CN105243259A

CN105243259A - Extreme learning machine based rapid prediction method for fluctuating wind speed

Info

Publication number: CN105243259A
Application number: CN201510559076.2A
Authority: CN
Inventors: 李春祥; 迟恩楠; 曹黎媛
Original assignee: SHANGHAI UNIVERSITY
Current assignee: SHANGHAI UNIVERSITY
Priority date: 2015-09-02
Filing date: 2015-09-02
Publication date: 2016-01-13

Abstract

The present invention provides a fast prediction method of fluctuating wind speed based on extreme learning machine, which comprises the following steps: first step, using ARMA model to simulate and generate fluctuating wind speed samples of vertical space points; second step, calculating hidden layer output matrix and hidden nodes and The connection weight vector of the output neuron; the third step is to use the hidden layer output matrix calculated in the second step and the connection weight vector between the hidden node and the output neuron to establish a regression mathematical model; the fourth step: use the test sample and the limit Compare the fluctuating wind speed results predicted by the learning machine and PSO-MK-LSSVM, and calculate the average absolute error, root mean square error and correlation coefficient of the predicted wind speed and the actual wind speed at the same time, evaluate the effectiveness of the present invention, and use the particle swarm optimization PSO to optimize the combined kernel at the same time The least squares support vector machine of the same fluctuating wind speed is predicted, and the performance of the two methods is analyzed and compared. The invention has the advantages of fast learning speed and good generalization performance.

Description

Rapid prediction method of fluctuating wind speed based on extreme learning machine

技术领域technical field

本发明涉及一种采用单隐层前馈神经网络学习算法对单点脉动风速进行快速预测，改进传统数据驱动技术预测需要参数寻优和模型选择导致算法时间长的缺陷，具体的说是一种基于极限学习机(ExtremeLearningMachine，ELM)的脉动风速快速预测方法。The invention relates to a single hidden layer feed-forward neural network learning algorithm for rapid prediction of fluctuating wind speed at a single point, which improves the traditional data-driven technology prediction that requires parameter optimization and model selection to cause long algorithm time defects, specifically a kind of A fast prediction method of fluctuating wind speed based on extreme learning machine (Extreme Learning Machine, ELM).

背景技术Background technique

研究风荷载时，通常把风处理为在一定时距内不随时间变化的平均风速和随时间随机变化的脉动风速两部分，平均风速产生结构静态响应，而脉动风速产生动态响应。风作用在高层结构时，其正负风压对结构形成风荷载，同时钝体绕流还会引起结构抖振、旋涡脱落引起的横向振动和扭转振动。极端风荷载作用下产生的抖振和颤振会引起建筑物倒塌或严重破坏；动态位移超限易引起墙体开裂和附属构件破坏；大幅振动会造成居住和生活的不舒适；脉动风频繁作用也会使外墙面构件和附属物产生疲劳破坏。掌握完整的脉动风速时程资料对于结构设计、安全具有重要意义。When studying wind loads, the wind is usually treated as an average wind speed that does not change with time within a certain time interval and a fluctuating wind speed that varies randomly with time. The average wind speed produces a static response of the structure, while the fluctuating wind speed produces a dynamic response. When the wind acts on a high-rise structure, its positive and negative wind pressure will form a wind load on the structure. At the same time, the flow around the blunt body will also cause structural buffeting, lateral vibration and torsional vibration caused by vortex shedding. Buffeting and chattering under extreme wind loads can cause building collapse or serious damage; dynamic displacement exceeding the limit can easily cause wall cracking and damage to attached components; large vibrations can cause discomfort in living and living; frequent pulsating winds It will also cause fatigue damage to exterior wall components and appendages. It is of great significance to master the complete fluctuating wind speed time history data for structural design and safety.

基于数据驱动的样本学习训练为脉动风速速测提供可行的方法。目前脉动风速建模预测的方法主要有时间序列分析法、人工神经网络、支持向量机等方法。然而这些方法都存在着理论或应用上的不足，如时问序列模型高阶模型参数估计难度大、低阶模型预测精度低；支持向量机虽然通过核函数定义的非线性变换将输入空间变换到一个高维空间，在这个高维空间中寻找输入变量和输出变量之间的一种非线性关系，解决了“维数灾难”问题，但核函数的选择和参数优化决定了模型的特性；人工神经网络模型应用较为成熟，作为一种数据驱动算法，具有逼近任意非线性函数的能力，可以映射出序列问复杂的非线性关系，从而在风速和风功率预测中得到广泛应用，然而传统的人工神经网络方法存在一些问题，如算法运行时问长，容易陷入局部极小等。Data-driven sample learning training provides a feasible method for fluctuating wind speed measurement. At present, the methods of fluctuating wind speed modeling and prediction mainly include time series analysis, artificial neural network, support vector machine and other methods. However, these methods have theoretical or application deficiencies, such as the difficulty in estimating the high-order model parameters of the time sequence model, and the low prediction accuracy of the low-order model; although the support vector machine transforms the input space into A high-dimensional space, looking for a nonlinear relationship between input variables and output variables in this high-dimensional space, solves the "curse of dimensionality" problem, but the selection of kernel functions and parameter optimization determine the characteristics of the model; artificial The application of the neural network model is relatively mature. As a data-driven algorithm, it has the ability to approximate any nonlinear function, and can map complex nonlinear relationships between sequences, so it has been widely used in wind speed and wind power prediction. However, the traditional artificial neural network There are some problems in the network method, such as long running time of the algorithm, easy to fall into local minimum and so on.

