CN115374689A - Air quality index prediction method based on improved sparrow search algorithm optimization - Google Patents
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Abstract
The invention discloses an air quality index prediction method based on improved sparrow search algorithm optimization, which comprises the following steps of: s1: acquiring historical data of air quality, constructing a training set and a testing set, and S2: establishing a BP neural network structure; s3: optimizing the weight and the threshold of the BP neural network by using the improved sparrow search algorithm; s4: establishing an air quality index prediction model based on improved sparrow search algorithm optimization; s5: and performing air quality index prediction by using the model. The prediction method provided by the invention not only solves the defects that the sparrow search algorithm is low in convergence speed and easy to fall into a local optimal solution in the later iteration stage, improves the global search capability of the BP neural network, further improves the prediction precision of the air quality prediction model, but also provides a scientific and effective method for related departments to accurately predict the air quality.
Description
Technical Field
The invention belongs to the field of air quality index prediction. More specifically, the invention relates to an air quality index prediction method based on improved sparrow search algorithm optimization.
Background
In recent years, with the increasingly rapid industrialization process, the rapid development of economy and the increasing of population in China, the problem of air pollution has attracted social attention. The harm of the atmospheric pollutants to human health is continuously intensified, and a plurality of problems are brought to the life of people. Air quality prediction based on air pollution parameters has become an important subject in environmental science, and many mature prediction models are used for predicting different pollutants in the aspect of air quality prediction. The prediction of air pollutants can timely determine preventive measures to avoid harm caused by air pollution, so that real-time monitoring of air quality is achieved, and a model with high prediction accuracy is designed by means of the monitored air quality data and methods such as artificial intelligence and machine learning, so that the change condition of the air quality in a period of time in the future can be predicted. The method is not only beneficial to timely acquiring the information of the air quality, but also beneficial to helping residents reasonably plan outdoor travel according to the information, and is also beneficial to the urban managers to take appropriate measures to control air pollution so as to improve the air quality.
Sparrow search optimization (SSA) is an intelligent optimization algorithm derived from the natural activities of sparrows to forage and evade predation. Sparrows divide the population into discoverers and followers to forage according to a proportion, and a danger early warning mechanism is also superposed to prevent the populations from being predated. By calculating the fitness value of each individual and sequencing, the positions of the finder, the joiner and the alerter are continuously updated along with the increase of the iteration times, and the whole population is continuously close to the optimal solution, namely the position of the optimal food. The sparrow search algorithm is applied to many actual engineering fields due to strong optimizing capability, high convergence speed and good stability, and the problems of low convergence speed and low precision of the traditional BP neural network can be solved by utilizing the sparrow search algorithm to optimize the BP neural network.
Although the sparrow search algorithm can optimize the BP neural network to a certain extent, the same as other intelligent optimization algorithms, the problems that the population diversity is reduced and the local optimum is easy to fall into exist when the global optimum is approached are also existed.
Disclosure of Invention
The invention aims to provide an air quality index prediction method based on improved sparrow search algorithm optimization, aiming at the problems that a BP neural network is easy to fall into local optimization, low in precision and the like during prediction, and the weight and the threshold of the BP neural network are optimized by utilizing the advantages that sparrows have high convergence speed and high optimization precision compared with the traditional optimization algorithm. Meanwhile, considering the defects of reduced population diversity, low convergence speed and weak global search capability of sparrow search in the later iteration stage, the quality of an initial solution is improved by introducing cubic mapping, and the diversity of the initialized sparrow population is increased. And the capability of jumping out the local optimal solution by combining the butterfly optimization strategy is enhanced. And finally, establishing a corresponding model and applying the model to the field of air quality prediction so as to improve the prediction precision and efficiency.
To achieve these objects and other advantages in accordance with the purpose of the invention, there is provided an air quality index prediction method optimized based on an improved sparrow search algorithm, comprising the steps of:
s1: acquiring historical air quality data, and constructing a training set and a testing set;
s2: establishing a BP neural network structure;
s3: optimizing the weight and the threshold of the BP neural network by using the improved sparrow search algorithm;
s4: establishing an air quality index prediction model based on improved sparrow search algorithm optimization;
s5: and performing air quality index prediction by using the model.
