CN112329359A - Neural network prediction method for aerodynamic performance of wing section of wind turbine under open ice condition - Google Patents
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Abstract
The invention discloses a neural network prediction method for the aerodynamic performance of a wing section of a wind turbine under an open ice condition, which comprises the following steps: and establishing a neural network optimization model by taking the minimum training error as a design target and taking the threshold value of the neuron, the connection weight between the neurons and the switching parameter thereof as design variables. The position of the optimal particle is updated by combining a non-optimal particle potential well center updating mode of a social learning correction quantum particle group algorithm and a Levy flight and greedy algorithm, a selection process that a test error interferes with the global optimal particle is introduced, optimization is further performed by cooperating with a binary particle swarm algorithm, and a new neural network (SLLQPSO-BPNN) is further trained and constructed by adopting an error back propagation algorithm. And predicting the lift coefficient and the resistance coefficient of the NACA64618 airfoil with the open ice shape, comparing and analyzing the lift coefficient and the resistance coefficient with the result of an error back propagation algorithm, and providing a neural network prediction method for the aerodynamic performance of the wind turbine airfoil under the open ice condition. The method for predicting the aerodynamic performance of the airfoil of the open-ice wind turbine enables the aerodynamic performance analysis of the airfoil not to consider the high requirements and the high cost of the wind tunnel environment, equipment conditions and the like and the excessive calculation amount of a CFD (computational fluid dynamics) method.
Description
Technical Field
The invention belongs to the technical field of calculation of aerodynamic performance of wind turbine airfoils, and particularly relates to a method for solving an aerodynamic performance prediction neural network optimization model by using an improved quantum particle swarm algorithm in combination with a binary particle swarm algorithm and an error back propagation algorithm.
Background
In the present day that the environmental deterioration and other problems due to the utilization of fossil energy are becoming more serious, the development of renewable energy is receiving much attention from various countries. The wind energy has the advantages of wide distribution, no pollution, rich reserves and the like, and occupies an important position in the field of energy production. Wind turbines for converting wind energy into electric energy often encounter weather conditions of low ambient temperature, large moisture content, high mass fraction of supercooled water drops in air, and freezing rain or snow, so that the surface of a blade can be frozen. Icing can alter the aerodynamic profile of the blade and increase surface roughness, resulting in reduced wind energy conversion. The geometrical shape of the blade is determined by the airfoil and the distribution thereof along the spanwise direction of the blade, so that the adverse effect of icing can be reduced or eliminated by the profile design of the airfoil under the icing condition, but the accurate and rapid acquisition of the aerodynamic performance of the icing airfoil is the primary condition for designing and is a key problem to be solved urgently.
The scholars at home and abroad study the aerodynamic performance of the wing section of the wind turbine under the icing condition by either an icing wind tunnel test or a Computational Fluid Dynamics (CFD) method or by combining the icing wind tunnel test and the CFD method. The icing wind tunnel experiment has high requirements on wind tunnel environment, equipment conditions and the like, is high in cost and has certain limitations on the aspects of blade size, icing working conditions and the like; the CFD method has a high accuracy in solving the flow field control equation, but the amount of calculation is too large. The neural network can be used for building an aerodynamic performance prediction model of the icing wing profile due to the fact that the neural network has strong nonlinear mapping and rapid parallel computing capability and can learn useful knowledge from samples and input and output. And establishing a neural network model with ice-shaped geometric characteristic parameters as input and maximum lift coefficient as output and adopting an error back propagation algorithm to search for a weight and a threshold value. However, a non-global optimization error back propagation algorithm based on a gradient descent method is sensitive to initial parameters, so that a network model is easy to trap into local minimum, and the prediction precision is reduced. Random parameters can be introduced into the global optimization algorithm in the process of searching the optimal solution, so that traps of local extreme values can be jumped out. The quantum particle swarm algorithm with the strong global search capability is very suitable for processing the optimization problems of real value, rugged error curved surface and multiple peaks, but the convergence speed is low, and the later population diversity is reduced. By means of improving a potential well model, a potential well center updating mode, a potential well length control strategy, fusing advanced ideas (chaos, elite groups, diversity variation and the like) and the like, the population diversity and the convergence speed of a quantum particle population algorithm can be improved. In recent years, the method of fusing advanced ideas is only to perform variation on premature particles, and although the global search capability of the algorithm is improved, the population diversity of the algorithm is still reduced at a later stage. The social learning thought attaches importance to information exchange and learning among individuals, and the individuals can quickly improve themselves through social learning without generating individual trial and error cost. Based on this, Yuan and the like learn the particle potential well center to the individual optimal position and the population average optimal position of the sample particle to strengthen the inter-particle information exchange and improve the population diversity. However, studies in which the particle well center learns the particle well center and the population average well center by using a social learning mechanism have not been involved.
