CN105205495A - Non-stationary fluctuating wind speed forecasting method based on EMD-ELM - Google Patents

Non-stationary fluctuating wind speed forecasting method based on EMD-ELM Download PDF

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CN105205495A
CN105205495A CN201510556369.5A CN201510556369A CN105205495A CN 105205495 A CN105205495 A CN 105205495A CN 201510556369 A CN201510556369 A CN 201510556369A CN 105205495 A CN105205495 A CN 105205495A
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李春祥
钟旺
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University of Shanghai for Science and Technology
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Abstract

The invention provides a non-stationary fluctuating wind speed forecasting method based on EMD-ELM. The method comprises the following steps: generating a non-stationary fluctuating wind speed sample by utilizing a TARMA model in a simulated manner, and dividing the fluctuating wind speed sample into a training set and a test set two parts, and carrying out normalization processing on the sample by utilizing Matlab; carrying out EMD processing on time sequence of the non-stationary fluctuating wind speed sample, and decomposing non-stationary nonlinear fluctuating wind signals into a group of stationary and linear sequence sets; carrying out phase-space reconstruction on the group of IMFs, and establishing corresponding ELM prediction models respectively; and carrying out superposition on the forecast results of the group of IMFs to obtain forecasted non-stationary fluctuating wind speed of the point, meanwhile, comparing the test sample with the forecasted non-stationary fluctuating wind speed result, and calculating average error, root-mean-square error and correlation coefficient of the forecasted wind speed and the actual wind speed. The invention provides a fast-speed and good-effect method for non-stationary fluctuating wind speed prediction.

Description

Based on the non-stationary fluctuating wind speed Forecasting Methodology of EMD-ELM
Technical field
The present invention relates to a kind of single-point non-stationary fluctuating wind speed Forecasting Methodology adopting empirical mode decomposition (EMD) and extreme learning machine (ELM) to combine, a kind of non-stationary fluctuating wind speed Forecasting Methodology based on EMD-ELM specifically.
Background technology
For large span spatial structure, Longspan Bridge, high building structure, tall and slender structure, as buildingss such as stay-supported mast, television tower, chimneys, wind load is one of control load of structural wind resistance design.And first the Wind resistant analysis of carrying out structure will obtain the sample data of wind load, determine that the main research means of Wind Engineering has theoretical analysis, numerical simulation, wind tunnel test and field measurement etc. at present.Along with the develop rapidly of computer technology and people are to the further investigation of stochastic process numerical simulation technology, adopt method for numerical simulation the to obtain arbitrariness of the condition such as feature that Wind Velocity History curve can consider place, wind spectrum signature, buildings, the load that simulation is obtained is as far as possible close to the actual wind-force of structure, the arbitrariness of some statistical property can be met simultaneously, and more representative than physical record, be thus widely used in Practical Project.
Non-stationary property as the ubiquitous a kind of phenomenon of the various random load of occurring in nature, as atmospheric turbulence of boundary layer, thunderstorm high wind and earthquake etc.Its amplitude and frequency are all time dependent, therefore under some specific environment, carry out numerical simulation to fluctuating wind, and the non-stationary of wind is the factor that must consider.Particularly in downburst, namely strong in Thunderstorm Weather down draft clashes ground, and propagated along earth's surface to surrounding by rum point have sudden and destructive a kind of high wind, it is extremely strong non-stationaryly produces larger dynamic response to structure possibly.A large amount of actual test data analysis shows, under the complicated landform of harsher wind conditions, many wind speed records do not meet this stationarity requirement.Non-stationary fluctuating wind particularly under complicated landform harsher wind conditions, when adopting steady wind speed to suppose, Non-stationary Data needs to give up, and this can cause larger analytical error, as turbulence intensity value can be over-evaluated, and then affects the accuracy of subsequent analysis.
