CN111461390A - L IESN ocean surface wind speed prediction method based on genetic algorithm key parameter optimization - Google Patents
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Abstract
The invention discloses an L IESN ocean surface wind speed prediction method based on genetic algorithm key parameter optimization, which comprises the following steps of S1, building meteorological characteristics, building a L IESN model, calculating commonly used physical quantity parameters and commonly used combined physical quantity parameters in weather analysis forecast by combining basic physical quantity and wind speed forming conditions measured by a meteorological station, calculating correlation degree between the basic physical quantity and the combined physical quantity, obtaining correlation degree between the basic physical quantity and wind speed and correlation degree between the combined physical quantity and wind speed, selecting multi-dimensional characteristics with high effectiveness, building a L IESN model, calculating an output weight matrix W of L IESN, and calculatingoutThe method comprises the steps of S2, optimizing key parameters influencing L IESN effect through a genetic algorithm, S3, training a training sample through an R L S online learning algorithm to obtain a L IESN ocean surface wind speed prediction model based on optimization of the key parameters of the genetic algorithm, and carrying out optimization on a test sample through the modelAnd (6) line prediction. The method has high prediction precision and high fitting degree of the prediction curve.
Description
Technical Field
The invention relates to the technical field of ocean surface wind speed forecasting, in particular to a leakage integral echo state network (L IESN) ocean surface wind speed forecasting method based on genetic algorithm key parameter optimization.
Background
Wind is a natural phenomenon generated by air flow, and the strong wind on the ocean surface can often cause sea waves and even storm tides, and has great influence on economic activities such as ships, harbors, engineering buildings, marine transportation and the like. The wind speed is used as a characteristic for measuring the wind movement speed, and the research on the wind speed prediction method has very important practical significance.
At present, marine observation data mainly come from the following ways: satellite inversion data, ship buoy data, oil platform and sea island data. The data quality of the satellite inversion data is often poor due to the influence of errors of a remote sensing instrument and an inversion algorithm. The quality of the ship is uneven due to the influence of factors such as the navigation speed, the navigation direction, the instability of the ship and the like. The buoy is an effective means for collecting meteorological data, but the time for putting the buoy into a buoy testing station is relatively late in China, the number of the buoys is relatively small, and the observation data are not complete. The platform station in China is long in building time, and the forecasting of the wind speed of the exploration platform station under the existing condition is beneficial to being popularized in nearby sea areas, so that the platform station has important practical significance.
The echo state network belongs to an important branch of machine learning, and the echo state network is applied to meteorological research, thereby being beneficial to improving the informatization and intellectualization level of meteorological forecast service and having important significance on the meteorological research.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a leakage integral type echo state network (L IESN) ocean surface wind speed prediction method based on genetic algorithm key parameter optimization, meteorological features are constructed according to original meteorological physical quantities, feature selection is carried out, a leakage integral type echo state network online learning algorithm is utilized, network parameters are optimized through a genetic algorithm, and finally the leakage integral type echo state network wind speed prediction based on the genetic algorithm key parameter optimization is realized.
Therefore, the invention adopts the following technical scheme:
an L IESN ocean surface wind speed prediction method based on genetic algorithm key parameter optimization comprises the following steps:
s1, constructing meteorological features and building L IESN model, comprising the following steps:
(1) calculating a common physical quantity parameter and a common combined physical quantity parameter in weather analysis forecast by combining the basic physical quantity measured by the weather station and the wind speed forming condition;
(2) quantitatively solving the correlation degree between the basic physical quantity and the combined physical quantity according to the spearman correlation coefficient to obtain the correlation degree between the basic physical quantity and the wind speed and the correlation degree between the combined physical quantity and the wind speed, and selecting the multi-dimensional characteristics with higher effectiveness;
(3) an L IESN model is built, and the calculation formula is as follows:
y(n)＝g(Wout[x(n)；u(n)]) (8-2)
wherein:
u (n), x (n), y (n) are input at the time n, state at the time n and output at the time n of the network respectively;
c >0, time constant of L IESN;
α >0, the decay rate of the leakage integration unit;
Win，W，Wout，Wbackrespectively an input weight matrix, a reserve pool state weight matrix, an output weight matrix and a feedback connection weight matrix;
f (-) is a Sigmoid function;
g (-) is an output layer activation function, and an identity function or a Sigmoid function is often selected;
[; represents concatenation of vectors;
(4) calculating L IESN output weight matrix W through an R L S online learning algorithmout；
S2, optimizing key parameters, namely optimizing the key parameters influencing the L IESN effect through a genetic algorithm;
and S3, forecasting the wind speed, namely training the training sample by utilizing an R L S online learning algorithm to obtain a L IESN ocean surface wind speed forecasting model optimized based on key parameters of a genetic algorithm, and forecasting the test sample by utilizing the model.
