CN103208032B - A kind of periodic weighting Forecasting Methodology based on small echo and chaos optimization LSSVM - Google Patents
A kind of periodic weighting Forecasting Methodology based on small echo and chaos optimization LSSVM Download PDFInfo
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Abstract
The invention discloses a kind of periodic weighting Forecasting Methodology based on small echo and chaos optimization LSSVM, it is characterized in that the method utilizes Wavelet Decomposition Technology that selected sample set data decomposition is become the component of different frequency.Based on chaology, component phase space is reconstructed.Each reconstruct component uses the training of LSSVM model respectively, and wherein the parameter of LSSVM forecast model is optimized by Chaos particle swarm optimization algorithm.Finally, the anticipation component that each LSSVM model obtains is carried out small echo restructuring and obtain complete periodic weighting load prediction waveform.Mainly comprise the wavelet decomposition of cyclic loading, the load phase space reconfiguration based on chaology, the structure of least square method supporting vector machine, the chaotic particle swarm optimization of parameter.The present invention can in certain cycle of reconstruct ripple, and under the time series of load has the condition of certain chaotic property, predetermined period presses load ripple.The periodic weighting load that predict stent will be born can be widely used in.
Description
Technical field
The present invention relates to underground mining engineering cyclic loading forecasting problem, particularly relate to the periodic weighting Forecasting Methodology based on small echo and chaos optimization LSSVM.
Background technology
Hydraulic support in tunnel is the main member bearing roof pressure, will consider several factors when arranging support, and wherein the form of load and Changing Pattern are main investigation factors.How understand the load form of following hydraulic support according to existing data and Changing Pattern becomes key issue.Realize the safe and efficient production of workplace, its periodic weighting step pitch and intensity must be grasped.Therefore must carry out correct Prediction periodic weighting waveform with the method for science, traditional Forecasting Methodology mainly contains: empirical estimation method, Wilson's estimation algorithm, old roof construction equilibrium relation estimation algorithm etc.
Less for periodic weighting forecasting research, and the present situation of poor accuracy, the LSSVM method constructed based on small echo and chaos optimization is predicted.Use LSSVM and in conjunction with the decomposition of small echo or the optimization function of chaos, good result obtained to the prediction of sequential ripple.These achievements in research are applied to periodic weighting prediction.First the prediction of model utilizes Wavelet Decomposition Technology that selected sample set data are resolved into different components according to different frequency.Each component after decomposition uses chaology to carry out phase space reconfiguration.Reconstruct component uses the training of LS-SVM model, and the determination of the parameter of training LS-SVM is realized by Chaos particle swarm optimization algorithm.Finally, carrying out recombinates obtains complete predetermined period to press load waveform for predicting the outcome of being obtained by each LS-SVM model.Compared with the waveform predict result and adding-weight one-rank local-region method, BP neural network, chaos diagonal recurrent neural networks, the correctness of this model is described.
Summary of the invention
For in mining process, the main basis selecting support is the periodic weighting load that it will bear, and how to predict the problem of this periodic weighting load.The present invention proposes a kind of periodic weighting Forecasting Methodology based on small echo and chaos optimization LSSVM.
For being described summary of the invention better, first briefly introduce embodiment situation.
Build five survey line monitoring working resistance of support situations of change at workplace, the observation data choosing 10# is analyzed, and checks hydraulic support pressure, i.e. 8 hours sampled point time intervals when every order of classes or grades at school is handed over to the next shift, altogether 425 groups of data.10# support presses load actual waveform as shown in Article 1 curve in figure.
1. the determination of hydraulic support periodic weighting load chaotic property
The training sample of forecast model is by carrying out phase space reconfiguration generation to time series.First its chaotic property will be proved to the reconstruct in this space.Its chaotic property is identified by the dimension and Lyapunov characteristic exponent that calculate chaotic attractor.Hydraulic support periodic weighting load circulate under different cycles formed sequential chart as shown in Figure 4.
As can be seen from Figure 4, system when T=16 closer to chaos.Seasonal effect in time series correlation dimension d is calculated, Embedded dimensions m=2d+1 according to G-P algorithm.According to this number of cases according to asking m=3.Mutual information method is utilized to try to achieve time delay τ=2 of phase space reconfiguration.Utilize small data sets arithmetic try to achieve average period for T=15.44, Lyapunov index be λ >0.It can thus be appreciated that periodic weighting time series has chaotic characteristic.
