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31
Scalespace Properties of the Multiscale Morphological DilationErosion
 IEEE TRANS. ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1996
"... A multiscale morphological dilationerosion smoothing operation and its associated scalespace expansion for multidimensional signals are proposed. Properties of this smoothing operation are developed and, in particular a scalespace monotonic property for signal extrema is demonstrated. Scalespace ..."
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Cited by 64 (2 self)
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A multiscale morphological dilationerosion smoothing operation and its associated scalespace expansion for multidimensional signals are proposed. Properties of this smoothing operation are developed and, in particular a scalespace monotonic property for signal extrema is demonstrated. Scalespace fingerprints from this approach have advantages over Gaussian scalespace fingerprints in that they: are defined for negative values of the scale parameter; have
Extending the HOL theorem prover with a Computer Algebra System to Reason about the Reals
 Higher Order Logic Theorem Proving and its Applications (HUG `93
, 1993
"... In this paper we describe an environment for reasoning about the reals which combines the rigour of a theorem prover with the power of a computer algebra system. 1 Introduction Computer theorem provers are a topic of research interest in their own right. However much of their popularity stems from ..."
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Cited by 34 (4 self)
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In this paper we describe an environment for reasoning about the reals which combines the rigour of a theorem prover with the power of a computer algebra system. 1 Introduction Computer theorem provers are a topic of research interest in their own right. However much of their popularity stems from their application in computeraided verification, i.e. proving that designs of electronic or computer systems, programs, protocols and cryptosystems satisfy certain properties. Such proofs, as compared with the proofs one finds in mathematics books, usually involve less sophisticated central ideas, but contain far more technical Supported by the Science and Engineering Research Council, UK. y Supported by SERC grant GR/G 33837 and a grant from DSTO Australia. details and therefore tend to be much more difficult for humans to write or check without making mistakes. Hence it is appealing to let computers help. Some fundamental mathematical theories, such as arithmetic, are usually requi...
2006) Convergence Properties of the Likelihood of Computed Dynamic Models
 Econometrica
"... This paper studies the econometrics of computed dynamic models. Since these models generally lack a closedform solution, their policy functions are approximated by numerical methods. Hence, the researcher can only evaluate an approximated likelihood associated with the approximated policy function ..."
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Cited by 26 (3 self)
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This paper studies the econometrics of computed dynamic models. Since these models generally lack a closedform solution, their policy functions are approximated by numerical methods. Hence, the researcher can only evaluate an approximated likelihood associated with the approximated policy function rather than the exact likelihood implied by the exact policy function. What are the consequences for inference of the use of approximated likelihoods? First, we find conditions under which, as the approximated policy function converges to the exact policy, the approximated likelihood also converges to the exact likelihood. Second, we show that second order approximation errors in the policy function, which almost always are ignored by researchers, have first order effects on the likelihood function. Third, we discuss convergence of Bayesian and classical estimates. Finally, we propose to use a likelihood ratio test as a diagnostic device for problems derived from the use of approximated likelihoods.
Incipient Fault Diagnosis of Dynamical Systems Using OnLine Approximators
 IEEE Transactions on Automatic Control
, 1998
"... Detection of incipient (slowly developing) faults is crucial in automated maintenance problems where early detection of worn equipment is required. In this note, a general framework for modelbased fault detection and diagnosis of a class of incipient faults is developed. The changes in the system d ..."
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Cited by 18 (1 self)
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Detection of incipient (slowly developing) faults is crucial in automated maintenance problems where early detection of worn equipment is required. In this note, a general framework for modelbased fault detection and diagnosis of a class of incipient faults is developed. The changes in the system dynamics due to the fault are modeled as nonlinear functions of the state and input variables, while the time profile of the failure is assumed to be exponentially developing. An automated fault diagnosis architecture using nonlinear online approximators with an adaptation scheme is designed and analyzed. A simulation example of a simple nonlinear massspring system is used to illustrate the results. Keywords Nonlinear Estimator, Failure Detection, OnLine Approximators. I. Introduction Increased productivity requirements and stringent performance specifications lead to more demanding operating conditions of many modern engineering systems. Such conditions increase the possibility of sy...
HOL Light Tutorial (for version 2.20)
, 2007
"... The HOL Light theorem prover can be difficult to get started with. While the manual is fairly detailed and comprehensive, the large amount of background information that has to be absorbed before the user can do anything interesting is intimidating. Here we give an alternative ‘quick start ’ guide, ..."