In addition, neural networks are often over-trained due to redundancy of connections between neurons, resulting in reduced generalization capability. The over-training phenomenon can be avoided by monitoring the test error and terminating the neural network training when it reaches a certain value, but this approach does not reduce the connection redundancy. Leung proposes a three-layer forward neural network with weight connection switches to construct a partially connected network structure among neurons to reduce connection redundancy, and to adjust the connection switches and parameters thereof by adopting an improved genetic algorithm. And then, the optimal connection switch and parameters of the neural network are also searched by Xiao and the like, Tsai and the like and Zhao respectively by utilizing a GPSES method, an HTGA algorithm and a binary particle swarm cooperative PSO algorithm. However, no research is conducted on improving the generalization capability of the neural network by considering the test error in the optimization process of the neural network.
Based on the two points, the method adopts a non-optimal particle potential well center updating mode of a social learning correction quantum particle group algorithm, utilizes Levy flight combined with a greedy algorithm to update the position of the optimal particle, utilizes a test error to interfere the selection process of the global optimal particle, and cooperates with a binary particle swarm and an error back propagation algorithm to solve an optimization model of a three-layer forward neural network structure and parameters with a weight value connecting switch, so as to predict the aerodynamic performance of the airfoil profile under the open ice condition.
Disclosure of Invention
The invention provides a neural network prediction method for the wing type aerodynamic performance of a wind turbine under the open ice condition, which can adopt a non-optimal particle potential well center updating mode of a social learning correction quantum particle group algorithm, and update the position of optimal particles by using Levy flight combined with a greedy algorithm to obtain an improved quantum particle group (SLLQPSO) algorithm; introducing a selection process of testing error interference global optimum particles, optimizing a three-layer forward neural network structure and parameters with a weight connection switch by cooperating with a binary particle swarm algorithm, and further training and constructing a new neural network (SLLQPSO-BPNN) by adopting an error back propagation algorithm; the method is used for predicting the lift and resistance coefficients of the NACA64618 airfoil with the open ice shape, providing a neural network prediction method for the aerodynamic performance of the wind turbine airfoil under the open ice condition, and realizing the aerodynamic performance analysis without considering the high requirements, the expensive cost and the excessive calculation amount of a CFD method of the wind tunnel environment, the equipment condition and the like.
In order to solve the technical problems, the invention adopts the technical scheme that: a neural network prediction method for the aerodynamic performance of a wing section of a wind turbine under the open ice condition is characterized by comprising the following steps: the method comprises the following steps:
step (1), constructing a neural network optimization model: adopting a display space decomposition mode to decompose the optimization design of the neural network structure and parameters into three optimization problems of an inter-neuron connection switch, a connection weight from an input layer to a hidden layer and a hidden layer neuron threshold value, and a connection weight from the hidden layer to an output layer and an output layer neuron threshold value, and establishing an optimization model shown in figure 1;
step (2), quantum particle swarm algorithm improvement: when the non-optimal particles are learnt, the center of the potential well of the particles is directly learnt to the center of the potential well of the target particles and the population average level, and when the particles are not learnt, the center of the original potential well of the particles is kept unchanged, and a learning mechanism is introduced to update the center p 'of the potential well of the g-th dimension of the h-th non-optimal particle'h,gThe formula (t) is:
in the formula, pR,g(t) is the center of the potential well of the sample particle;is the center of the average potential well of the population,pa,g(t) is the center of the potential well in the g dimension of the a-th particle; r is1(t),r2(t),r3(t)∈U(0,1);r2(t)(pR,g(t)-ph,g(t)) is a part of learning to the sample particles;is part of learning to the social average level; epsilon is a social influence factor, epsilon is xi G/B, xi is a proportionality coefficient, and 0.01 is taken; phThe update probability of the h-th non-optimal particle potential well center.
