本文關(guān)鍵詞：基于Napofics多維泰勒網(wǎng)的非線性時(shí)間序列建模及預(yù)測(cè)研究　出處：《東南大學(xué)》2016年博士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 多維泰勒網(wǎng) 非線性時(shí)間序列 自適應(yīng) 建模 預(yù)測(cè) 正負(fù)反饋交替論 穩(wěn)定性分離 多尺度

【摘要】：時(shí)間序列的相鄰數(shù)據(jù)之間存在著內(nèi)在聯(lián)系,這種內(nèi)在聯(lián)系是時(shí)間序列的一個(gè)本質(zhì)特征。時(shí)間序列建模及預(yù)測(cè)就是根據(jù)系統(tǒng)的觀測(cè)值,建立能反映時(shí)間序列中所包含的動(dòng)態(tài)關(guān)系的數(shù)學(xué)模型,揭示系統(tǒng)的運(yùn)動(dòng)規(guī)律,預(yù)測(cè)其未來的變化發(fā)展規(guī)律和走勢(shì),是預(yù)測(cè)方法體系中的重要組成部分。通過綜合運(yùn)用系統(tǒng)的輸入輸出數(shù)據(jù),而非機(jī)理,建立非線性時(shí)間序列的解析模型,特別是建立具有量變到質(zhì)變現(xiàn)象的系統(tǒng)的解析模型尤為重要。因此,對(duì)時(shí)間序列建模及預(yù)測(cè)方法的研究,無論是在揭示系統(tǒng)運(yùn)動(dòng)規(guī)律或某一現(xiàn)象與其它現(xiàn)象之間的內(nèi)在關(guān)系及運(yùn)動(dòng)規(guī)律,進(jìn)一步發(fā)展現(xiàn)有理論,提升對(duì)系統(tǒng)運(yùn)動(dòng)規(guī)律探索與認(rèn)知這樣的科學(xué)研究層面,還是在重大工程結(jié)構(gòu)和重要基礎(chǔ)設(shè)施的垮塌等破壞性災(zāi)害預(yù)報(bào)、環(huán)境污染監(jiān)測(cè)這樣的科學(xué)應(yīng)用層面,都具有重大意義。為此,本文針對(duì)非線性時(shí)間序列建模和預(yù)測(cè)問題,特別是針對(duì)物質(zhì)系統(tǒng)由量變到質(zhì)變而呈現(xiàn)“平穩(wěn)→劇變→再平穩(wěn)→再劇變”這一變化規(guī)律的時(shí)間序列展開對(duì)其建模以及預(yù)測(cè)的研究。首先,針對(duì)非線性時(shí)間序列,提出一種新型的、可用于時(shí)間序列預(yù)測(cè)的網(wǎng)絡(luò)模型——多維泰勒網(wǎng),并結(jié)合該模型,提出了一種新型的非線性時(shí)間序列預(yù)測(cè)方法：其次,在多維泰勒網(wǎng)單步預(yù)測(cè)的基礎(chǔ)上,將該多維泰勒網(wǎng)應(yīng)用于混沌系統(tǒng)的多步預(yù)測(cè),建立多步自適應(yīng)模型,通過數(shù)據(jù)窗口的滑動(dòng)自適應(yīng)建模,實(shí)現(xiàn)對(duì)具有混沌特性的非線性時(shí)間序列的多步預(yù)測(cè)；再次,針對(duì)實(shí)際物質(zhì)系統(tǒng)中,一些系統(tǒng)的狀態(tài)變化往往存在由量變到質(zhì)變,由一個(gè)穩(wěn)定階段過渡到另一個(gè)穩(wěn)定階段的現(xiàn)象,從而不斷呈現(xiàn)出“平穩(wěn)→劇變→再平穩(wěn)→再劇變”的演變規(guī)律,在本文導(dǎo)師嚴(yán)洪森教授經(jīng)過多年方法論研究而提出的正負(fù)反饋交替論(Alternate positive negative feedbackics,簡(jiǎn)稱Napofic s)的基礎(chǔ)上,提出了一種新穎的、對(duì)該變化規(guī)律進(jìn)行動(dòng)態(tài)數(shù)學(xué)描述的正負(fù)反饋交替論模型,并結(jié)合多維泰勒網(wǎng)模型,提出了基于該正負(fù)反饋交替論的非線性時(shí)間序列預(yù)測(cè)方法；最后,結(jié)合物質(zhì)系統(tǒng)由量變到質(zhì)變而呈現(xiàn)“平穩(wěn)→劇變→再平穩(wěn)→再劇變”這一變化規(guī)律,將等效正、負(fù)反饋?zhàn)饔玫呐卸ǔ叨韧卣篂槎喑叨?即以狀態(tài)變化速度作為第一尺度、狀態(tài)變化加速度作為第二尺度,根據(jù)狀態(tài)變化劇烈程度以及劇烈變化趨勢(shì),將狀態(tài)穩(wěn)定性分離,提出了基于多維泰勒網(wǎng)的多尺度正負(fù)反饋交替論模型并應(yīng)用于預(yù)報(bào)仿真。具體說來,主要在以下幾個(gè)方面進(jìn)行了研究：1.針對(duì)非線性時(shí)間序列,提出了一種新型的、不同于以往常用研究方法的網(wǎng)絡(luò)模型——多維泰勒網(wǎng)。該網(wǎng)絡(luò)是一種新型的、在建立系統(tǒng)解析模型方面具有突出優(yōu)勢(shì)的新型網(wǎng)絡(luò)模型。首先詳細(xì)介紹了該模型的結(jié)構(gòu)和工作原理。證明了多維泰勒網(wǎng)模型構(gòu)建形式的可行性,并確定了模型中各加權(quán)項(xiàng)的具體表達(dá)形式。在此基礎(chǔ)上,提出了一種新型的基于多維泰勒網(wǎng)的時(shí)間序列預(yù)測(cè)方法。該新型預(yù)測(cè)方法的特點(diǎn)是僅利用非線性時(shí)間序列的觀測(cè)數(shù)據(jù),通過多維泰勒網(wǎng)得到n元一階多項(xiàng)式差分方程組,在無需待預(yù)測(cè)系統(tǒng)的任何先驗(yàn)知識(shí)和機(jī)理的情況下獲得動(dòng)力學(xué)特性描述,實(shí)現(xiàn)對(duì)非線性時(shí)間序列的預(yù)測(cè)。最后通過典型Lorenz混沌時(shí)間序列以及某大型建筑的工程監(jiān)測(cè)數(shù)據(jù)算例驗(yàn)證了方法的有效性和可行性。2.針對(duì)在實(shí)際系統(tǒng)中廣泛存在的混沌現(xiàn)象,提出了一種新的基于多維泰勒網(wǎng)的多步自適應(yīng)預(yù)測(cè)方法,對(duì)混沌時(shí)間序列這一典型非線性時(shí)間序列進(jìn)行多步預(yù)測(cè)。定義了多維泰勒多項(xiàng)式,并證明了該多項(xiàng)式可以對(duì)定義在有界閉集上的多元函數(shù)進(jìn)行逼近。證明了多維泰勒網(wǎng)n階差分輸入形式的正確性。在此基礎(chǔ)上提出的自適應(yīng)多步預(yù)測(cè)方法不同于一般進(jìn)行相空間重構(gòu)的混沌時(shí)間序列預(yù)測(cè)方法,它不以嵌入維數(shù)和時(shí)間延遲這兩個(gè)相空間重構(gòu)方法中的關(guān)鍵參數(shù)的選取為前提。無需系統(tǒng)的先驗(yàn)知識(shí)和機(jī)理,基于具有混沌特性的時(shí)間序列數(shù)據(jù),建立多維泰勒網(wǎng)模型,通過數(shù)據(jù)窗口的滑動(dòng)自適應(yīng)建模,從而實(shí)現(xiàn)對(duì)混沌時(shí)間序列的多步預(yù)測(cè)。最后,通過應(yīng)用實(shí)例驗(yàn)證了該基于多維泰勒網(wǎng)的混沌時(shí)間序列多步自適應(yīng)預(yù)測(cè)方法的可行性和實(shí)用性。3.針對(duì)實(shí)際物質(zhì)系統(tǒng)中,一些系統(tǒng)的狀態(tài)變化往往存在由量變到質(zhì)變,從一個(gè)穩(wěn)定階段過渡到另一個(gè)穩(wěn)定階段的現(xiàn)象,從而不斷呈現(xiàn)出“平穩(wěn)→劇變→再平穩(wěn)→再劇變”的演變規(guī)律,引入等效正負(fù)反饋的思想,并將該思想與系統(tǒng)狀態(tài)這一演變過程相結(jié)合,提出了一種新穎的、對(duì)該變化規(guī)律進(jìn)行動(dòng)態(tài)數(shù)學(xué)描述的正負(fù)反饋交替論模型,以及基于該正負(fù)反饋交替論模型的非線性時(shí)間序列預(yù)測(cè)方法。