Aircraft high-dimensional temperature prediction method under wide-area high-altitude task environment

Abstract

The application provides a wide-range high-altitude task environment aircraft high-dimensional temperature prediction method, comprising the following steps: step one: temperature-time first prediction based on regression analysis; step two: temperature-time secondary prediction based on nonlinear fitting and error random representation; step three: temperature-height prediction based on empirical formula and dynamic interpolation; step four: temperature-longitude and latitude prediction based on dynamic interpolation; and step five: high-dimensional temperature fusion prediction. The application comprehensively utilizes mathematical statistics methods such as regression analysis, nonlinear fitting, linear (nonlinear) interpolation and empirical formula to construct a temperature factor prediction model related to four-dimensional variables including time, height, longitude and latitude, so that a reasonable temperature long-term prediction value can be output when any four-dimensional coordinate in the given aircraft task process, thereby providing guidance for the task process.

Description

Technical Field

[0001] This invention provides a method for predicting the high-dimensional temperature of aircraft in a wide-area high-altitude mission environment. It involves a long-term prediction technology for high-dimensional temperature environmental factors based on a comprehensive empirical model and statistical model, including regression analysis, nonlinear fitting, and dynamic interpolation. It belongs to the field of equipment environmental engineering. Background Technology

[0002] Temperature, as one of the most typical natural environmental factors during spacecraft missions, has a continuous impact on the performance and functionality of spacecraft. Taking missiles as an example, temperature significantly affects many aspects, including missile engine thrust, aerodynamic drag, flight lift, guidance accuracy, and warhead materials, thus directly influencing missile launch decisions, performance levels, and functional realization. If the temperature conditions during a spacecraft mission can be predicted in advance, it not only allows for a preliminary assessment of its reliability, safety, and mission success, but also provides guidance for mission initiation decisions and the implementation of compensatory measures during the mission. Therefore, reasonable and accurate temperature prediction is of great guiding significance for the performance of the spacecraft itself and the success of the mission. Specifically, the temperature characteristics during a spacecraft mission typically exist in a four-dimensional "space" interwoven with time, altitude, longitude, and latitude, and the high-dimensional spatiotemporal coupling effect presents a significant challenge to the reasonable and accurate prediction of temperature.

[0003] Current temperature prediction methods mainly fall into two categories: mathematical statistics and intelligent prediction. However, existing methods primarily focus on predicting temperature with respect to single variables such as altitude or time, and are mainly geared towards short-term predictions. They lack research on long-term temperature prediction considering latitude and longitude, as well as high-dimensional spatiotemporal coupling. Therefore, there is an urgent need to study predictive methods for high-dimensional spatiotemporal temperature factors. Summary of the Invention

[0004] (1) Purpose of the invention: The invention comprehensively utilizes mathematical statistics methods and empirical formulas such as regression analysis, nonlinear fitting, and linear (nonlinear) interpolation to construct a predictive model of temperature factors with respect to four-dimensional variables including time, altitude, longitude, and latitude. The goal is to output a reasonable long-term temperature prediction value for any four-dimensional coordinate during a given spacecraft mission, thereby providing guidance for the mission process.

[0005] (2) Technical solution:

[0006] The technical solution of the present invention is as follows: A method for predicting the high-dimensional temperature of an aircraft in a wide-area high-altitude mission environment, comprising the following steps:

[0007] Step 1: Initial temperature-time prediction based on regression analysis; specifically including the following steps:

[0008] a) Determining the four-dimensional spatial range and resolution of the spacecraft's mission environment: time, altitude, longitude, and latitude.

[0009] First, the four-dimensional spatial range that the aircraft may experience during the mission is clearly defined; second, the data resolution of the four dimensions is set respectively: in this invention, the time resolution is set to 6h / data point, the altitude resolution is set to 1km / data point, and the longitude and latitude resolutions are both set to 0.25 degrees / data point.