Calculating population average potential well center by utilizing potential well center containing more particle information and obtained after social learning is introducedAnd the distance between the particles is adopted to control the length of a potential well, and the position X of the g dimension of the h non-optimal particle in the next iteration after descending order arrangementh,g(t +1) is:
in the formula, Xh,g(t) is the position of the particle h at the tth iteration; u. ofh,j(t) is in the interval [0, 1 ]]Random numbers are uniformly distributed throughout the course of administration.
During t iterations, if the position of the H-th particle after descending order arrangement is the global optimal position, the H-th particle must be the individual optimal position, so that the updated information of the H position of the particle is less, and a local optimal solution is trapped; in order to make the particles escape from the local part and enlarge the search range, the position of the particles H is updated by adopting the Levy flight with the characteristics of short-distance frequent search and long-distance minority search, and the final position X of the optimal particles is determined by utilizing a greedy algorithmH(t+1):
In the formula (f)fitnessIs a function of the fitness value;carrying out the position with the minimum fitness value when the particle H flies in the Levy mode, wherein q is the flying time of the particle H, q belongs to {0, 1, 2.. multidot.L }, and L is the maximum flying time; gbest (t) is a global optimal position of the population;
introducing a social learning and correction non-optimal particle potential well center updating mode, updating the position of the optimal particle by using Levy flight and a greedy algorithm, and providing an improved quantum particle swarm (SLLQPSO) algorithm, wherein the basic flow is shown in FIG. 2;
step (3), solving a neural network prediction model: searching an optimal value of a parameter of a connection switch between neurons by using a binary particle swarm algorithm, and searching a connection weight from an input layer to a hidden layer, a hidden layer neuron threshold value, a connection weight from the hidden layer to an output layer and an optimal value of an output layer neuron threshold value by using an SLLQPSO algorithm; in order to further improve the precision of the neural network, the optimized weight and threshold are used as initial parameters, and an error back propagation algorithm with strong local search capability is adopted to train the network again;
and (4) realizing the neural network (SLLQPSO-BPNN) prediction method of the aerodynamic performance of the wind turbine airfoil under the open ice condition shown in the figure 3 through the steps (1) to (3).
Due to the adoption of the technical scheme, compared with the prior art, the neural network prediction method for the wing type aerodynamic performance of the wind turbine under the open ice condition updates the position of the optimal particle by utilizing the social learning correction quantum particle swarm algorithm in the non-optimal particle potential well center updating mode and the Levy flight combined greedy algorithm, so that the population diversity and the convergence speed of the quantum particle swarm algorithm can be improved; the generalization capability of the neural network can be improved by applying the selection process of the test error interference global optimum particles; the three-layer forward neural network structure and parameter optimization model with the weight connecting switch is solved by cooperating with the binary particle swarm and the error back propagation algorithm, the precision of the neural network can be further improved, and then the rising and resistance coefficients of the NACA64618 wing section after the open ice is formed are predicted. The method solves the problems and provides technical support and important reference for calculating the aerodynamic performance of the wind turbine airfoil under the open ice condition.
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The advantages and realisation of the invention will be more apparent from the following detailed description, given by way of example, with reference to the accompanying drawings, which are given for the purpose of illustration only, and which are not to be construed in any way as limiting the invention, and in which:
FIG. 1 is a diagram of a three-layer forward neural network optimization model with a weight connection switch according to the present invention;
FIG. 2 is a basic flow diagram of the improved Quantum particle swarm (SLLQPSO) algorithm of the present invention;
FIG. 3 is a flow chart of the construction of the aerodynamic performance prediction neural network of the airfoil of the wind turbine under the open ice condition;
FIG. 4a is a graph of the lift coefficient prediction for an NACA64618 airfoil under open ice conditions and the absolute error from experimental values for the airfoil of the present invention;
FIG. 4b is a graph of the prediction of drag coefficient for an NACA64618 airfoil under open ice conditions and the absolute error from experimental values for the airfoil under open ice conditions.
Detailed Description
The invention will be further described with reference to the following examples and figures:
the invention relates to a neural network prediction method for the aerodynamic performance of a wing section of a wind turbine under the open ice condition, which is based on the following design idea:
1. introducing an updating mode of modifying the center of the non-optimal particle potential well through social learning, updating and determining the position of the optimal particle by using Levy flight combined with a greedy algorithm, so as to improve the population diversity and the convergence speed of the quantum particle group algorithm;
2. and (3) utilizing the selection process of the test error interference global optimum particles, and applying an SLLQPSO algorithm in cooperation with a binary particle swarm and an error back propagation algorithm to solve an optimization model of a three-layer forward neural network structure and parameters with a weight connecting switch so as to improve the generalization capability of the neural network in the optimization process.