Phase space reconfiguration thinks that the evolution of each component of system all receives other component influences be associated.Therefore when reconstructing, investigate one-component, and using it certain regular time postpone on measurement as increasing dimension, determine certain multi-dimension space a bit, continuous repetition said process also measures each retardation for different time, just can produce point so in a large number, and many character of such attractor just remain, just can by the one-component reconstruct motive power system model of employing system, the dimension of the true phase space of preliminary certainty annuity.
If the periodic weighting payload data of 10# support is { x (t) }, t=1,2 ..., n, wherein n is number of samples.According to Takens theorem, chaos time sequence just can be reconstructed such as formula (3) by time delay (τ) and embedding dimension (m).
X
n＝(x
n,x
n+τ,…,x
n+(m-1)τ)(3)
C-C method equally also can be adopted to carry out phase space reconfiguration.
2. the chaotic particle swarm optimization of least square method supporting vector machine parameter
The kernel function of the support vector machine adopted is radial basis function, such as formula (4).The regression model of last LSSVM is such as formula (5).
In formula: α
iregression coefficient; B threshold values; σ represents radial basis check figure width.
As can be seen from formula (5), the effect of carrying out regretional analysis depends on γ (representing kernel functional parameter, unlisted associated expression), the parameters such as σ.Chaos-Particle Swarm Optimization is adopted to be optimized γ and σ in model.Chaotic particle swarm optimization is exactly a kind of stochastic global optimization algorithm, and it has fast convergence rate, and the feature that precision is high.The concrete steps of chaotic particle swarm optimization:
1). initialization population.Comprise: algorithm parameter, iterations, chaos masking number of times.
2). according to the basic particle group algorithm formula more speed of new particle and position.
3). to globally optimal solution P
gcarry out chaotization process.By P
gin each element p
gi(i=1,2 ..., n) be mapped in [0,1] field of definition of Logistic () equation; z
i=(p
gi-a
i)/(b
i-a
i), then, carry out iteration with Logistic () equation and produce Chaos Variable sequence z
i(m) (m=1,2 ...), then Chaos Variable sequence is got back to former solution space by inverse transformation mapping, obtain P
g(m).In each feasible solution that former solution space is set up Chaos Variable
calculate fitness value, retain optimum P
*;
4). select a particle P pre-group from working as at random
*replace.
5) if. reach requirement, then terminate.Otherwise carry out second step.
3. based on small echo and chaos optimization LSSVM forecast model prediction flowage structure as shown in Figure 5.
Accompanying drawing explanation
Fig. 1 support 10# wavelet decomposition figure.
The decomposable process of Fig. 2 Mallat algorithm.
The building-up process of Fig. 3 Mallat algorithm.
The chaos situation of system under Fig. 4 different cycles.
Note: (D, C)
t=20=(1.484,0.9749), (D, C)
t=18=(1.481,0.9826), (D, C)
t=16=(1.464,0.9876), (D, C)
t=14=(1.485,0.9782), wherein D is correlation dimension, and C is related coefficient.
Fig. 5 predicts flow process based on small echo and chaos optimization LSSVM.
The prediction curve of Figure 64 model and the comparison diagram of actual curve.
Embodiment
For making above-mentioned purpose of the present invention, feature and advantage become apparent more, and below in conjunction with the correlation theory used and embodiment, the present invention is further detailed explanation.
Embodiment is certain exploiting field 1212, ore deposit two coal face, and it is positioned to the west of 2 12 coal transporting something containerized lanes, north, and adjacent northern two 1210-1 goafs, exploiting field, north, southern side is unworked country.Workplace design mining height 4.0 meters, advances along top board.Adopt inclined longwall retrusive comprehensive mechanized coal mining method.Feed mode is cut sth. askew feed in end, and return toward once cutting two cutter coals, cyclic advance is 0.8m.
1212 workplaces are opened and cut specification is 8.4m × 3.5m, adopts 8m anchor cable, wire netting, steel band combined supporting.The working face mining initial stage adopts one-way coal cutting, from tail toward head pushing and sliding.One is to adjust transporter and the reasonable lap of splice of elevating conveyor.Two is enter rib to ensure that support is parallel, and set cap starts after entering rib to carry out read-record to support huge pillar tensimeter.
Build five surveys line monitoring working resistance of support situations of change at workplace, survey line position is arranged in about 10#, 35#, 60#, 85#, 107# support, each circulation to stent strut pressure gauge reading not once, and as record result.The observation data choosing 10# is analyzed, and checks hydraulic support pressure, i.e. 8 hours sampled point time intervals when every order of classes or grades at school is handed over to the next shift, altogether 425 groups of data.10# support presses load actual waveform as shown in Article 1 curve in Fig. 1.
