A Manifold Modeling Method for Environmental Parameter Space

Abstract

The present invention relates to a manifold modeling method for environmental parameter space, comprising the following steps: pre-processing environmental parameter data of a candidate region to establish a numerical space model of the environmental parameters of the region; using the geometric structure and spatial characteristics of a Riemann manifold to construct a manifold space representation corresponding to the environmental numerical parameters; performing manifold space representation on simulation parameters according to the manifold space positions of the candidate region at different times; performing manifold space representation on simulation parameters and calculating the corresponding geodesic distance, outputting the geodesic distance between the environmental simulation parameters and the historical environmental parameters of the region in the manifold space; combining the geodesic distance of the environmental simulation parameters in the manifold space, and finally evaluating the reliability of the environmental simulation parameters. The present invention targets a large amount of historical data of environmental parameters, effectively utilizes the geometric structure of the data, and performs manifold modeling on the numerical space of environmental parameters.

Description

Technical Field

[0001] The present invention relates to the technical field of environmental simulation and machine learning, and in particular provides a manifold modeling method oriented to environmental parameter space. Background Art

[0002] According to the environmental parameter information such as sunlight, average temperature, wind speed, rainfall, relative humidity, longitude, latitude, etc. in the real environment, there are some objective physical connections between various parameters, such as geographical location (precision and latitude) affects sunlight, regional light intensity affects the surface temperature of the area, rainfall affects relative humidity, etc., directly modeling many parameters in the real environment in Euclidean space may lead to the following problems:

[0003] (1) Since the coordinates in Euclidean space are mutually orthogonal, if modeling is performed directly in Euclidean space, it is assumed that the parameters in the real environment are mutually exclusive (unrelated). Obviously, this assumption does not match the relationship between the actual parameters.

[0004] (2) There are many parameters in the real environment. In order to improve the reliability and accuracy of the environmental parameter model, if all parameters are modeled, the dimension of the parameter space may be too high and the calculation is complicated.

[0005] To solve the above problems, based on the mutual relationship between environmental parameters, the manifold space in non-Euclidean geometry is used to construct a geometric model in the real scene environmental parameter space, and provide corresponding confidence evaluation results for the environmental parameters in the simulation model. Summary of the invention

[0006] In view of this, the purpose of the present invention is to provide a manifold modeling method for environmental parameter space to solve the problem of deep network interpretability.

[0007] The technical solution provided by the present invention is: a manifold modeling method for environmental parameter space, comprising the following steps:

[0008] 1) Preprocess the environmental parameter data of the candidate area and establish a numerical spatial model of the environmental parameters of the area;

[0009] 2) Using the geometric structure and spatial characteristics of Riemannian manifolds, we construct a manifold space representation corresponding to the numerical parameters of the environment;

[0010] 3) Perform manifold spatial representation of simulation parameters according to the manifold spatial positions of the candidate regions at different times;

[0011] 4) Perform manifold space representation on the simulation parameters and calculate the corresponding geodesic distance, and output the geodesic distance between the environmental simulation parameters and the historical environmental parameters of the area in the manifold space;

[0012] 5) Combined with the geodesic distance of the environmental simulation parameters in the manifold space, the reliability of the environmental simulation parameters is finally evaluated.

[0013] The method of establishing the numerical spatial model of the environmental parameters of the region comprises the following steps:

[0014] For a candidate region, the environmental database contains environmental parameter samples for n days, that is, the environmental parameter sample space of the region is represented as A = {V1, V2, …, V n},in V i Represents the d-dimensional environmental parameter data vector measured in the area at different times, including wind speed, temperature, altitude, and light.

[0015] The geometric structure and spatial characteristics of the Riemann manifold are used to construct a manifold space representation corresponding to the environmental numerical parameters, and specifically, the covariance matrix is ​​used to perform a manifold representation on the measured real environmental data.

[0016] The manifold spatial representation of the simulation parameters according to the manifold spatial positions of the candidate regions at different times comprises the following steps:

[0017] Through simulation, the d-dimensional environmental parameter data vectors of the candidate area at different periods are obtained;

[0018] The covariance matrix is ​​used to characterize the manifold of the environmental data of the simulation parameters.