The invention carries out innovative design from the aspects of updating mode of non-optimal particle potential well center, updating and determining optimal particle position, improving neural network generalization ability and the like:
1. improvement of quantum particle swarm algorithm
In view of the problems that the convergence speed of the quantum particle swarm algorithm is low, the later population diversity is reduced, the generalization capability of a neural network is reduced due to the fact that connection redundancy among neurons is over-trained, and the like, the SLLQPSO algorithm which introduces social learning correction non-optimal particle potential well center updating mode and utilizes Levy flight and greedy algorithm to update and determine the optimal particle position is provided.
2. Neural network prediction of wind turbine airfoil aerodynamic performance under open ice condition
Establishing an optimization model of a three-layer forward neural network structure with a weight connecting switch and parameters, searching an optimal value of the parameters of the connecting switch between the neurons by using a binary particle swarm algorithm, and searching a connection weight from an input layer to a hidden layer, a hidden layer neuron threshold value, a connection weight from the hidden layer to an output layer and an optimal value of an output layer neuron threshold value by using an SLLQPSO algorithm; in order to further improve the precision of the neural network, the optimized weight and threshold are used as initial parameters, the network is retrained again by adopting an error back propagation algorithm with strong local search capability, and then the aerodynamic performance prediction neural network (SLLQPSO-BPNN) of the wind turbine airfoil under the open ice condition is constructed.
The invention discloses a neural network prediction method for the aerodynamic performance of a wing section of a wind turbine under an open ice condition, which comprises the following steps of:
step (1), constructing a neural network optimization model: adopting a display space decomposition mode to decompose the optimization design of the neural network structure and parameters into three optimization problems of an inter-neuron connection switch, a connection weight from an input layer to a hidden layer and a hidden layer neuron threshold value, and a connection weight from the hidden layer to an output layer and an output layer neuron threshold value, and establishing an optimization model shown in figure 1;
step (2), quantum particle swarm algorithm improvement: when the non-optimal particles are learnt, the center of the potential well of the particles is directly learnt to the center of the potential well of the target particles and the population average level, and when the particles are not learnt, the center of the original potential well of the particles is kept unchanged, and a learning mechanism is introduced to update the center p 'of the potential well of the g-th dimension of the h-th non-optimal particle'h,gThe formula (t) is:
in the formula, pR,g(t) is the center of the potential well of the sample particle;is the center of the average potential well of the population,pa,g(t) is the center of the potential well in the g dimension of the a-th particle; r is1(t),r2(t),r3(t)∈U(0,1);r2(t)(pR,g(t)-ph,g(t)) is a part of learning to the sample particles;is part of learning to the social average level; epsilon is a social influence factor, epsilon is xi G/B, xi is a proportionality coefficient, and 0.01 is taken; phThe update probability of the h-th non-optimal particle potential well center.
Calculating population average potential well center by utilizing potential well center containing more particle information and obtained after social learning is introducedAnd the distance between the particles is adopted to control the length of a potential well, and the position X of the g dimension of the h non-optimal particle in the next iteration after descending order arrangementh,g(t +1) is:
in the formula, Xh,g(t) is the position of the particle h at the tth iteration; u. ofh,j(t) is in the interval [0, 1 ]]Random numbers are uniformly distributed throughout the course of administration.