Preferably, the training data comprises PM 2.5 、PM 10 、SO 2 、CO、NO 2 、O 3 And the like.
Preferably, the parameters of the BP neural network include weight values and threshold values of the BP neural network.
Preferably, the objective function of the improved sparrow search algorithm is the error rate E of the training set of the BP neural network train Error rate E with test set test The sum, expressed as:
fitness＝argmin(E train +E test )
preferably, the step S3 specifically includes the steps of:
s31: initializing parameters of a sparrow search algorithm, including the sparrow population number n, the follower number P, the joiner number S and the population maximum iteration number t max A population warning value R;
s32: carrying out population initialization by utilizing cubic mapping;
s33: establishing a fitness function and sequencing;
s34: the positions of discoverers are updated by fusing butterfly optimization strategies, so that the global search performance of the algorithm is enhanced
S35: updating the follower position;
s36: randomly selecting an alertor and updating the position of the alertor;
s37: calculating and sequencing the updated fitness value;
s38: and (4) judging whether the iteration stop condition is met, if so, exiting and outputting a result, otherwise, repeatedly executing the steps S32-S36.
Preferably, in step S32, the cubic mapping formula is:
y(n+1)＝4y(n) 3 -3y(n) (2)
wherein n is the mapping degree, y (n) is epsilon (-1, 0) U (0, 1), and y (n) is the nth mapping value.
In order to prevent the value generated by chaotic mapping from exceeding the weight and threshold value optimization range of the BP neural network, the mapping value is adjusted to a uniform interval by using the formula (2).
X i ＝X lb +0.5(X lb -X ub )(y i +1) (3)
Wherein, X lb 、X ub The upper and lower boundaries of the dimensionality of the individuals in the sparrow population; x i The actual position value of the sparrow individual is obtained.
Preferably, in step S34, the location update formula of the finder is:
wherein the content of the first and second substances,
indicating that the ith sparrow is in the d-dimensional position at the t-th iteration. X gbest Is the current global optimum position, f i The smell of the ith butterfly is expressed, the value of the smell depends on the fitness, and r is a random number of 0-1. Q is a random number following a standard normal distribution. L is a single row of all 1 matrices in d dimensions. R is an early warning value and the value range is [0,1 ]]. ST is an alert value with a value range of [0.5,1']。
When R < ST, which means that there are no predators around the foraging environment at this time, the finder can perform an extensive search operation. When R is more than or equal to ST, the method indicates that some sparrows in the population have found predators and gives an alarm to other sparrows in the population, and all sparrows need to quickly fly to other safe places to forage.
Preferably, in step S35, the location update formula of the follower is:
wherein the content of the first and second substances,
for the t +1 th iteration the optimal position of the finder is found,
the global worst position for the t-th iteration. A is a single row of d-dimensional matrices in which each element is randomly assigned a value of 1 or-1, and A + ＝A T (AA T ) -1 And n is the total number of sparrows. When i is>n/2, this indicates that the ith participant with lower fitness value does not obtain food, is in a state of full hunger, and needs to fly to other places to find food to obtain moreEnergy; when i is less than or equal to n/2, a part of the participants can forage around the best discoverer, and the participants and the discoverer can compete for food, so that the participants change into discoverers.
Preferably, in step S36, the position update formula of the alert person is:
wherein, the first and the second end of the pipe are connected with each other,
for the t-th iteration global optimum position, beta is a step size control parameter, and K is [ -1,1]A random number in between. Xi is a very small constant to avoid when f i ＝f w When the denominator is 0. f. of i 、f g 、f w Representing the current, best and worst fitness, respectively. When f is i >f g This indicates that the sparrow is now at the border of the population and is extremely vulnerable to predators. f. of i ＝f g This indicates that sparrows in the middle of the population are aware of the danger and need to be close to other sparrows to minimise their risk of being prey.
The invention at least comprises the following beneficial effects:
firstly, the weight and the threshold of the BP neural network are optimized by utilizing the advantages of high search precision and strong stability of a sparrow search algorithm, and the prediction efficiency and precision are improved.
Secondly, the invention adopts cubic mapping to realize population initialization, thereby increasing the diversity of the population and avoiding the premature convergence.