Extreme learning machine (ExtremeLearningMachine, ELM) be a kind of novel Single hidden layer feedforward neural networks (SLFNs) learning method, this algorithm is under the prerequisite of Stochastic choice input layer weights and hidden neuron threshold value, calculate by means of only a step and can try to achieve network output weights, compare with traditional neural network, extreme learning machine drastically increases generalization ability and the pace of learning of network, has stronger nonlinear fitting ability.Its basic thought is: arrange suitable the number of hidden nodes before training, and only need for input weights and hidden layer are biased random assignment in the process of implementation, whole process once completes, and without the need to iteration, and produces unique optimum solution.Fluctuating wind speed simulation generated, as learning training sample, is set up regression model and is effectively predicted single-point fluctuating wind speed.
Summary of the invention
Technical matters to be solved by this invention is to provide a kind of non-stationary fluctuating wind speed Forecasting Methodology based on EMD-ELM, autoregressive moving-average model (Time-VaryingAuto-RegressiveandMovingAverage is become when it utilizes, TARMA) simulation generates non-stationary fluctuating wind speed sample, based on empirical mode decomposition (EMD) and sort reorganization method, set up the model of extreme learning machine (ELM), utilize this model to predict single-point non-stationary fluctuating wind speed.Calculate the validity that the average error (AE) of actual wind speed and prediction of wind speed, root-mean-square error (RMSE) and related coefficient (R) evaluate this method simultaneously.
According to foregoing invention design, the present invention adopts following technical proposals: the non-stationary fluctuating wind speed Forecasting Methodology that the present invention is based on EMD-ELM comprises the following steps:
The first step: become autoregressive moving-average model simulation when utilizing and generate non-stationary fluctuating wind speed sample, fluctuating wind speed sample is divided into training set, test set two parts, and adopts Matlab to samples normalization process;
Nonlinear for this non-stationary fluctuating wind signal decomposition is one group of stable state and linear sequence sets, i.e. intrinsic mode function by second step: carry out empirical mode decomposition process to the time series of this non-stationary fluctuating wind speed sample;
3rd step: phase space reconfiguration is carried out to this group intrinsic mode function component, and set up corresponding extreme learning machine forecast model respectively according to their respective features, study prediction is carried out to this non-stationary fluctuating wind speed time series;
4th step: predicting the outcome of this group intrinsic mode function component is carried out superposing the prediction of wind speed that just can obtain the non-stationary fluctuating wind of this point, simultaneously by the non-stationary fluctuating wind speed Comparative result of test sample book and prediction, the average error of computational prediction wind speed and actual wind speed, root-mean-square error and related coefficient, evaluate the validity of this method.
Preferably, in the above-mentioned first step, in time, becomes autoregressive moving-average model simulation m and ties up non-stationary fluctuating wind speed and be expressed as following formula:
U ( t ) = Σ i = 1 p A i ( t ) U ( t - i Δ t ) + Σ j = 0 q B j ( t ) X ( t - j Δ t )
Wherein, U (t) is zero-mean nonstationary random process vector, A i(t) for time become autoregressive coefficient matrix, B j(t) for time become slip regression coefficient matrix, p is Autoregressive, and q is slip regression order, and to be variance be X (t) 1, the white noise sequence of normal distribution.
Preferably, in the above-mentioned first step, time become the Autoregressive p=4 of autoregressive moving-average model, slip regression order q=1; Simulation points is positioned at along downburst moving direction and distance downburst thunderstorm center 3500m; Downburst Wind speed model adopts Oseguera and Bowles mean wind speed model, the vertical distributed model of Vicroy, maximum wind velocity V in vertical distribution wind speed max=80m/s, residing height and position Z max=67m; The radial maximum wind velocity V of certain At The Height in wind speed field r, max=47m/s, with downburst central horizontal distance r max=1000m, radical length scale-up factor R r=700m; Thunderstorm intensity time variations following formula represents:
Π = t / 5 , ( 0 ≤ t ≤ 5 min ) e - ( t - 5 ) / 20 , ( t > 5 min )
In formula, ∏ represents thunderstorm intensity, and t represents the time, and e is natural constant, downburst point-to-point speed V o=8m/s; Upper cut-off frequency is 2 π rad, N=2^11, consider that downburst self moves, simulated time interval of delta t=0.5s, simulation duration is 1000s, totally 2000 sample points simultaneously.