During t iterations, if the position of the H-th particle after descending order arrangement is the global optimal position, the H-th particle must be the individual optimal position, so that the updated information of the H position of the particle is less, and a local optimal solution is trapped; in order to make the particles escape from the local part and enlarge the search range, the position of the particles H is updated by adopting the Levy flight with the characteristics of short-distance frequent search and long-distance minority search, and the final position X of the optimal particles is determined by utilizing a greedy algorithmH(t+1):
In the formula (f)fitnessIs a function of the fitness value;carrying out the position with the minimum fitness value when the particle H flies in the Levy mode, wherein q is the flying time of the particle H, q belongs to {0, 1, 2.. multidot.L }, and L is the maximum flying time; gbest (t) is a global optimal position of the population;
introducing a social learning and correction non-optimal particle potential well center updating mode, updating the position of the optimal particle by using Levy flight and a greedy algorithm, and providing an improved quantum particle swarm (SLLQPSO) algorithm, wherein the basic flow is shown in FIG. 2;
step (3), solving a neural network prediction model: searching an optimal value of a parameter of a connection switch between neurons by using a binary particle swarm algorithm, and searching a connection weight from an input layer to a hidden layer, a hidden layer neuron threshold value, a connection weight from the hidden layer to an output layer and an optimal value of an output layer neuron threshold value by using an SLLQPSO algorithm; in order to further improve the precision of the neural network, the optimized weight and threshold are used as initial parameters, and an error back propagation algorithm with strong local search capability is adopted to train the network again;
and (4) realizing the neural network (SLLQPSO-BPNN) prediction method of the aerodynamic performance of the wind turbine airfoil under the open ice condition shown in the figure 3 through the steps (1) to (3).
Nothing in this specification is said to apply to the prior art.
Example (b):
1. the low-speed airfoil NACA64618 of the American national aviation council is selected as a research object, and the NACA64618 is an airfoil with the maximum relative thickness of 18%, the maximum relative camber of 20% at the chord length and the simple camber line.
2. Neural network prediction of wind turbine airfoil aerodynamic performance under open ice condition
Establishing a connection switch population X1, a connection weight from an input layer to a hidden layer and a hidden layer neuron threshold populationX2, and a hidden layer-to-output layer connection weight and an output layer neuron threshold population X3, and each population calculates a fitness value by using global optimal particle information of other populations. To prevent the generalization ability of the neural network from being reduced due to over-training, a comprehensive error E is selectedsThe smallest particle is the globally optimal particle, EsThe calculation formula of (2) is as follows:
in the formula, EtIn order to train the error, the user can,Ecin order to test for errors in the test,N1,N2the capacities of the training and test samples, respectively.
Predicting NACA64618 wing profile at Re 2 × 10 by respectively adopting SLLQPSO-BPNN and error back propagation neural network6The results of the rise and the resistance coefficients are shown in fig. 4a and 4b, and the average absolute error, the linear correlation coefficient and the average relative error of the predicted values and the experimental values of the two neural networks are calculated. Basic parameters of SLLQPSO-BPNN: the number of hidden layer neurons is 15; in the binary particle swarm algorithm, the population size is 50, and a learning factor c1=c22.05, the weight coefficient omega is controlled by adopting a linear decreasing strategy,wherein ω ismaxAnd ωminThe maximum and minimum weight coefficients, ω, respectivelymax=0.9,ωmin0.4, T and TmaxRespectively the current and maximum iteration times; in the SLLQPSO algorithm, the population scale is 50, the contraction-expansion coefficient is 0.05, the proportionality coefficient is 0.01, and the maximum Levy flight time is 100; in the error back propagation algorithm, the learning rate is 0.003. Hidden layer neuron number and SLLQPSO-The BPNN network is consistent, and the Levenberg-Marquardt is adopted as the training algorithm.
Compared with an error back propagation neural network, the SLLQPSO-BPNN network has the advantages that the prediction result of the lift and resistance coefficients of the NACA64618 airfoil profile is closer to an experimental value except for individual attack angles, the prediction error and the error fluctuation amplitude are obviously reduced, and the prediction precision is remarkably improved; the average absolute error and the average relative error of the SLLQPSO-BPNN neural network are both smaller than that of the error back propagation network, and the average relative error is smaller than 4%; the predicted values of the two networks and the experimental result are in positive correlation, and the linear correlation coefficient of the SLLQPSO-BPNN network is closer to 1, so that the prediction effect of the SLLQPSO-BPNN network is more ideal and effective, and a reliable tool is provided for the pneumatic performance analysis of the wind turbine airfoil under the open ice condition.
The embodiments of the present invention have been described in detail, but the description is only for the preferred embodiments of the present invention and should not be construed as limiting the scope of the present invention. All equivalent changes and modifications made within the scope of the present invention should be covered by the present patent.
