CN104376214A - Fluctuating wind velocity simulation method based on data driving - Google Patents

Abstract

The invention provides a fluctuating wind velocity simulation method based on a data driving technology. The method comprises the steps that first, a certain number of fluctuating wind velocities, distributed in the height direction, of a super high-rise building are obtained with an AR method through numerical simulation and serve as sample data, then, three technological methods based on data driving including a BP neural network, an SVM and an LS-SVM are used for learning and training the sample data in some height areas with an interpolation method, a regression forecasting model is built, and the fluctuating wind velocities of other height areas are simulated and predicted. The correlation coefficient of a prediction simulation value and a target value (original data), a root-mean-square error and the time needed by simulation are adopted as evaluation indexes. Through comparison between the evaluation indexes, the result shows that the BP neural network is short in consumed time but poor in simulation accuracy; the SVM is high in simulation accuracy but high in time consumption; the LS-SVM is high in accuracy and short in consumed time.

Description

Based on the fluctuating wind speed analogy method of data-driven

Technical field

The present invention relates to a kind of fluctuating wind speed analogy method based on data-driven.

Background technology

Wind load is one of design load causing engineering structure important, and for the flexible structure such as high, large, thin, long, wind load usually plays main even decisive role.Usually keep watch and be divided into average wind and fluctuating wind to be analyzed, wherein fluctuating wind has random character, the charming appearance and behaviour random vibration that it will make structure that the forms such as Along-wind vibration, acrosswind galloping, vortex shedding, torsional divergence vibration and other coupled vibrations may occur.The vibration of these forms not only affects the internal force distribution of structure, the more important thing is, structure will be made to produce dynamic buckling phenomenon, thus greatly reduce the ultimate bearing capacity of structure reality.Therefore, consider in engineering that the dynamic response of wind is extremely important.In existing Wind Engineering, determine that the Main Means of engineering structure wind load has wind tunnel test, field measurement, Numerical Simulations etc. at present.Along with the popularization and application of computing machine and the further investigation of numerical analysis method, the Wind Velocity History curve obtained by method for numerical simulation can meet the arbitrariness of some statistical property, and has more representativeness than physical record, so be widely adopted in Practical Project.Wherein, linear filtering method calculated amount is little, speed fast, is widely deployed in the time series analysis of fluctuating wind.

In recent years, along with developing rapidly of information science technology, method based on data driven technique becomes focus in many fields and developing direction gradually, do not need the mathematical models of consideration system, it is the feature that the describes sample data main criteria as modeling, utilizes these data of controlled system to realize the method for the forecast of system running state, evaluation, scheduling, monitoring, diagnosis, the various desired function such as decision-making and optimization.Wherein, the utilization of neural network and support vector machine is ripe gradually, and embodies respective advantage in the research work in each field.BP neural network is a kind of multilayer feedforward neural network, the principal feature of this network is that signal is to front transfer, error back propagation, to in front transfer, neuronic activation value is propagated to output layer from input layer through each hidden layer, the input response of network is obtained at each neuron of output layer, then according to the direction of the error reduced between network output with actual output sample, input layer is got back to reverses through each hidden layer from output layer, thus progressively revise each connection weights and threshold, BP neural network prediction is exported and constantly approaches desired output.Support vector machine (Support VectorMachines, SVM) is a kind of novel machine learning method that Vapnik grows up on the basis of Statistical Learning Theory, and it concludes the approximate of principle to structural risk minimization.It can avoid the network structure of Artificial Neural Network to be difficult to determine, cross study and owe the problems such as study, can solve again small sample, non-linear, high dimension drawn game portion minimal point etc. preferably and ask.Least square method supporting vector machine (Least Squares Support Vector Machine, LS-SVM) put forward at first by Suykens, it improves the one of SVM, change the inequality constrain in traditional SVM into equality constraint, quadratic programming problem will be solved change into and solve system of linear equations, and change empiric risk into quadratic power by the first power of deviation, avoid insensitive loss function, greatly reduce complexity, in nonlinear prediction method, have more advantage.

