereof is shown in the following table:
[0038] Table 1 Commonly used vegetation index calculation formulas
[0039]
[0040]
[0041] Among them, r, g, and b in the formula are the RGB sensor band data, r is the red band, g is the green band, and b is the blue band; R R , R G , R B , R NIR , R Red-edge is the multispectral sensor band data, R R is the red band, R Gv is the green band, R B is the blue band, R NIR is the near infrared band, R Red-edge It is the red edge band.
[0042] Step 3) The growth environment characteristics and fertilizer application parameter characteristic data of rice in the experimental area are collected through the influencing factor data acquisition module, wherein the growth environment characteristic data can be one or more of the ambient temperature, ambient humidity, moisture content, average sunshine, etc., and the fertilizer application parameter characteristic data can be one or more of the application type, application amount and application time of fertilizers and pesticides.
[0043] Step 4), using the yield measurement module to sample and weigh the mature rice in the experimental area using the ground measurement method to obtain the measured data of rice yield.
[0044] Step 5), the correlation coefficient between the common vegetation index value and the rice yield value in each growth period of the experimental area is calculated by the yield correlation analysis module, and the common vegetation index with a correlation coefficient within the correlation threshold [0.7, 1] is selected as the evaluation time domain vegetation index, wherein the calculation formula of the correlation coefficient is:
[0045]
[0046] In the formula, ρ kt is the correlation coefficient between the tth commonly used vegetation index value and the rice yield value in the kth growth period; x kt is the value of the tth commonly used vegetation index in the kth growth period; is the mean value of the tth commonly used vegetation index value in the kth growth period; y μ is the measured value of rice yield in the μth experimental area; λ is the number of experimental areas; is the mean of the measured rice yield,
[0047] Step 6), gray correlation analysis is performed on the acquired rice growth environment characteristic data and fertilizer application parameter characteristic data and rice yield value in the experimental area through the yield correlation analysis module, and the weight of each influencing factor on rice yield is determined according to the analysis results. The specific steps are as follows:
[0048] s61, construct a data sequence of influencing factor values and rice yield values based on the acquired influencing factor values and rice yield value data, and the sequence expression is:
[0049] E=(E l )
[0050] F=(F1,F2,...,F j , ..., F n )
[0051] Where, E is the data sequence of rice yield value; F is the data sequence of influencing factor value; E l is the rice yield value of the lth experimental area; Fj is the j-th influencing factor set;
[0052] s62, standardize the data in the data sequence, the calculation formula is:
[0053]
[0054] In the formula, E l ' is the standardized value of rice yield in the first experimental area; e lh is the measured value of rice yield in the lth experimental area at the hth time; is the mean of the measured rice yield in the lth experimental area, H is the total number of times the output is measured; F jh is the normalized value of the hth measured value of the jth influencing factor; f jh is the h-th measured value of the j-th influencing factor; is the mean of the measured values of the jth influencing factor,
[0055] s63, calculate the correlation coefficient of all data points in the data sequence, the calculation formula is:
[0056]
[0057] In the formula, ξ jh is the correlation coefficient between each data point in the data sequence F and the data sequence E; where min[min(|E l '-F jh |)] is to take |E l '-F jh |Calculate the minimum value of the result and then take the minimum value of all calculated minimum values; max[max(|E l '-F jh |)] is to take |E l '-F jh |After calculating the maximum value of the result, take the maximum value of all the calculated maximum values; ρ is the resolution coefficient, and its value range is (0,1];
[0058] s64, calculate the correlation value according to the calculation result of the correlation coefficient, the calculation formula is:
[0059]
[0060] In the formula, R j is the correlation value between the jth influencing factor and rice yield value;
[0061] s65, determine the weight of the influencing factor based on the obtained correlation, and the calculation formula is:
[0062]
[0063] Step 7), constructing a mapping matrix table V→P of the evaluative temporal vegetation index and influencing factors to the rice yield value according to the acquired data through the model building module, wherein the specific expression of the mapping matrix table is:
[0064]
[0065] In the formula, a li It is expressed as the i-th evaluation time-domain vegetation index value of the l-th experimental area; L is the total number of experimental areas; b lj It is expressed as the weighted value of the jth influencing factor in the lth experimental area, P l It is represented by the measured value of rice yield in the lth experimental area; m represents the total number of evaluation time-domain vegetation index values, and n represents the total number of influencing factor values.
[0066] Step 2: Collect rice data in the area to be tested for yield prediction
[0067] The specific steps are:
[0068] Step 8), obtaining the growth environment characteristics and fertilizer application parameter characteristic data of rice in the tested area.
