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2013 | Buch

Introduction and Overview Kapitel lesen Erstes Kapitel lesen

System Identification Using Regular and Quantized Observations

Applications of Large Deviations Principles

verfasst von: Qi He, Le Yi Wang, G. George Yin

Verlag: Springer New York

Buchreihe : SpringerBriefs in Mathematics

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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SUCHEN

Über dieses Buch

​This brief presents characterizations of identification errors under a probabilistic framework when output sensors are binary, quantized, or regular. By considering both space complexity in terms of signal quantization and time complexity with respect to data window sizes, this study provides a new perspective to understand the fundamental relationship between probabilistic errors and resources, which may represent data sizes in computer usage, computational complexity in algorithms, sample sizes in statistical analysis and channel bandwidths in communications.

Inhaltsverzeichnis

Frontmatter
1. Introduction and Overview
Abstract
Traditional system identification taking noise measurement into consideration concentrates on convergence in suitable senses (such as in mean square, in distribution, or with probability one) and rates of convergence. Such asymptotic analysis is inadequate in applications that require precise probability error bounds beyond what are provided by the law of large numbers or the central limit theorem. Especially, for system diagnosis and prognosis and their related complexity analysis, it is essential to understand probabilities of identification errors over a finite data window. For example, in real-time diagnosis, parameter values must be evaluated to determine whether they belong to a “normal” region or a “fault” has occurred. This set-based identification amounts to hypothesis testing, which relies on an accurate probabilistic characterization of parameter estimates.
Qi He, Le Yi Wang, G. George Yin
2. System Identification: Formulation
Abstract
Consider a single-input–single-output (SISO) linear time-invariant (LTI) stable discrete-time system
$$y(t) =\displaystyle\sum\limits_{ i=0}^{\infty }a_{ i}u(t - i) + d(t),\quad t = t_{0} + 1,\ldots,$$
(2.1)
where {y(t)} is the noise corrupted observation, {d(t)} is the disturbance, {u(t)} is the input with u(t) = 0 for t < 0, and \(a =\{ a_{i},i = 0,1,\ldots \},\) satisfying
$$\|a\|_{1} =\displaystyle\sum\limits_{ i=0}^{\infty }\vert a_{ i}\vert < \infty.$$
To proceed, we define
$$\begin{array}{ll} & \theta = (a_{0},a_{1},\ldots,a_{m_{0}-1})^{\prime} \in {\mathbb{R}}^{m_{0} }, \\ & \widetilde{\theta } = (a_{m_{0}},a_{m_{0}+1},\ldots )^{\prime}, \end{array}$$
(2.2)
where z′ denotes the transpose of z.
Qi He, Le Yi Wang, G. George Yin
3. Large Deviations: An Introduction
Abstract
The theory of large deviations characterizes probabilities and moments of certain sequences that are associated with “rare” events. In a typical application, consider the sum of N independent and identically distributed random variables. The deviations from the mean of the sum by a given bound become “rarer” as N becomes larger. Large deviations principles give asymptotically accurate probabilistic descriptions of such rare events as a function of N. Large deviations theory has been applied in diversified areas in probability theory, statistics, operations research, communication networks, information theory, statistical physics, financial mathematics, and queuing systems, among others.
Qi He, Le Yi Wang, G. George Yin
4. LDP of System Identification under Independent and Identically Distributed Observation Noises
Abstract
We first consider system identification under i.i.d. noise. Extension to correlated noises will be treated in Chapter 5. Beginning with the following assumptions, we should emphasize here that since we consider open-loop identification problems, the input signal u is part of experimental design and can be selected to enhance the identification process.
Qi He, Le Yi Wang, G. George Yin
5. LDP of System Identification under Mixing Observation Noises
Abstract
Up to this point, the observation noises are assumed to be uncorrelated. In this chapter, we demonstrate that a much larger class of noise processes can be treated.
Qi He, Le Yi Wang, G. George Yin
6. Applications to Battery Diagnosis
Abstract
This chapter uses a battery diagnosis problem to illustrate the use of the LDP in industrial applications. Management of battery systems plays a pivotal role in electric and hybrid vehicles, and in support of distributed renewable energy generation and smart grids. The state of charge (SOC), the state of health (SOH), internal impedance, open circuit voltage, and other parameters indicate jointly the state of the battery system. Battery systems’ behavior varies significantly among individual cells and demonstrates time-varying and nonlinear characteristics under varying operating conditions such as temperature, charging/discharging rates, and different SOCs. Such complications in capturing battery features point to a common conclusion that battery monitoring, diagnosis, and management should be individualized and adaptive. Although battery health diagnosis has drawn substantial research effort recently [26, 56] using various estimation methods or signal-processing algorithms [6, 43], the LDP has never been used before in this application. In the following, we describe a joint estimation algorithm for real-time battery parameter and SOC estimation that supports a diagnosis method using LDPs. For further reading on power control and battery systems, see [4, 5, 9, 13, 20, 21, 24, 25, 34, 44, 52] and references therein.
Qi He, Le Yi Wang, G. George Yin
7. Applications to Medical Signal Processing
Abstract
Heart and lung sounds are of essential importance in medical diagnosis of patients with lung or heart diseases. To obtain reliable diagnosis and detection, it is critically important that cardiac and respiratory auscultation obtain sounds of high clarity. However, heart and lung sounds interfere with each other in auscultation, corrupting sound quality and causing difficulties in diagnosis. For example, the main frequency components of heart sounds, which are in the range of 50–100 Hz, often produce an intrusive interference that masks the clinical interpretation of lung sounds over the low-frequency band. It is highly desirable, especially in computerized heart/lung sound analysis, to separate the overlapped heart and lung sounds before using them for diagnosis.
Qi He, Le Yi Wang, G. George Yin
8. Applications to Electric Machines
Abstract
Electric machines are essential systems in electric vehicles and are widely used in other applications. In particular, permanent magnet direct current (PMDC) motors have been extensively employed in industrial applications such as electric vehicles and battery-powered devices such as wheelchairs, power tools, guided vehicles, welding equipment, X-ray and tomographic systems, and computer numerical control (CNC) machines. PMDC motors are physically smaller and lighter for a given power rating than induction motors. The unique features of PMDC motors, including their high torque production at lower speed and flexibility in design, make them preferred choices in automotive transmissions, gear systems, lower-power traction utility, and other fields [12, 18, 22, 47, 54]. For efficient torque/speed control, thermal management, motor-condition monitoring, and fault diagnosis of PMDC motors, it is essential that their characteristics be captured in real-time operations. This is a system identification problem that can be carried out by using standard identification methods [35, 48].
Qi He, Le Yi Wang, G. George Yin
9. Remarks and Conclusion
Abstract
For clarity, this book assumes that the input is designed to be periodic. Advantages of using full rank and periodic inputs in quantized identification problems have been extensively discussed in [62]. Note that such a choice is not a fundamental limitation, and aperiodic inputs can also be used. As a first attempt at using LDPs in complexity analysis, we will not explore this direction in detail here, but only highlight the main steps. To illustrate the basic ideas and computational processes for quantized identification under aperiodic inputs, we use the basic case of a binary sensor with threshold C and gain identification problems.
Qi He, Le Yi Wang, G. George Yin
Backmatter
Metadaten
Titel
System Identification Using Regular and Quantized Observations
verfasst von
Qi He
Le Yi Wang
G. George Yin
Copyright-Jahr
2013
Verlag
Springer New York
Electronic ISBN
978-1-4614-6292-7
Print ISBN
978-1-4614-6291-0
DOI
https://doi.org/10.1007/978-1-4614-6292-7

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