2004年由南洋理工大学黄广斌副教授提出极限学习机是一种简单易用、有效的单隐层前馈神经网络学习算法。该算法在随机选择输入层权值和隐层神经元的前提下，仅通过一步计算即可求得网络输出权值，同传统神经网络相比，极限学习机极大地提高了网络的泛化能力和学习速度，具有较强的非线性拟合能力。极限学习机只需要设置网络的隐层节点个数，在算法执行过程中不需要调整网络的输入权值以及隐元的偏置，并且产生唯一的最优解，因此具有学习速度快且泛化性能好的优点。In 2004, associate professor Huang Guangbin of Nanyang Technological University proposed that the extreme learning machine is an easy-to-use and effective single-hidden-layer feed-forward neural network learning algorithm. Under the premise of randomly selecting the input layer weights and hidden layer neurons, the algorithm can obtain the network output weights only through one-step calculation. Compared with the traditional neural network, the extreme learning machine greatly improves the generalization ability of the network. And learning speed, has strong nonlinear fitting ability. The extreme learning machine only needs to set the number of hidden layer nodes of the network, and does not need to adjust the input weights of the network and the bias of the hidden elements during the algorithm execution process, and produces the only optimal solution, so it has fast learning speed and generalization The advantages of good performance.

发明内容Contents of the invention

本发明所要解决的技术问题是提供一种基于极限学习机的脉动风速快速预测方法，解决传统的传统数据驱动技术预测模耗时严重等问题，通过数值模拟出脉动风速样本与新型数据驱动技术ELM结合，利用数值模拟为数据驱动模拟提供样本数据，再通过数据驱动技术预测所需后续时间的脉动风速，为抗风设计提供所需的完整风速时程曲线的预测方法，节约了大量的时间成本，并计算实际风速与预测风速的平均绝对误差(MAE)、均方根误差(RMSE)以及相关系数(R)评价本方法的精度。The technical problem to be solved by the present invention is to provide a fast prediction method of pulsating wind speed based on extreme learning machine, which solves the problem of serious time-consuming prediction model of traditional data-driven technology, and simulates the pulsating wind speed samples through numerical simulation and the new data-driven technology ELM In combination, use numerical simulation to provide sample data for data-driven simulation, and then use data-driven technology to predict the fluctuating wind speed in the required follow-up time, and provide a prediction method for the complete wind speed time history curve required for wind resistance design, saving a lot of time and cost , and calculate the mean absolute error (MAE), root mean square error (RMSE) and correlation coefficient (R) of actual wind speed and predicted wind speed to evaluate the accuracy of this method.

根据上述发明构思，本发明采用下述技术方案：一种基于极限学习机的脉动风速快速预测方法，其特征在于，其包括以下步骤：According to the above-mentioned inventive concept, the present invention adopts the following technical scheme: a method for fast prediction of fluctuating wind speed based on extreme learning machine, characterized in that it comprises the following steps:

第一步，利用ARMA模型模拟生成垂直空间点脉动风速样本，将每一个空间点的脉动风速样本分为训练集、测试集两部分，对其分别进行归一化处理，取嵌入维数k＝10对进行样本数据进行相空间重构；In the first step, the ARMA model is used to simulate and generate fluctuating wind speed samples of vertical spatial points, and the fluctuating wind speed samples of each spatial point are divided into two parts: training set and test set, which are normalized respectively, and the embedding dimension k = 10 Perform phase space reconstruction on the sample data;

第二步，给定训练样本N＝{(x_i,t_i)|x_i∈Rⁿ,t_i∈Rⁿ,i＝1,…,N}；激励函数g(x)和隐含层节点数M，由于激活函数可以无穷可微，只需要在训练之前设置适当的隐含层节点数，为输入权和隐含层偏差进行随机赋值，建立单隐层前馈神经网络学习数学模型，计算隐藏层输出矩阵和隐藏节点与输出神经元的连接权向量；In the second step, given training samples N={( _xi ,t _i )| _xi ∈R ⁿ ,t _i ∈R ⁿ ,i=1,…,N}; activation function g(x) and hidden layer The number of nodes is M. Since the activation function can be infinitely differentiable, it is only necessary to set an appropriate number of nodes in the hidden layer before training, randomly assign values to the input weight and hidden layer deviation, and establish a single hidden layer feedforward neural network learning mathematical model. Calculate the hidden layer output matrix and the connection weight vector between hidden nodes and output neurons;

