CN111582541A - Firefly algorithm-based inland inundation model prediction method - Google Patents
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Abstract
The invention belongs to the technical field of waterlogging models, and particularly relates to a waterlogging model prediction method based on a firefly algorithm, which comprises the following steps: step 1, training a weight and a threshold of a neural network by using a training error of the neural network as a fitness function of a firefly individual to obtain an optimal parameter; step 2, constructing an inland inundation prediction model by using the optimal parameters obtained in the step 1; according to the firefly algorithm-based waterlogging prediction model provided by the invention, the weight and the threshold of a neural network are trained by adopting a firefly group algorithm, and the trained neural network model is adopted to predict waterlogging; the method overcomes the defects that the traditional rainfall ponding model needs a large amount of basic data information and requires a precise hydrologic physical process, and the like, simultaneously solves the defect that a neural network is easy to fall into a local minimum, and has important significance for realizing accurate prediction of urban waterlogging and accelerating the progress of an intelligent city.
Description
Technical Field
The invention belongs to the technical field of waterlogging models, and particularly relates to a waterlogging model prediction method based on a firefly algorithm.
Background
Along with the development of the society, the industrialization process is accelerated, so that the ecological environment is damaged, the waterlogging disasters are frequent, the waterlogging can not only cause traffic paralysis, but also cause great loss to the personal safety and property of people. The method is particularly important for the research of the waterlogging model and the waterlogging prediction. The urban waterlogging is forecasted in advance, the forecasting accuracy is improved, the influence of the urban waterlogging can be effectively reduced, and the progress of the smart city is accelerated.
Traditional rainfall ponding models, SWMM and the like, require a large amount of basic data information and require a thorough hydrological physical process, which limits the accuracy and use of the models. Along with the development of smart cities, the improvement of a drainage network management monitoring system can remotely obtain rainfall and liquid level data in real time, weather and rainfall information can be collected in real time, and an inland inundation prediction model can be constructed by using the monitoring data to predict inland inundation of cities and reduce loss.
Disclosure of Invention
The invention aims to overcome the defects of the existing waterlogging model and overcome the defect that a neural network is easy to fall into local minimum, and provides a waterlogging model prediction method based on a firefly algorithm.
In order to achieve the purpose, the invention adopts the following technical scheme:
an inland inundation model based on a firefly algorithm comprises the following steps:
step 1, training a threshold value and a weight of a neural network by using a training error of the neural network as a fitness function of a firefly individual to obtain a trained neural network;
and 2, constructing an inland inundation prediction model by using the neural network obtained in the step 1.
Compared with the prior art, the invention has the following technical effects:
according to the firefly algorithm-based inland inundation model prediction method, threshold values and weight values of a neural network are optimized by adopting a firefly swarm optimization algorithm, and inland inundation prediction is carried out by adopting a trained neural network model; the method overcomes the defects that the traditional rainfall ponding model needs a large amount of basic data information and requires a precise hydrologic physical process, and the like, simultaneously solves the defect that a neural network is easy to fall into a local minimum, and has important significance for realizing accurate prediction of urban waterlogging and accelerating the progress of an intelligent city.
Additional features and advantages of the invention will be set forth in the detailed description which follows.
Drawings
Fig. 1 is a schematic flow chart of a firefly algorithm-based inland inundation model prediction method provided by the invention.
Detailed Description
In order to make the technical means, the creation characteristics, the achievement purposes and the effects of the invention easy to understand, the invention is further clarified below by combining the attached drawings.
As shown in fig. 1, the invention provides a firefly algorithm-based inland inundation model prediction method, which comprises the following steps:
step 1, training a threshold value and a weight of a neural network by using a training error of the neural network as a fitness function of a firefly individual to obtain a trained neural network;
the step 1 specifically comprises:
step 1.1: initialization
Step 1.1.1: the number of neurons in the input, hidden and output layers of a neural network is divided inton, m, g; characterizing individuals using real number encoding, which contains a hidden layer threshold bjOutput layer threshold θkWeight v between input layer and hidden layerijWeight w between hidden layer and output layerjkIf the number of the parameters to be optimized by the neural network is n × m + m + m × g + g;
assuming that there are h fireflies in a firefly group, the p-th firefly individual is marked as xpP is 1, …, h and xp＝(v11，…，vnm，b1，…，bm，w11，…，wmg，θ1，…θg) Defining the fluorescein volatilization factor of the pth firefly in the h fireflies as rho, the fluorescein update rate as gamma, the dynamic decision domain update rate as β, the threshold value of the number of the fireflies contained in the neighborhood set as T, and the perception radius as
Initial fluorescein value of lp(0) Initial dynamic decision domain radius of
Defining the iteration times as t; the maximum number of iterations is iter _ max;
for example, the threshold value of the number of fireflies included in the neighborhood set, such as fluorescein volatility factor ρ of 0.4, fluorescein update rate γ of 0.6, and dynamic decision domain update rate β of 0.08, is T of 50, and the sensing radius is
Initial fluorescein value of lp(0) Initial dynamic decision field radius of 5
Step 1.1.2: initializing basic parameters of a BP neural network model, comprising: training times N, learning rate eta and the like;
for example, the number of training times of the BP neural network is 3000, and the learning rate is 0.01.