Thirdly, the invention integrates the butterfly optimization strategy to enhance the global search performance of the algorithm and reduce the risk of the algorithm falling into the local optimum.
And fourthly, the model established after the algorithm is improved is used for predicting the air quality index, and compared with other models, the model is remarkably improved in the aspects of prediction accuracy, convergence rate and global search performance, and can be well applied to the actual AQI prediction.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention.
Drawings
FIG. 1 is a flow chart of an air quality index prediction method based on improved sparrow search algorithm optimization according to the invention;
FIG. 2 is a flow chart of an improved sparrow search algorithm according to the present invention;
FIG. 3 is a diagram of a BP neural network according to the present invention;
Detailed Description
As shown in fig. 1, an air quality index prediction method based on improved sparrow search algorithm optimization includes the following steps:
s1: acquiring historical air quality data, and constructing a training set and a testing set;
s2: establishing a BP neural network structure;
s3: optimizing the weight and the threshold of the BP neural network by using the improved sparrow search algorithm;
s4: establishing an air quality index prediction model optimized based on an improved sparrow search algorithm;
s5: and performing air quality index prediction by using the model.
Further, the training data includes influence factors such as PM2.5, PM10, SO2, CO, NO2, O3, and the like.
Further, the parameters of the BP neural network include a weight value and a threshold value of the BP neural network.
Further, the objective function of the improved sparrow search algorithm is the error rate E of the neural network training set train Error rate E with test set test The expression is as follows:
fitness＝argmin(E train +E test )
further, in step S3, the method specifically includes the following steps:
s31: parameter initialization for sparrow search algorithmIncluding the sparrow population number n, the follower number P, the joiner number S, the population maximum iteration number t max A population warning value R;
s32: carrying out population initialization by utilizing cubic mapping;
s33: establishing a fitness function and sequencing;
s34: the positions of discoverers are updated by fusing butterfly optimization strategies, so that the global search performance of the algorithm is enhanced
S35: updating the follower position;
s36: randomly selecting an alertor and updating the position of the alertor;
s37: calculating and sequencing the updated fitness value;
s38: and (4) judging whether the iteration stop condition is met, if so, exiting and outputting a result, otherwise, repeatedly executing the steps S32-S36.
Compared with the traditional optimization algorithm, the sparrow search algorithm has the advantages of high convergence rate and high optimization precision, and the prediction precision and the convergence rate of the BP neural network are improved by optimizing the weight and the threshold of the BP neural network. However, the sparrow search algorithm has the defects of reduced population diversity, low convergence rate and weak global search capability in the later iteration stage, so that the sparrow search algorithm is easy to fall into a local optimal solution. The invention improves the algorithm, mainly comprising the following two points:
1. and the cubic mapping is adopted to complete population initialization, so that the population diversity is increased, and the premature convergence phenomenon is avoided.
2. And the positions of the discoverers are updated by fusing the butterfly optimization strategy, so that the global search performance of the algorithm is enhanced, and the risk of trapping the algorithm into a local optimal solution is reduced.
The algorithm flow chart is shown in fig. 2.
When the sparrow search algorithm initializes the population, a random generation mode is adopted, and the sparrow population is unevenly distributed in the mode, so that later iterative optimization is influenced. In order to improve the global search capability of the algorithm and avoid the reduction of population diversity in the later iteration stage, the chaotic sequence is utilized to initialize the positions of sparrow individuals in consideration of the characteristics of randomness, ergodicity, regularity and the like of chaotic mapping. The uniformity and the ergodicity of the cubic mapping are superior to those of the classical Logistic mapping, so that the initialization of the population is completed by adopting the cubic mapping in the invention. The cubic mapping formula is as follows:
y(n+1)＝4y(n) 3 -3y(n) (2)
wherein n is the mapping number, y (n) ∈ (-1, 0) U (0, 1), and y (n) is the nth mapping value.
In order to prevent the value generated by chaotic mapping from exceeding the weight and threshold value optimization range of the BP neural network, the mapping value is adjusted to a uniform interval by using the formula (2).
X i ＝X lb +0.5(X lb -X ub )(y i +1) (3)
Wherein X lb 、X ub The upper and lower boundaries of the dimensionality of the individuals in the sparrow population; x i The actual position value of the sparrow individual is obtained.