[0010] b) Design and train a temperature-time linear regression model using nearby data as a benchmark; this includes selecting nearby data and designing and training the linear regression model:

[0011] First, the latest year's data in the historical data is selected as the benchmark. In this invention, the nearest data is the historical temperature information of 2022.

[0012] Secondly, we designed and trained linear regression models: using the inter-year increase in monthly average temperature as the dependent variable and the year as the independent variable, we constructed linear regression models Δy for the dependent variable of January, February, March, ..., December on the year. i (x)=k i (x-x0)+b i In this formula, i represents the month, x represents the year, x0 represents the initial year of the historical data, and Δy i (x) represents the increase in the average temperature of month i in year x compared to the same period of the previous year, k i and b i Let represent the slope and intercept of the linear regression model for month i, respectively. Furthermore, by training the linear regression model using MATLAB software, the coefficients of the linear regression model can be obtained.

[0013] Step 2: Temperature-time quadratic prediction based on nonlinear fitting and random error characterization; specifically including the following steps:

[0014] a) Temperature-time prediction based on nonlinear fitting:

[0015] Even after the linear regression prediction in "Step One," a certain deviation still exists between the predicted and actual values ​​of the temperature increment (due to factors such as dimensionality compression and long-term prediction). ξ i (x) represents the difference between the predicted and actual values ​​of the average temperature level increment in month i of year x after "step one". Through statistical analysis and fitting of historical data, this invention uses a trigonometric function to characterize the deviation between the predicted and actual values, specifically expressed as:

[0016] ξ i (x)=A i sin(B i(x-x0)+C i ), (1)

[0017] In the formula, A i B i and C i represents the unknown parameters in the nonlinear model for the i-th month, which can be obtained by fitting historical data using MATLAB software; x and x0 represent the year to be determined and the initial year of the historical data, respectively.

[0018] b) Temperature-time prediction based on random error characterization:

[0019] After regression analysis and nonlinear fitting, the predicted values ​​are quite close to the true values. However, due to the limited number of training samples, errors still exist between them. To address this, this invention introduces a randomized value method to characterize the error ξ2 in this case. i (x), i.e., ξ2 i (x)=rand(min i ,max i In this formula, 'rand' represents a random value selection function, and min... i This represents the minimum error in the training sample set for this stage, while max represents the minimum error in the training sample set for this stage. i This indicates the corresponding maximum error value.

[0020] c) Temperature-time integrated prediction model:

[0021] By superimposing linear regression, nonlinear regression and error stochastic characterization models, and using formula (2), long-term temperature prediction can be achieved using historical temperature data of the region under given latitude, longitude and altitude conditions.

[0022] y i,j (x)=y i,j (2022)+k i (x-2018)+b i +A i sin(B i (x-2018)+C i )+rand(min i ,max i (2)

[0023] In this formula, i represents the month, j represents the specific time of the point to be predicted within the month, and y i,j (x) and y i,j (2022) represents the temperature at a specific time j in any future year and in the i-th month of 2022, respectively.

[0024] Step 3: Temperature-height prediction based on empirical formulas and dynamic interpolation; specifically including the following steps:

[0025] a) Tropospheric temperature-height prediction based on empirical formulas:

[0026] The primary heat source for the troposphere is the Earth's surface; therefore, the energy received decreases with increasing altitude, leading to a decrease in atmospheric temperature with increasing altitude. In the troposphere, the relationship between temperature and altitude can be approximated by a generally accepted empirical formula:

[0027] T=T0-6×Δy, (3)

[0028] In the formula, T represents the temperature at the current altitude; T0 represents the temperature at the known altitude; and Δy represents the altitude difference in km. The altitude range of the troposphere varies with latitude, averaging 17–18 km in low latitudes, 10–12 km in mid-latitudes, and 8–9 km in polar regions. Therefore, when using empirical formulas for tropospheric temperature-altitude prediction, the application range of the formulas needs to be flexibly adjusted according to the latitude of the target location.