In fluctuating wind speed actual measurement and wind tunnel test, the actual measurement of wind speed sample not only needs to arrange measurement mechanism, and increases cost, and traditional numerical simulation technology needs to be simulated by each wind speed simulation point, also very time-consuming.Therefore, obtain unknown wind speed sample by known wind speed sample to be of practical significance very much.By prediction, we can obtain the characteristic information of wind speed sample, save wind speed actual measurement cost, contribute to us like this and more fund of scientific research is applied to the place more needed.

Summary of the invention

The object of the present invention is to provide a kind of fluctuating wind speed analogy method based on data-driven, thus solve the problem such as cost consuming time, means of testing complexity being obtained wind speed sample by actual high wind record, wind tunnel experiment.The wind speed sample that data driven technique simulation obtains can meet the arbitrariness of some statistical property, and has more representativeness than physical record.

For achieving the above object, the present invention adopts following technical proposals:

Based on a fluctuating wind speed analogy method for data-driven, by interpolation study and the training of the fluctuating wind speed sample data of some height, predict the fluctuating wind speed time series of other height; Concrete steps are as follows:

1) select high-rise building, determine the parameter required for numerical simulation fluctuating wind speed: the building height of simulation and each height, the mean wind speed of these 10 meters of height in place, surface roughness values, ground roughness exponent, the simulation related function of simulation wind speed point.

2) fluctuating wind speed time series that the some generated by AR method numerical simulation is distributed along high uniformity, as limited original systolic wind speed sample data; And the analogue value of power spectral density of the wind speed, autocorrelation function and cross correlation function and the degree of agreement of respective objects value are tested, to verify the feasibility based on AR modeling high-rise building Wind Velocity History;

3) BP neural network, SVM, LS-SVM tri-kinds of data driven technique methods are adopted respectively, sample data in some height region is carried out to study and the training of interpolation method, set up forecast model, by the sample data that input interval is two-layer, export the fluctuating wind speed of middle layer corresponding time;

4) adopt the related coefficient of prognosis modelling value and desired value, root-mean-square error and time required for simulating as evaluation index, result is analyzed, acquisition different pieces of information driving method simulation Pros and Cons separately.

Above-mentioned steps 2) in AR model following formula represent:

$v\left(t\right)=-\underset{k=1}{\overset{p}{\mathrm{\Σ}}}{\mathrm{\ψ}}_k\·v(t-\mathrm{k\Δt})+N\left(t\right)---\left(1\right)$

In formula: it is vectorial at the fluctuating wind speed time series of t and t-k Δ t that v (t), v (t-k Δ t) are respectively space M point; P is the exponent number of AR model; Δ t is the time step of simulation wind speed; ψ _kbeing AR model autoregressive coefficient matrix, is M × M rank square formation; N (t)=Ln (t), L is lower triangular matrix, and n (t) is that M ties up average to be 0 variance be 1 separate white noise vector.

Above-mentioned steps 3) in SVM regression model regression problem by introduce loss function solve, according to data sample set T={ (x _i, y _i) ..., (x _l, y _l) (wherein x _ifor input value, y _ifor output valve), find R ⁿon a function f (x), according to this function, a given new input data x, just can judge that the real number corresponding to it exports y; Wherein: x _i∈ R ⁿ, y _i∈ R, i=1,2,3 ..., l; Main contents are as follows:

1) given sample data collection T, considers, with function g (x)=(ω x)+b, to carry out matching, and make the distance between f and g minimum to sample data;

2) according to structural risk minimization, and linear regression is generalized to non-linear regression, structure optimization problem:

$\min [\frac{1}{2}{\left|\right|\mathrm{\ω}\left|\right|}^2+C\underset{i=1}{\overset{l}{\mathrm{\Σ}}}({\mathrm{\ξ}}_i+{\mathrm{\ξ}}_i^{*})]$