Specifically, in step S34, the location update formula of the finder is:
wherein the content of the first and second substances,
indicating that the ith sparrow is in the d-dimensional position at the t-th iteration. X gbest Is the current global optimum position, f i The smell of the ith butterfly is expressed, the value of the smell depends on the fitness, and r is a random number of 0-1. Q is a random number following a standard normal distribution. L is a single row of all 1 matrices in d dimensions. R is an early warning value and the value range is [0,1 ]]. ST is an alert value with a value range of [0.5,1]. When R is<ST, which means that there are no predators around the foraging environment at this time, the finder may perform an extensive search operation. When R ≧ ST, this indicates that some sparrows in the population have found predators and raised an alarm to other sparrows in the population, at which time all sparrows need to fly quickly to other safe locations for foraging.
Specifically, in step S35, the location update formula of the follower is:
wherein, the first and the second end of the pipe are connected with each other,
for the t +1 th iteration the optimal position of the finder is found,
the global worst position for the t-th iteration. A is a single row of d-dimensional matrices in which each element is randomly assigned a value of 1 or-1, and A + ＝A T (AA T ) -1 And n is the total number of sparrows. When i is>n/2, this shows that the ith subscriber with lower fitness value does not obtain food, is in a state of full hunger, and needs to fly to other places to find food at this time to obtain more energy; when i is less than or equal to n/2, a part of the participants can forage around the best discoverer, and the participants and the discoverer can compete for food, so that the participants change into discoverers.
Specifically, in step S36, the position update formula of the guardian is:
wherein the content of the first and second substances,
for the t-th iteration global optimum position, beta is a step size control parameter, and K is [ -1,1]A random number in between. Xi is a very small constant to avoid when f i ＝f w When the denominator is 0. f. of i 、f g 、f w Representing the current, best and worst fitness respectively. When f is i >f g This indicates that the sparrow is now at the border of the population and is extremely vulnerable to predators. f. of i ＝f g This indicates that sparrows in the middle of the population are aware of the danger and need to be close to other sparrows to minimise their risk of being prey.
The BP neural network is a multi-layer feedforward network comprising an input layer, a hidden layer and an output layer, and the BP neural network topology comprises the input layer, the hidden layer and the output layer. The main characteristics are that the input signal is transmitted in the forward direction and the error is propagated in the reverse direction. The error of the neural network is a function of the internal link weights. The training process of the network is to iteratively improve the weight and the threshold value through the gradient reduction of the error function so as to make the actual output value of the network continuously approach the expected output value. The network neural structure is shown in fig. 3.
The weights and thresholds of the output layer and the hidden layer are trained and corrected in a gradient descending manner, and the correction formula is as follows:
wherein the content of the first and second substances,
eta is learning rate, x i (i =1,L, n) is an input value of the neural network, d j (j =1,l, p) is the output value of the hidden layer, i.e. the input value of the output layer. y is k (k =1,L, q) is the actual predicted value of the network, o k (k =1,L, q) is the actual output value of the network, θ j For hidden layer neuron thresholds, β k Is the output layer neuron threshold. w is a ij As a weight between the input layer and the hidden layer, w jk The weights from the hidden layer to the output layer.
The weight and the threshold value of the BP neural network training are randomly generated, and the stability and the precision of the search result are influenced, so the parameters of the neural network are optimized through the improved sparrow search algorithm, and the convergence speed and the precision of the model are improved.
The above embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the protection scope of the present invention.
Claims (9)
1. The air quality index prediction method based on the optimization of the improved sparrow search algorithm is characterized by comprising the following steps of:
s1: acquiring historical air quality data, and constructing a training set and a testing set;
s2: establishing a BP neural network structure;
s3: optimizing the weight and the threshold of the BP neural network by using the improved sparrow search algorithm;
s4: establishing an air quality index prediction model based on improved sparrow search algorithm optimization;
s5: and (5) performing air quality index prediction by using the model.
2. The improved sparrow search algorithm optimized air quality index prediction method according to claim 1, wherein the training data comprises influence factors of PM2.5, PM10, SO2, CO, NO2, O3, and the like.
3. The improved sparrow search algorithm optimization-based air quality index prediction method according to claim 1, wherein the parameters of the BP neural network comprise weight values and threshold values of the BP neural network.
