Identification of Physical Systems (eBook)

Applications to Condition Monitoring, Fault Diagnosis, Soft Sensor and Controller Design

Rajamani Doraiswami, Maryhelen Stevenson, Chris Diduch (Autoren)

eBook Download: EPUB

2014
John Wiley & Sons (Verlag)
978-1-118-53649-0 (ISBN)

Infos

Identification of a physical system deals with the problem of identifying its mathematical model using the measured input and output data. As the physical system is generally complex, nonlinear, and its input–output data is corrupted noise, there are fundamental theoretical and practical issues that need to be considered. 

Identification of Physical Systems addresses this need, presenting a systematic, unified approach to the problem of physical system identification and its practical applications.  Starting with a least-squares method, the authors develop various schemes to address the issues of accuracy, variation in the operating regimes, closed loop, and interconnected subsystems. Also presented is a non-parametric signal or data-based scheme to identify a means to provide a quick macroscopic picture of the system to complement the precise microscopic picture given by the parametric model-based scheme.  Finally, a sequential integration of totally different schemes, such as non-parametric, Kalman filter, and parametric model, is developed to meet the speed and accuracy requirement of mission-critical systems.

Key features:

• Provides a clear understanding of theoretical and practical issues in identification and its applications, enabling the reader to grasp a clear understanding of the theory and apply it to practical problems
• Offers  a self-contained guide by including the background necessary to understand this interdisciplinary subject
• Includes case studies for the application of identification on physical laboratory scale systems, as well as number of illustrative examples throughout the book

Identification of Physical Systems is a comprehensive reference for researchers and practitioners working in this field and is also a useful source of information for graduate students in electrical, computer, biomedical, chemical, and mechanical engineering.

Autor

Rajamani Doraiswami, Professor Emeritus, Electrical and Computer Engineering Department, University of New Brunswick, USA Rajamani Doraiswami is Professor Emeritus in the Department of Electrical and Computer Engineering at the University of New Brunswick. Dr. Doraiswami is known internationally as an excellent researcher, has held an NSERC operating grant continually since 1981 and has published more than 60 papers in refereed journals and 90 conference papers. Dr. Doraiswami's research interests focus on control, signal processing, pattern classification and algorithms. One of his most successful collaborations has been in the development of laboratories for the teaching of analysis and design of control and signal processing systems in real-time. Chris Diduch is a Professor in the Department of Electrical and Computer Engineering at the University of New Brunswick. His research is in the fields of control systems and digital systems. Maryhelen Stevenson is a Professor in the Department of Electrical and Computer Engineering at the University of New Brunswick. Her research is in the fields of pattern classification, speech and signal processing, adaptive systems and time-frequency representations.

Textauszug

Preface

The topic of identification and its applications is interdisciplinary, covering the areas of estimation theory, signal processing, and control with a rich background in probability and stochastic processes and linear algebra. Applications include control system design and analysis, fault detection and isolation, health monitoring, condition-based maintenance, fault diagnosis of a sensor network, and soft sensing. A soft sensor estimates variables of interest from the process output measurements using a maintenance-free software, instead of a hardware, device.

The Kalman filter forms the backbone of the work presented in this book, in view of its key property, namely, the residual is a zero-mean white noise process if and only if there is no mismatch between the model of the system and that employed in the design of the Kalman filter. This property is termed the residual property of the Kalman filter. The structure of the identification model is selected to be that of the Kalman filter so as to exploit the residual property. If the error between the system output and its estimate obtained using the identified model is a zero-mean white noise process, then the identified model is the best fit to the system model. Fault detection and isolation is based on analyzing the Kalman filter residual. If the residual property holds, then it is asserted that there is a fault and the residual is then further analyzed to isolate the faulty subsystems. A bank of Kalman filters is employed for fault diagnosis in a sensor network because of the distributed nature of the latter. At the core of a soft sensor is a Kalman filter, which generates the estimates of the unmeasured variable from the output measurements.

Chapters 1-5 provide a background for system identification and its applications including modeling of signals and systems, deterministic and random signals, characterization of signals, and estimation theory, as explained below.

Modeling of Signals and Systems

Chapter 1 describes state-space and linear regression models of systems subject to disturbance and measurement noise. The disturbances may include effects such as the gravity load, electrical power demand, fluctuations in the flow in a fluid system, wind gusts, bias, power frequency signal, dc offset, crew or passenger load in vehicles such as space-crafts, ships, helicopters, and planes, and process faults. Measurement noise is a random signal inherent in all physical components. The most common source of noise is thermal noise, due to the motion of thermally agitated free electrons in a conductor.

A signal is modeled as an output of a linear time-invariant system driven by an impulse (delta) function if it is deterministic, and by a zero-mean white noise process if it is random. An integrated model is developed that includes the model of the disturbance and the measurement noise. The integrated model is driven by both the system input and the zero-mean white noise processes that generate the random disturbances and measurement noise. This model sets the stage for developing the model of the Kalman filter for the system.

Temporal and Spectral Characterization of Signals: Correlation and Spectral Density (Coherence)

Characterization of the signals in terms of the correlation and its frequency-domain counterpart, the power spectral density, are treated in Chapter 2. The correlation is a measure of the statistical similarity or dissimilarity between two waveforms, whereas the magnitude-squared coherence spectrum measures the spectral similarity or dissimilarity between two signals. This measure (coherence spectrum) is the frequency-domain counterpart of the correlation coefficient which preserves only the shape of the correlation function. The coherence spectrum is widely used in many areas including medical diagnosis, performance monitoring, and fault diagnosis. Non-parametric identification of a system in terms of its frequency response may be obtained simply by dividing the cross-power spectral density of the system input and its output, by the spectral density of the input at each frequency. The non-parametric identification serves to cross check the result of the parametric identification of the system.