[0019] The covariance matrix is ​​obtained by the following formula:

[0020] Construct the covariance matrix space X R :

[0021]

[0022] Among them, V i Represents the d-dimensional environmental parameter data vector at different times, u R is the corresponding mean;

[0023]

[0024] The output of the geodesic distance between the environment simulation parameter and the historical environment parameter of the place in the manifold space comprises the following steps:

[0025] The geodesic distance between the simulated data and the measured real data reference point in the manifold space:

[0026]

[0027] Where X and Y are any two points on the covariance matrix of the simulated parameter data and the measured real environment data, trace(·) represents the trace of the matrix, and log(·) represents the logarithmic function of the matrix.

[0028] The step of combining the geodesic distance of the environment simulation parameters in the manifold space and finally evaluating the reliability of the environment simulation parameters comprises the following steps:

[0029] Set the credibility threshold to τ;

[0030] If the geodesic distance d(X,Y)≤τ between the simulated data and the measured real data reference point in the manifold space, the obtained simulation environment parameters are considered to have high reliability; otherwise, the obtained simulation environment parameters are considered to have low reliability.

[0031] The environmental parameter data include wind speed, temperature, altitude, and light.

[0032] The present invention provides a manifold modeling method for environmental parameter space, which has the following beneficial effects:

[0033] Utilizing the geometric structure and spatial characteristics of Riemann manifolds, we construct a manifold space representation corresponding to the environmental numerical parameters, define the manifold space position of a fixed location at different times, and output the geodesic distance between the environmental simulation parameters and the historical environmental parameters of the location in the manifold space by performing manifold space representation of the simulation parameters and calculating their corresponding geodesic distances. By using the geometric representation method of Riemann manifolds, we can effectively reduce the amount of calculation in the original high-dimensional parameter space, improve the computing power of the model by combining the coupling relationship between the parameters, and finally evaluate the reliability of the environmental simulation parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments:

[0035] Figure 1 A schematic flow chart of a manifold modeling method for an environmental parameter space provided by the present invention;

[0036] Figure 2 A sample diagram of environmental parameter data in a manifold modeling method for an environmental parameter space provided by the present invention.

[0037] Figure 3 A manifold representation diagram of environmental parameters in a manifold modeling method for an environmental parameter space provided by the present invention.

[0038] Figure 4 This is the geodesic distance calculation result diagram of the simulation environment parameter data. DETAILED DESCRIPTION

[0039] The present invention will be further explained below in conjunction with specific implementation schemes, but the present invention is not limited thereto.

[0040] The present invention discloses a manifold modeling method for environmental parameter space, and the method flow includes five parts: environmental parameter input, numerical space construction, manifold space representation, geodesic distance output, and simulation parameter reliability evaluation. The present invention first performs numerical space modeling on environmental parameters, and for a large amount of environmental data in a fixed area, establishes a numerical space model of the environmental parameters of the area;

[0041] Afterwards, the geometric structure and spatial characteristics of the Riemann manifold are used to construct the manifold space representation corresponding to the environmental numerical parameters, and the manifold space position of a fixed location at different times is defined. By performing manifold space representation on the simulation parameters and calculating their corresponding geodesic distances, the geodesic distances between the environmental simulation parameters and the historical environmental parameters of the location in the manifold space are output, and finally the reliability of the environmental simulation parameters is evaluated.

[0042] The present invention targets a large amount of historical data of environmental parameters, effectively utilizes the geometric structure of the data, performs manifold modeling on the numerical space of the environmental parameters, and provides a method for evaluating the reliability of environmental simulation parameters by calculating the geodesic distance of the environmental parameters in the manifold space for the environmental simulation parameter data generated by simulation.

[0043] A manifold modeling method for environmental parameter space, comprising:

[0044] Step 1: Input environmental parameter data.

[0045] Step 2: pre-process the input environmental parameter data, and for a large amount of environmental data in a fixed area, establish a numerical spatial model of the environmental parameters of the area.

[0046] Step three, construct the manifold space representation corresponding to the environment numerical parameters.

[0047] Step 4: Define the manifold space position of a fixed location at different times and characterize the simulation parameters in manifold space.