第三步，利用第二步中计算的隐藏层输出矩阵和隐藏节点与输出神经元的连接权向量建立回归数学模型，利用该模型对脉动风速测试集样本进行预测；The third step is to use the hidden layer output matrix calculated in the second step and the connection weight vector between hidden nodes and output neurons to establish a regression mathematical model, and use this model to predict the fluctuating wind speed test set samples;

第四步：将测试样本与分别利用极限学习机和PSO-MK-LSSVM预测的脉动风速结果对比，同时计算预测风速与实际风速的平均绝对误差、均方根误差以及相关系数，评价本发明的有效性，同时利用粒子群PSO优化组合核的最小二乘支持向量机对同样脉动风速进行预测，分析比较两种方法的性能。Step 4: compare the test sample with the fluctuating wind speed results predicted by the extreme learning machine and PSO-MK-LSSVM respectively, and calculate the average absolute error, root mean square error and correlation coefficient of the predicted wind speed and the actual wind speed at the same time, and evaluate the method of the present invention At the same time, the least squares support vector machine of the particle swarm PSO optimization combined kernel is used to predict the same fluctuating wind speed, and the performance of the two methods is analyzed and compared.

优选地，所述第一步中ARMA模型模拟m维脉动风速表示为下式：Preferably, in the first step, the ARMA model simulates the m-dimensional fluctuating wind speed and is expressed as the following formula:

$U u ((t t)) = = {Σ Σ}_{i i = = 11}^{p p} {A A}_{i i} X x ((t t - - i i Δ Δ t t)) + + {Σ Σ}_{j j = = 00}^{q q} {B B}_{j j} X x ((t t - - i i Δ Δ t t))$

式中，U(t)为脉动风速；A_i,B_j分别是m×m阶AR和MA模型的系数矩阵；X(t)为m×1阶正态分布白噪声序列；P为自回归阶数、q为滑动回归阶数，t为时间。where U(t) is fluctuating wind speed; A _i and B _j are the coefficient matrices of m×m order AR and MA models respectively; X(t) is m×1 order normal distribution white noise sequence; P is autoregressive The order, q is the sliding regression order, and t is the time.

优选地，所述第二步中单隐层前馈神经网络学习数学模型，对于N个不同样本(x_i,t_i)，隐含层节点数目是M，激励函数为g(x)，其中x_i＝[x_i1,x_i2,…,x_in]^T∈Rⁿ，t_i＝[t_i1,t_i2,…,t_im]^T∈R^m，其单隐层前馈神经网络学习数学模型SLFN的数学模型为：Preferably, in the second step, the single hidden layer feedforward neural network learns a mathematical model, for N different samples ( _xi , t _i ), the number of hidden layer nodes is M, and the activation function is g(x), where x _i ＝[x _i1 ,x _i2 ,…,x _in ] ^T ∈ R ⁿ , t _i ＝[t _i1 ,t _i2 ,…,t _im ] ^T ∈ R ^m , its single hidden layer feedforward neural network learning mathematics The mathematical model of the model SLFN is:

${Σ Σ}_{i i = = 11}^{M m} {β β}_{i i} {g g}_{i i} (({x x}_{j j})) = = {Σ Σ}_{i i = = 11}^{M m} {β β}_{i i} g g (({a a}_{i i} \cdot &Center Dot; {x x}_{j j} + + {b b}_{i i})) = = {t t}_{j j},, j j = = 11,, ... ...,, N N$

式中，a_i＝[a_i1,a_i2,…,a_in]^T是连接第i个隐含层结点的输入权值；b_i是第i个隐含层结点的偏差；β_i＝[a_i1,a_i2,…,a_im]^T是连接第i个隐含层结点的输出权值；激励函数g(x)可以是“Sigmoid”、“Sine”等；t_j为第j个节点的输出值。In the formula, a _i ＝[a _i1 ,a _i2 ,…,a _in ] ^T is the input weight connecting the i-th hidden layer node; b _i is the bias of the i-th hidden layer node; β _i ＝[a _i1 ,a _i2 ,…,a _im ] ^T is the output weight connected to the i-th hidden layer node; the activation function g(x) can be "Sigmoid", "Sine" and so on; t _j is the The output value of j nodes.

优选地，所述第三步中，设置隐层结点数M＝20、激励函数g(x)为“Sigmoid”，计算的隐层输出矩阵和隐层结点与输出神经元的连接权向量，建立回归数学模型Hβ＝T，对测试集进行预测，式中T为输出节点的输出矩阵。Preferably, in the third step, set the number of hidden layer nodes M=20, the activation function g(x) to be "Sigmoid", the calculated hidden layer output matrix and the connection weight vector of hidden layer nodes and output neurons, Establish a regression mathematical model Hβ=T to predict the test set, where T is the output matrix of the output node.