$s.t.\left\{\begin{array}{c}{y}_i-(\mathrm{\ω}\·\mathrm{\Φ}\left(x_i\right)+b)\≤\mathrm{\ϵ}{\mathrm{\ξ}}_i\\ (\mathrm{\ω}\·\mathrm{\Φ}\left(x_i\right)+b)-y_i\≤\mathrm{\ϵ}+{\mathrm{\ξ}}_i^{*}\\ {\mathrm{\ξ}}_i,{\mathrm{\ξ}}_i^{*}\≥0,i\mathrm{1,2,3},...,l\end{array}\right.---\left(2\right)$

In formula, ω and b is weights and threshold respectively, and C is penalty factor, realizes the compromise of empiric risk and fiducial range; ξ _i, for relaxation factor; ε is loss function, namely fitting precision; For the dual problem of derived expression (2), utilize Lagrange function to change, optimization aim will be following form:

$\min [\frac{1}{2}\underset{i=1}{\overset{l}{\mathrm{\Σ}}}({\mathrm{\α}}_i^{*}-{\mathrm{\α}}_i)({\mathrm{\α}}_j^{*}-{\mathrm{\α}}_j)(\mathrm{\Φ}\left(x_i\right)\·\mathrm{\Φ}\left(x_j\right))+\mathrm{\ϵ}\underset{i=1}{\overset{l}{\mathrm{\Σ}}}({\mathrm{\α}}_i^{*}+{\mathrm{\α}}_i)-\underset{i=1}{\overset{l}{\mathrm{\Σ}}}{y}_i({\mathrm{\α}}_i^{*}-{\mathrm{\α}}_i)]$

$s.t.\left\{\begin{array}{c}\underset{i=1}{\overset{l}{\mathrm{\Σ}}}({\mathrm{\α}}_i^{*}-{\mathrm{\α}}_i)=0\\ 0\≤{\mathrm{\α}}_i^{(*)}\≤C,i=\mathrm{1,2,3},...,l\end{array}\right.---\left(3\right)$

In formula, α _iwith for the Lagrange factor;

3) by kernel function K (x _i, x _j)=(Φ (x _i) Φ (x _j)) be transformed into higher dimensional space, now can solve and obtain returning decision function:

$f\left(x\right)=\mathrm{\ω}\·\mathrm{\Φ}\left(x\right)+b=\underset{i=1}{\overset{l}{\mathrm{\Σ}}}({\mathrm{\α}}_i^{*}-{\mathrm{\α}}_i)K(x,x_i)+b^{*}---\left(4\right).$

Above-mentioned steps 3) in LS-SVM change the inequality constrain in SVM into equality constraint, quadratic programming problem will be solved and change into and solve system of linear equations, and change empiric risk into quadratic power by the first power of deviation:

$\min [\frac{1}{2}{\left|\right|\mathrm{\ω}\left|\right|}^2+\frac{1}{2}C\underset{i=1}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\ξ}}_i^2]$

s.t.[y _i-(ω·Φ(x _i)+b)＝ξ _i],i＝1,2,3,…,l (5)

Introduce Lagrange function, transform its dual problem, and according to KKT (Karush-Kuhn-Tucher) condition in Optimum Theory, obtain following equation and constraint condition:

$\left\{\begin{array}{c}\mathrm{\ω}=\underset{i=1}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\α}}_i{y}_i\mathrm{\Φ}\left(x_i\right)\\ \underset{i=1}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\α}}_i{y}_i=0\\ {\mathrm{\α}}_i=C{\mathrm{\ξ}}_i\\ \mathrm{\ω}\·\mathrm{\Φ}\left(x_i\right)+b+{\mathrm{\ξ}}_i-y_i=0\end{array}\right.---\left(6\right)$

Finally obtain decision function:

$f\left(x\right)=\underset{i=1}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\α}}_{i}K(x,x_i)+b---\left(7\right).$

Compared with prior art, the present invention has following outstanding substantive distinguishing features and significant advantage:

In theory, the present invention adopts SVM and LS-SVM data driven technique, and they not only have the solid theoretical foundation of Statistical Learning Theory, and have to close geometric interpretation and perfect mathematical form.