Preferably, the basic physical quantities in step (1) include: latitude, longitude, barometric pressure at the survey station platform, barometric pressure at sea level, temperature at the survey station platform, dew point temperature, relative humidity, water vapor pressure, 2min average wind speed, and 10min average wind speed.
Preferably, the combined physical quantity parameter in step (1) includes: maximum pressure difference, maximum temperature difference, temperature-dew point difference, water vapor density and total energy.
Further, the feature of higher effectiveness in step (2) is 6 dimensions, which are respectively: air pressure, dew point, relative humidity, water vapor density, total energy, and historical wind speed along the shore site.
Calculating an output weight matrix W at the moment i through an online learning algorithm in the step (4)outThe process of (2) is as follows:
wherein P is the length of the time sequence, mu is a forgetting factor, the range of the forgetting factor is 0< mu <1, and the forgetting factor is exponentially changed,
1) initialization of network parameters:
setting the dimensions of an input layer, a reserve pool and an output layer of the network;
setting the size of a reserve pool and the leakage attenuation rate of a leakage integral unit in the model;
to form a uniform distribution of [ -1,1 [)]Input matrix W ofinConnected to feedbackWeight matrix Wback；
The forgetting factor 0< μ <1, typically μ ≈ 1, is set.
2) Updating the output weight value:
updating the state of the reserve pool according to the following formula (10), and setting a cascade matrix of the state and the input as d (n) ═ x (n-1); u (n), the output at time n is:
the error at time n is as follows:
e(n)＝y(n)-fout(Wout(n-1)d(n)) (11)
the output weight value at the moment n is updated as follows:
Wout(n)＝Wout(n-1)+e(n)KT(n) (12)
wherein, the gain vector at n moments is:
P(n)＝μ-1[P(n-1)-K(n)xT(n)P(n-1)](14)
the corner marks H, T represent the conjugate transpose and transpose of the matrix.
3) And executing the step 2) to update the output weight until the time sequence is ended.
The step of optimizing the key parameters affecting the L IESN effect by genetic algorithm in step S2 is as follows:
(1) carrying out binary coding cascade coding on the scale N of a key parameter reservoir, the spectral radius SR of an internal connection matrix, the scale IS of an input unit, the sparsity degree SD of the reservoir and the leakage attenuation rate α in L IESN by adopting a uniform design method to generate a group of chromosomes of key parameters of a L IESN prediction model to form a population;
(2) substituting chromosomes representing key parameters in L IESN in the population into L IESN to establish a L IESN prediction model, loading training samples into the established model to perform wind speed prediction to obtain NRMSE of a prediction result, substituting the NRMSE into fitness calculation formulas (15-1) and (15-2) to obtain the fitness of the population, wherein in the ith iterative optimization, the fitness function is as follows:
wherein: sigma2Is the variance of the predicted sequence; b is the total number of test samples; c. CmIs a larger constant and has the main function of ensuring that the fitness function is not negative.
(3) According to the fitness function value of the population, adopting a roulette method to enable the individuals with higher fitness to enter the next generation according to the probability; exchanging genes in the paired individuals according to probability by a uniform crossing method; then carrying out mutation operation according to a set probability to change a certain gene in the code;
(4) repeating the steps (2) and (3) until the maximum genetic algebra is reached;
(5) and recording the individual codes of the optimal results to obtain key parameter values.
The invention has the characteristics and beneficial effects that:
the invention adopts the genetic algorithm as the network parameter optimization of the leakage integral echo state network, and improves the network parameter optimization efficiency and the system prediction performance. Compared with the classical echo state network and the time series ARMA prediction method, the echo state network based on the genetic algorithm network parameter optimization has higher prediction precision and higher fitting degree of a prediction curve. Therefore, the method provided by the invention is suitable for wind speed forecasting based on physical quantity data of the meteorological station.
Drawings
FIG. 1 is a graph of NRMSE change in accordance with an embodiment of the present invention;
FIG. 2 is a comparison of ARMA predicted results and actual output;
FIG. 3 is a comparison of a classical ESN prediction result with an actual output;
FIG. 4 is a comparison of predicted results and actual outputs, respectively, for an embodiment of the present invention.