[0029] b) Stratospheric temperature-height prediction based on dynamic interpolation:

[0030] The stratosphere mainly extends from the top of the troposphere to 50 km. At the bottom of the stratosphere (approximately below 25 km), temperature changes very slowly with altitude, with a rate of change approximately zero. Between 25 km and 50 km, due to the dominance of solar radiation, temperature increases with altitude. Therefore, within the stratosphere, this invention performs temperature-altitude prediction in stages, determining the altitude envelope of the point to be predicted at a given resolution, and estimating the temperature value of the point to be predicted by interpolating the temperatures at the endpoints of the interval.

[0031] Specifically, in the case of the height resolution (1km / data point) utilized in this invention, the height h to be predicted is selected. X The envelope interval, h X ∈(h1,h2), where h1 and h2 represent the two endpoints of the height envelope, respectively. The temperature T of the height to be predicted. X Satisfy: T X =(h2-h X )T1+(h X -h1)T2, where T1 and T2 represent the temperatures at the envelope endpoints, respectively.

[0032] The implementation diagram of this step is as follows: Figure 2 As shown.

[0033] Step 4: Temperature-latitude / longitude prediction based on dynamic interpolation;

[0034] Temperature variations with latitude and longitude are influenced by complex and difficult-to-quantify factors such as topography. Therefore, within the two-dimensional space of latitude and longitude, the finite two-dimensional space is divided into several grids based on the resolution of historical data. Given a point to be predicted, its envelope grid is determined, and the distances d1, d2, d3, d4 between the point to be predicted and the boundary points of the envelope grid are calculated (see Appendix). Figure 3 ), respectively using formula and Calculate two predicted values ​​for the point to be predicted; where T i (i = 1, 2, 3, 4) represents the temperature value at the endpoint of the envelope grid, and T' and T” represent the temperature prediction values ​​under the diagonal envelope, respectively. Furthermore, the temperature value of the point to be predicted is calculated using the formula T = (T' + T”) / 2.

[0035] Step 5: Fusion prediction of high-dimensional temperature; specifically includes the following steps:

[0036] a) Determine the four-dimensional envelope range of the point to be predicted:

[0037] For any point to be predicted, its 4D envelope range is determined at a given resolution. The number of envelope points in the latitude and longitude layer is usually 4, the number of envelope points in the altitude layer is usually 2, and one point that satisfies the resolution and is closest to that moment is selected in the time layer.

[0038] b) Determine the predicted temperature values ​​for several points within the envelope:

[0039] At a given resolution, the predicted temperature values ​​for several points within the envelope are calculated through "Step One". Specifically, an initial temperature-time prediction based on regression analysis is first performed, followed by a secondary temperature-time prediction based on nonlinear fitting and random error characterization. Through this process, the time-level temperature prediction for several points within the envelope is completed.

[0040] c) High-dimensional temperature fusion prediction in priority order:

[0041] Following the priority order of altitude and latitude / longitude, the temperature values ​​at several points within the envelope of the altitude to be predicted are first calculated through "Step Three." Specifically, depending on whether the point to be predicted is in the troposphere or stratosphere, the appropriate temperature-elevation prediction model is selected. Empirical formulas are used in the troposphere, while dynamic interpolation methods are used in the stratosphere.

[0042] Then, using "Step Four", the envelope grid of latitude and longitude is determined, and two predicted values ​​T' and T" are calculated. The final predicted temperature value of the point to be predicted is obtained by using T = (T' + T") / 2.

[0043] (3) Advantages and benefits:

[0044] This invention provides a method for predicting the high-dimensional temperature of an aircraft in a wide-area high-altitude mission environment, the advantages of which are:

[0045] ①This invention addresses the high-dimensional temperature environment factors during spacecraft missions by conducting predictive research from the perspectives of time, altitude, latitude and longitude, which can significantly improve the rationality and accuracy of long-term temperature prediction;

[0046] ②This invention combines regression analysis, nonlinear interpolation and random error characterization to construct a temperature-time prediction model, which can significantly improve the prediction accuracy of temperature with respect to the time dimension;

[0047] ③ The empirical formulas and dynamic interpolation methods used in this invention provide insights into solving the problem of predicting temperature with respect to altitude and latitude and longitude, and promote research on the prediction of high-dimensional environmental factors;

[0048] ④ The method described in this invention is scientific, has good processability, and has broad application value. Attached Figure Description

[0049] Figure 1 This is a flowchart of the method described in this invention.