Claims (3)
1. A neural network prediction method for the aerodynamic performance of a wing section of a wind turbine under the open ice condition is characterized by comprising the following steps: the method comprises the following steps:
step (1), constructing a neural network optimization model: adopting a display space decomposition mode to decompose the optimization design of the neural network structure and parameters into three optimization problems of an inter-neuron connection switch, a connection weight from an input layer to a hidden layer and a hidden layer neuron threshold value, and a connection weight from the hidden layer to an output layer and an output layer neuron threshold value, and establishing a corresponding optimization model;
step (2), quantum particle swarm algorithm improvement: when the non-optimal particles are learnt, the center of the potential well of the particles is directly learnt to the center of the potential well of the target particles and the population average level, and when the particles are not learnt, the center of the original potential well of the particles is kept unchanged, and a learning mechanism is introduced to update the center p 'of the potential well of the g-th dimension of the h-th non-optimal particle'h,gThe formula (t) is:
in the formula, pR,g(t) is the center of the potential well of the sample particle;is the center of the average potential well of the population,pa,g(t) is the center of the potential well in the g dimension of the a-th particle; r is1(t),r2(t),r3(t)∈U(0,1);r2(t)(pR,g(t)-ph,g(t)) is a part of learning to the sample particles;is part of learning to the social average level; epsilon is a social influence factor, epsilon is xi G/B, xi is a proportionality coefficient, and 0.01 is taken; phThe update probability of the h-th non-optimal particle potential well center.
Calculating population average potential well center by utilizing potential well center containing more particle information and obtained after social learning is introducedAnd the distance between the particles is adopted to control the length of a potential well, and the position X of the g dimension of the h non-optimal particle in the next iteration after descending order arrangementh,g(t +1) is:
in the formula, Xh,g(t) is the position of the particle h at the tth iteration; u. ofh,j(t) is in the interval [0, 1 ]]Random numbers are uniformly distributed throughout the course of administration.
In t iterations, if the position of the H-th particle after descending order is the global optimum bitIf the particle H position is the local optimal position, the particle H position is required to be the individual optimal position, so that the updated information of the particle H position is less, and a local optimal solution is trapped; in order to make the particles escape from the local part and enlarge the search range, the position of the particles H is updated by adopting the Levy flight with the characteristics of short-distance frequent search and long-distance minority search, and the final position X of the optimal particles is determined by utilizing a greedy algorithmH(t+1):
In the formula (f)fitnessIs a function of the fitness value;carrying out the position with the minimum fitness value when the particle H flies in the Levy mode, wherein q is the flying time of the particle H, q belongs to {0, 1, 2.. multidot.L }, and L is the maximum flying time; gbest (t) is a global optimal position of the population;
introducing a potential well center updating mode for correcting the non-optimal particles through social learning, updating the position of the optimal particles by using Levy flight and a greedy algorithm, and providing an improved quantum particle swarm (SLLQPSO) algorithm;
step (3), solving a neural network prediction model: searching an optimal value of a parameter of a connection switch between neurons by using a binary particle swarm algorithm, and searching a connection weight from an input layer to a hidden layer, a hidden layer neuron threshold value, a connection weight from the hidden layer to an output layer and an optimal value of an output layer neuron threshold value by using an SLLQPSO algorithm; in order to further improve the precision of the neural network, the optimized weight and threshold are used as initial parameters, and an error back propagation algorithm with strong local search capability is adopted to train the network again;
and (4) realizing a neural network (SLLQPSO-BPNN) prediction method for the aerodynamic performance of the wind turbine airfoil under the open ice condition through the steps (1) to (3).
2. The neural network prediction method for the aerodynamic performance of a wind turbine airfoil under open ice conditions according to claim 1, characterized in that: after an optimization model of a three-layer forward neural network structure with a weight value connecting switch and parameters is established in the step (1) and a non-optimal particle potential well center updating mode of a social learning correction quantum particle group algorithm and a Levy flight and greedy algorithm are combined to update the position of the optimal particle in the step (2), a selection process of the global optimal particle is interfered by a test error, the optimization model is solved by cooperating with a binary particle swarm and an error back propagation algorithm, and then the aerodynamic performance of the wind turbine airfoil under the open ice condition is predicted.
3. A neural network prediction method of the aerodynamic performance of a wind turbine airfoil under open ice conditions according to claim 1 or 2, characterized in that: the prediction values of the SLLQPSO-BPNN of the NACA64618 airfoil and the error back propagation neural network and the experimental values are in positive correlation, and the linear correlation coefficient of the SLLQPSO-BPNN network is closer to 1, so that the prediction effect of the SLLQPSO-BPNN network is more ideal and effective.
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