From practical application, the forecast model set up by above-mentioned data driven technique, by the sample data that input interval is two-layer, can dope the fluctuating wind speed of middle layer corresponding time more accurately.Therefore, the present invention is adopted can to reach cost-saving, time saving effect.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of the fluctuating wind speed analogy method based on data-driven.

Fig. 2,3,4 is the fluctuating wind speed of AR method numerical simulation and simulated power spectrum, autocorrelation function compares with desired value.

Fig. 5,6 is the fluctuating wind speed cross correlation function of AR method numerical simulation and comparing of target cross correlation function.

Fig. 7 simulates based on the fluctuating wind speed of BP Neural Network Data Driving technique.

Fig. 8 simulates based on the fluctuating wind speed of SVM data driven technique.

Fig. 9 simulates based on the fluctuating wind speed of LS-SVM data driven technique.

Embodiment

Below in conjunction with accompanying drawing, enforcement of the present invention is further described.

As shown in Figure 1, a kind of fluctuating wind speed analogy method based on data-driven, concrete steps are as follows:

The first step, selects certain city's centre-height to be the high-rise building of 200 meters, gets every the point of 10 meters as each simulation wind speed point along short transverse.Other correlation parameters are in table 1:

Table 1 associated analog parameter

represent the mean wind speed of 10m At The Height.

Second step, the fluctuating wind speed time series that the some generated by AR method numerical simulation is distributed along high uniformity, as limited original systolic wind speed sample data.Simulated power spectrum adopts Davenport spectrum, and only consider the spatial coherence of short transverse, related function is got: C _x=C _y=0, C _z=10.Get 4 rank autoregressive model exponent numbers, namely p gets 4, sets up 20 dimension AR autoregressive models, generates the fluctuating wind speed time series curve of 20 simulations wind speed point 1000s (5000 time interval Δ t).Calculate the power spectrum density of these analogues value, autocorrelation function, cross correlation function, and compare with desired value.As can be seen from Fig. 2 to Fig. 6, the analogue value and desired value more identical, simulate effect is more satisfactory.

In order to verify the validity based on data driven technique prediction, need a part of sample data group to be used for machine learning, another part sample data group is for predicting the fluctuating wind speed that verification msg Driving technique is simulated.The sample data of AR model generation is divided into two parts by the present invention: get front 200s (1000 Δ t) fluctuating wind speed value as learning sample, and 200s air speed value is then as checking sample.Second step has 1000s data, here only with 400s, does not know to be mistake, please check.

3rd step, adopt BP neural network, SVM, LS-SVM respectively, the interpolation machine learning carried out based on data driven technique is trained, and sets up prediction regression model.Interpolation machine learning is: get the fluctuating wind speed learning sample in several groups of two layer height districts that are separated by as input, the wind speed learning sample of middle layer height, as output, is trained, thus set up forecast model.Such as: the fluctuating wind speed time series sample at 10m and 50m, 40m and 80m, 140m and 180m place is as input, and the fluctuating wind speed time series at 50m, 60m, 160m place, as output, carries out learning training and forecast test.BP neural network of the present invention comprises 20 neuronic hidden layers, and the activation function of input layer and hidden layer adopts " tansig ", and output layer activation function adopts " trainlm ".SVM model and LS-SVM model all adopt Radial basis kernel function, and adopt the method for 5 folding crosschecks and grid-search to determine optimum regularization parameter C and nuclear parameter g.

Using the checking sample of rear 200s as input, by prediction regression model, export the fluctuating wind speed time series in middle layer, see Fig. 7-9.

4th step, calculate the coefficient R of the inter-layer prediction analogue value and desired value (raw data), root-mean-square error RMSE and time required for simulating as evaluation index, result is analyzed, in table 2.

