Air quality prediction method based on rough set and structural risk minimization

Abstract

The present application relates to a kind of air quality prediction method based on rough set and structural risk minimization, comprising: obtaining environmental parameter sample data related to air quality;Establish air quality evaluation system to the environmental parameter sample data obtained from meteorological monitoring station Grade evaluation creates air quality index decision table;According to air quality index decision table, the empirical error of conditional attribute subset is calculated using rough set theory and structural risk minimization theory and the mutual information of conditional attribute subset and decision attribute;And optimal conditional attribute subset is calculated using genetic algorithm, and the conditional attribute in optimal conditional attribute subset is used as the conditional attribute of rough set classifier to predict air quality with the environmental parameter data of target monitoring point, the prediction model of the present application by rough set theory combines structural risk minimization, on the premise of not reducing the prediction accuracy, while taking into account the complexity of model, the stability and robustness of prediction are enhanced.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of air quality prediction, and particularly relates to an air quality prediction method based on rough set and structural risk minimization. BACKGROUND

[0002] The environmental pollution problem has caused strong reaction in the society at present, because the serious air pollution problem has affected the health and life of people, the main pollutants composing the air quality index are PM2.5, PM10, S02, NO2, CO, O3, TSP (suspended particulate matter), DF (dust fall) and eight items, and the AQI (Air Quality Index) can be associated with one or more pollutant factors.

[0003] In real life, the data of the main pollutants is the key to compose the AQI, however, due to the error in the data acquisition of the pollutants, the pollutant data can be incomplete or redundant, which will increase the difficulty of the air quality analysis and prediction.

[0004] The rough set theory is a mathematical tool for processing incomplete and uncertain knowledge proposed by Z. Pawlak in 1982. The rough set can effectively analyze and process various incomplete information, and find the implicit information law. At present, most of the air quality prediction is carried out by using the rough set, but the rough set theory needs to be established on the indiscernible relation, that is, the equivalence relation, because the requirement of the equivalence relation is relatively strict, and the tolerance of the error information is low, when there is a large amount of noise in the data set, the generalization of the rough set is generally weak, which leads to the instability of the prediction accuracy. SUMMARY

[0005] In order to solve the problems in the prior art that due to the error in the data acquisition of the pollutants, the pollutant data can be incomplete or redundant, which increases the difficulty of the air quality analysis and prediction, and the rough set theory needs to be established on the indiscernible relation, that is, the equivalence relation, because the requirement of the equivalence relation is relatively strict, and the tolerance of the error information is low, when there is a large amount of noise in the data set, the generalization of the rough set is generally weak, which leads to the instability of the prediction accuracy, the present application provides an air quality prediction method based on rough set and structural risk minimization, which comprises the following steps:

[0006] S1: obtaining the environmental parameter sample data related to the air quality from the meteorological monitoring station;

[0007] S2: establishing the air quality evaluation system to grade the environmental parameter sample data obtained from the meteorological monitoring station to obtain the air quality index grade of the environmental parameter sample;

[0008] S3: creating an air quality index decision table according to environmental parameters related to air quality as condition attributes and air quality index grades of the environmental parameter samples as decision attributes based on the environmental parameter sample data;

[0009] S4: generating a limited number of condition attribute subsets according to the condition attributes in the air quality index decision table, and calculating the empirical error of the condition attribute subsets and the mutual information between the condition attribute subsets and the decision attributes by using rough set theory and structural risk minimization theory;

[0010] S5: calculating the optimal condition attribute subset by using a genetic algorithm according to the empirical error of the condition attribute subsets and the mutual information between the condition attribute subsets and the decision attributes;

[0011] S6: taking the condition attributes in the optimal condition attribute subset as the condition attributes of a rough set classifier to predict the air quality based on the environmental parameter data of the target monitoring point, and obtaining the air quality result.

[0012] The present application has at least the following beneficial effects

[0013] The present application combines rough set theory with structural risk minimization criteria, uses the quantitative analysis of rough set theory to infer and explain the relationship between data, adds structural risk minimization criteria to balance the prediction error and complexity, and improves the stability and robustness of air quality prediction. BRIEF DESCRIPTION OF DRAWINGS

[0014] Figure 1 The method flowchart of the present application;

[0015] Figure 2 The structural risk minimization criteria diagram of the present application;

[0016] Figure 3 The genetic algorithm flowchart of the present application. DETAILED DESCRIPTION

[0017] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the protection scope of the present application.

