遲滯現象之系統建模

Abstract

遲滯是與時間進程無關的記憶現象，遲滯系統的輸出訊號與其輸入訊號變動的速度是無關的。遲滯現象在許多物理研究領域上出現，例如：電磁學、電子學、熱力學、可塑性材料科學、以及機械力學等等。然而，這種與速率無關的記憶特質，使得遲滯系統模型非常難以建立。 現存的遲滯系統模型可以分為「局部記憶」及「非局部記憶」兩種。局部記憶模型只考慮目前的輸入輸出值，亦即，在系統的輸入輸出圖譜上的每一點，至多可以有二條曲線經過，當輸入值上升時，系統的輸出沿上升曲線變化，而當輸入值下降時，則由下降曲線決定輸出值。另外，非局部記憶模型在決定系統之輸出值時，則廣泛參考過去發生過的輸入極值。這兩種模型各有其缺點：局部記憶模型不能如非局部記憶模型有效的逼近一個真實的系統；而非局部記憶模型則需要大量的記憶空間，而且在系統運作上之計算也更為複雜。 因此，本文將新發展一個有效率的遲滯系統模型。在此之前，則先檢驗傳統的系統模型，例如：有限訊號回應模型、迴歸輸入模型、時間延遲神經網路、回饋式神經網路等等，測試其是否具有模擬遲滯現象的能力。文中首先以數位訊號處理的角度定義遲滯現象，然後分別以理論分析及數學程式模擬兩方面驗證傳統的系統模型不具有遲滯性質。 接下來，本文提出一個新的遲滯系統模型，此模型結合三個模組，亦即梯度分析、極值暫存、及輸出函數三部分。這樣的架構在接收到一個輸入的極值時，就決定一條啟動函數以供後續輸入值對應到系統輸出值。值得注意的是，此一啟動函數是由存放在極值暫存區的多項之前的數值所決定，因此這個模型同時具有非局部記憶而在工作型態上又同時具有類似局部記憶模型的方便性。 本文所提出的遲滯系統模型將應用在模擬地下水位及地層下陷之間的關係。而經濟學上的領先指標與共同指標之間的關連亦提出來討論。實驗結果顯示新提出的模型對於這些系統的模擬效果遠優於傳統的系統模型。這也意函地層下陷與經濟指標這些系統具有「與速率無關的記憶」。 在新提出的系統基礎上，本文另外發展一個新的語音辨識方法。有鑑於發音的速度不一致性，使得傳統語音辨識演算法複雜而困難，我們在此將引入新的遲滯模型，並以模型中所決定的參數作為固定長度的語音特徵，藉此將可在線性的時間複雜度內辨識出單一語音。 本文首先對遲滯現象提出數學定義，藉此驗證傳統的系統模型不具有遲滯性質。接下來則發展一個有效率的遲滯系統模型，並以此模型解釋地層下陷及經濟指標等遲滯相關系統的數據資料，最後則又將此模型應用在語音訊號的辨識。

Hysteresis is a unique type of dynamics. The output of a hysteresis system is independent of input speed. This property is known as rate-independence, the defining characteristic of hysteresis behavior. Hysteresis phenomena are frequently observed in physical research domains, including magnetism, plasticity, electronics, thermodynamics, materials, and mechanics. However, the unique property of rate independence makes modeling hysteresis behaviors extremely difficult. Existing hysteresis models can be categorized into local and nonlocal memory models. Local memory models consider the current I/O values locally: a maximum of two curves pass through each working point in the I/O diagram. For an increasing input, the curve rises. If the input decreases, then a falling curve is traced. Meanwhile, nonlocal memory models globally refer to past extreme inputs while transducing the new input value to its corresponding output. Both of these models have disadvantages. Local memory models cannot approximate actual systems as closely as do nonlocal memory models, whereas nonlocal memory models require amount of memory to record past extreme values and are computationally difficult. Before developing a newly efficient hysteresis model, we must examine whether conventional memory-related models, such as finite impulse response (FIR) models, autoregressive external input (ARX) models, time delay neural networks (TDNN), and recurrent neural networks (RNN) can simulate hysteresis behavior. This study defines hysteretic memory (rate-independent memory) and then conducts both of theoretical analysis and numerical simulations to examine that conventional system models are not hysteresis systems. Subsequently, this study presents a novel model of hysteresis phenomena. Combining three major blocks - the Gradient Investigator (GI), Extreme-value Template (ET), and Output Function (OF) - the proposed model approximates hysteresis behavior, conveniently by determining an active polynomial function once an extreme input value is reached. Notably, this model includes nonlocal memory in the ET block and is as computationally easy as local memory models of hysteresis. The proposed model is applied to model the relation between ground-water level and land subsidence. The connection between the economic leading and coincident indicators is also studied. Experimental results reveal that our model approximates the measured data more closely than conventional short-term memory models do. This fact implies that the systems of land subsidence and economic indicators are involved with rate independent memory. Based on the proposed model, this study also presents a novel means of recognizing voice signals. Assuming that the dynamic speed of speaking primarily complicates speech recognition, we adopt the parameters of our model as the fixed-length feature for recognition. Accordingly, reference words can be recognized in linear time. Experiments employ the voice signals of numbers, from zero to nine, spoken in Mandarin Chinese. The proposed method is verified to recognize voice signals efficiently. Restated, this study defines hysteretic memory (rate-independent memory) and examines that conventional system models are not hysteresis systems. Consequently, we develop an efficient hysteresis model and apply this model to explain the relation between ground-water level and land subsidence, as well as the connection between the economic leading and coincident indicators. Finally, the proposed model is also applied to voice signal recognition.