Step 1.2: a fluorescein updating stage;
step 1.2.1: calculating the p th firefly x in the t th iteration by the formula (1)pThe fitness function value f (i);
wherein y isiIn order to be the actual value of the measurement,
is a model predicted value;
is the training error of the neural network.
Step 1.2.2: calculating the p th firefly x in the t th iteration by the formula (2)p(t) fluorescein value lp(t)：
lp(t)＝(1-ρ)×lp(t-1)+γF(xp(t)) (2)
Equation (2) shows the position x of the p-th firefly at the t-th iterationp(t) corresponding fitness value F (x)p(t)) conversion to the fluorescein value lp(t)；
Step 1.3: a firefly individual movement stage;
step 1.3.1: calculating the p-th firefly x at the t-th iterationpHamming distance to other n-1 fireflies in ith firefly xpDynamic decision domain radius of
In the method, individuals with larger fluorescein value than self are selected to form a neighborhood set Mp(t); and the neighborhood set MpThe total number of fireflies in (t) is expressed as | Mp(t)|，
Step 1.3.2: calculating the p th firefly x in the t th iteration by the formula (3)pMoving to M within the neighborhood setpThe s-th of (t)Firefly xsProbability p ofps(t)：
In formula (3), s, b is 1,2, …, Mp(t); p firefly x at the t iterationpMoving to firefly x with the highest probabilitys；
pps(t) the larger the firefly p selects the corresponding firefly s and the larger the probability that the firefly p moves to the firefly s, after the moving target s is determined, the firefly p moves to the firefly p, and the position updating formula is as follows:
wherein e is the step length;
firefly algorithm simulation firefly's in nature luminous behavior, firefly attract the mate through the luminescence and call for a couple or seek food, and the luminous of individual firefly is brighter then the appeal is big more, so, and other most firefly are attracted by the lightest firefly, gather near this firefly, and this firefly is exactly the optimal solution.
The firefly algorithm generates oscillation phenomenon in the later period, which is caused by improper step length selection, the invention introduces the concept of variable step length, the step length is larger in the initial period of iteration, the search speed can be increased, the step length is smaller in the later period of iteration, the highest in the local part can be conveniently obtained, the optimal solution can not be skipped because the step length is too large, and the specific formula is as follows:
e(t)＝emaxec·g(t)
wherein
g (t) and tmaxFor the current iteration number and the maximum iteration number, emaxAnd eminRespectively representing the maximum and minimum values of e.
Step 1.4: a dynamic decision domain updating stage;
obtaining the t +1 th iteration using equation (5)Time of flight p firefly xpDynamic decision domain radius of
Step 1.5: outputting an optimal solution;
judging whether t +1 > iter _ max is true, if true, outputting the pth firefly x in the t +1 iterationpPosition x ofp(t +1) is used as the optimal solution, otherwise, the t +1 is assigned to the t, and the step 1.2 is returned to be executed in sequence;
step 1.6: the position of the firefly individual with the highest fitness is the optimal solution, and the optimal solution is the optimal threshold and weight of the neural network model.
And 2, constructing an inland inundation prediction model by using the optimal parameters obtained in the step 1.
The step 2 specifically comprises the following steps: the model input layer is liquid level, rainfall and meteorological data (including observation station, historical rainfall, current rainfall, highest temperature, lowest temperature, wind speed and evaporation capacity), a digital elevation model and a pipeline type, and the output layer is future water level and waterlogging grade.
And (4) inputting the data of the input layer into the waterlogging prediction model obtained in the step (1) to predict the future water level and the waterlogging level.
The method provided by the invention overcomes the defects that the traditional rainfall ponding model needs a large amount of basic data information, requires the elaboration of the hydrological physical process and the like, simultaneously solves the defect that a neural network is easy to fall into a local minimum, and has important significance for realizing accurate prediction of urban waterlogging, guaranteeing the life and property safety of people and accelerating the progress of an intelligent city.
The foregoing shows and describes the general principles, essential features, and inventive features of this invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (3)
1. A firefly algorithm-based inland inundation model prediction method is characterized by comprising the following steps:
step 1, training a threshold value and a weight of a neural network by using a training error of the neural network as a fitness function of a firefly individual to obtain a trained neural network;
and 2, constructing an inland inundation prediction model by using the neural network obtained in the step 1.