[0050] Figure 2 This is a schematic diagram of the temperature-altitude prediction method in this invention.

[0051] Figure 3 This is a schematic diagram of the temperature-latitude and longitude prediction method in this invention. Detailed Implementation

[0052] To make the above-mentioned objects and advantages of the present invention clearer and easier to understand, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments;

[0053] This invention provides a method for predicting the high-dimensional temperature of an aircraft in a wide-area high-altitude mission environment, the implementation flowchart of which is shown below. Figure 1 As shown, the specific implementation method is as follows;

[0054] Step 1: Initial temperature-time prediction based on regression analysis; specifically, it consists of the following steps:

[0055] a) Determination of the four-dimensional spatial range and resolution of the spacecraft mission environment (time, altitude, longitude, latitude).

[0056] The mission space of the spacecraft is set to a latitude and longitude range of 115–121 degrees East and 23–29 degrees North; the altitude range is set to 0–50 km. The time resolution is set to 6 hours per data point; the latitude and longitude resolution is 0.25 degrees per data point; and the altitude resolution is 1 km per data point. Three points to be predicted are selected, and their four-dimensional coordinates are shown in Table 1.

[0057] Table 1. Four-dimensional coordinates of the points to be predicted

[0058]

[0059] b) Design and train a temperature-time regression model based on nearby data.

[0060] Using the temperature data for the entire year of 2022 in this region as the nearest neighboring data, a linear regression model was used to model the interannual increment of the monthly average temperature level, i.e., the formula Δy. i =k i Δx+b i in, Δy i k represents the change in the average temperature level of the i-th month between two consecutive years. i and b i This represents the parameters of the incremental linear regression model for month i. The regression model was trained using all historical temperature data for the region from 2018 to 2022 in MATLAB software, and the parameters of the linear regression model for 12 months were obtained, as shown in Table 2.

[0061] Table 2. Parameters of the linear regression model for the annual increase in monthly average temperature over time.

[0062]

[0063] Step 2: Temperature-time quadratic prediction based on nonlinear fitting and random error characterization; specifically including the following steps:

[0064] a) Temperature-time prediction based on nonlinear fitting

[0065] After the linear regression calculation in "Step One," there is still a discrepancy between the actual and predicted values ​​of the annual increase in monthly average temperature. Therefore, a nonlinear fitting method is chosen to further fit the discrepancy. The nonlinear fitting formula used in this invention is as follows:

[0066] ξ i (x)=A i sin(B i (x-x0)+C i For any given month, the nonlinear model was fitted using the "cftool" toolbox in MATLAB software to determine three parameters to be found. The results are shown in Table 3.

[0067] Table 3. Parameters of the interannual increment of monthly average temperature - time nonlinear fitting model

[0068]

[0069] b) Temperature-time prediction based on random error characterization

[0070] Using formula ξ2 i (x)=rand(min i ,max i Calculate the random error term ξ2 i (x), the results are shown in Table 4.

[0071] Table 4. Parameters of the stochastic characterization model for the interannual increment of monthly average temperature.

[0072]

[0073] c) Integrated temperature-time prediction

[0074] By superimposing linear regression, nonlinear regression and error stochastic characterization models, and using formula (2) to calculate the temperature value of the point to be predicted under fixed latitude, longitude and altitude conditions.

[0075] Step 3: Temperature-height prediction based on empirical formulas and dynamic interpolation;

[0076] a) Tropospheric temperature-height prediction based on empirical formulas

[0077] Determine the envelope interval containing the altitude of the point to be predicted, and calculate the temperature of the point to be predicted using the temperature values ​​at the endpoints of the interval and the formula T = T0 - 6 × Δy. It is easy to see that "point 1 to be predicted" is located in the troposphere; therefore, the empirical formula for this step is used to predict its altitude.