2. the wavelet decomposition of cyclic loading
Predicted data sample set is various and exists necessarily non-stationary, nonlinear, and the precision of prediction of LSSVM can be affected.In order to address this problem, utilize the multiresolution analysis of wavelet analysis method, data are processed by different level.The sampled point of supports loading, for the time, is discrete in time.For this situation, Mallat fast algorithm implementation wavelet transform can be used.Mallat algorithm is the filtering using wavelet filter discrete signal to be carried out to low pass and high pass.
If the low frequency component on the i-th yardstick is a
i, high fdrequency component is d
i, orthogonal wavelet filter is respectively h (low pass) and g (high pass), then the wavelet decomposition on certain yardstick and the Mallat algorithmic notation of synthesis are such as formula (1) and formula (2).Decomposition and building-up process are as shown in Figures 2 and 3
Press load to decompose with Mallat wavelet analysis method to this 10# support, use the Orthogonal Wavelets (db4) of dwt in matlab to carry out 3 grades of decomposition, be divided into and solve 4 components, wherein, a
1for low frequency component (trend term), d
1, d
2, d
3for each grade high fdrequency component.Decompose component map respectively as the 2nd in Fig. 1,3,4,5 figure.
The training sample of forecast model is by carrying out phase space reconfiguration generation to time series.First its chaotic property will be proved to the reconstruct in this space.Its chaotic property is identified by the dimension and Lyapunov characteristic exponent that calculate chaotic attractor.Hydraulic support periodic weighting load circulate under different cycles formed sequential chart as shown in Figure 4.
As can be seen from Figure 4, system when T=16 closer to chaos.Seasonal effect in time series correlation dimension d is calculated, Embedded dimensions m=2d+1 according to G-P algorithm.According to this number of cases according to asking m=3.Mutual information method is utilized to try to achieve time delay τ=2 of phase space reconfiguration.Utilize small data sets arithmetic try to achieve average period for T=15.44, Lyapunov index be λ >0.It can thus be appreciated that periodic weighting time series has chaotic characteristic.
Phase space reconfiguration thinks that the evolution of each component of system all receives other component influences be associated.Therefore when reconstructing, investigate one-component, and using it certain regular time postpone on measurement as increasing dimension, determine certain multi-dimension space a bit, continuous repetition said process also measures each retardation for different time, just can produce point so in a large number, and many character of such attractor just remain, just can by the one-component reconstruct motive power system model of employing system, the dimension of the true phase space of preliminary certainty annuity.
If the periodic weighting payload data of 10# support is { x (t) }, t=1,2 ..., n, wherein n is number of samples.According to Takens theorem, chaos time sequence just can be reconstructed such as formula (3) by time delay (τ) and embedding dimension (m).
X
n＝(x
n,x
n+τ,…,x
n+(m-1)τ)(3)
C-C method equally also can be adopted to carry out phase space reconfiguration.
Suykens etc. propose least square method supporting vector machine (LSSVM) on the basis of standard support vector machine, loss function in standard support vector type is set to error sum of squares by it, inequality constrain is made into equality constraint, reduce undetermined parameter, again the problem solving quadratic programming is changed into solving of linear KKT (karushkuhnkucker) system of equations, reduce the complicacy solved.The kernel function of the support vector machine adopted is radial basis function, such as formula (4).The regression model of last LSSVM is such as formula (5).
As can be seen from formula (5), the effect of carrying out regretional analysis depends on γ (representing kernel functional parameter, unlisted associated expression), the parameters such as σ.Current parameter selection method mainly contains gradient descent algorithm, Searching algorithm, particle swarm optimization algorithm and genetic algorithm etc., and gradient descent algorithm is responsive to initial value; Searching algorithm, calculated amount is large, and search speed is slow; Genetic algorithm and particle cluster algorithm, be very easily absorbed in local optimum.Adopt Chaos particle swarm optimization algorithm to be optimized the parameter γ of LSSVM and σ for this reason.
Carry out the training of LSSVM, its parameter will be set in advance.The method of Selecting parameter is a lot, and we expect that use has global optimization ability, and fast convergence rate, the algorithm that result precision is high carries out Selecting parameter.Chaos sequence is produced based on the optimal location that Chaos-Particle Swarm Optimization mainly utilizes the ergodicity of chaotic motion to search by current whole population.The optimal location particle produced in chaos sequence is replaced at random a particle position in current particle group.Improve particle cluster algorithm and be easily absorbed in Local Extremum, later stage of evolution restrains the low shortcoming of slow precision.
The concrete steps of chaotic particle swarm optimization:
1. initialization population.Comprise: algorithm parameter, iterations, chaos masking number of times.