2. The firefly algorithm-based inland inundation model prediction method according to claim 1, wherein the step 1 specifically comprises the following steps:
step 1.1: initialization
Step 1.1.1: the number of the neurons of an input layer, a hidden layer and an output layer of the neural network is divided into n, m and g; characterizing individuals using real number encoding, which contains a hidden layer threshold bjOutput layer threshold θkWeight v between input layer and hidden layerijWeight w between hidden layer and output layerjkIf the number of the parameters to be optimized by the neural network is n × m + m + m × g + g;
assuming that there are h fireflies in a firefly group, the p-th firefly individual is marked as xpP is 1, …, h and xp＝(v11,…,vnm,b1,…,bm,w11,…,wmg,θ1,…θg) Defining the fluorescein volatilization factor of the pth firefly in the h fireflies as rho, the fluorescein update rate as gamma, the dynamic decision domain update rate as β, the threshold value of the number of the fireflies contained in the neighborhood set as T, and the perception radius as
Initial fluorescein value of lp(0) Initial dynamic decision domain radius of
Defining the iteration times as t; the maximum number of iterations is iter _ max;
step 1.1.2: initializing basic parameters of a BP neural network model, comprising: training times N, learning rate eta and the like;
step 1.2: a fluorescein updating stage;
step 1.2.1: calculating the p th firefly x in the t th iteration by the formula (1)pThe fitness function value f (i);
wherein y isiIn order to be the actual value of the measurement,
is a model predicted value;
is the training error of the neural network;
step 1.2.2: calculating the p th firefly x in the t th iteration by the formula (2)p(t) fluorescein value lp(t)：
lp(t)＝(1-ρ)×lp(t-1)+γF(xp(t)) (2)
Equation (2) shows the position x of the p-th firefly at the t-th iterationp(t) corresponding fitness value F (x)p(t)) conversion to the fluorescein value lp(t)；
Step 1.3: a firefly individual movement stage;
step 1.3.1: calculating the p-th firefly x at the t-th iterationpEuclidean distance to other n-1 fireflies, at the ith fireflies xpDynamic decision domain radius of
In the method, individuals with larger fluorescein value than self are selected to form a neighborhood set Mp(t); and the neighborhood set MpThe total number of fireflies in (t) is expressed as | Mp(t)|，
Step 1.3.2: calculating the p th firefly x in the t th iteration by the formula (3)pMoving to M within the neighborhood setp(t) S th firefly xsProbability p ofps(t)：
In formula (3), s, b is 1,2, …, Mp(t); p firefly x at the t iterationpMoving to firefly x with the highest probabilitys；
pps(t) the larger the firefly p selects the corresponding firefly s and the larger the probability that the firefly p moves to the firefly s, after the moving target s is determined, the firefly p moves to the firefly p, and the position updating formula is as follows:
wherein e is the step length;
step 1.4: a dynamic decision domain updating stage;
obtaining the p-th firefly x at the t +1 th iteration by using the formula (5)pDynamic decision domain radius of
Step 1.5: outputting an optimal solution;
judging whether t +1 > iter _ max is true, if true, outputting the p-th firefly in the t +1 th iterationxpPosition x ofp(t +1) is used as the optimal solution, otherwise, the t +1 is assigned to the t, and the step 1.2 is returned to be executed in sequence;
step 1.6: the position corresponding to the firefly individual with the highest fitness is the optimal solution, and the optimal solution is the threshold and the weight of the neural network model.
3. The firefly algorithm-based inland inundation model prediction method according to claim 1, wherein the step 2 is specifically as follows:
the model input layer is liquid level, rainfall and meteorological data (including observation station, historical rainfall, current rainfall, highest temperature, lowest temperature, wind speed and evaporation capacity), a digital elevation model and a pipeline type, and the output layer is future water level and waterlogging grade;
and (4) inputting the data of the input layer into the waterlogging model obtained in the step (1) to predict the future water level and the waterlogging level.
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| CN113761789A (en) * | 2021-07-23 | 2021-12-07 | 江苏大学 | Method for estimating SOC of battery based on BP neural network optimized by firefly swarm algorithm |
| CN116046079A (en) * | 2023-04-03 | 2023-05-02 | 山东省地质调查院(山东省自然资源厅矿产勘查技术指导中心) | Geological environment thematic data integrated management system based on position |
| CN116861317A (en) * | 2023-09-04 | 2023-10-10 | 北京建筑大学 | Cell waterlogging early warning method and system based on BP neural network |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN113538125A (en) * | 2021-06-29 | 2021-10-22 | 百维金科(上海)信息科技有限公司 | Risk rating method for optimizing Hopfield neural network based on firefly algorithm |
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| CN113344305A (en) * | 2021-08-05 | 2021-09-03 | 中国水利水电科学研究院 | Rapid prediction method for rainstorm waterlogging event |
| CN116046079A (en) * | 2023-04-03 | 2023-05-02 | 山东省地质调查院(山东省自然资源厅矿产勘查技术指导中心) | Geological environment thematic data integrated management system based on position |
| CN116046079B (en) * | 2023-04-03 | 2023-06-30 | 山东省地质调查院(山东省自然资源厅矿产勘查技术指导中心) | Geological environment thematic data integrated management system based on position |
| CN116861317A (en) * | 2023-09-04 | 2023-10-10 | 北京建筑大学 | Cell waterlogging early warning method and system based on BP neural network |
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