[0078] b) Stratospheric temperature-altitude prediction based on dynamic interpolation

[0079] It is not difficult to see that "point 2 to be predicted" is located in the stratosphere where the temperature changes very slowly with altitude. Therefore, at the data resolution set by this invention, the temperature value of the point is replaced by the endpoint value of the altitude range containing "point 2 to be predicted".

[0080] For "point 3 to be predicted", it falls within a range where temperature varies significantly with altitude. Therefore, at a given resolution, using the temperatures T1 and T2 at the endpoints of the altitude range containing "point 2 to be predicted", the temperature can be calculated using formula T. X =(h2-h X )T1+(h X The temperature at that point is obtained by calculating -h1)T2.

[0081] Step 4: Temperature-latitude / longitude prediction based on dynamic interpolation;

[0082] It is not difficult to see that, at the latitude and longitude level, both "point 2 to be predicted" and "point 3 to be predicted" are at the data resolution set by this invention, so there is no need to perform this interpolation step on these two points.

[0083] For "point 1 to be predicted", in the two-dimensional space of latitude and longitude, calculate the distances from this point to the four endpoints of the latitude and longitude envelope grid: d1 = 0.224, d2 = 0.25, d1 = 0.158, d1 = 0.112.

[0084] Using the formulas respectively and Calculate the two predicted values ​​for "point 1 to be predicted";

[0085] The final predicted temperature value of "point 1 to be predicted" is calculated using the formula T = (T' + T') / 2.

[0086] Step 5: Fusion prediction of high-dimensional temperature; specifically includes the following steps:

[0087] a) Determine the four-dimensional envelope of the point to be predicted.

[0088] For any point to be predicted that is not on the resolution grid, its 4D envelope points are determined. The number of envelope points at the latitude and longitude level is typically 4, the number at the altitude level is typically 2, and one approximate point is selected at the time level. The envelope ranges of the three points to be predicted are shown in Table 5.

[0089] b) Determine the predicted temperature values ​​for several points within the envelope;

[0090] At a given resolution, the predicted temperature values ​​of several envelope points were calculated through "Step 1", and the results are shown in Table 5.

[0091] Table 5. Predicted temperature values ​​of coordinate points within the envelope of the three points to be predicted.

[0092]

[0093] a) High-dimensional temperature fusion prediction in priority order

[0094] Following the priority order of altitude and latitude / longitude, the temperature values ​​of several points within the altitude envelope are first calculated through "Step 3"; finally, the temperature values ​​of several points within the latitude / longitude envelope are merged using "Step 4" to obtain the final temperature value of the point to be predicted, as shown in Table 6.

[0095] Table 6. Long-term temperature prediction results for the three points to be predicted.

[0096]

[0097] It is not difficult to conclude that the high-dimensional long-term temperature prediction method proposed in this invention can obtain relatively reasonable temperature values. Furthermore, by comparing the prediction results of three points to be predicted, it can be found that as the number of dimensions that meet the historical data resolution of the points to be predicted increases, the temperature prediction value becomes more accurate.

[0098] In summary, this invention relates to a high-dimensional temperature prediction method for aircraft in a wide-area high-altitude mission environment. It involves a long-term prediction technique for high-dimensional temperature environmental factors based on regression analysis, nonlinear fitting, and dynamic interpolation. The specific steps of this method are: 1. Initial temperature-time prediction based on regression analysis; 2. Secondary temperature-time prediction based on nonlinear fitting and random error characterization; 3. Temperature-altitude prediction based on empirical formulas and dynamic interpolation; 4. Temperature-latitude / longitude prediction based on dynamic interpolation; 5. Fusion prediction of high-dimensional temperature. This invention is applicable to high-dimensional spatiotemporal temperature prediction research for aircraft with wide-area high-altitude mission environment characteristics, significantly improving the rationality and accuracy of long-term predictions and providing effective information input for mission decision-making.