[0018] Please refer to Figure 1 The present application provides an air quality prediction method based on rough set and structural risk minimization, comprising:

[0019] S1: Obtain environmental parameter sample data related to air quality from a meteorological monitoring site;

[0020] The main pollutants that constitute the air quality index are PM2.5, PM10, S02, NO2, CO, O3, TSP (suspended particulate matter), DF (dust fall), etc. Therefore, the environmental parameters collected by the present application are PM2.5, PM10, S02, NO2, CO, O3, TSP (suspended particulate matter), and DF (dust fall). The environmental parameter sample data are the pollutant concentrations corresponding to PM2.5, PM10, S02, NO2, CO, O3, TSP (suspended particulate matter), and DF (dust fall).

[0021] S2: Establish an air quality evaluation system to grade the environmental parameter sample data obtained from the meteorological monitoring site to obtain the air quality index grade of the environmental parameter sample;

[0022] The air quality evaluation system refers to the national standard GB 3095-2012 for dividing six air quality index grades, namely, excellent, good, light pollution, moderate pollution, heavy pollution, and severe pollution. The air quality index grade evaluation system is established. The air quality index 0-50 is grade one; the air quality index 51-100 is grade two; the air quality index 101-150 is grade three; the air quality index 151-200 is grade four; the air quality index 201-300 is grade five; and the air quality index greater than 300 is grade six, as shown in Table 1:

[0023] Table 1 Air quality evaluation table

[0024]

[0025] According to the national standard GB 3095-2012, the grade concentration limits of various environmental parameters are divided into three intervals, which are coded as low, medium, and high. Low indicates that the environmental parameter is not over standard, medium indicates that the environmental parameter is over standard, and high indicates that the environmental parameter is seriously over standard. Let A1, A2, A3, A4, A5, A6, A7, and A8 represent the environmental parameters PM2.5, PM10, S02, NO2, CO, O3, TSP (suspended particulate matter), and DF (dust fall), respectively, to obtain the environmental parameter evaluation table.

[0026] According to the environmental parameter evaluation table, the environmental parameter sample data in the environmental parameter sample data are evaluated, and the air quality index grade corresponding to the environmental parameter sample data is obtained according to the air quality index evaluation table.

[0027] S3: According to the environmental parameter sample data, the environmental parameters related to air quality are taken as condition attributes, and the air quality index decision table is created with the air quality index level of the environmental parameter sample as the decision attribute, as shown in Table 2:

[0028] Table 2 Air quality index decision table

[0029] Domain [A1] [A2] [A3] [A4] [A5] [A6] [A7] [A8] D x1 Low Low Low Medium Low Low Medium Medium Rank 2 x2 Low Low High Medium Low Low High Medium Rank 3 x3 Low Low Low Medium Low Low Low Medium Rank 1 x4 Low Medium Low Medium Low Medium Low Medium Rank 2 x5 Medium Medium Medium High Medium Medium Medium High Rank 2 x6 High Medium High High High Medium High Rank 4 Low x7 Medium Medium High Low Medium Medium High Rank 3 High x8 Medium High High High Medium High Rank 5 Figure 2 Figure 3 … … … … … … … … … …

[0030] wherein x1 represents the first environmental parameter sample data, x2 represents the second environmental parameter sample data, and so on, and D represents the air quality index level corresponding to the environmental parameter sample data.

[0031] Rough set theory:

[0032] Rough set is a new mathematical method for processing inaccurate, uncertain and incomplete data, which can discover the implicit knowledge and reveal the potential law through data analysis and reasoning. It can determine the approximate description of uncertain target set through a pair of accurate sets: upper approximation and lower approximation.

[0033] Let S be an information table, S is represented as: S = (U, At = C U {d}, {V a |a∈At}, {I a |a∈At})

[0034] U is a finite object set, referred to as the universe; At is a finite non-empty attribute set; Va represents the attribute value range of attribute a∈At, i.e. the value range of attribute a; Ia is an information function, representing the value of object x at a.

[0035] The indiscernible relation on the universe U is:

[0036] Obviously, the indiscernible relation is an equivalence relation, which divides the universe U into U / R B , U / R B = {X1, X2, …, X m} The equivalence class set formed by the equivalence relation R B . The equivalence class [x] B = {y | (x, y) ∈ R B} is the basic knowledge granule in rough set.