Estimation theory: Estimation theory is a branch of statistics with wide application in science and engineering. It especially forms the backbone of the system identification field. Because of its pivotal role in System identification, estimation theory has been thoroughly addressed in three complete chapters (Chapters 3-5) which provide its foundational knowledge and results.

Estimation of a Deterministic Parameter

The problem of estimating a deterministic parameter from noisy measurements is developed in Chapter 3. The measurement model is assumed to be linear. The output measurement is a linear function of the unknown parameter with additive noise. The probability density function of the measurement is not restricted to be Gaussian. Commonly occurring heavy tailed probability density functions (PDFs) such as the Laplacian, the exponential, and Cauchy PDFs are considered. If the PDF governing the measurement is unknown except for its mean and variance, a worst-case PDF, which is a partly Gaussian and partly exponential, is employed. The worst-case PDF is derived using min-max theory. A thin-tailed PDF, such as the Gaussian one, characterizes “good” measurement data, while those with thick tails characterize bad measurement data. A popular lower bound used in estimation theory to define the efficiency of an estimator, namely the Cramer - Rao lower bound, is derived for the error covariance of the estimator. An estimator is termed efficient if its estimation error covariance is equal to the Cramer-Rao lower bound, and is unbiased if the true value of the parameter is equal to the expected value of its estimate. Approaches to the estimation of deterministic non-random parameters are developed, including maximum likelihood and the least-squares methods.

Estimation of Random Parameter

Chapter 4 deals with random parameter estimation. It is shown that the optimal estimate in the sense of minimum mean-squared error is the conditional mean of the parameter given the past and present measurement. Extension of the random parameter estimation to the optimum mean-squared error estimation of random process, including the states and output of a system, leads to the development of the Kalman filter.

Least-Squares Estimation

Chapter 5 deals with the widely used least-squares method for estimating the unknown deterministic parameter from the measurement signal which is corrupted by colored or white noise. Properties of the least-squares estimate are derived. Expressions for the bias error and covariance of the estimation error are obtained for the case when the number of data samples is both finite and infinitely large. The least-squares and its generalized version of the weighted least-squares method produces an estimator that is unbiased and is the best linear unbiased estimator (BLUE estimator). Most importantly, the optimal estimate is a solution of a set of linear equations which can be efficiently computed using the Singular Value Decomposition (SVD) technique. Moreover, the least-squares estimation has a very useful geometric interpretation. The residual can be shown to be actually orthogonal to the hyper-plane generated by the columns of the data matrix. This is called the orthogonality principle.

Kalman Filter

The Kalman filter is developed in Chapter 6. It is widely used in a plethora of science and engineering applications including tracking, navigation, fault diagnosis, condition-based maintenance, performance (or health or product quality) monitoring, soft sensing, estimation of a signal of a known class buried in noise, speech enhancement, and controller implementation. It also plays a crucial role in system identification as the structure of the identification model is chosen to be the same as that of the Kalman filter. It is an optimal recursive estimator of the states of a dynamical system that is very well suited for systems that can be non-stationary, unlike the Wiener filter which is limited to stationary processes only. Further extensions of the Kalman filter have taken it into the realms of non-Gaussian and nonlinear systems and have spawned a variety of powerful filters, ranging from the well-known extended KF to the most general particle filter (PF). In a KF, the system is modeled in a state-space form driven by a zero-mean white Gaussian noise process. The Kalman filter consists of two sets of equation, a static (or algebraic) and a dynamic equation. The dynamic equation, or state equation, is driven by the input of the system and the residual. The algebraic (or static) equation, also known as the output equation, contains an additive white Gaussian noise which represents the measurement noise. The Kalman filter is designed for the integrated model of the system formed of the models of the system, the disturbance and the measurement noise. There are two approaches to deriving the Kalman filter: one relies on the stochastic estimation theory and the other on the deterministic theory. A deterministic approach is adopted herein. The structure of the Kalman filter is determined using the internal model principle, which establishes the necessary and sufficient condition for the tracking of the output of a dynamical system. In accordance with this principle, the Kalman filter consists of (i) a copy of the system model driven by the residuals and (ii) a gain term, termed the Kalman gain, used to stabilize the filter. The internal model principle provides a...

Produkt-Details

• Erscheint lt. Verlag: 29.7.2014
• Sprache: englisch
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Schlagworte: Approach • Complex • Control Process & Measurements • Data • Deals • Electrical & Electronics Engineering • Elektrotechnik u. Elektronik • fundamental • generally • Identification • Input • inputoutput • Maschinenbau • mathematical model • mechanical engineering • Messtechnik • Mess- u. Regeltechnik • Noise • Physical • Physical Systems • Practical • Problem • Regelungstechnik • Sensoren, Instrumente u. Messung • Sensors, Instrumentation & Measurement • Sensortechnik • System • Systematic • Systems Engineering & Management • Systemtechnik • Systemtechnik u. -management • Theoretical
• ISBN-10: 1-118-53649-5 / 1118536495
• ISBN-13: 978-1-118-53649-0 / 9781118536490