[0048] Step 5: Characterize the simulation parameters in manifold space and calculate their corresponding geodesic distances.

[0049] Step six, output the geodesic distance between the environmental simulation parameters and the historical environmental parameters of the area in the manifold space, combine the geodesic distance of the environmental simulation parameters in the manifold space, and finally evaluate the reliability of the environmental simulation parameters.

[0050] The second step preprocesses the input environmental parameter data to establish a numerical spatial model of the environmental parameters of the region, and the parameter spatial modeling includes the following steps:

[0051] Step 2-1, for the environmental parameter model in the real space, select the measured environmental data of a fixed area in a certain year as the relevant database for constructing the environmental parameter model.

[0052] Step 2-2, construct sample data based on daily data in a fixed region and filter out some invalid data.

[0053] Step 2-3: For a fixed area, the corresponding large number of environmental databases contain environmental parameter samples for n days, that is, the environmental parameter sample space of the area can be expressed as A = {V1, V2, ..., V n},in V i Represents the d-dimensional environmental parameter data vector measured every day in the area, including factors such as wind speed, temperature, altitude, and light.

[0054] like Figure 2 The actual environmental measured data of Taoxian Airport in May is shown. For the environmental parameter model in real space, the measured environmental data of Taoxian Airport in Shenyang, Liaoning Province in 2019 was selected as the relevant database for constructing the environmental parameter model, which contains the following parameters:

[0055] 1) Station name;

[0056] 2) Site number;

[0057] 3) Date;

[0058] 4) Average wind speed (knots);

[0059] 5) Maximum sustained wind speed (knots);

[0060] 6) Maximum instantaneous wind speed (knots);

[0061] 7) Latitude, longitude;

[0062] 8) visibility (mi);

[0063] 9) precipitation (in);

[0064] 10) Dew point temperature (F);

[0065] 11) Height (m);

[0066] 12) Average temperature (℃), daily maximum temperature (℃), daily minimum temperature (℃);

[0067] 13) Average relative humidity (%), minimum relative humidity (%);

[0068] 14) Small evaporation capacity (mm);

[0069] 15) Average station pressure (hPa), daily maximum station pressure (hPa), daily minimum station pressure (hPa).

[0070] The measured environmental data of Taoxian Airport are as follows: Figure 2 As shown, the data is taken daily as the unit, and a total of 365 data items are included in 2019. The data comes from the official meteorological website. After filtering out some invalid data, there are a total of 360 data items.

[0071] The step three includes using the geometric structure and spatial characteristics of the Riemann manifold to construct a manifold space representation corresponding to the environmental numerical parameters.

[0072] Since the measured data is in vector form, the key issue in constructing the manifold space of real environmental data is how to represent the vector data in the manifold space. For the manifold representation of environmental parameters, this patent uses a positive definite symmetric manifold representation method to represent the measured environmental parameters in the Riemann manifold space. The reasons for using a positive definite symmetric manifold structure to establish an environmental space model are as follows:

[0073] Since there are many parameters in the real environment space, the dimension of the positive symmetric manifold is only related to the intrinsic dimension of the parameters and has nothing to do with the amount of data of the environmental parameters. That is, the complexity of the established manifold environmental parameter model is not affected by the amount of measured data.

[0074] The covariance matrix is ​​used to represent the manifold of the measured real environmental data. For the historical environmental data of different periods, the correlation of environmental parameters is calculated and the covariance matrix space is constructed.

[0075] The step four includes characterizing the environmental parameters using a positive definite symmetric manifold.

[0076] The covariance matrix shows good applicability in target classification, target detection and target tracking. The covariance matrix of the image can characterize the relationship between each different feature dimension in the image area. For environmental parameter data, the covariance matrix can represent the relationship between each environmental parameter dimension. Therefore, for the 360 ​​measured environmental parameter data of Taoxian Airport in 2019, according to the 12 months, a monthly environmental parameter matrix consisting of 30 days of measured environmental data for each month is constructed. The corresponding covariance matrix calculation results for the 12 months of the year are as follows: Figure 3 shown.

[0077] The step 5 includes characterizing the simulation parameters in manifold space and calculating the corresponding geodesic distance. By characterizing the simulation parameters in a positive definite symmetric manifold space, the Euclidean logarithmic Riemann distance formula is used to calculate the geodesic distance between the environmental simulation parameters and the historical environmental parameters of the area in the manifold space.