Detailed Description
The invention is further illustrated with reference to specific embodiments below.
According to basic physical quantities measured by a weather station, combined with commonly used combined physical quantity parameters in weather analysis and forecast, a spearman correlation coefficient method is adopted for feature selection, 6-dimensional features with high effectiveness are selected, a leakage integral type echo state network online learning algorithm is utilized, key parameters are optimized through a genetic algorithm, and finally the leakage integral type echo state network wind speed prediction based on genetic algorithm key parameter optimization is achieved.
The ocean surface wind speed prediction method of the present invention will be described in detail with reference to specific examples.
Example one
A leakage integral echo state network ocean surface wind speed prediction method based on genetic algorithm key parameter optimization comprises the following steps:
s1, constructing meteorological features, and building a leakage integral echo state network (L IESN) model:
(1) the data of the embodiment is derived from actually measured data of a Bohai Bay A platform meteorological station provided by Tianjin urban meteorology office, the time range is 2006-2016, and the data has partial missing values. The missing values in the original data are processed as follows: if a certain missing value is discontinuous in time or the missing value is not long in continuous time, filling missing data in a linear interpolation mode; if the deletion continues and the duration is longer, the whole case is deleted. The data after collation was about 86000 pieces.
The physical quantities included in the measured data of the platform meteorological station A comprise: latitude (°), longitude (°), barometric pressure at the survey station platform (hPa), barometric pressure at sea level (hPa), temperature at the survey station platform (° c), dew point temperature (° c), relative humidity (%), vapor pressure (hPa), 2min average wind speed (m/s), and 10min average wind speed (m/s).
Deleting repeated longitude and latitude information in each piece of information, selecting the average wind speed of 2 minutes after 3 hours at the current moment as a wind speed pre-reporting label, taking other physical quantities as original meteorological characteristics, and arranging the data as shown in table 1:
TABLE 1A platform raw data
Calculating some commonly used physical quantity parameters and commonly used composite physical quantity parameters in weather analysis forecast by combining the basic physical quantity measured by the meteorological station and considering the wind speed forming condition, wherein the commonly used composite physical quantity parameters are as follows:
a. maximum differential pressure (DevPRS): the value of the air pressure variation at the adjacent time, which is selected as the maximum pressure difference at the current time and has the maximum variation 6 hours before the current time, is taken as the unit of hPa.
b. Maximum temperature difference (DevTEM): the value of the temperature variation of the adjacent time, which is selected as the maximum temperature difference of the current time and has the maximum variation 6 hours before the current time, is taken as the unit of temperature variation of the current time.
c. Temperature-dew point difference (T-T)d): is a physical quantity for measuring the air humidity in the actual weather forecast analysis. When T is equal to TdWhen it is, it means that the air humidity is completely saturated, (T-T)d) Smaller values indicate that the air is closer to full saturation.
d. Water vapor density (p)v): is a physical quantity that measures the mass of water vapor in a unit volume of air. The water vapor density cannot be directly measured by using a conventional method and needs to be calculated by the water vapor pressure. The specific calculation formula is as follows:
wherein e is the vapor pressure and T is the temperature.
e. Total energy (E)t): the main energies that can directly determine the atmospheric motion state are: the total energy is the sum of the apparent heat energy, the latent heat energy, the potential energy and the kinetic energy.
For a unit mass of air, there are: total energy is apparent heat energy + latent heat energy + potential energy + kinetic energy; the formula is described as follows:
under the condition that part of meteorological station equipment is relatively lagged behind, observation data are directly used for calculation, and therefore, a calculation formula of total energy relative to temperature-total temperature is introduced by thunderstorm weather and the like:
wherein the dry air ratio constant pressure heat capacity cp＝1004.07J·Kg-1·K-1(ii) a Acceleration of gravity g ═ 9.8m · s-2The altitude Z unit is m, the gasification heat energy of water is L ≈ 250 J.g-1(ii) a The unit of specific humidity q is g.kg-1(ii) a The unit of the wind speed V is m.s-1The pressure p is expressed in hPa.
The degree of correlation between the variables was analyzed by the spearman correlation coefficient method. The correlation degree of the original physical quantity with the wind speed and the correlation degree of the combined physical quantity with the wind speed are shown in tables 2 and 3.