Preferably, in described second step, the time series of the non-stationary fluctuating wind speed sample obtained being carried out empirical mode decomposition process, is one group of stable state and linear sequence sets, i.e. intrinsic mode function by nonlinear for this non-stationary fluctuating wind signal decomposition.
Preferably, in described 3rd step, this group intrinsic mode function component obtained is carried out phase space reconfiguration, just can determine the basic structure of extreme learning machine according to the dimension of sample vector after phase space reconfiguration and the extreme learning machine hidden neuron number of specifying; Then set up corresponding extreme learning machine forecast model respectively according to this group intrinsic mode function component feature separately, study prediction is carried out to this non-stationary fluctuating wind speed time series; Finally predicting the outcome of this group intrinsic mode function component is carried out superposing the prediction of wind speed that just can obtain the non-stationary fluctuating wind of this point.
Preferably, empirical mode decomposition non-stationary Wind Velocity History U (t) be expressed as intrinsic mode function component and add final surplus r n(t), as shown in the formula:
U ( t ) = Σ j = 1 n c j ( t ) + r n ( t )
In formula, c jt () represents a jth intrinsic mode function component, n represents that empirical mode decomposition becomes the quantity of intrinsic mode function, r nt () represents surplus.
The non-stationary fluctuating wind speed Forecasting Methodology that the present invention is based on EMD-ELM has following advantage: non-linear and non-stationary for each spatial point fluctuating wind speed, and forecast model has good learning ability for the intrinsic mode function component after empirical mode decomposition and training error is little.Meanwhile, adopt extreme learning machine to predict, guarantee the accuracy that non-stationary fluctuating wind speed is predicted.Show according to operation result, predict that the non-stationary fluctuating wind speed that obtains and actual non-stationary fluctuating wind speed coincide very well based on EMD-ELM method, can as a kind of effective ways of single-point non-stationary fluctuating wind speed prediction.
Accompanying drawing explanation
Fig. 1 be based on time become 20 meters of At The Height fluctuating wind speed sample schematic diagram that autoregressive moving-average model method simulates;
Fig. 2 is the empirical mode decomposition schematic diagram of 20 meters of At The Height non-stationary fluctuating wind speed analog samples;
Fig. 3 is based on EMD-ELM non-stationary fluctuating wind speed Forecasting Methodology design framework figure schematic diagram;
Fig. 4 is based on extreme learning machine fluctuating wind speed Forecasting Methodology process flow diagram;
Fig. 5 is that 20 meters of At The Height EMD-ELM prediction of wind speed and actual wind speed contrast schematic diagram;
Fig. 6 is that 20 meters of At The Height EMD-ELM prediction of wind speed and actual wind speed autocorrelation function contrast schematic diagram;
Fig. 7 is that 20 meters of At The Height EMD-ELM prediction of wind speed and actual wind speed power spectral density function contrast schematic diagram.
Embodiment
Design of the present invention is as follows: first carry out empirical mode decomposition to the non-stationary fluctuating wind speed of this point, is decomposed into a series of component relatively stably; Then each component is predicted respectively, adopt extreme learning machine to become autoregressive moving-average model in time to the method that each component is predicted; Predicting the outcome to superpose and obtain final prediction of wind speed finally to each component of this point.
The non-stationary fluctuating wind speed Forecasting Methodology that the present invention is based on EMD-ELM comprises the steps:
The first step, becomes autoregressive moving-average model (TARMA) simulation and generates non-stationary fluctuating wind speed sample, fluctuating wind speed sample is divided into training set, test set two parts, and adopts Matlab to samples normalization process when utilizing;
In the described first step, in time, becomes autoregressive moving-average model simulation m and ties up non-stationary fluctuating wind speed and be expressed as following formula (1):
U ( t ) = Σ i = 1 p A i ( t ) U ( t - i Δ t ) + Σ j = 0 q B j ( t ) X ( t - j Δ t ) - - - ( 1 )
In formula, U (t) is zero-mean nonstationary random process vector, A i(t) for time become autoregressive coefficient matrix, B j(t) for time become slip regression coefficient matrix, p is Autoregressive, and q is slip regression order, and to be variance be X (t) 1, the white noise sequence of normal distribution.