[0078] The step six includes setting a threshold parameter based on the geodesic distance of the environment simulation parameter in the manifold space, determining the relationship between the threshold parameter and the calculated geodesic distance, and evaluating the reliability of the environment simulation parameter.

[0079] like Figure 1 As shown, the present invention provides a manifold modeling method for environmental parameter space, comprising the following steps:

[0080] Step 1: Input environmental parameter data and quantize the environmental parameter data. In practice, the relevance and validity of the data are judged, and environmental factors with low relevance are selected.

[0081] Step 2: Establish a numerical spatial model of environmental parameters. For the environmental parameter model in real space, select the measured environmental data of a fixed area in a certain year as the relevant database for building the environmental parameter model. Construct sample data based on the daily data of the fixed area and filter out some invalid data. For a fixed area, the corresponding large number of environmental databases contain environmental parameter samples for n days, that is, the environmental parameter sample space of the area can be expressed as

[0082] A={V1,V2,…,V n},

[0083] in V i Represents the d-dimensional environmental parameter data vector measured every day in the area, including factors such as wind speed, temperature, altitude, and light.

[0084] Step 3: Use the covariance matrix to represent the measured real environment data. For historical environment data from different periods, calculate the correlation of environmental parameters and construct the covariance matrix space:

[0085]

[0086] Where V i Represents the historical measured data of environmental parameters in different periods, u R is the corresponding mean. R The calculation formula is:

[0087]

[0088] Step four, use positive definite symmetric manifolds to represent the environmental parameter data in manifold space. The covariance matrix shows good applicability in target classification, target detection and target tracking. The covariance matrix of the image can characterize the relationship between each different feature dimension in the image area. Similarly, for environmental parameter data, the covariance matrix can represent the relationship between each environmental parameter dimension. Therefore, for the 360 ​​measured environmental parameter data of Taoxian Airport in 2019, according to 12 months, a monthly environmental parameter matrix consisting of 30 days of measured environmental data for each month is constructed. Figure 3 The manifold representation of the real environment measured data of Taoxian Airport in 2019 is shown.

[0089] Step 5, by performing manifold space representation on the simulation parameters and calculating the corresponding geodesic distance, outputting the geodesic distance between the environmental simulation parameters and the historical environmental parameters of the area in the manifold space, including the following steps:

[0090] Calculate the geodesic distance between the simulation parameter data and the Riemannian geometry center in the manifold space:

[0091]

[0092] Where X and Y represent any two points on the positive definite symmetric manifold, trace(·) represents the trace of the matrix, and log(·) represents the logarithmic function of the matrix.

[0093] Step six, the simulation data for the test are mainly divided into two categories: one is reasonable simulation data, which is obtained based on the actual environmental data measured in a certain month; the other is unreasonable simulation data, which is used to test the effectiveness of the environmental parameter manifold space model.

[0094] The calculated positive definite symmetric manifold matrix for May is used as the real data reference point in the manifold parameter space. The simulation test data are tested respectively, and the geodesic distance between the simulation data and the real data reference point of each month in the manifold space is calculated. Finally, the calculated manifold geodesic distance is used as the basis for evaluating the reliability and rationality of the simulation parameters.

[0095] Specifically, the credibility threshold is set to τ. If the calculated geodesic distance d(X,Y) between the simulation data and the reference point of the real data of each month in the manifold space is ≤τ, the obtained simulation environment parameters are considered to have high reliability; otherwise, if the calculated geodesic distance d(X,Y) between the simulation data and the reference point of the real data of each month in the manifold space is >τ, the obtained simulation environment parameters are considered to have low reliability.

[0096] The schematic diagram of the sample library used in the manifold modeling method for the environment parameter space proposed by the present invention is as follows: Figure 2 The experimental test results are shown in Figure 3 shown.

[0097] The simulation data of the experimental test are mainly divided into two categories: one is reasonable simulation data, which is obtained based on the actual environmental data measured in a certain month; the other is unreasonable simulation data, which is used to test the effectiveness of the environmental parameter manifold space model.