TABLE 2 correlation degree of original physical quantity with wind speed
TABLE 3 correlation of Combined meteorological features with wind speed
The features thus selected include: the air pressure, the dew point, the relative humidity, the water vapor density, the total energy and the historical wind speed of the coastal station are 6-dimensional characteristics. The 6-dimensional feature contains most of the original physical quantities and effectively reduces the input feature dimensions.
(2) The online learning algorithm of the leakage integral echo state network introduces a step parameter on the basis of a state updating equation of a classical echo state network, and the calculation formula is as follows:
y(n)＝g(Wout[x(n)；u(n)]) (8-2)
wherein, u (n), x (n), y (n) are input of the network at the moment n, state at the moment n and output at the moment n respectively; c. C>0, time constant of L IESN, α>0, attenuation ratio of leakage integration unit, Win，W，Wout，WbackRespectively an input weight matrix, a reserve pool state weight matrix, an output weight matrix and a feedback connection weight matrix; f (-) is a Sigmoid function; g (-) is an output layer activation function, and an identity function or a Sigmoid function is often selected; [;]representing a concatenation of vectors.
Compared with the state updating equation of the classical echo state network, the leakage integral type echo state network added with the step length is added with an item
This term increases the previous state and can be adjusted with time constants and step sizes, increasing the memory of the neural network.
The on-line learning algorithm adopts a recursive least square algorithm R L S.R L S algorithm, can avoid the inversion calculation process of a large matrix, reduces the calculation complexity, has good convergence and numerical stability, and when the R L S algorithm is applied to the on-line learning of L IESN, the output weight matrix W at the moment ioutDuring the updating process, the following conditions should be satisfied:
wherein, P is the length of time sequence, mu is forgetting factor, the range is 0< mu <1, and the change is exponential.
The steps of the R L S-based L IESN online learning algorithm are as follows:
1) initialization of network parameters:
setting the dimensions of an input layer, a reserve pool and an output layer of the network;
setting parameters such as the size of a reserve pool, the leakage attenuation rate of a leakage integral unit and the like in the model;
to form a uniform distribution of [ -1,1 [)]Input matrix W ofinWeight matrix W connected with feedbackback；
The forgetting factor 0< μ <1, typically μ ≈ 1, is set.
2) Updating the output weight value:
updating the state of the reserve pool according to the following formula (10), and setting a cascade matrix of the state and the input as d (n) ═ x (n-1); u (n), the output at time n is:
the error at time n is as follows:
e(n)＝y(n)-fout(Wout(n-1)d(n)) (11)
the output weight value at the moment n is updated as follows:
Wout(n)＝Wout(n-1)+e(n)KT(n) (12)
wherein, the gain vector at n moments is:
P(n)＝μ-1[P(n-1)-K(n)xT(n)P(n-1)](14)
the corner marks H, T represent the conjugate transpose and transpose of the matrix.
3) And executing the step 2) to update the output weight until the time sequence is ended.
S2, optimizing key parameters:
the scale N of a key parameter reserve pool, the spectrum radius SR of an internal connection matrix, the input unit scale IS, the sparsity degree SD of the reserve pool and the leakage attenuation rate α contained in the network reserve pool in the echo state are required to be reasonably valued so that the system can generate the optimal performance.
Referring to fig. 1, the algorithm for optimizing the parameters of the leaky integration type echo state network by using the genetic algorithm comprises the following steps:
(1) l expression of key parameters in IESN in genetic algorithms:
the SR, IS, SD and α parameters in L IESN are subjected to binary coding cascade coding by adopting a uniform design method, a group of chromosomes of L IESN prediction model key parameters are generated, and a population IS formed.
(2) The chromosome representing the key parameters in L IESN in the population is substituted into L IESN to realize the establishment of L IESN prediction model, the training samples are loaded into the established model to carry out wind speed prediction to obtain the normalized mean square error (NRMSE) of the prediction result, and the normalized mean square error (NRMSE) is substituted into a fitness calculation formula (15) to obtain the fitness of the population, in the ith iterative optimization, the fitness function is as follows:
wherein: sigma2To predict the variance of the sequence, b is the total number of test samples. c. CmIs a larger constant and has the main function of ensuring that the fitness function is not negative.
(3) According to the fitness function value of the population, adopting a roulette method to enable the individuals with higher fitness to enter the next generation according to the probability; exchanging genes in the paired individuals according to probability by a uniform crossing method; then mutation operation is carried out according to the set probability, and genes of certain positions in the codes are changed.