證明了用正負(fù)反饋交替論模型描述系統(tǒng)呈現(xiàn)出的“平穩(wěn)→劇變→再平穩(wěn)→再劇變”的演變規(guī)律的可行性。根據(jù)數(shù)據(jù)的變化劇烈程度,將狀態(tài)穩(wěn)定性分離,用疊加多個(gè)死區(qū)函數(shù)反映系統(tǒng)狀態(tài)不同劇變期由于能量爆發(fā)造成的正反饋?zhàn)饔?將系統(tǒng)狀態(tài)穩(wěn)定性分離,不從系統(tǒng)內(nèi)在的機(jī)理出發(fā),而是通過系統(tǒng)內(nèi)在機(jī)理的外部表征數(shù)據(jù),建立系統(tǒng)的動(dòng)力學(xué)模型,以從動(dòng)態(tài)數(shù)學(xué)模型的角度描述系統(tǒng)狀態(tài)由量變到質(zhì)變而呈現(xiàn)出“平穩(wěn)→劇變→再平穩(wěn)→再劇變”的這一變化規(guī)律。最后通過算例實(shí)例仿真,驗(yàn)證了該正負(fù)反饋交替論模型在非線性時(shí)間序列建模及預(yù)測(cè)中的有效性。4.結(jié)合物質(zhì)系統(tǒng)由量變到質(zhì)變而呈現(xiàn)“平穩(wěn)→劇變→再平穩(wěn)→再劇變”這一變化規(guī)律,以及多維泰勒網(wǎng),引入多尺度概念,提出了一種基于多維泰勒網(wǎng)的多尺度正負(fù)反饋交替論模型。證明了用多個(gè)尺度描述系統(tǒng)的上述演變規(guī)律和建立其多尺度模型的正確性。將狀態(tài)的變化速度和變化加速度分別作為等效正、負(fù)反饋的第一和第二界定尺度,根據(jù)狀態(tài)變化劇烈程度以及劇烈變化趨勢(shì),將狀態(tài)穩(wěn)定性分離。以動(dòng)力學(xué)方程形式表述物質(zhì)系統(tǒng)的上述變化規(guī)律。該模型是一種能夠?qū)ⅰ捌椒�(wěn)→劇變→再平穩(wěn)→再劇變”這一變化過程中的劇烈變化階段系統(tǒng)狀態(tài)變化量和變化趨勢(shì)以顯性函數(shù)的形式表達(dá)的、基于觀測(cè)數(shù)據(jù)的通用模型。最后,將該模型應(yīng)用于非線性時(shí)間序列預(yù)測(cè),以具有典型量變積累到質(zhì)變的實(shí)際系統(tǒng)實(shí)測(cè)數(shù)據(jù)為基礎(chǔ),進(jìn)行系統(tǒng)建模及預(yù)報(bào)的仿真研究。結(jié)果表明,該模型能較準(zhǔn)確反映系統(tǒng)的變化規(guī)律,能有效進(jìn)行預(yù)報(bào)、且精度高,為具有此類演變規(guī)律的復(fù)雜系統(tǒng)建模及預(yù)測(cè)提供了一種新穎而有效的手段。
[Abstract]:There is a connection between adjacent data time series, this relation is an essential feature of time series. The modeling and forecasting of time series is based on the observation value, establish mathematical model can reflect the dynamic relationship contained in the time series, reveals the movement of the system, forecast its future development law and the trend is an important part of prediction system. Through the input and output data of the integrated use of the system, rather than a mechanism, an analytical model of nonlinear time series, especially to establish a quantitative change to qualitative change phenomenon of the analytical model of system is particularly important. Therefore, the research on time series modeling and forecasting methods, either the intrinsic relationship between the motion rules and reveal the law of motion of the system or a phenomenon and other phenomena, the further development of existing theories, to enhance the system movement rules The law of exploration and cognition such scientific research level, or in the important project and the important infrastructure collapse and destructive disaster forecasting, environmental pollution monitoring such scientific level, are of great significance. Therefore, based on the nonlinear time series modeling and forecasting of time series, especially for the material system from quantitative to qualitative change show "smooth, smooth, and then again to change the variation of the upheaval of the research on Modeling and prediction. Firstly, aiming at the nonlinear time series, puts forward a new type, can be used, the multi-dimensional Taylor network model for time series prediction network, combined with the model, a method is proposed for predicting the model of nonlinear time series. Secondly, based on the multi-dimensional Taylor network and single step prediction, the multi-dimensional Taylor network applied to chaotic systems with multi step prediction, establish Adaptive model, adaptive modeling by sliding data window, realize multi-step prediction for nonlinear time series have chaotic characteristics; thirdly, according to the actual state of material system, some system changes