[0098] The experimental results are as follows:

[0099] (1) When the test data is reasonable simulation data, the measured environmental parameter data of Taoxian Airport in May is selected as a reference to generate 6 possible reasonable simulation environmental parameters. The geodesic distance between the parameters and the manifold reference point of that month is calculated. If the distance is less than the threshold, the simulation parameters are considered reasonable.

[0100] (2) Similarly, for unreasonable simulation parameter data, the geodesic distance between the data and the reference point of the lunar manifold is calculated. If the distance is greater than the threshold, the simulation parameter is considered unreasonable.

[0101] The calculation results of two types of simulation environment parameter data are as follows Figure 4 As shown, the distance value of the first type of simulation data is 9.7051, while the distance value of the second type of simulation data is 58.8508. The output result is that the first type of data is reasonable and the second type of data is unreasonable, which verifies the effectiveness of this model.

[0102] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

Claims

1. A manifold modeling method for environmental parameter space, characterized in that The following steps are involved: 1) Preprocess the environmental parameter data of the candidate area and establish a numerical spatial model of the environmental parameters of the area; 2) Using the geometric structure and spatial characteristics of Riemannian manifolds, we construct a manifold space representation corresponding to the numerical parameters of the environment; 3) Perform manifold spatial representation of simulation parameters according to the manifold spatial positions of the candidate regions at different times; 4) Perform manifold space representation on the simulation parameters and calculate the corresponding geodesic distance, and output the geodesic distance between the environmental simulation parameters and the historical environmental parameters of the area in the manifold space; 5) Combined with the geodesic distance of the environmental simulation parameters in the manifold space, the reliability of the environmental simulation parameters is finally evaluated.

2. The method for manifold modeling in an environmental parameter space according to claim 1, characterized in that: The method of establishing the numerical spatial model of the environmental parameters of the region comprises the following steps: For a candidate region, the environmental database contains environmental parameter samples for n days, that is, the environmental parameter sample space of the region is represented as A = {V1, V2, …, V n },in V i Represents the d-dimensional environmental parameter data vector measured in the area at different times, including wind speed, temperature, altitude, and light.

3. The method for manifold modeling in an environmental parameter space according to claim 1, characterized in that: The geometric structure and spatial characteristics of the Riemann manifold are used to construct a manifold space representation corresponding to the environmental numerical parameters, and specifically, the covariance matrix is ​​used to perform a manifold representation on the measured real environmental data.

4. The method for manifold modeling in an environmental parameter space according to claim 1, characterized in that: The manifold spatial representation of the simulation parameters according to the manifold spatial positions of the candidate regions at different times comprises the following steps: Through simulation, the d-dimensional environmental parameter data vectors of the candidate area at different periods are obtained; The covariance matrix is ​​used to characterize the manifold of the environmental data of the simulation parameters.

5. A manifold modeling method for environmental parameter space according to claim 3 or 4, characterized in that: The covariance matrix is ​​obtained by the following formula: Construct the covariance matrix space X R : Among them, V i Represents the d-dimensional environmental parameter data vector at different times, u R is the corresponding mean; 6. The method for manifold modeling in an environmental parameter space according to claim 1, characterized in that: The output of the geodesic distance between the environment simulation parameter and the historical environment parameter of the place in the manifold space comprises the following steps: The geodesic distance between the simulated data and the measured real data reference point in the manifold space: Where X and Y are any two points on the covariance matrix of the simulated parameter data and the measured real environment data, trace(·) represents the trace of the matrix, and log(·) represents the logarithmic function of the matrix.

7. The method for manifold modeling in an environmental parameter space according to claim 1, characterized in that: The step of combining the geodesic distance of the environment simulation parameters in the manifold space and finally evaluating the reliability of the environment simulation parameters comprises the following steps: Set the credibility threshold to τ; If the geodesic distance d(X,Y)≤τ between the simulated data and the measured real data reference point in the manifold space, the obtained simulation environment parameters are considered to have high reliability; otherwise, the obtained simulation environment parameters are considered to have low reliability.

8. The method for manifold modeling in an environmental parameter space according to claim 1, characterized in that: The environmental parameter data include wind speed, temperature, altitude, and light.

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