(4) And (5) repeating the steps (2) and (3) until the maximum genetic algebra is reached.
(5) And recording the individual codes of the optimal results to obtain key parameter values.
The parameter optimizing process is to encode the parameters according to their characteristics, and the encoded set is called chromosome. Initializing the population according to a coding method, and selecting a superior chromosome from potential solutions according to the survival principle of a fittest. After each iteration, excellent genes are inherited, and new excellent genes are reselected after a new generation of population is generated through crossing and mutation. In this way, the newly generated gene is superior to the previous generation gene, resulting in a near optimal solution for the parameters.
S3, wind speed prediction:
in this embodiment, historical measured data of a platform of a Bohai Bay A is used as sample data, the data acquisition interval is 1 hour, the time range is 6 months to 2016 months and 12 months in 2006, and 86000 pieces are total. Training sets and test sets were randomly selected for data from 6 months 2006 to 12 months 2015 according to a 4:1 ratio. Data from 2016, 1 month to 2016, 12 months was selected as the validation set.
Because the original data has different dimensions and dimension units, the direct use of the original data can affect the result of data analysis, and in order to eliminate the influence caused by different dimensions among the data, the original data is suitable for model training, and the normalization processing is carried out on the data range, and the method comprises the following steps:
in the above formula, x1(n) actual data at time n, xminIs the minimum value in the sample set X, XmaxIs the maximum value in sample set X.
L the range of key parameters SR, IS, SD and α in IESN IS set as SR ∈ [0.001, 1], IS ∈ [0.001, 1], SR ∈ [0.001, 1], α∈ [0.001, 1], each parameter IS set as individual according to 8-bit coding by adopting a cascade coding method, the number of the individual in each population IS 16, and the maximum iteration number IS 20.
S4, analysis of results:
table 4 shows the normalized mean square error minimum result and the values of the key parameters in each generation of the genetic algorithm. The variation of normalized mean square error with the increase of genetic algebra of genetic algorithm is shown in FIG. 1.
TABLE 4 genetic algorithm optimization results
From the results shown in fig. 1, it can be seen that, as the genetic algebra increases, the overall prediction error of the model decreases and gradually becomes stable, which indicates that the genetic algorithm can find the optimal value of the key parameter in the network, so that the performance of the model is improved. From the results shown in table 4, it can be seen that the optimal value found by the genetic algorithm in each generation is unstable, but the combination effect can reach the practical use requirement.
And substituting the parameters searched by the genetic algorithm into the network model to predict the wind speed in the future 3 hours. The classical ESN, time series prediction model ARMA and the method proposed by the present invention are shown in table 5 for the same time wind speed prediction error pair. The comparison of the predicted results of the 3 models with the actual output is shown in fig. 2-4.
Error comparison of 53 prediction models in Table
In FIG. 2, prediction point 0 represents 2016, month 11, day 1, 00, prediction point 1 represents 2016, month 11, day 1, 03, prediction occurs every 3 hours, and so on, until prediction point 200 is 2016, month 11, day 25, 21.
As can be seen from table 5 and fig. 2-4, the echo state network optimized based on the GA algorithm of the present invention has higher prediction accuracy and higher fitting degree of the prediction curve compared to the classical echo state network and the time series ARMA prediction method. Therefore, the method is suitable for wind speed forecasting based on physical quantity data of the meteorological station.
Claims (6)
1. An L IESN ocean surface wind speed prediction method based on genetic algorithm key parameter optimization comprises the following steps:
s1, constructing meteorological features and building L IESN model, comprising the following steps:
(1) calculating a common physical quantity parameter and a common combined physical quantity parameter in weather analysis forecast by combining the basic physical quantity measured by the weather station and the wind speed forming condition;
(2) quantitatively solving the correlation degree between the basic physical quantity and the combined physical quantity according to the spearman correlation coefficient to obtain the correlation degree between the basic physical quantity and the wind speed and the correlation degree between the combined physical quantity and the wind speed, and selecting the multi-dimensional characteristics with high effectiveness;
(3) an L IESN model is built, and the calculation formula is as follows:
y(n)＝g(Wout[x(n)；u(n)]) (8-2)
wherein:
u (n), x (n), y (n) are input at the time n, state at the time n and output at the time n of the network respectively;
c >0, time constant of L IESN;
α >0, the decay rate of the leakage integration unit;
Win，W，Wout，Wbackrespectively an input weight matrix, a reserve pool state weight matrix, an output weight matrix and a feedback connection weight matrix;
f (-) is a Sigmoid function;
g (-) is an output layer activation function, and an identity function or a Sigmoid function is often selected;
[; represents concatenation of vectors;
(4) calculating L IESN output weight matrix W through an R L S online learning algorithmout；
S2, optimizing key parameters, namely optimizing the key parameters influencing the L IESN effect through a genetic algorithm;
and S3, forecasting the wind speed, namely training the training sample by utilizing an R L S online learning algorithm to obtain a L IESN ocean surface wind speed forecasting model optimized based on key parameters of a genetic algorithm, and forecasting the test sample by utilizing the model.