[0069] Step 9), the yield prediction module calculates the matching degree between the growth environment characteristics of rice in the test area and the fertilizer application parameter characteristic data and the basis of the data set in the mapping matrix table, and determines the predicted yield threshold of rice in the test area through the matching degree. The matching degree calculation formula is:
[0070]
[0071] Where Md is the matching value; α, β are constant coefficients, and α∈(0,1), β∈(0,1), α+β=1; a i is the i-th evaluation time-domain vegetation index value of rice in the tested area; b' lj It is expressed as the measured value of the jth influencing factor in the lth experimental area; b j is the jth influencing factor value of rice in the tested area; is the weight of the jth influencing factor on rice yield.
[0072] The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.
Claims
1. A rice yield prediction method based on drone images, characterized in that: include: Collect UAV remote sensing images and influencing factor data of rice in various growth stages in the experimental area, including growth environment characteristics and fertilizer application parameter characteristics, interpret remote sensing images, and obtain common vegetation index characteristic data; The ground measurement method is used to sample and weigh the rice at maturity to obtain the measured data of rice yield; Calculating the correlation coefficient between each of the commonly used vegetation index values and the rice yield value in each growth period, and selecting the commonly used vegetation index whose correlation coefficient is within the correlation threshold range as the evaluative time-domain vegetation index; Conduct grey correlation analysis on the acquired growth environment characteristic data, fertilizer application parameter characteristic data and rice yield value, and determine the weight of the influencing factors on rice yield based on the analysis results; Constructing a mapping matrix table V→P of the evaluative temporal vegetation index and the influencing factors to rice yield values; The evaluative temporal vegetation index and the influencing factor value of rice in the test area are obtained as the value to be evaluated, and the matching degree between the value to be evaluated and the basis of the number set V in the mapping matrix table is calculated, and the predicted yield threshold of rice in the test area is determined by the matching degree, wherein the calculation formula of the matching degree is: Where Md is the matching value; α, β are constant coefficients, and α∈(0,1), β∈(0,1), α+β=1; a i b' is the evaluative temporal vegetation index value of the i-th item of rice in the tested area; lj It is expressed as the measured value of the influencing factor of the jth item in the lth experimental area; b j is the jth influencing factor value of rice in the tested area; is the weight of the jth influencing factor on rice yield; The specific expression of the mapping matrix table is: In the formula, a li It is expressed as the time-domain vegetation index value of the i-th item of the l-th experimental area; L is the total number of experimental areas; b lj It is expressed as the weighted value of the influencing factor of the jth item in the lth experimental area, P l It is expressed as the measured value of rice yield in the lth experimental area; m is the total number of evaluation time-domain vegetation index values, and n is the total number of influencing factor values; The method for determining the weights of influencing factors on rice yield includes the following steps: s1, construct the data sequence of influencing factor values and rice yield values based on the acquired influencing factor values and rice yield value data. The sequence expression is: And=(And l ) F=(F1,F2,...,F j ,...,F n ) Where, E is the data sequence of rice yield value; F is the data sequence of influencing factor value; E l is the rice yield value of the lth experimental area; F j is the j-th influencing factor set; s2, standardize the data in the data sequence, the calculation formula is: In the formula, E l ' is the standardized value of rice yield in the first experimental area; e lh is the measured value of rice yield in the lth experimental area at the hth time; is the mean of the measured rice yield in the lth experimental area, H is the total number of times the output is measured; F jh is the normalized value of the hth measured value of the jth influencing factor; f jh is the h-th measured value of the j-th influencing factor; is the mean of the measured values of the jth influencing factor, s3, calculate the correlation value of all data points in the data sequence, the calculation formula is: In the formula, ξ jh is the correlation coefficient between each data point in the data sequence F and the data sequence E; where min[min(|E l '-F jh |)] is to take |E l '-F jh |Calculate the minimum value of the result and then take the minimum value of all calculated minimum values; max[max(|E l '-F jh |)] is to take |E l '-F jh |After calculating the maximum value of the result, take the maximum value of all the calculated maximum values; ρ is the resolution coefficient, and its value range is (0,1]; s4, calculate the correlation value according to the calculation result of the correlation coefficient, the calculation formula is: In the formula, R j is the correlation between the jth influencing factor and rice yield value; s5, determine the weight of the influencing factor based on the obtained correlation, and the calculation formula is:
2. The rice yield prediction method based on drone images according to claim 1 is characterized in that: The formula for calculating the correlation coefficient is: In the formula, ρ kt is the correlation coefficient between the tth commonly used vegetation index value and the rice yield value in the kth growth period; x kt is the value of the tth commonly used vegetation index in the kth growth period; is the mean value of the tth commonly used vegetation index value in the kth growth period; y μ is the measured value of rice yield in the μth experimental area; λ is the number of experimental areas; is the mean of the measured rice yield, 3. The rice yield prediction method based on drone images according to claim 1 is characterized in that: The correlation threshold value range is [0.7, 1].