2. according to the basic particle group algorithm formula more speed of new particle and position.
3. couple globally optimal solution P
gcarry out chaotization process.By P
gin each element p
gi(i=1,2 ..., n) be mapped in [0,1] field of definition of Logistic () equation; z
i=(p
gi-a
i)/(b
i-a
i), then, carry out iteration with Logistic () equation and produce Chaos Variable sequence z
i(m) (m=1,2 ...), then Chaos Variable sequence is mapped p by inverse transformation
gi=a
i+ (b
i-a
i) z
im () gets back to former solution space, obtain P
g(m).In each feasible solution that former solution space is set up Chaos Variable
calculate fitness value, retain optimum P
*;
4. select a particle P pre-group from working as at random
*replace.
If 5. reach requirement, then terminate.Otherwise carry out second step.
So chaotic particle swarm optimization is exactly a kind of stochastic global optimization algorithm, and it has fast convergence rate, and the feature that precision is high.Selecting parameter when meeting LSSVM training in this model optimizes requirement.
By above-mentioned discussion, the prediction flowage structure based on small echo and chaos optimization LSSVM forecast model of proposition as shown in Figure 5.
Here 4 time series waveforms after using wavelet decomposition are predicted, use front 350 points of time series as training set, and rear 75 points are as simulation contrast set.The Selecting parameter of LSSVM carries out according to Section 5.The parameter relevant to chaos, to have calculated in Section 3 for this example and has listed.4 time series ripples of each frequency that prediction is formed carry out wavelet reconstruction and form final periodic weighting load prediction ripple.
For contrasting the performance of this model, construct 3 models here, identical with correlated condition in data, and simulate when each model reaches optimum.In order to evaluation model performance, adopt square error (meansquarederror, and average relative percentage error (meanabsolutepercenterror MSE), MPAE) as model performance evaluation index, their definition are respectively such as formula (6) and formula (7).The prediction curve of several model as shown in Figure 6.Several model construction and evaluation result as shown in table 1.
In formula: x
trepresent the actual observed value of support periodic weighting load,
represent the predicted value of load, n represents sample number.
Table 14 Construction of A Model and evaluation index result
Model 1 is adding-weight one-rank local-region method, and its prediction is realized by linear fit time series.Its advantage is that computation structure complexity is low, convenience of calculation, and speed is the fastest in these 4 models.But the periodic weighting load suffered by support is chaos to a great extent, is nonlinear.Precision be in this way minimum.
Model 2 uses BP neural network.The self-adaptation nonlinear structure of neural network, be suitable for predicting nonlinear system, its precision is higher than model 1.But BP network learning method is empirical risk minimization principle, easily occurs over-fitting, its precision is seriously reduced.Meanwhile, use the time cost of neural network larger than model 1.
Compared with model 3 is predicted with BP NEURAL NETWORK, there is good prediction effect, speed of convergence is accelerated, and improves precision of prediction.To the discussion of chaos diagonal recurrent neural networks forecast model, illustrate that model 3 is prediction scheme more outstanding at present.
The performance of this model is as shown in table 1, with regard to MSE and MAPE, improves a lot than traditional model 1 and model 2 performance.Compared with the chaos diagonal recurrent neural networks forecast model proposed not long ago, the performance still progress to some extent of prediction.But the cost that performance improves is exactly the seriously higher of time cost.There is the phase space of certain chaotic property for formed non-linear of this data of hydraulic support periodic weighting load, use the result carrying out predicting based on small echo and chaos optimization LSSVM model can be more accurate.