本发明极限学习机的脉动风速快速预测方法具有如下优点：相比于传统的神经网络算法，ELM在训练的过程中不需要调整输入权值和偏置，只需根据相应算法来调整输出权值β，便可获得一个全局最优解；相对于PSO-MK-LSSVM，其参数选择较为容易，训练速度显著提升，且不会陷入局部最优，在时间消耗很少的前提下能达到很好的准确率。The rapid prediction method of the pulsating wind speed of the extreme learning machine of the present invention has the following advantages: Compared with the traditional neural network algorithm, the ELM does not need to adjust the input weight and bias in the training process, and only needs to adjust the output weight according to the corresponding algorithm β, a global optimal solution can be obtained; compared with PSO-MK-LSSVM, its parameter selection is easier, the training speed is significantly improved, and it will not fall into a local optimal solution, and it can achieve a very good solution with little time consumption. the accuracy rate.

附图说明Description of drawings

图1是沿地面垂直方向20米处脉动风速模拟样本示意图。Figure 1 is a schematic diagram of a simulated sample of fluctuating wind speed at 20 meters along the vertical direction of the ground.

图2是沿地面垂直方向50米处脉动风速模拟样本示意图。Figure 2 is a schematic diagram of a simulated sample of fluctuating wind speed at 50 meters along the vertical direction of the ground.

图3是20米ELM与PSO-LSSVM预测风速与模拟风速对比示意图。Figure 3 is a schematic diagram of the comparison between the predicted wind speed and the simulated wind speed of the 20-meter ELM and PSO-LSSVM.

图4是20米ELM与PSO-LSSVM预测风速与模拟风速自相关函数对比示意图。Figure 4 is a schematic diagram of the comparison of the autocorrelation function between the predicted wind speed and the simulated wind speed of the 20-meter ELM and PSO-LSSVM.

图5是50米ELM与PSO-LSSVM预测风速与模拟风速对比示意图。Figure 5 is a schematic diagram of the comparison between the predicted wind speed and the simulated wind speed of the 50-meter ELM and PSO-LSSVM.

图6是50米ELM与PSO-LSSVM预测风速与模拟风速自相关函数对比示意图。Figure 6 is a schematic diagram of the comparison of the autocorrelation function between the predicted wind speed and the simulated wind speed of the 50-meter ELM and PSO-LSSVM.

具体实施方式detailed description

下面结合附图给出本发明较佳实施例，以详细说明本发明的技术方案。The preferred embodiments of the present invention are given below in conjunction with the accompanying drawings to describe the technical solution of the present invention in detail.

本发明极限学习机的脉动风速快速预测方法包括以下步骤：The pulsating wind speed fast prediction method of the extreme learning machine of the present invention comprises the following steps:

第一步，利用ARMA(Auto-RegressiveandMovingAverageModel，自回归滑动平均)模型模拟生成垂直空间点脉动风速样本，将每一个空间点的脉动风速样本分为训练集、测试集两部分，对其分别进行归一化处理，取嵌入维数k＝10对进行样本数据进行相空间重构；确定单点脉动风速样本的ARMA模型各参数，ARMA模型的自回归阶数p＝4，滑动回归阶数q＝1。模拟某100米的超高层建筑，沿高度方向取每隔10米的点作为各模拟风速点。其他相关参数见表1：In the first step, the ARMA (Auto-Regressive and Moving Average Model) model is used to simulate and generate fluctuating wind speed samples at vertical spatial points, and the fluctuating wind speed samples at each spatial point are divided into two parts: the training set and the testing set, and normalized respectively. Normalization processing, taking the embedding dimension k=10 to carry out phase space reconstruction of the sample data; determining the parameters of the ARMA model of the single-point fluctuating wind speed sample, the autoregressive order of the ARMA model p=4, and the sliding regression order q= 1. To simulate a 100-meter super high-rise building, take points every 10 meters along the height direction as the simulated wind speed points. Other relevant parameters are shown in Table 1:

表1相关模拟参数表Table 1 Related simulation parameter table

模拟功率谱采用Kaimal谱，只考虑高度方向的空间相关性。模拟生成20、50米脉动风速样本分别见图1、图2。The simulated power spectrum adopts Kaimal spectrum, and only considers the spatial correlation in the height direction. The simulated fluctuating wind speed samples at 20 and 50 meters are shown in Figure 1 and Figure 2, respectively.

第一步中，ARMA模型模拟m维脉动风速表示为下式(1)：In the first step, the ARMA model simulates the m-dimensional fluctuating wind speed expressed as the following formula (1):

$U u ((t t)) = = {Σ Σ}_{i i = = 11}^{p p} {A A}_{i i} X x ((t t - - i i Δ Δ t t)) + + {Σ Σ}_{j j = = 00}^{q q} {B B}_{j j} X x ((t t - - i i Δ Δ t t)) ... ... ((11))$

将得到的脉动风速按式(2)进行归一化处理：The obtained fluctuating wind speed is normalized according to formula (2):

${y the y}_{i i}^{* *} = = \frac{{y the y}_{i i} - - {y the y}_{m m a a x x}}{{y the y}_{m m a a x x} - - {y the y}_{m m i i n no}} ... ... ((22))$

式中，为归一化后脉动风速，y_i为实际脉动风速样本，y_max为实际脉动风速最大值，y_min实际脉动风速最小值。In the formula, is the fluctuating wind speed after normalization, y _i is the actual fluctuating wind speed sample, y _max is the maximum value of the actual fluctuating wind speed, and y _min is the minimum value of the actual fluctuating wind speed.