Time become the Autoregressive p=4 of autoregressive moving-average model, slip regression order q=1.Simulation points is positioned at along downburst moving direction and distance downburst thunderstorm center 3500m.Downburst Wind speed model adopts Oseguera and Bowles mean wind speed model, the vertical distributed model of Vicroy, maximum wind velocity V in vertical distribution wind speed max=80m/s, residing height and position Z max=67m; The radial maximum wind velocity V of certain At The Height in wind speed field r, max=47m/s, with downburst central horizontal distance r max=1000m, radical length scale-up factor R r=700m; Thunderstorm intensity time variations following formula (2) represents:
Π = t / 5 , ( 0 ≤ t ≤ 5 min ) e - ( t - 5 ) / 20 , ( t > 5 min ) - - - ( 2 )
In formula, ∏ represents thunderstorm intensity, and t represents the time, and e is natural constant, downburst point-to-point speed V 0=8m/s.Upper cut-off frequency is 2 π rad, N=2 11, consider that downburst self moves, simulated time interval of delta t=0.5s, simulation duration is 1000s, totally 2000 sample points simultaneously.The time spectrum of the non-stationary fluctuating wind speed simulation of 20m At The Height as shown in Figure 1.
Second step: empirical mode decomposition (EMD) process is carried out to the time series of this non-stationary fluctuating wind speed sample, be one group of stable state and linear sequence sets by nonlinear for this non-stationary fluctuating wind signal decomposition, i.e. intrinsic mode function (IMF);
That empirical mode decomposition non-stationary Wind Velocity History U (t) is expressed as intrinsic mode function component (IMFs) and add final surplus r n(t), as shown in the formula (3):
U ( t ) = Σ j = 1 n c j ( t ) + r n ( t ) - - - ( 3 )
Wherein, c jt () represents a jth intrinsic mode function component, n represents that empirical mode decomposition becomes the quantity of intrinsic mode function, r nt () represents surplus.
Empirical mode decomposition is carried out to the non-stationary fluctuating wind speed at 20m place, obtains intrinsic mode function component and the surplus of this spatial point, as shown in Figure 2.
3rd step: phase space reconfiguration is carried out to this group intrinsic mode function component, and set up corresponding extreme learning machine forecast model respectively according to their respective features, study prediction is carried out to this non-stationary fluctuating wind speed time series;
This group intrinsic mode function component obtained is carried out phase space reconfiguration, just can determine the basic structure of extreme learning machine according to the dimension of sample vector after phase space reconfiguration and the extreme learning machine hidden neuron number of specifying; Then set up corresponding extreme learning machine forecast model respectively according to this group intrinsic mode function component feature separately, study prediction is carried out to this non-stationary fluctuating wind speed time series; Finally predicting the outcome of this group intrinsic mode function component is carried out superposing the prediction of wind speed that just can obtain the non-stationary fluctuating wind of this point.
Be specially, first, consider that research object of the present invention is point speed in units of 0.5 second, sample number is 2000 time points altogether 1000s, thus choose front 1000 time points altogether 500s form training set, and then rear 1000 time points are total to 500s as test set.Then, in order to reflect this non-stationary fluctuating wind speed sample Evolution in time, carry out phase space reconfiguration to the intrinsic mode function component that this non-stationary fluctuating wind speed obtains after empirical mode decomposition, time delay τ=1 chosen during reconstruct, Embedded dimensions is m=10.Because Embedded dimensions is 10, so the sample of training set is 990 10 dimensional vectors, test set is 1000 10 dimensional vectors.Therefore, the structure of extreme learning machine is: input layer 10 neurons, hidden layer 20 neurons, output layer are 1 neuron, so just determine the structure of extreme learning machine non-stationary fluctuating wind speed forecast model.Last just with this ELM forecast model, decompose through EMD the IMFs produced to this non-stationary fluctuating wind speed and carry out study prediction, the process flow diagram of the Forecasting Methodology of ELM as shown in Figure 4.