4. The improved sparrow search algorithm optimization-based air quality index prediction method according to claim 1, wherein the objective function of the improved sparrow search algorithm is an error rate E of a BP neural network training set train Error rate with test set E test The sum, expressed as:
fitness＝argmin(E train +E test ) (1) 。
5. the improved sparrow search algorithm optimization-based air quality index prediction method according to claim 1, wherein in the step S3, the method specifically comprises the following steps:
s31: initializing parameters of a sparrow search algorithm, including the sparrow population number n, the follower number P, the joiner number S and the population maximum iteration number t max A population warning value R;
s32: carrying out population initialization by utilizing cubic mapping;
s33: establishing a fitness function and sequencing;
s34: the positions of discoverers are updated by fusing butterfly optimization strategies, so that the global search performance of the algorithm is enhanced
S35: updating the follower position;
s36: randomly selecting an alertor and updating the position of the alertor;
s37: calculating and sequencing the updated fitness value;
s38: and (4) judging whether the iteration stopping condition is met, if so, exiting and outputting a result, otherwise, repeatedly executing the steps S32-S36.
6. The improved sparrow search algorithm optimization-based air quality index prediction method according to claim 5, wherein in step S32, the cubic mapping formula is as follows:
y(n+1)＝4y(n) 3 -3y(n) (2)
wherein n is the mapping degree, y (n) is epsilon (-1, 0) U (0, 1), and y (n) is the nth mapping value.
In order to prevent the value generated by chaotic mapping from exceeding the weight and threshold value optimization range of the BP neural network, the mapping value is adjusted to a uniform interval by using the formula (2).
X i ＝X lb +0.5(X lb -X ub )(y i +1) (3)
Wherein, X lb 、X ub The upper and lower boundaries of the dimensionality of the individuals in the sparrow population; x i The actual position value of the sparrow individual is obtained.
7. The improved sparrow search algorithm optimization-based air quality index prediction method according to claim 5, wherein in step S34, the discoverer location update formula is as follows:
wherein the content of the first and second substances,
indicating that the ith sparrow is in the d-dimensional position at the t-th iteration. X gbest Is the current global optimum position, f i The smell of the ith butterfly is expressed, the value of the smell depends on the fitness, and r is a random number of 0-1. Q is a random number following a standard normal distribution. L is a single row of all 1 matrices in d dimensions. R is an early warning value and has a value range of [0,1')]. ST is an alert value with a value range of [0.5,1']. When R is<ST, which means that there are no predators around the foraging environment at this time, the finder can perform extensive search operations. When R ≧ ST, this indicates that some sparrows in the population have found predators and raised an alarm to other sparrows in the population, at which time all sparrows need to fly quickly to other safe locations for foraging.
8. The improved sparrow search algorithm optimization-based air quality index prediction method according to claim 5, wherein in step S35, the position update formula of the follower is as follows:
wherein the content of the first and second substances,
for the t +1 th iteration the optimal position of the finder is found,
the global worst position for the t-th iteration. A is a single row d-dimensional matrix in which each element followsA machine value of 1 or-1, and A + ＝A T (AA T ) -1 And n is the total number of sparrows. When i is>n/2, this shows that the ith participant with lower fitness value does not obtain food, is in a state of full hunger, and needs to fly to other places to forage to obtain more energy; when i is less than or equal to n/2, a part of the participants can forage around the best discoverer, and the participants and the discoverer can compete for food, so that the participants change into discoverers.
9. The optimized air quality index prediction method based on the improved sparrow search algorithm as claimed in claim 5, wherein in step S36, the position update formula of the alerter is as follows:
wherein the content of the first and second substances,
for the t-th iteration global optimum position, beta is a step size control parameter, and K is [ -1,1]A random number in between. Xi is a very small constant to avoid when f i ＝f w When the denominator is 0. f. of i 、f g 、f w Representing the current, best and worst fitness, respectively. When f is i >f g This indicates that the sparrow is now at the border of the population and is extremely vulnerable to predators. f. of i ＝f g This indicates that sparrows in the middle of the population are perceived as dangerous and need to be close to other sparrows to minimize their risk of being prey.
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