第二步，给定训练样本N＝{(x_i,t_i)|x_i∈Rⁿ,t_i∈Rⁿ,i＝1,…,N}；激励函数g(x)和隐含层节点数M，由于激活函数可以无穷可微，只需要在训练之前设置适当的隐含层节点数，为输入权和隐含层偏差进行随机赋值，建立单隐层前馈神经网络学习数学模型，计算隐藏层输出矩阵和隐藏节点与输出神经元的连接权向量；根据极限学习机ELM原理，激励函数为“Sigmoid”和隐含层结点数为M＝20，给定训练样本N＝{(x_i,t_i)|x_i∈Rⁿ,t_i∈Rⁿ,i＝1,…,N}，得到ELM的算法为：In the second step, given training samples N={( _xi ,t _i )| _xi ∈R ⁿ ,t _i ∈R ⁿ ,i=1,…,N}; activation function g(x) and hidden layer The number of nodes is M. Since the activation function can be infinitely differentiable, it is only necessary to set an appropriate number of nodes in the hidden layer before training, randomly assign values to the input weight and hidden layer deviation, and establish a single hidden layer feedforward neural network learning mathematical model. Calculate the hidden layer output matrix and the connection weight vector between hidden nodes and output neurons; according to the principle of extreme learning machine ELM, the activation function is "Sigmoid" and the number of hidden layer nodes is M=20, given training samples N={(x _i ,t _i )| _xi ∈R ⁿ ,t _i ∈R ⁿ ,i=1,…,N}, the algorithm to get ELM is:

(1)随机选取权值a_i，偏置b_i(i＝1,…,M)；(1) randomly select weight a _i , bias b _i (i=1,...,M);

(2)计算隐层输出矩阵 $H = [\begin{matrix} g (a_{1} \cdot x_{1} + b_{1}) & ... & g (a_{N} \cdot x_{1} + b_{M}) \\ ... & ... & ... \\ g (a_{1} \cdot x_{N} + b_{1}) & ... & g (a_{N} \cdot x_{N} + b_{M}) \end{matrix}];$ (2) Calculate the hidden layer output matrix $h = [\begin{matrix} g (a_{1} &Center Dot; x_{1} + b_{1}) & ... & g (a_{N} \cdot x_{1} + b_{m}) \\ ... & ... & ... \\ g (a_{1} \cdot x_{N} + b_{1}) & ... & g (a_{N} &Center Dot; x_{N} + b_{m}) \end{matrix}];$

(3)计算输出权重β：β＝H²T。(3) Calculate the output weight β: β=H ² T.

第二步中，单隐层前馈神经网络学习数学模型建立：In the second step, the single hidden layer feedforward neural network learning mathematical model is established:

对于N个不同样本(x_i,t_i)，隐含层节点数目是M，激励函数为g(x)，其中x_i＝[x_i1,x_i2,…,x_in]^T∈Rⁿ，t_i＝[t_i1,t_i2,…,t_im]^T∈R^m，其单隐层前馈神经网络学习数学模型SLFN的数学模型为：For N different samples ( _xi ,t _i ), the number of hidden layer nodes is M, and the activation function is g(x), where x _i =[ _xi1 , _xi2 ,…,x _in ] ^T ∈ R ⁿ , t _i ＝[t _i1 ,t _i2 ,…,t _im ] ^T ∈ R ^m , the mathematical model of the single hidden layer feedforward neural network learning mathematical model SLFN is:

${Σ Σ}_{i i = = 11}^{M m} {β β}_{i i} {g g}_{i i} (({x x}_{j j})) = = {Σ Σ}_{i i = = 11}^{M m} {β β}_{i i} g g (({a a}_{i i} \cdot \cdot {x x}_{j j} + + {b b}_{i i})) = = {t t}_{j j},, j j = = 11,, ... ...,, N N ... ... ((33))$

网络的训练相当于零误差逼近N个训练样本，即式(3)可以表示为矩阵方程(4)：Network training is equivalent to approaching N training samples with zero error, that is, equation (3) can be expressed as matrix equation (4):

Hβ＝T……………(4)Hβ=T……………(4)

式中， $H = [\begin{matrix} g (a_{1} \cdot x_{1} + b_{1}) & ... & g (a_{N} \cdot x_{1} + b_{M}) \\ ... & ... & ... \\ g (a_{1} \cdot x_{N} + b_{1}) & ... & g (a_{N} \cdot x_{N} + b_{M}) \end{matrix}], β = {[\begin{matrix} β_{1}^{T} \\ ... \\ β_{M}^{T} \end{matrix}]}_{M \times m}, T = {[\begin{matrix} t_{1}^{T} \\ ... \\ t_{N}^{T} \end{matrix}]}_{N \times m} .$ In the formula, $h = [\begin{matrix} g (a_{1} &Center Dot; x_{1} + b_{1}) & ... & g (a_{N} \cdot x_{1} + b_{m}) \\ ... & ... & ... \\ g (a_{1} \cdot x_{N} + b_{1}) & ... & g (a_{N} &Center Dot; x_{N} + b_{m}) \end{matrix}], β = {[\begin{matrix} β_{1}^{T} \\ ... \\ β_{m}^{T} \end{matrix}]}_{m \times m}, T = {[\begin{matrix} t_{1}^{T} \\ ... \\ t_{N}^{T} \end{matrix}]}_{N \times m} .$