The evaluation index of table 2 three kinds of method simulations

As can be seen from Fig. 7-9 and table 2, although BP neural network analog rate is short, ratio of precision is poor, and network struction is comparatively complicated, and need to determine hidden layer neuron number, anticipation error etc., the setting of these values all produces larger impact to result.SVM is based on structural risk minimization, overcome neural network local minimum points problem, cross study and the problem such as deficient problem concerning study, Model Selection collection dimension disaster, it has good generalization ability, so simulation precision is higher than BP neural network, but more time-consuming, and this utilizes quadratic standard forms optimisation technique to solve dual problem mainly due to SVM, a large amount of matrix operations is carried out in quadratic form searching process, need very large internal memory, cause training algorithm slow, holding time.LS-SVM is the improvement of SVM, has solid theoretical foundation equally, also can ensure that the function obtained has minimum forecasting risk and best generalization ability.Further, LS-SVM replaces the quadratic programming optimization in SVM by one group of system of linear equations, and improve speed of convergence, solving speed is fast.

Claims (4)

1., based on a fluctuating wind speed analogy method for data-driven, by interpolation study and the training of the fluctuating wind speed sample data of some height, predict the fluctuating wind speed time series of other height; It is characterized in that, concrete steps are as follows:

1) select high-rise building, determine the parameter required for numerical simulation fluctuating wind speed: the building height of simulation and each height, the mean wind speed of these 10 meters of height in place, surface roughness values, ground roughness exponent, the simulation related function of simulation wind speed point;

2) fluctuating wind speed time series that the some generated by AR method numerical simulation is distributed along high uniformity, as limited original systolic wind speed sample data; And the analogue value of power spectral density of the wind speed, autocorrelation function and cross correlation function and the degree of agreement of respective objects value are tested, to verify the feasibility based on AR modeling high-rise building Wind Velocity History;

3) BP neural network, SVM, LS-SVM tri-kinds of data driven technique methods are adopted respectively, sample data in some height region is carried out to study and the training of interpolation method, set up forecast model, by the sample data that input interval is two-layer, export the fluctuating wind speed of middle layer corresponding time;

4) adopt the related coefficient of prognosis modelling value and desired value, root-mean-square error and time required for simulating as evaluation index, result is analyzed, acquisition different pieces of information driving method simulation Pros and Cons separately.

2. the fluctuating wind speed analogy method based on data-driven according to claim 1, is characterized in that, described step 2) in AR model following formula represent:

$v\left(t\right)=-\underset{k=1}{\overset{p}{\mathrm{\Σ}}}{\mathrm{\ψ}}_k\·v(t-\mathrm{k\Δt})+N\left(t\right)---\left(1\right)$

In formula: it is vectorial at the fluctuating wind speed time series of t and t-k Δ t that v (t), v (t-k Δ t) are respectively space M point; P is the exponent number of AR model; Δ t is the time step of simulation wind speed; ψ _kbeing AR model autoregressive coefficient matrix, is M × M rank square formation; N (t)=Ln (t), L is lower triangular matrix, and n (t) is that M ties up average to be 0 variance be 1 separate white noise vector.

3. the fluctuating wind speed analogy method based on data-driven according to claim 1, is characterized in that, described step 3) in SVM regression model regression problem by introduce loss function solve, according to data sample set T={ (x _i, y _i) ..., (x _l, y _l) (wherein x _ifor input value, y _ifor output valve), find R ⁿon a function f (x), according to this function, a given new input data x, just can judge that the real number corresponding to it exports y; Wherein: x _i∈ R ⁿ, y _i∈ R, i=1,2,3 ..., l; Main contents are as follows:

1) given sample data collection T, considers, with function g (x)=(ω x)+b, to carry out matching, and make the distance between f and g minimum to sample data;

2) according to structural risk minimization, and linear regression is generalized to non-linear regression, structure optimization problem:

$\min [\frac{1}{2}{\left|\right|\mathrm{\ω}\left|\right|}^2+C\underset{i=1}{\overset{l}{\mathrm{\Σ}}}({\mathrm{\ξ}}_i+{\mathrm{\ξ}}_i^{*})]$