Claims (3)
1. the method for periodic weighting prediction, it is characterized in that, the method utilizes Wavelet Decomposition Technology that selected sample set data decomposition is become the component of different frequency, based on chaology, component phase space is reconstructed, each reconstruct component respectively life cycle presses the training of LSSVM model, wherein the parameter of periodic weighting LSSVM forecast model is optimized by Chaos particle swarm optimization algorithm, finally, the anticipation component that each periodic weighting LSSVM model obtains is carried out small echo restructuring and obtain complete periodic weighting load prediction waveform, it comprises the steps: the wavelet decomposition of cyclic loading, based on the load phase space reconfiguration of chaology, the structure of periodic weighting least square method supporting vector machine, the chaotic particle swarm optimization of periodic weighting model parameter, in certain cycle of reconstruct ripple, under the time series of load has the condition of certain chaotic property, predetermined period presses load ripple, utilize the multiresolution analysis of wavelet analysis method, data are processed by different level, the sampled point of supports loading is for the time, discrete in time, for this situation, use Mallat fast algorithm implementation wavelet transform, Mallat algorithm is the filtering using wavelet filter discrete signal to be carried out to low pass and high pass, if the low frequency component on the i-th yardstick is a
i, high fdrequency component is d
i, orthogonal wavelet filter is respectively h low pass and g high pass, then the wavelet decomposition on certain yardstick and the Mallat algorithmic notation of synthesis such as formula (1) and formula (2),
Press load to decompose with Mallat wavelet analysis method to support, use the Orthogonal Wavelets of dwt in matlab to carry out 3 grades of decomposition, be divided into and solve 4 components, wherein, a
1for low frequency component, d
1, d
2, d
3for each grade high fdrequency component, the defining method of hydraulic support periodic weighting load chaotic property, hydraulic support periodic weighting load circulate under different cycles formed time series chaotic property can by change its cycle T, dimension and the Lyapunov characteristic exponent of chaotic attractor is calculated under different cycles T, determine that the T when cycle dimension is minimum or related coefficient is maximum is the chaos cycle, periodic weighting least square method supporting vector machine parameter is optimized by Chaos-Particle Swarm Optimization, the kernel function of periodic weighting support vector machine is radial basis function, the regression model of periodic weighting LSSVM such as formula for:
Adopt Chaos-Particle Swarm Optimization to be optimized about γ and σ of load in formula, note: in above formula, the implication of each variable is: n is number of samples, k is a kth sample information, and i is i-th yardstick, a
ibe the low frequency component on the i-th yardstick, d
ibe the high fdrequency component on the i-th yardstick, h is for decomposing low-pass filter, and g is for decomposing Hi-pass filter, α
ifor regression coefficient, b is the threshold values set in regression model, and σ is radial basis check figure width.
2. a kind of method for periodic weighting prediction according to claim 1, is characterized in that,
The concrete steps of parameters of loading chaotic particle swarm optimization:
1). initialization population, comprising: algorithm parameter, iterations, chaos masking number of times;
2). according to the basic particle group algorithm more speed of new particle and position;
3). to globally optimal solution P
gcarry out chaotization process, by P
gin each element p
gi(i=1,2 ..., n) be mapped in [0,1] field of definition of Logistic () equation; z
i=(p
gi-a
i)/(b
i-a
i), then, carry out iteration with Logistic () equation and produce Chaos Variable sequence z
i(m) (m=1,2 ...), then Chaos Variable sequence is mapped p by inverse transformation
gi=a
i+ (b
i-a
i) z
im () gets back to former solution space, obtain P
gm (), in each feasible solution that former solution space experiences Chaos Variable
calculate fitness value, retain optimum P
*;
4). select a particle P pre-group from working as at random
*replace;
5) if. reach requirement, then terminate, otherwise carry out second step, note: P
gfor globally optimal solution, p
gi(i=1,2 ..., n) be each element in globally optimal solution, z
ifor a ground i element map of optimum solution is to the value in Logistic () equation, a
ibe the low frequency component on the i-th yardstick, b
ibe the threshold values that the i-th yardstick sets, z
i(m) (m=1,2 ...) be the Chaos Variable sequence drawn with Logistic () Equation Iterative.
3. a kind of method for periodic weighting prediction according to claim 1, is characterized in that, predicts flow process based on small echo and chaos optimization periodic weighting LSSVM.
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| CN103498699A (en) * | 2013-09-04 | 2014-01-08 | 中国矿业大学 | Predicating system of mine operation face roof weight |
| CN104333005B (en) * | 2014-08-18 | 2016-04-13 | 西南交通大学 | Based on frequency dynamic Forecasting Methodology after the Power System Disturbances of support vector regression |
| CN110083910B (en) * | 2019-04-19 | 2020-11-17 | 西安交通大学 | NSGA-II based chaotic time sequence prediction sample acquisition method |
| CN110672319B (en) * | 2019-10-11 | 2021-04-23 | 大连海事大学 | Large ship shafting centering safety state evaluation method based on attractor |
| CN111472827B (en) * | 2020-04-10 | 2021-05-28 | 太原理工大学 | Intelligent decision-making method for hydraulic support group following propulsion behavior |
| CN111828095B (en) * | 2020-07-09 | 2021-11-19 | 郑州普泽能源科技有限公司 | Dynamic prediction method for top plate incoming pressure |
| CN114792177B (en) * | 2022-06-24 | 2022-09-23 | 中煤科工开采研究院有限公司 | Multi-hydraulic support load prediction method and device for fully mechanized mining face and electronic equipment |
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