H为网络隐层输出矩阵，H的第i列表示第i个隐层结点对应于输入x₁,x₂…,x_N的第i个隐层神经元的输出向量，β表示输出权重。H is the output matrix of the hidden layer of the network, the i-th column of H represents the output vector of the i-th hidden layer neuron corresponding to the input x ₁ , x ₂ ..., x _N of the i-th hidden layer node, and β represents the output weight.

通过定理表明：当隐含层节点的数目足够多的时候，且输入权随机取值，SLFN可以逼近任何连续函数。为了使SLFN具有良好的泛化性能，通常使M<<N。因此，当输入权以随机赋值的方式确定后，所得隐藏层权值可以通过线性方程(5)的最小二乘解解决。The theorem shows that when the number of hidden layer nodes is large enough and the input weight is randomly selected, SLFN can approximate any continuous function. In order to make SLFN have good generalization performance, M<<N is usually made. Therefore, when the input weights are determined by random assignment, the obtained hidden layer weights can be solved by the least squares solution of the linear equation (5).

min_β||Hβ-T||……………(5)min _β ||Hβ-T||……………(5)

其解为如下式(6)：Its solution is the following formula (6):

β＝H²T……………(6)β=H ² T……………(6)

式中，H²为隐层输出矩阵H的Moore-Penrose广义逆矩阵，β表示输出权重。求出β后就完成了极限学习机的训练过程。In the formula, H ² is the Moore-Penrose generalized inverse matrix of the hidden layer output matrix H, and β represents the output weight. After obtaining β, the training process of the extreme learning machine is completed.

第三步，利用第二步中计算的隐藏层输出矩阵和隐藏节点与输出神经元的连接权向量建立回归数学模型，利用该模型对脉动风速测试集样本进行预测。取采样时间1000s的20m、50m脉动风速样本，嵌入维数k＝10，对样本数据进行相空间重构。将1-790s脉动风速作为训练集，791-990s脉动风速作为测试集，用以考察预测精度，将训练集输入进行学习训练得到隐层输出矩阵H和输出权重β，建立ELM回归模型，对791-990s的脉动风速进行泛化预测。第三步中，设置隐层结点数M＝20、激励函数g(x)为“Sigmoid”，计算的隐层输出矩阵和隐层结点与输出神经元的连接权向量，建立回归数学模型Hβ＝T，对测试集进行预测。The third step is to use the hidden layer output matrix calculated in the second step and the connection weight vector between hidden nodes and output neurons to establish a regression mathematical model, and use this model to predict the samples of the fluctuating wind speed test set. Take 20m and 50m fluctuating wind speed samples with a sampling time of 1000s, embedding dimension k=10, and reconstruct the phase space of the sample data. The pulsating wind speed of 1-790s is used as the training set, and the pulsating wind speed of 791-990s is used as the test set to examine the prediction accuracy. The training set is input for learning and training to obtain the hidden layer output matrix H and output weight β, and the ELM regression model is established. For 791 -990s fluctuating wind speed for generalization prediction. In the third step, the number of hidden layer nodes is set to M=20, the activation function g(x) is "Sigmoid", the calculated hidden layer output matrix and the connection weight vector between hidden layer nodes and output neurons, and the regression mathematical model Hβ is established = T, make predictions on the test set.

