本文選題：多分辨分析　切入點：小波包　出處：《西安科技大學(xué)》2013年碩士論文　論文類型：學(xué)位論文

【摘要】：煤礦瓦斯災(zāi)害是煤礦五大自然災(zāi)害之一，嚴(yán)重威脅煤礦的安全生產(chǎn)。瓦斯涌出量是研究瓦斯災(zāi)害的一個重要指標(biāo)，，為防止瓦斯災(zāi)害事故的發(fā)生，對瓦斯涌出量進行預(yù)測尤為重要。從系統(tǒng)的觀點來看，瓦斯涌出是一個復(fù)雜的非線性動力系統(tǒng)，其涌出量作為一種時間序列，依其數(shù)據(jù)的大小和順序蘊含著大量有關(guān)系統(tǒng)動態(tài)演化過程的痕跡和特征，本文針對這一特點結(jié)合小波理論中的多分辨分析和小波包分析對礦井瓦斯涌出量進行了預(yù)測。主要內(nèi)容和結(jié)論如下。 通過小波多分辨分析把瓦斯涌出量這一非平穩(wěn)時間序列分解為若干層近似意義上的平穩(wěn)時間序列，再用AR模型對其單只重構(gòu)序列建立模型（即建立了基于多分辨分析的預(yù)測模型），分析了不同小波基函數(shù)和同一小波基函數(shù)分解層數(shù)不同對預(yù)測效果的影響。經(jīng)過仿真驗證，基于多分辨分析的預(yù)測結(jié)果與直接用AR模型預(yù)測的結(jié)果相比較好。 多分辨分析只能在固定的頻率空間上分解時間軸，對于時間分辨率比較高的時間序列，可能會因為選取了比較低的頻率尺度，導(dǎo)致某些在頻率較高空間中反映瓦斯涌出系統(tǒng)狀態(tài)特征的信息丟失。瓦斯涌出量常具有混沌特性且規(guī)律不易顯現(xiàn)。因此，本文選用可以自適應(yīng)選擇頻帶的小波包變換對瓦斯涌出量的混沌時間序列進行分解和重構(gòu)，在其混沌特性判別的基礎(chǔ)上，改進了傳統(tǒng)的小波包—混沌預(yù)測模型，對模型中小波包重構(gòu)的每組序列的預(yù)測結(jié)果引入了權(quán)重，建立了加權(quán)小波包—混沌預(yù)測模型。仿真結(jié)果表明，此模型不但提高了預(yù)測精度還改善了預(yù)測誤差的不穩(wěn)定性，增加了可預(yù)測范圍；鑒于最優(yōu)小波包在分解層數(shù)一定的情況下重構(gòu)結(jié)點數(shù)會盡可能少的優(yōu)點，本文提出了用最優(yōu)小波包進行分解的加權(quán)最優(yōu)小波包—混沌預(yù)測模型，它不但保留了加權(quán)小波包—混沌預(yù)測模型的優(yōu)點，還減小了計算量，經(jīng)仿真驗證，具有較好的預(yù)測效果。 最后，本文用小波神經(jīng)網(wǎng)絡(luò)代替最優(yōu)小波包—混沌預(yù)測模型中的加權(quán)一階局域法，利用小波神經(jīng)網(wǎng)絡(luò)強大的非線性映射能力，建立了最優(yōu)小波包—混沌—小波神經(jīng)網(wǎng)絡(luò)模型，對瓦斯涌出量進行預(yù)測。經(jīng)過仿真實驗和比較分析，最優(yōu)小波包—混沌—小波神經(jīng)網(wǎng)絡(luò)模型預(yù)測精度較高，具有一定的推廣和實用價值。
[Abstract]:Gas disaster in coal mine is one of the five natural disasters in coal mine, which seriously threatens the safe production of coal mine. The quantity of gas emission is an important index to study gas disaster, in order to prevent the occurrence of gas disaster accident, From the point of view of system, gas emission is a complex nonlinear dynamic system, and its emission is a time series. According to the size and order of the data, there are a lot of traces and characteristics about the dynamic evolution of the system. In this paper, combined with multi-resolution analysis and wavelet packet analysis in wavelet theory, the mine gas emission is predicted. The main contents and conclusions are as follows. The non-stationary time series of gas emission is decomposed into stationary time series in the sense of approximation by wavelet multi-resolution analysis. Then the AR model is established for its single reconstruction sequence (that is, a prediction model based on multi-resolution analysis is established, and the influence of different wavelet basis functions and different decomposition layers of the same wavelet basis function on the prediction results is analyzed. The prediction result based on Multiresolution analysis is better than that with AR model directly. Multiresolution analysis can only decompose the time axis in a fixed frequency space. For a time series with a higher time resolution, it may be possible to select a lower frequency scale. This results in the loss of some information which reflects the state characteristics of the gas emission system in the higher frequency space. The gas emission is often characterized by chaos and the law is not easy to appear. In this paper, the wavelet packet transform, which can adaptively select the frequency band, is used to decompose and reconstruct the chaotic time series of gas emission. On the basis of discriminating its chaotic characteristics, the traditional wavelet packet-chaos prediction model is improved. The weight is introduced into the prediction results of each set of sequences reconstructed by wavelet packets, and a weighted wavelet packet-chaotic prediction model is established. The simulation results show that the model not only improves the prediction accuracy but also improves the instability of prediction errors. In view of the advantage that the number of nodes reconstructed by optimal wavelet packets is as small as possible when the number of decomposition layers is constant, a weighted optimal wavelet packet-chaotic prediction model is proposed. It not only retains the advantages of the weighted wavelet packet-chaotic prediction model, but also reduces the computational complexity. The simulation results show that it has a good prediction effect. Finally, in this paper, wavelet neural network is used to replace the weighted first-order local method in the optimal wavelet packet-chaos prediction model, and the optimal wavelet packet-chaos wavelet neural network model is established by using the powerful nonlinear mapping ability of the wavelet neural network. The simulation experiment and comparative analysis show that the prediction accuracy of the optimal wavelet packet chaotic wavelet neural network model is high and has certain popularization and practical value.
【學(xué)位授予單位】：西安科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：TD712.5

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