Claims

1. A method for predicting the high-dimensional temperature of an aircraft in a wide-area high-altitude mission environment, characterized in that, Includes the following steps: Step 1: Initial temperature-time prediction based on regression analysis; including: Step 1.1: Determine the four-dimensional spatial range and resolution of the spacecraft mission environment, including time, altitude, longitude, and latitude; Step 1.2: Design and train a temperature-time linear regression model based on nearby data; Step 2: Temperature-time quadratic prediction based on nonlinear fitting and random error characterization; including: Step 2.1: Temperature-time prediction based on nonlinear fitting; Step 2.2: Temperature-time prediction based on random error characterization; Step 2.3: Temperature-Time Integrated Prediction Model; Step 3: Temperature-height prediction based on empirical formulas and dynamic interpolation; including: Step 3.1: Tropospheric temperature-height prediction based on empirical formulas; Step 3.2: Stratospheric temperature-height prediction based on dynamic interpolation; Step 4: Temperature-latitude / longitude prediction based on dynamic interpolation; Within the two-dimensional space of latitude and longitude, the two-dimensional finite space is divided into several grids based on the resolution of historical data; Step 5: Fusion prediction of high-dimensional temperature; including: Step 5.1: Determine the four-dimensional envelope range of the point to be predicted; Step 5.2: Determine the predicted temperature values ​​for several points within the envelope; Step 5.3: High-dimensional temperature fusion prediction in priority order.

2. The method for predicting the high-dimensional temperature of an aircraft in a wide-area high-altitude mission environment according to claim 1, characterized in that: In step 1.1, the four-dimensional spatial range that the aircraft may experience during the mission is first defined; then, the data resolution of the four dimensions is set respectively: the time resolution is set to 6h / data point, the altitude resolution is set to 1km / data point, and the longitude and latitude resolutions are both set to 0.25 degrees / data point.

3. The method for predicting the high-dimensional temperature of an aircraft in a wide-area high-altitude mission environment according to claim 1 or 2, characterized in that: Step 1.2 specifically includes the selection of neighboring data and the design and training of the linear regression model: First, the latest year's data in the historical data was selected as the benchmark, and the historical temperature information of 2022 was used. Secondly, we designed and trained linear regression models: using the inter-year increase in monthly average temperature as the dependent variable and the year as the independent variable, we constructed linear regression models Δy for the dependent variable of January, February, March, ..., December on the year. i (x)=k i (x-x0)+b i In this formula, i represents the month, x represents the year, x0 represents the initial year of the historical data, and Δy i (x) represents the increase in the average temperature of month i in year x compared to the same period of the previous year, k i and b i Let represent the slope and intercept of the linear regression model for month i, respectively. Then, the linear regression model is trained using MATLAB software to obtain its coefficients.

4. The method for predicting the high-dimensional temperature of an aircraft in a wide-area high-altitude mission environment according to claim 1, characterized in that: In step 2.1, there is still a certain deviation between the predicted and actual values ​​of the temperature increment; ξ i (x) represents the difference between the predicted and actual values ​​of the average temperature level increment in month i of year x after step one; through statistical analysis and fitting of historical data, a trigonometric function is selected to characterize the deviation between the predicted and actual values, and the specific expression is: x i (x)=A i sin(B i (x-x0)+C i ), (1) In the formula, A i B i and C i represents the unknown parameters in the nonlinear model for the i-th month, obtained by fitting historical data using MATLAB software; x and x0 represent the year to be determined and the initial year of the historical data, respectively.

5. The method for predicting the high-dimensional temperature of an aircraft in a wide-area high-altitude mission environment according to claim 1, characterized in that: In step 2.2, the error ξ2 in this case is characterized by introducing a random value. i (x), i.e., ξ2 i (x)=rand(min i ,max i In this formula, 'rand' represents a random value selection function, and min... i This represents the minimum error in the training sample set for this stage, while max represents the minimum error. i This indicates the corresponding maximum error value.