第四步：将测试样本与分别利用ELM和PSO-MK-LSSVM预测的脉动风速结果对比，同时计算预测风速与实际风速的平均绝对误差(MAE)、均方根误差(RMSE)以及相关系数(R)，评价本发明的有效性，同时利用粒子群PSO优化组合核的最小二乘支持向量机(PSO-MK-LSSVM)对同样脉动风速进行预测，分析比较两种方法的性能。第四步中，将ELM预测结果与实际风速进行对比，包括风速幅值、自相关函数，计算预测结果的误差指标，包括平均绝对误差(MAE)、均方根误差(RMSE)以及相关系数(R)，评价预测方法的精度，同时利用PSO-MK-LSSVM对该风速样本进行预测比较两种数据驱动技术在时间上的消耗程度和精度效果。图3、图4分别为ELM和PSO-MK-LSSVM对20米高度处脉动风速与模拟风速幅值比较、自相关函数比较；图5、图6分别为ELM和PSO-MK-LSSVM对50米高度处脉动风速与模拟风速幅值比较、自相关函数比较；根据图3、图5显示ELM预测风速与模拟风速吻合很好，与采用组合核函数的PSO-MK-LSSVM的效果相当；根据图4、图6显示ELM预测风速与模拟风速的相关性吻合很好，与采用组合核函数的PSO-MK-LSSVM的效果相当。Step 4: Compare the test samples with the fluctuating wind speed results predicted by ELM and PSO-MK-LSSVM respectively, and calculate the mean absolute error (MAE), root mean square error (RMSE) and correlation coefficient ( R), evaluate the effectiveness of the present invention, utilize the least squares support vector machine (PSO-MK-LSSVM) of particle swarm PSO optimization combined kernel simultaneously to predict the same fluctuating wind speed, analyze and compare the performance of two kinds of methods. In the fourth step, the ELM prediction results are compared with the actual wind speed, including wind speed amplitude and autocorrelation function, and the error indicators of the prediction results are calculated, including mean absolute error (MAE), root mean square error (RMSE) and correlation coefficient ( R), evaluate the accuracy of the prediction method, and use PSO-MK-LSSVM to predict the wind speed sample and compare the time consumption and accuracy effect of the two data-driven technologies. Fig. 3 and Fig. 4 respectively show the comparison of fluctuating wind speed and simulated wind speed amplitude and autocorrelation function comparison between ELM and PSO-MK-LSSVM at a height of 20 meters; Fig. 5 and Fig. Comparison of fluctuating wind speed at height with simulated wind speed amplitude and autocorrelation function; Fig. 3 and Fig. 5 show that ELM predicted wind speed is in good agreement with simulated wind speed, which is equivalent to the effect of PSO-MK-LSSVM using combined kernel function; according to Fig. 4. Figure 6 shows that the correlation between ELM predicted wind speed and simulated wind speed is very good, which is equivalent to the effect of PSO-MK-LSSVM using combined kernel functions.

上面的步骤是基于Matlab平台编制的基于极限学习机的脉动风速快速预测方法的计算程序进行分析和验证的，预测结果和时间消耗对比见表2。The above steps are analyzed and verified based on the calculation program of the extreme learning machine-based rapid prediction method of fluctuating wind speed compiled on the Matlab platform. The prediction results and time consumption comparison are shown in Table 2.

表2两方法预测结果指标对比表Table 2 Comparison table of prediction result indicators of the two methods

分析结果显示，ELM预测精度达到组合核函数MK-LSSVM的精度但是时间消耗缺大大降低；由于支持向量机模型需要优化寻参需要反复迭代消耗时间较多，20米处组合核的最小二乘支持向量机所用时间将近是ELM的7倍，50米处组合核的最小二乘支持向量机所用时间是ELM的6倍左右，相对于组合核的最小二乘支持向量机，ELM参数选择较为容易，只需要设定隐含层节点数，使训练速度显著提升，且不会陷入局部最优，在时间消耗很少的前提下能达到很好的准确率，能够为脉动风速预测提供一种准确高效的方法。The analysis results show that the prediction accuracy of ELM reaches the accuracy of the combined kernel function MK-LSSVM, but the time consumption is greatly reduced; because the support vector machine model needs to optimize the parameter search, it takes more time to iterate repeatedly, and the least squares support of the combined kernel at 20 meters The time used by the vector machine is nearly 7 times that of the ELM, and the time used by the least squares support vector machine with the combined kernel at 50 meters is about 6 times that of the ELM. Compared with the least squares support vector machine with the combined kernel, the parameter selection of the ELM is easier. It only needs to set the number of hidden layer nodes, so that the training speed can be significantly improved, and it will not fall into a local optimum. It can achieve a good accuracy rate under the premise of little time consumption, and can provide an accurate and efficient method for fluctuating wind speed prediction. Methods.

本发明的构思如下：通过ARMA数值模拟出脉动风速样本与新型数据驱动技术ELM结合，利用数值模拟为ELM模拟提供样本数据，建立单隐层前馈神经网络学习数学模型，计算隐层输出矩阵和隐层结点与输出神经元的连接权向量，再通过该模型预测所需后续时间的脉动风速。The idea of the present invention is as follows: combine the pulsating wind speed samples through ARMA numerical simulation and the new data-driven technology ELM, use numerical simulation to provide sample data for ELM simulation, establish a single hidden layer feedforward neural network learning mathematical model, and calculate the hidden layer output matrix and The connection weight vector between the hidden layer node and the output neuron, and then predict the fluctuating wind speed in the required subsequent time through the model.