2. The L IESN ocean surface wind speed prediction method of claim 1, wherein the basic physical quantities in step (1) include latitude, longitude, barometric pressure at the instrumented platform, barometric pressure at sea level, temperature at the instrumented platform, dew point temperature, relative humidity, water vapor pressure, 2min average wind speed, and 10min average wind speed.
3. The L IESN ocean surface wind speed prediction method of claim 1, wherein the combined physical quantity parameters in step (1) include maximum pressure difference, maximum temperature difference, temperature-dew point difference, water vapor density, total energy.
4. The L IESN ocean surface wind speed prediction method of claim 1, wherein the higher effectiveness in step (2) is characterized by 6 dimensions, respectively, air pressure, dew point, relative humidity, water vapor density, total energy, and coastal site historical wind speed.
5. The L IESN ocean surface wind speed prediction method of claim 1, wherein in step (4), the output weight matrix W at time i is calculated by an online learning algorithmoutThe process of (2) is as follows:
wherein P is the length of the time sequence, mu is a forgetting factor, the range of the forgetting factor is 0< mu <1, and the forgetting factor is exponentially changed,
1) initialization of network parameters:
setting the dimensions of an input layer, a reserve pool and an output layer of the network;
setting the size of a reserve pool and the leakage attenuation rate of a leakage integral unit in the model;
to form a uniform distribution of [ -1,1 [)]Input matrix W ofinWeight matrix W connected with feedbackback；
The forgetting factor 0< μ <1, typically μ ≈ 1, is set.
2) Updating the output weight value:
updating the state of the reserve pool according to the following formula (10), and setting a cascade matrix of the state and the input as d (n) ═ x (n-1); u (n), the output at time n is:
the error at time n is as follows:
e(n)＝y(n)-fout(Wout(n-1)d(n)) (11)
the output weight value at the moment n is updated as follows:
Wout(n)＝Wout(n-1)+e(n)KT(n) (12)
wherein, the gain vector at n moments is:
P(n)＝μ-1[P(n-1)-K(n)xT(n)P(n-1)](14)
the corner marks H, T represent the conjugate transpose and transpose of the matrix.
3) And executing the step 2) to update the output weight until the time sequence is ended.
6. The method for predicting wind speed at an ocean surface of L IESN according to claim 1, wherein the step of optimizing the key parameters affecting the effect of L IESN by genetic algorithm in step S2 is as follows:
(1) carrying out binary coding cascade coding on the scale N of a key parameter reservoir, the spectral radius SR of an internal connection matrix, the scale IS of an input unit, the sparsity degree SD of the reservoir and the leakage attenuation rate α in L IESN by adopting a uniform design method to generate a group of chromosomes of key parameters of a L IESN prediction model to form a population;
(2) substituting chromosomes representing key parameters in L IESN in the population into L IESN to establish a L IESN prediction model, loading training samples into the established model to perform wind speed prediction to obtain NRMSE of a prediction result, substituting the NRMSE into fitness calculation formulas (15-1) and (15-2) to obtain the fitness of the population, wherein in the ith iterative optimization, the fitness function is as follows:
wherein: sigma2Is the variance of the predicted sequence; b is the total number of test samples; c. CmIs a larger constant and has the main function of ensuring that the fitness function is not negative.
(3) According to the fitness function value of the population, adopting a roulette method to enable the individuals with higher fitness to enter the next generation according to the probability; exchanging genes in the paired individuals according to probability by a uniform crossing method; then carrying out mutation operation according to a set probability to change a certain gene in the code;
(4) repeating the steps (2) and (3) until the maximum genetic algebra is reached;
(5) and recording the individual codes of the optimal results to obtain key parameter values.
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