4. The rice yield prediction method based on drone images according to claim 1, characterized in that: The commonly used vegetation indices include at least one of the normalized vegetation index, green normalized vegetation index, renormalized vegetation index, ratio vegetation index, terrestrial chlorophyll index, vegetation extraction color index, overgreen vegetation index, green leaf vegetation index, plant pigment ratio, red, green and blue vegetation index, terrestrial chlorophyll index, moisture index, improved red edge ratio vegetation index and vegetation attenuation index.
5. The rice yield prediction system based on drone images is characterized by: The system includes a remote sensing image acquisition module, a vegetation index acquisition module, an influencing factor data acquisition module, a yield measurement module, a yield correlation analysis module, a yield relevance analysis module, a model building module, and a yield prediction module; The remote sensing image acquisition module is used to collect UAV remote sensing images of rice in the experimental area and the area to be tested at various growth stages; The vegetation index acquisition module is used to interpret the acquired remote sensing images and obtain common vegetation index feature data; The influencing factor data acquisition module is used to collect the growth environment characteristics and fertilizer application parameter characteristic data of rice in the experimental area and the area to be tested; The yield measurement module uses a ground measurement method to sample and weigh the mature rice in the experimental area to obtain measured data of rice yield; The yield correlation analysis module is connected to the vegetation index acquisition module, and is used to calculate the correlation coefficient between the common vegetation index value and the rice yield value in each growth period of rice in the experimental area, and screen out the common vegetation index whose correlation coefficient is within the correlation threshold [0.7,1] as the evaluation time domain vegetation index; The yield correlation analysis module is connected to the influencing factor data acquisition module, and is used to perform grey correlation analysis on the acquired growth environment characteristic data and fertilizer application parameter characteristic data and rice yield value, and determine the weight of each influencing factor on rice yield according to the analysis result. The method for determining the weight of the influencing factor on rice yield includes the following steps: s1, construct the data sequence of influencing factor values and rice yield values based on the acquired influencing factor values and rice yield value data. The sequence expression is: And=(And l ) F=(F1,F2,...,F j ,...,F n ) Where, E is the data sequence of rice yield value; F is the data sequence of influencing factor value; E l is the rice yield value of the lth experimental area; F j is the j-th influencing factor set; s2, standardize the data in the data sequence, the calculation formula is: In the formula, E l ' is the standardized value of rice yield in the first experimental area; e lh is the measured value of rice yield in the lth experimental area at the hth time; is the mean of the measured rice yield in the lth experimental area, H is the total number of times the output is measured; F jh is the normalized value of the hth measured value of the jth influencing factor; f jh is the h-th measured value of the j-th influencing factor; is the mean of the measured values of the jth influencing factor, s3, calculate the correlation value of all data points in the data sequence, the calculation formula is: In the formula, ξ jh is the correlation coefficient between each data point in the data sequence F and the data sequence E; where min[min(|E l '-F jh |)] is to take |E l '-F jh |Calculate the minimum value of the result and then take the minimum value of all calculated minimum values; max[max(|E l '-F jh |)] is to take |E l '-F jh |After calculating the maximum value of the result, take the maximum value of all the calculated maximum values; ρ is the resolution coefficient, and its value range is (0,1]; s4, calculate the correlation value according to the calculation result of the correlation coefficient, the calculation formula is: In the formula, R j is the correlation between the jth influencing factor and rice yield value; s5, determine the weight of the influencing factor based on the obtained correlation, and the calculation formula is: The model building module is connected with the yield measurement module, the yield correlation analysis module and the yield relevance analysis module, and is used to build a mapping matrix table V→P of the evaluative temporal vegetation index and the influencing factors to the rice yield value according to the acquired data. The specific expression of the mapping matrix table is: In the formula, a li It is expressed as the time-domain vegetation index value of the i-th item of the l-th experimental area; L is the total number of experimental areas; b lj It is expressed as the weighted value of the influencing factor of the jth item in the lth experimental area, Among them, b' lj It is expressed as the measured value of the influencing factor of the jth item in the lth experimental area; P l It is expressed as the measured value of rice yield in the lth experimental area; m is the total number of evaluation time-domain vegetation index values, and n is the total number of influencing factor values; The yield prediction module is connected to the model building module, and is used to calculate the matching degree between the growth environment characteristics and fertilizer application parameter characteristic data of rice in the test area and the basis of the data set in the mapping matrix table, and determine the predicted yield threshold of rice in the test area through the matching degree, wherein the calculation formula of the matching degree is: Where Md is the matching value; α, β are constant coefficients, and α∈(0,1), β∈(0,1), α+β=1; a i is the evaluative temporal vegetation index value of the rice in the tested area as described in item i; b j is the jth influencing factor value of rice in the tested area; is the weight of the jth influencing factor on rice yield.
6. The rice yield prediction system based on drone images according to claim 5, characterized in that: The system also includes a memory, a processor, and an electronic program stored in the memory and capable of running on the processor, wherein the processor can implement the steps of the method according to any one of claims 1 to 4 when running the electronic program.
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