[0037] For each subset X ∈ U and equivalence relation R, the upper approximation and lower approximation of X are defined as follows:

[0038]

[0039]

[0040] The universe of discourse U is partitioned into the positive region POS R (X), the negative region NEG R (X) and the boundary region BNG R (X) three disjoint regions, where

[0041] Positive region: POS R (X) = R X;

[0042] Negative region:

[0043] Boundary region:

[0044] Approximation quality is used to describe the dependency between attributes. If the value of attribute Q is completely determined by P, it is said that Q is determined by P, denoted as Let P, Q ∈ At, the degree of dependency of Q on P is k (0 ≤ k ≤ 1), denoted as:

[0045]

[0046] S4: Generate a finite number of condition attribute subsets according to the condition attributes in the air quality index decision table, and calculate the empirical error of the condition attribute subsets and the mutual information between the condition attribute subsets and the decision attribute using rough set theory and structural risk minimization theory;

[0047] S41: Obtain the decision information system of the air quality index decision table according to rough set theory:

[0048] Where, let S = (U, C ∪ D, V, f) be a decision information system, where U = {x1, x2, …, x n} is a non-empty finite object set also known as the universe of discourse, x i is denoted as the i-th environmental parameter sample data. C = {A1, A2, …, A m} is a non-empty finite attribute set, where A i is denoted as the concentration of gases and suspended particles such as PM2.5, PM10, SO2, NO2, CO, O3, TSP, etc. B is a subset of the condition attribute set C. D is the decision attribute, which is represented by air quality index level here, which is divided into six levels according to the severity of air quality. is the value domain, where V a represents the value domain of attribute a, and f is the information function.

[0049] S42: Calculate the empirical error of the condition attribute subset according to the degree of dependency of the decision attribute subset D on the condition attribute subset B in the decision information system;

[0050] Remp (B) = 1 - γ B (D),

[0051]

[0052] where | · | denotes the cardinality of a set, i.e., the number of elements in the set. A partition derived from the condition attribute subset B is U / IND(B) = {X1, X2,..., Xn}, where Xi is one equivalence class. n}, X i is one equivalence class.[x] D A partition derived from the decision attribute D is U / IND(D).

[0053] For example, according to Table 2, let U = {x1, x2, x3, x4, x5, x6, x7, x8} be an environmental sample dataset, where C = {A1, A2, A3, A4, A5, A6, A7, A8} represents a set of PM2.5, PM10, S02, NO2, CO, O3, TSP, DF ring parameters; D represents a decision attribute (an air quality index level corresponding to the environmental parameter sample data). When the condition attributes A1A2A3A4 are used as a partition, the condition attribute subset B = {PM2.5, PM10, S02, NO2}, and the equivalence class set derived from the condition attribute B is U / IND(B) = {{x1, x3}, {x2}, {x4}, {x5}, {x7}, {x6, x8}}. When the decision attribute D is used as a partition, U / IND(D) = {{x3}, {x1, x4, x5}, {x2, x7}, {x6}, {x8}}. At this time, the dependency degree of the decision attribute D on the condition attribute B is:

[0054] B = {PM2.5, PM10, S02, NO2}, and the equivalence class set derived from the condition attribute B is U / IND(B) = {{x1, x3}, {x2}, {x4}, {x5}, {x7}, {x6, x8}}. When the decision attribute D is used as a partition, U / IND(D) = {{x3}, {x1, x4, x5}, {x2, x7}, {x6}, {x8}}. At this time, the dependency degree of the decision attribute D on the condition attribute B is:

[0055] Therefore R emp (B) = 1 - γ B (D) = 1 - 0.625 = 0.375.

[0056] S43: introducing a mutual information regularization function according to a structural risk minimization criterion to calculate the mutual information between the condition attribute subset and the decision attribute;

[0057] See ​ Structural risk minimization (SRM) is a strategy proposed to prevent overfitting. Structural risk minimization is equivalent to regularization. The structural risk adds a regularizer or penalty term representing the model complexity to the empirical risk. The definition of the structural risk is:

[0058]

[0059] where J(f) is a function of model complexity, λ≥0 is a coefficient used to balance the empirical risk and model complexity. The strategy of structural risk minimization considers that the model with the minimum structural risk is the optimal model:

[0060]

[0061] The structural risk minimization requires that the empirical risk and the model complexity are both small, so that the model has better generalization.