6. A method for predicting the high-dimensional temperature of an aircraft in a wide-area high-altitude mission environment according to claim 1, 4, or 5, characterized in that: In step 2.3, linear regression, nonlinear regression and error stochastic characterization model are superimposed, and using formula (2), the long-term temperature prediction is achieved using the historical temperature data of the region under the given latitude, longitude and altitude conditions; y i,j (x)=y i,j (2022)+k i (x-2018)+b i +A i sin(B i (x-2018)+C i )+rand(min i ,max i ) (2) In this formula, i represents the month, j represents the specific time of the point to be predicted within the month, and y i,j (x) and y i,j (2022) represents the temperature at a specific time j in any future year and in the i-th month of 2022, respectively.

7. The method for predicting high-dimensional temperature of an aircraft in a wide-area high-altitude mission environment according to claim 1, characterized in that: In step 3.1, in the troposphere, the relationship between temperature and altitude can be approximated by a generally accepted empirical formula: T=T0-6×Δy, (3) In the formula, T represents the temperature at the current altitude; T0 represents the temperature at the known altitude; Δy represents the altitude difference in km; the altitude range of the troposphere varies with latitude, with an average range of 17-18 km in low latitudes, 10-12 km in mid-latitudes, and 8-9 km in polar regions.

8. A method for predicting the high-dimensional temperature of an aircraft in a wide-area high-altitude mission environment according to claim 1 or 7, characterized in that: In step 3.2, in the stratosphere, temperature-altitude prediction is carried out in stages to determine the altitude envelope of the point to be predicted at the specified resolution, and the temperature value of the point to be predicted is estimated by interpolating the temperature at the endpoints of the interval. Select the height h to be predicted X The envelope interval, h X ∈(h1,h2), where h1 and h2 represent the two endpoints of the height envelope, respectively; the temperature T of the height to be predicted. X Satisfy: T X =(h2-h X )T1+(h X -h1)T2, where T1 and T2 represent the temperatures at the envelope endpoints, respectively.

9. The method for predicting the high-dimensional temperature of an aircraft in a wide-area high-altitude mission environment according to claim 1, characterized in that: In step four, given a point to be predicted, its envelope grid is determined, and the distances d1, d2, d3, and d4 between the point to be predicted and the boundary points of the envelope grid are calculated using the formulas respectively. and Calculate two predicted values ​​for the point to be predicted; where T i (i = 1, 2, 3, 4) represents the temperature value at the endpoint of the envelope grid, and T' and T” represent the temperature prediction values ​​under the diagonal envelope twice, respectively; further, the temperature value of the point to be predicted is calculated using the formula T = (T' + T”) / 2.

10. The method for predicting the high-dimensional temperature of an aircraft in a wide-area high-altitude mission environment according to claim 1, characterized in that: In step 5.1, for any point to be predicted, under a given resolution, its 4-dimensional envelope range is determined; where the number of envelope points in the latitude and longitude dimension is 4, the number of envelope points in the altitude dimension is 2, and in the time dimension, one point that meets the resolution and is closest to that moment is selected. In step 5.2, the temperature prediction values ​​of several points within the envelope are calculated at a given resolution. First, a temperature-time prediction based on regression analysis is carried out, and then a second temperature-time prediction is carried out based on nonlinear fitting and random error characterization. Through this step, the temperature prediction of several points within the envelope at the time level is completed. In step 5.3, the specific steps are as follows: according to the priority order of altitude and latitude and longitude, the temperature values ​​of several points within the envelope of the altitude to be predicted are first calculated; depending on whether the point to be predicted is in the troposphere or the stratosphere, the corresponding temperature prediction model with respect to altitude is selected; empirical formulas are used in the troposphere, while dynamic interpolation methods are used in the stratosphere. Then, using the envelope grid of the latitude and longitude layer, two predicted values ​​T' and T” are calculated. The final predicted temperature value of the point to be predicted is obtained by using T = (T' + T”) / 2.

Images