4th step: predicting the outcome of this group intrinsic mode function component is carried out superposing the prediction of wind speed that just can obtain the non-stationary fluctuating wind of this point, simultaneously by the non-stationary fluctuating wind speed Comparative result of test sample book and prediction, the average error (AE) of computational prediction wind speed and actual wind speed, root-mean-square error (RMSE) and related coefficient (R), evaluate the validity of this method.In addition, the result that EMD-ELM predicts can be contrasted with predicting the outcome of EMD-BPNN.
Matching performance for extreme learning machine is subject to the impact of network structure to a certain extent, this method is used for the extreme learning machine model of forecasting wind speed, input layer number is the input saturation dimension of phase space reconfiguration, output layer has a neuron, what unique needs were specified is hidden layer neuron number, and this method adopts the extreme learning machine structure comprising 20 hidden neurons.
Fig. 5 is 20 meters of At The Height prediction of wind speed and the comparing of actual wind speed; Fig. 6 is 20 meters of At The Height EMD-ELM prediction of wind speed and the comparing of actual wind speed autocorrelation function; Fig. 7 is 20 meters of At The Height EMD-ELM prediction of wind speed and the comparing of actual wind speed power spectral density function.The average error (AE) of computational prediction wind speed and actual wind speed, root-mean-square error (RMSE) and related coefficient (R), evaluate validity of the present invention.
Step is above that the calculation procedure based on empirical mode decomposition and extreme learning machine fluctuating wind speed Forecasting Methodology worked out based on Matlab platform carries out analysis & verification.The evaluation index that predicts the outcome of EMD-ELM and EMD-BPNN is shown in Table 1.
Table 1 predicts the outcome each evaluation index table
Evaluation index Forecasting Methodology EMD-BPNN EMD-ELM
AE 0.6209 0.5617
RSME 1.1940 0.9374
R 0.9972 0.9977
Above step can reference diagram 3, gives implementing procedure of the present invention intuitively.Analysis result shows, and EMD-ELM and the EMD-BPNN related coefficient that predicts the outcome all is greater than 0.99 and namely illustrates there is very strong correlation, and square error shows EMD-ELM and predicts the outcome and better converge on actual wind speed.And, can find out that predicting the outcome of EMD-ELM is all better than EMD-BPNN in average error, root-mean-square error and related coefficient these three, so the estimated performance of EMD-ELM to non-stationary fluctuating wind speed is more excellent, the travelling speed of extreme learning machine is far faster than reverse transmittance nerve network simultaneously.The present invention is that the prediction of non-stationary fluctuating wind speed provides that a speed is faster, the method for better effects if.
Above-described specific embodiment; the technical matters of solution of invention, technical scheme and beneficial effect are further described; be understood that; the foregoing is only specific embodiments of the invention; be not limited to the present invention; within the spirit and principles in the present invention all, any amendment made, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (6)

1., based on a non-stationary fluctuating wind speed Forecasting Methodology of EMD-ELM, it is characterized in that, it comprises the following steps:
The first step: become autoregressive moving-average model simulation when utilizing and generate non-stationary fluctuating wind speed sample, fluctuating wind speed sample is divided into training set, test set two parts, and adopts Matlab to samples normalization process;
Nonlinear for this non-stationary fluctuating wind signal decomposition is one group of stable state and linear sequence sets, i.e. intrinsic mode function by second step: carry out Empirical Mode Decomposition Algorithm process to the time series of this non-stationary fluctuating wind speed sample;
3rd step: phase space reconfiguration is carried out to this group intrinsic mode function component, and set up corresponding extreme learning machine forecast model respectively according to their respective feature, study prediction is carried out to this non-stationary fluctuating wind speed time series;
4th step: predicting the outcome of this group intrinsic mode function component is carried out superposing the prediction of wind speed of the non-stationary fluctuating wind just obtaining this point, simultaneously by the non-stationary fluctuating wind speed Comparative result of test sample book and prediction, the average error of computational prediction wind speed and actual wind speed, root-mean-square error and related coefficient, evaluate the validity of this method.