are from quantitative to qualitative change, from a stable phase transition to another stable stage of the phenomenon, so as to continuously present "the evolution of smooth, smooth, and then again to upheaval upheaval", in the positive and negative mentor Yan Hongsen professor after many years of research methodology of feedback theory (Alternate positive negative feedbackics alternate, referred to as Napofic s) on the basis of a novel, the variation of positive and negative dynamic mathematical description the alternate feedback theory model, and combined with the multi-dimensional Taylor network model, proposed the alternating positive and negative feedback nonlinear time series method based on prediction theory; finally, combined with the The material system from quantitative to qualitative change and showed a "smooth, smooth, and then again, drastic upheaval" the regularity is equivalent, expand the criteria the negative feedback function for multi scale, i.e. to state change rate as the first scale, state change of acceleration as second scale, according to the state of the degree of change and drastic change trend the state, stability of separation, the multi-level network feedback on alternating positive and negative Dovi Taylor model and its application in prediction based on simulation. Specifically, research mainly in the following aspects: 1. according to the non linear time series, we put forward a new network, the model is different from the commonly used research methods -- Dovi Taylor network. The network is a new type of model, network model has advantages in establishing the analytic model of system. First introduces the model and structure of The working principle has been proved. The feasibility of constructing form multi-dimensional Taylor network model, and to determine the specific forms of expression of the weighted model. On this basis, we put forward a new time series prediction method based on multi-dimensional Taylor network. The characteristics of this new prediction method is only using the observation data of nonlinear time series through the multi-dimensional Taylor network N first order polynomial difference equations to describe the dynamic characteristics, without any prior knowledge and mechanism to predict the system's situation, realize the prediction of the nonlinear time series. Finally, through the typical Lorenz chaotic time series and the engineering monitoring data of a large building of the method was verified the effectiveness and feasibility of.2. in chaotic phenomenon widely exists in the actual system, proposes a new adaptive multi step prediction method based on multi-dimensional Taylor network, the The chaotic time series which is a typical nonlinear time series multi-step prediction. The definition of multidimensional Taylor polynomials, and proves that the polynomials can be defined in the bounded closed set of multivariate function approximation. It is proved that the multi-dimensional Taylor network and the difference of n order correct input form. Different adaptive prediction method of chaotic time series is presented in this on the basis of multi step prediction method to reconstruct the phase space, it is not to select the embedding dimension and time delay of the two key parameters of phase space reconstruction method in the premise. Without a priori knowledge of the system and mechanism, time series data are based on chaotic characteristics, establish multi-dimensional Taylor network model. By sliding window adaptive modeling data, so