[0062] On this basis, the mutual information regularization term I(B;D) is introduced into the selected rough set model, which is expressed as

[0063] I(B;D) = H(D) - H(D|B)

[0064] where H(D) is the information entropy of the decision attribute D, H(D|B) is the conditional information entropy of the decision attribute D with respect to the attribute subset B, and I(B;D) represents the mutual information between the attribute subset B and the decision attribute D. The mutual information regularization term is added to the selected rough set model to improve the stability and robustness of the air quality prediction by using the characteristics of rough set theory that can quantitatively analyze and infer and explain the relationship between data.

[0065]

[0066] Please refer to ​ , S5: calculating the optimal conditional attribute subset according to the empirical error of the conditional attribute subset and the mutual information between the conditional attribute subset and the decision attribute using a genetic algorithm;

[0067] S51: encoding the conditional attribute subset and taking the encoded conditional attribute subset as the initial chromosome population of the genetic algorithm;

[0068] S52: calculating the expected error of the conditional attribute subset according to the empirical error of the conditional attribute subset and the mutual information between the conditional attribute subset and the decision attribute;

[0069] The expected error of the conditional attribute subset includes:

[0070] minR reg (B) = R emp (B) + αI(B;D);

[0071] where minR reg (B) represents the expected error of the attribute subset B, R emp (B) represents the empirical error of the subset B, I(B;D) represents the mutual information between the attribute subset B and the decision attribute D, and α is a hyperparameter, α≥0. ​

[0072] S53: The initial chromosome is processed by selection, crossover and mutation operators of genetic algorithm to obtain a crossover and mutation chromosome. The selection operator selects the roulette method, the crossover operator adopts single-point crossover, and the mutation operator adopts basic bit mutation;

[0073] According to the expected error of each initial chromosome, the roulette method is selected, and the specific operation is as follows:

[0074] (1) Let the population size be M (the number of initial chromosomes), and calculate the fitness f of each individual (initial chromosome) in the population (i=1, 2,..., M) (expected error);

[0075] (2) Calculate the probability of each individual (initial chromosome) being inherited into the next generation population;

[0076]

[0077] (3) Calculate the cumulative probability q of each individual (initial chromosome) x i (i=1, 2,..., n); i ;

[0078]

[0079] (4) Generate a uniformly distributed pseudo-random number r in the interval [0, 1];

[0080] (5) If r < q1, select individual 1, otherwise, select individual k, so that: q k-1 <r≤q k is established;

[0081] (6) Repeat (4), (5) for M times as the preset number of times.

[0082] When performing the crossover operation, the individuals are selected to participate in the crossover according to a certain probability, a crossover point is randomly selected from the two random chromosomes, and then the substring after the crossover point is exchanged to generate the next generation individual.

[0083] The basic bit mutation operation refers to the mutation operation of the gene value of one or several loci randomly specified in the individual code string with a mutation probability P m . The operation process is as follows:

[0084] (1) For each locus of the individual (initial chromosome), specify it as a mutation point with a probability P m ;

[0085] (2) Perform mutation operation on the specified mutation point.

[0086] S54: the chromosome after the crossover mutation is taken as the initial chromosome of the next iteration of the genetic algorithm, and steps S52-S54 are repeatedly executed until a preset iteration number is reached; and the condition attribute subset with the minimum expected error is taken as the optimal condition attribute subset. The application reduces the feature dimension without reducing the classification accuracy in combination with the genetic algorithm, thereby improving the speed of air quality prediction.

[0087] S6: the condition attributes in the optimal condition attribute subset are taken as the condition attributes of the rough set classifier to predict the air quality based on the environmental parameter data of the target monitoring point, thereby obtaining the air quality result.

[0088] For example, according to Table 2, let U = {x1, x2, x3, x4, x5, x6, x7, x8} be an environmental sample data set, wherein C = {A1, A2, A3, A4, A5, A6, A7, A8} represents a PM2.5, PM10, SO2, NO2, CO, O3, TSP, DF ring parameter set; and D represents a decision attribute (air quality index level corresponding to the environmental parameter sample data). Assuming that the optimal attribute subset obtained according to the above operation is A1A2A3, the optimal condition attribute subset B = {PM2.5, PM10, SO2} at this time, and the equivalence class set derived from the condition attribute B is U / IND(B) = {{x1, x3}, {x2}, {x4}, {x5}, {x7}, {x6, x8}}. The rule set derived from the decision table is γ(B) = {γ1, γ2, γ3, γ4, γ5, γ6}. Given a to-be-tested environmental sample data X,

[0089] X = {low, low, high, medium, low, high, medium, medium}, at this time, according to the rule set derived from the decision table, X has a probability of 1 to be air quality index level 3.