$s.t.\left\{\begin{array}{c}{y}_i-(\mathrm{\ω}\·\mathrm{\Φ}\left(x_i\right)+b)\≤\mathrm{\ϵ}+{\mathrm{\ξ}}_i\\ (\mathrm{\ω}\·\mathrm{\Φ}\left(x_i\right)+b)-y_i\≤\mathrm{\ϵ}+{\mathrm{\ξ}}_i^{*}\\ {\mathrm{\ξ}}_i,{\mathrm{\ξ}}_i^{*}\≥0,i=\mathrm{1,2,3},\·\·\·,l\end{array}\right.---\left(2\right)$

In formula, ω and b is weights and threshold respectively, and C is penalty factor, realizes the compromise of empiric risk and fiducial range; ξ _i, for relaxation factor; ε is loss function, namely fitting precision; For Φ (x _i) replace the x after linear graduation for Nonlinear Indexing _i; For the dual problem of derived expression (2), utilize Lagrange function to change, optimization aim will be following form:

$\min [\frac{1}{2}\underset{i=1}{\overset{l}{\mathrm{\Σ}}}({\mathrm{\α}}_i^{*}-{\mathrm{\α}}_i)({\mathrm{\α}}_j^{*}-{\mathrm{\α}}_j)(\mathrm{\Φ}\left(x_i\right)\·\mathrm{\Φ}\left(x_j\right))+\mathrm{\ϵ}\underset{i=1}{\overset{l}{\mathrm{\Σ}}}({\mathrm{\α}}_i^{*}+{\mathrm{\α}}_i)-\underset{i=1}{\overset{l}{\mathrm{\Σ}}}{y}_i({\mathrm{\α}}_i^{*}-{\mathrm{\α}}_i)]$

$s.t.\left\{\begin{array}{c}\underset{i=1}{\overset{l}{\mathrm{\Σ}}}({\mathrm{\α}}_i^{*}-{\mathrm{\α}}_i)=0\\ 0\≤{\mathrm{\α}}_i^{(*)}\≤C,i=\mathrm{1,2,3},\·\·\·,l\end{array}\right.---\left(3\right)$

In formula, α _iwith for the Lagrange factor;

3) by kernel function K (x _i, x _j)=(Φ (x _i) Φ (x _j)) be transformed into higher dimensional space, now can solve and obtain returning decision function:

$f\left(x\right)=\mathrm{\ω}\·\mathrm{\Φ}\left(x\right)+b=\underset{i=1}{\overset{l}{\mathrm{\Σ}}}({\mathrm{\α}}_i^{*}-{\mathrm{\α}}_i)K(x,x_i)+b^{*}---\left(4\right).$

4. the fluctuating wind speed analogy method based on data-driven according to claim 1, it is characterized in that, described step 3) in LS-SVM change the inequality constrain in SVM into equality constraint, quadratic programming problem will be solved change into and solve system of linear equations, and change empiric risk into quadratic power by the first power of deviation:

$\min [\frac{1}{2}{\left|\right|\mathrm{\ω}\left|\right|}^2+\frac{1}{2}C\underset{i=1}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\ξ}}_i^2]$

s.t.[y _i-(ω·Φ(x _i)+b)＝ξ _i],i＝1,2,3,…,l (5)

Introduce Lagrange function, transform its dual problem, and according to KKT (Karush-Kuhn-Tucher) condition in Optimum Theory, obtain following equation and constraint condition:

$\left\{\begin{array}{c}\mathrm{\ω}=\underset{i=1}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\α}}_i{y}_i\mathrm{\Φ}\left(x_i\right)\\ \underset{i=1}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\α}}_i{y}_i=0\\ {\mathrm{\α}}_i=C{\mathrm{\ξ}}_i\\ \mathrm{\ω}\·\mathrm{\Φ}\left(x_i\right)+b+{\mathrm{\ξ}}_i-y_i=0\end{array}\right.---\left(6\right)$

Finally obtain decision function:

$f\left(x\right)=\underset{i=1}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\α}}_{i}K(x,x_i)+b---\left(7\right).$