2. the non-stationary fluctuating wind speed Forecasting Methodology based on EMD-ELM according to claim 1, is characterized in that, in the described first step, time becomes autoregressive moving-average model simulation m and ties up non-stationary fluctuating wind speed and be expressed as following formula:
U ( t ) = Σ i = 1 p A i ( t ) U ( t - i Δ t ) + Σ j = 0 q B j ( t ) X ( t - j Δ t )
In formula, U (t) is zero-mean nonstationary random process vector, A i(t) for time become autoregressive coefficient matrix, B j(t) for time become slip regression coefficient matrix, p is Autoregressive, and q is slip regression order, and to be variance be X (t) 1, the white noise sequence of normal distribution.
3. the non-stationary fluctuating wind speed Forecasting Methodology based on EMD-ELM according to claim 1, is characterized in that, in the described first step, time become the Autoregressive p=4 of autoregressive moving-average model, slip regression order q=1; Simulation points is positioned at along downburst moving direction and distance downburst thunderstorm center 3500m; Downburst Wind speed model adopts Oseguera and Bowles mean wind speed model, the vertical distributed model of Vicroy, maximum wind velocity V in vertical distribution wind speed max=80m/s, residing height and position Z max=67m; The radial maximum wind velocity V of certain At The Height in wind speed field r, max=47m/s, with downburst central horizontal distance r max=1000m, radical length scale-up factor R r=700m; Thunderstorm intensity time variations following formula represents:
Π = t / 5 , ( 0 ≤ t ≤ 5 min ) e - ( t - 5 ) / 20 , ( t > 5 min )
In formula, ∏ represents thunderstorm intensity, and t represents the time, and e is natural constant, downburst point-to-point speed V o=8m/s; Upper cut-off frequency is 2 π rad, N=2^11, consider that downburst self moves, simulated time interval of delta t=0.5s, simulation duration is 1000s, totally 2000 sample points simultaneously.
4. the non-stationary fluctuating wind speed Forecasting Methodology based on EMD-ELM according to claim 1, it is characterized in that, in described second step, the time series of the non-stationary fluctuating wind speed sample obtained is carried out empirical mode decomposition process, be one group of stable state and linear sequence sets, i.e. intrinsic mode function by nonlinear for this non-stationary fluctuating wind signal decomposition.
5. the non-stationary fluctuating wind speed Forecasting Methodology based on EMD-ELM according to claim 1, is characterized in that, in described second step, that empirical mode decomposition non-stationary Wind Velocity History U (t) is expressed as intrinsic mode function component and add final surplus r n(t), as shown in the formula:
U ( t ) = Σ j = 1 n c j ( t ) + r n ( t )
Wherein, c jt () represents a jth intrinsic mode function component, n represents that empirical mode decomposition becomes the quantity of intrinsic mode function, r nt () represents surplus.
6. the non-stationary fluctuating wind speed Forecasting Methodology based on EMD-ELM according to claim 1, it is characterized in that, in described 3rd step, this group intrinsic mode function component obtained is carried out phase space reconfiguration, just can determine the basic structure of extreme learning machine according to the dimension of sample vector after phase space reconfiguration and the extreme learning machine hidden neuron number of specifying; Then set up corresponding extreme learning machine forecast model respectively according to this group intrinsic mode function component feature separately, study prediction is carried out to this non-stationary fluctuating wind speed time series; Finally predicting the outcome of this group intrinsic mode function component is carried out superposing the prediction of wind speed that just can obtain the non-stationary fluctuating wind of this point.
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