[0090] The air quality result is predicted, and the relevant enterprises are fed back in a timely manner to reduce the emission of pollutants and improve the environmental quality of the target monitoring point.

[0091] Although the embodiments of the application have been shown and described, it can be understood by those of ordinary skill in the art that various changes, modifications, replacements and variations can be made to the embodiments without departing from the principles and spirits of the application, and the scope of the application is defined by the appended claims and their equivalents.

Claims

1. An air quality prediction method based on rough set theory and structural risk minimization, characterized in that, include: S1: Obtain sample data of environmental parameters related to air quality from meteorological monitoring stations; S2: Establish an air quality assessment system to evaluate the environmental parameter sample data obtained from meteorological monitoring stations and obtain the air quality index level of the environmental parameter sample; S3: Based on the environmental parameter sample data, use the environmental parameters related to air quality as conditional attributes, and use the air quality index level of the environmental parameter sample as the decision attribute to create an air quality index decision table; S4: Generate a finite number of condition attribute subsets based on the condition attributes in the air quality index decision table, and use rough set theory and structural risk minimization theory to calculate the empirical error of the condition attribute subsets and the mutual information between the condition attribute subsets and the decision attributes. The calculation of the empirical error of the conditional attribute subset and the mutual information between the conditional attribute subset and the decision attribute using rough set theory and structural risk minimization theory includes: S41: A decision information system that derives the air quality index decision table based on rough set theory; S42: Calculate the empirical error of the conditional attribute subset D based on the dependency of the decision attribute subset D on the conditional attribute subset B in the decision information system. S43: Based on the structural risk minimization criterion, a mutual information regularization function is introduced to calculate the mutual information between the conditional attribute subset and the decision attribute; S5: The optimal conditional attribute subset is calculated using a genetic algorithm based on the empirical error of the conditional attribute subset and the mutual information between the conditional attribute subset and the decision attribute. The empirical error of the conditional attribute subset includes: in, The cardinality of a set is the number of elements in the set. This represents a partition derived from a subset B of conditional attributes. This represents an equivalence class in the partition. This represents a partition derived from decision attribute D. ; The mutual information between the subset of conditional attributes and the decision attributes includes: in For decision attributes Information entropy Subset of conditional attributes Regarding decision attributes Conditional information entropy, Represents a subset of attributes With decision attributes Mutual information; S6: Use the conditional attributes in the optimal conditional attribute subset as the conditional attributes of the rough set classifier to predict air quality using environmental parameter data of the target monitoring point, and obtain the air quality result.

2. The air quality prediction method based on rough set theory and structural risk minimization according to claim 1, characterized in that, The optimal conditional attribute subset, calculated using a genetic algorithm based on the empirical error of the conditional attribute subset and the mutual information between the conditional attribute subset and the decision attribute, includes: S51: Encode the subset of conditional attributes and use the encoded subset of conditional attributes as the initial chromosome population for the genetic algorithm; S52: Calculate the expected error of the conditional attribute subset based on the empirical error of the conditional attribute subset and the mutual information between the conditional attribute subset and the decision attribute; S53: The initial chromosomes are processed using selection, crossover, and mutation operators of a genetic algorithm to obtain crossover and mutated chromosomes. The selection operator uses the roulette wheel method, the crossover operator uses single-point crossover, and the mutation operator uses basic bit mutation. S54: Use the chromosome after crossover mutation as the initial chromosome for the next iteration of the genetic algorithm, and repeat steps S52-S54 until the preset number of iterations is reached; use the subset of conditional attributes with the smallest expected error as the optimal subset of conditional attributes.

3. The air quality prediction method based on rough set theory and structural risk minimization according to claim 1, characterized in that, The expected error of the conditional attribute subset includes: in, Represents a subset of attributes The expected error Representing a subset empirical error, Represents a subset of attributes With decision attributes mutual information, As a hyperparameter .

4. The air quality prediction method based on rough set theory and structural risk minimization according to claim 1, characterized in that, The environmental parameters related to air quality include PM2.5, PM10, SO2, NO2, CO, O3, TSP, and DF.

5. The air quality prediction method based on rough set theory and structural risk minimization according to claim 1, characterized in that, The air quality assessment system is based on the national standard GB 3095-2012, which divides the air quality into six levels: excellent, good, lightly polluted, moderately polluted, heavily polluted, and severely polluted. An air quality index level assessment system is established.

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