System Modeling of Hysteresis Phenomena
|關鍵字:||遲滯現象;有限訊號回應模型;迴歸輸入模型;前傳式神經網路;時間延遲神經網路;回饋式神經網路;hysteresis phenomenon;FIR model;ARX model;feed forward neural network;time delay neural network;recurrent neural network|
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.
|Appears in Collections:||Thesis|