本发明通过ARMA模型数值模拟出脉动风速样本与新型数据驱动技术ELM结合，为抗风设计提供所需的完整风速时程曲线的预测方法。该方法只要设置网络的隐层节点个数，在算法执行过程中不需要调整网络的输入权值以及隐元的偏置，并且产生唯一的最优解，具有学习速度快且泛化性能好的优点。利用该模型对单点脉动风速进行预测，计算预测结果的MAE、RMSE、R评价预测性能，同时与PSO-MK-LSSVM进行比较，突出ELM的优异性能。The invention combines the fluctuating wind speed samples numerically simulated by the ARMA model with the novel data-driven technology ELM to provide a prediction method for the complete wind speed time-history curve required for wind resistance design. This method only needs to set the number of hidden layer nodes of the network, and does not need to adjust the input weights of the network and the bias of hidden elements during the algorithm execution process, and generates a unique optimal solution, which has fast learning speed and good generalization performance. advantage. The model is used to predict the fluctuating wind speed at a single point, and the MAE, RMSE, and R of the prediction results are calculated to evaluate the prediction performance. At the same time, it is compared with PSO-MK-LSSVM to highlight the excellent performance of ELM.

以上所述的具体实施例，对本发明的解决的技术问题、技术方案和有益效果进行了进一步详细说明，所应理解的是，以上所述仅为本发明的具体实施例而已，并不用于限制本发明，凡在本发明的精神和原则之内，所做的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。The specific embodiments described above have further described the technical problems, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above descriptions are only specific embodiments of the present invention and are not intended to limit In the present invention, any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. a method for fast prediction of fluctuating wind speed based on extreme learning machine, is characterized in that, it comprises the following steps:

In the first step, the ARMA model is used to simulate and generate fluctuating wind speed samples of vertical spatial points, and the fluctuating wind speed samples of each spatial point are divided into two parts: training set and test set, which are normalized respectively, and the embedding dimension k = 10 Perform phase space reconstruction on the sample data;

In the second step, given training samples N={( _xi ,t _i )| _xi ∈R ⁿ ,t _i ∈R ⁿ ,i=1,…,N}; activation function g(x) and hidden layer The number of nodes is M. Since the activation function can be infinitely differentiable, it is only necessary to set an appropriate number of nodes in the hidden layer before training, randomly assign values to the input weight and hidden layer deviation, and establish a single hidden layer feedforward neural network learning mathematical model. Calculate the hidden layer output matrix and the connection weight vector between hidden nodes and output neurons;

The third step is to use the hidden layer output matrix calculated in the second step and the connection weight vector between hidden nodes and output neurons to establish a regression mathematical model, and use this model to predict the fluctuating wind speed test set samples;

Step 4: compare the test sample with the fluctuating wind speed results predicted by the extreme learning machine and PSO-MK-LSSVM respectively, and calculate the average absolute error, root mean square error and correlation coefficient of the predicted wind speed and the actual wind speed at the same time, and evaluate the method of the present invention At the same time, the least squares support vector machine of the particle swarm PSO optimization combined kernel is used to predict the same fluctuating wind speed, and the performance of the two methods is analyzed and compared.

2. the rapid prediction method of fluctuating wind speed based on extreme learning machine according to claim 1, is characterized in that, in the first step, ARMA model simulates m-dimensional fluctuating wind speed and is expressed as following formula:

U u ((t t)) = = {Σ Σ}_{i i = = 11}^{p p} {A A}_{i i} X x ((t t - - i i Δ Δ t t)) + + {Σ Σ}_{j j = = 00}^{q q} {B B}_{j j} X x ((t t - - i i Δ Δ t t))

where U(t) is fluctuating wind speed; A _i and B _j are the coefficient matrices of m×m order AR and MA models respectively; X(t) is m×1 order normal distribution white noise sequence; P is autoregressive The order, q is the sliding regression order, and t is the time.

3. the fluctuating wind speed prediction method based on extreme learning machine according to claim 1 is characterized in that, in the second step, single hidden layer feed-forward neural network learning mathematical model, for N different samples ( _xi , t _i ), the number of hidden layer nodes is M, and the activation function is g(x), where x _i =[x _i1 , _xi2 ,…,x _in ] ^T ∈ R ⁿ , t _i =[t _i1 ,t _i2 ,…,t _im ] ^T ∈ R ^m , the mathematical model of its single hidden layer feedforward neural network learning mathematical model SLFN is:

{Σ Σ}_{i i = = 11}^{M m} {β β}_{i i} {g g}_{i i} (({x x}_{j j})) = = {Σ Σ}_{i i = = 11}^{M m} {β β}_{i i} g g (({a a}_{i i} \cdot \cdot {x x}_{j j} + + {b b}_{i i})) = = {t t}_{j j},, j j = = 11,, ... ...,, N N

In the formula, a _i ＝[a _i1 ,a _i2 ,…,a _in ] ^T is the input weight connecting the i-th hidden layer node; b _i is the bias of the i-th hidden layer node; β _i ＝[a _i1 ,a _i2 ,…,a _im ] ^T is the output weight connected to the i-th hidden layer node; the activation function g(x) can be "Sigmoid", "Sine" and so on; t _j is the The output value of j nodes.

4. the pulsating wind speed fast prediction method based on extreme learning machine as claimed in claim 1, is characterized in that, in the 3rd step, hidden layer node number M=20, excitation function g (x) are set as " Sigmoid " , the calculated hidden layer output matrix and the connection weight vector between hidden layer nodes and output neurons, establish a regression mathematical model Hβ=T, and predict the test set.