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Cited by 10 (0 self)
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The HOL Light theorem prover can be difficult to get started with. While the manual is fairly detailed and comprehensive, the large amount of background information that has to be absorbed before the user can do anything interesting is intimidating. Here we give an alternative ‘quick start ’ guide, aimed at teaching basic use of the system quickly by means of a graded set of examples. Some readers may find it easier to absorb; those who do not are referred after all to the standard manual. “Shouldn’t we read the instructions?”
Chain rules for higher derivatives
 The Mathematical Intelligencer
, 2006
"... We define a notion of higherorder directional derivative of a smooth function and use it to establish three simple formulae for the nth derivative of the composition of two functions. These three “higherorder chain rules ” are alternatives to the classical Faa ̀ di Bruno formula. They are less exp ..."
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Cited by 5 (0 self)
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We define a notion of higherorder directional derivative of a smooth function and use it to establish three simple formulae for the nth derivative of the composition of two functions. These three “higherorder chain rules ” are alternatives to the classical Faa ̀ di Bruno formula. They are less explicit than Faa ̀ di Bruno’s formula, but are much simpler and avoid Diophantine or combinatorial complications.
The Integral: An Easy Approach after Kurzweil and Henstock.
"... A simple definition. Riemann’s integral of 1867 can be summarized as f(t)dt = lim � f(τi)(ti − ti−1). This summary conceals some of the complexity—for example, the limit is of a net, not a sequence—but it displays what we wish to emphasize: The integral is formed by combining the values f(τi) in a v ..."
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Cited by 4 (0 self)
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A simple definition. Riemann’s integral of 1867 can be summarized as f(t)dt = lim � f(τi)(ti − ti−1). This summary conceals some of the complexity—for example, the limit is of a net, not a sequence—but it displays what we wish to emphasize: The integral is formed by combining the values f(τi) in a very direct fashion. The values of f are used less directly in Lebesgue’s integral (1902), which � b can be described as limn→ ∞ a gn(t)dt. The approximating functions gn must be chosen carefully, using deep, abstract notions of measure theory. Simpler definitions are possible—for example, functional analysts might consider the metric completion of C[0, 1] using the L1 norm—but such a definition does not give us easy access to the Lebesgue integral’s simple and powerful properties such as the Monotone Convergence Theorem. We generally think in terms of those simple properties, rather than the various complicated definitions, when we actually use the Lebesgue integral.
Neural Network Based Robust Fault Diagnosis in Robotic Systems
 IEEE Transactions on Neural Networks
, 1997
"... Fault diagnosis plays an important role in the operation of modern robotic systems. A number of researchers have proposed fault diagnosis architectures for robotic manipulators using the modelbased analytical redundancy approach. One of the key issues in the design of such fault diagnosis scheme ..."
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Cited by 4 (0 self)
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Fault diagnosis plays an important role in the operation of modern robotic systems. A number of researchers have proposed fault diagnosis architectures for robotic manipulators using the modelbased analytical redundancy approach. One of the key issues in the design of such fault diagnosis schemes is the effect of modeling uncertainties on their performance. This paper investigates the problem of fault diagnosis in rigidlink robotic manipulators with modeling uncertainties. A learning architecture with sigmoidal neural networks is used to monitor the robotic system for offnominal behavior due to faults. The robustness and stability properties of the fault diagnosis scheme are rigorously established. Simulation examples are presented to illustrate the ability of the neural network based robust fault diagnosis scheme to detect and accommodate faults in a twolink robotic manipulator. 1 1 Introduction Robotic systems are integral components of many complex engineering system...
Adaptive Nonlinear Design Without a Priori Knowledge of Control Directions
, 1998
"... Detection of incipient (slowly developing) faults is crucial in automated maintenance problems where early detection of worn equipment is required. In this paper, a general framework for modelbased fault detection and diagnosis of a class of incipient faults is developed. The changes in the system ..."
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Cited by 2 (0 self)
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Detection of incipient (slowly developing) faults is crucial in automated maintenance problems where early detection of worn equipment is required. In this paper, a general framework for modelbased fault detection and diagnosis of a class of incipient faults is developed. The changes in the system dynamics due to the fault are modeled as nonlinear functions of the state and input variables, while the time profile of the failure is assumed to be exponentially developing. An automated fault diagnosis architecture using nonlinear online approximators with an adaptation scheme is designed and analyzed. A simulation example of a simple nonlinear massspring system is used to illustrate the results. Index TermsFailure detection, nonlinear estimator, online approximators. I. INTRODUCTION Increased productivity requirements and stringent performance specifications lead to more demanding operating conditions of many modern engineering systems. Such conditions increase the possibility Man...