as to realize the multi step prediction of chaotic time series. Finally, the application example of the multi-dimensional Taylor network based on chaotic time sequence Column.3. adaptive multi step prediction of the feasibility and practicability of the method according to the actual state of material system, some system changes are from quantitative to qualitative change, from a stable phase transition to another steady stage phenomenon, and constantly showing smooth evolution, smooth, and then to upheaval upheaval. "The introduction of the equivalent positive and negative feedback of thought, and the thought and system state of the evolution process of the combination, this paper presents a novel, on the variation of positive and negative feedback on alternating dynamic mathematical description model, and based on the alternating positive and negative feedback nonlinear time series theory model forecasting method. Proved by positive and negative feedback replace the theory model to describe the system showing a" smooth, smooth, and then again, change the evolution of upheaval is feasible. According to the data of the degree of change, the stability of state separation And with the superposition of a plurality of dead zone function reflect different system state upheaval period due to a positive feedback effect caused by a burst of energy, the stability of system state separation, not starting from the mechanism inherent in the system, but through the external data representation of the internal mechanism of the system, the dynamic model of system is set up by a quantitative change to qualitative change from the dynamic mathematical model of the angle of system state description shows the variation of stable, smooth, and then again to drastic upheaval ". Finally through the example simulation, verified the positive and negative feedback on alternating combination of material system from quantitative change to qualitative model.4. is effective in modeling and prediction of nonlinear time series in the present", and then change smoothly smooth, then shift "the regularity and multi-dimensional Taylor network, introduced the concept of multi-scale, presents a multi-scale and multi-dimensional Taylor network based on alternating feedback The model is proved by the evolution. Describe the system with multiple scales and establish the multiscale model is correct. The state change rate and the change of acceleration as the equivalent is, first and second negative feedback definition scale, according to the state of the degree of change and drastic change trend, the state of separation. The variation law of stability expression of substance system in the form of dynamic equation. The model is a "smooth, smooth, and then again to upheaval upheaval in the course of this change change stage system state variation and change trend of expression by dominant function in the form of the general model, based on observation data. Finally, the application of the model in the nonlinear time series prediction, which has typical accumulated to the actual system data qualitative basis for simulation modeling and forecasting system. Results It shows that the model can accurately reflect the change rule of the system, and it can predict effectively, and it has high accuracy. It provides a new and effective means for modeling and forecasting complex systems with such evolution rules.

【學(xué)位授予單位】：東南大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：O211.61

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