Connections Between Classical and Generalised Trajectories of a State/Signal System

In our earlier article “Well-posed state/signal systems in continuous time”, we originally defined the notion of a trajectory of a state/signal system by means of a generating subspace. However, it was left as an open problem whether the generating subspace is uniquely determined by a given family of all generalised trajectories of a well-posed state/signal system. In this article we give a positive answer to this question and show how this insight simplifies some formulations in the theory of well-posed state/signal systems. The main contribution of the article is an explicit convolution scheme for constructing classical trajectories approximating an arbitrary generalised trajectory. We apply this scheme by studying relationships between classical and generalised trajectories of continuous-time state/signal systems under very weak assumptions. Among others, we show that there exists a space of classical trajectories that is invariant under differentiation and dense in the space of generalised trajectories. Some of our results generalise known results for strongly continuous semigroups and input/state/output systems, but we make no use of decompositions of the signal space into an input space and an output space, and in particular, none of our results depend on well-posedness.     

Statistical methods for automatic crack detection based on vibrothermography sequence‐of‐images data

Vibrothermography is a relatively new nondestructive evaluation technique for finding cracks through frictional heat generated from crack surface vibrations under external excitations. The vibrothermography inspection method provides a sequence of infrared images as the output. We use a matched filter technique to increase the signal‐to‐noise ratio of the sequence‐of‐images data. An automatic crack detection criterion based on the features extracted from the matched filter output greatly increases the sensitivity of the vibrothermography inspection method. In this paper, we develop a three‐dimensional matched filter for the sequence‐of‐images data, which presents the statistical analysis for the matched filter output, and evaluate the probability of detection. Our results show the crack detection criterion based on the matched filter output provides an improved detection capability. Copyright © 2010 John Wiley & Sons, Ltd.     

Computation of Controllability and Observability Matrices – Duality and Automatic Differentiation

During the last decades, many new methods for controller and observer design for nonlinear state‐space systems have been developed. Several of these design methods require Lie derivaties and Lie brackets. These derivatives are also needed to compute controllability and observability matrices of nonlinear systems. Up to now, these derivatives have been computed symbolically. An alternative approach based on automatic differentiation is presented.     

Improving envelopment in Data Envelopment Analysis under variable returns to scale

In a Data Envelopment Analysis model, some of the weights used to compute the efficiency of a unit can have zero or negligible value despite of the importance of the corresponding input or output. This paper offers an approach to preventing inputs and outputs from being ignored in the DEA assessment under the multiple input and output VRS environment, building on an approach introduced in Allen and Thanassoulis (2004) for single input multiple output CRS cases. The proposed method is based on the idea of introducing unobserved DMUs created by adjusting input and output levels of certain observed relatively efficient DMUs, in a manner which reflects a combination of technical information and the decision maker’s value judgements. In contrast to many alternative techniques used to constrain weights and/or improve envelopment in DEA, this approach allows one to impose local information on production trade-offs, which are in line with the general VRS technology. The suggested procedure is illustrated using real data.     

Multi-harmonic measurements and numerical simulations of nonlinear vibrations of a beam with non-ideal boundary conditions

This study presents a direct comparison of measured and predicted nonlinear vibrations of a clamped–clamped steel beam with non-ideal boundary conditions. A multi-harmonic comparison of simulations with measurements is performed in the vicinity of the primary resonance. First of all, a nonlinear analytical model of the beam is developed taking into account non-ideal boundary conditions. Three simulation methods are implemented to investigate the nonlinear behavior of the clamped–clamped beam. The method of multiple scales is used to compute an analytical expression of the frequency response which enables an easy updating of the model. Then, two numerical methods, the Harmonic Balance Method and a time-integration method with shooting algorithm, are employed and compared one with each other. The Harmonic Balance Method enables to simulate the vibrational stationary response of a nonlinear system projected on several harmonics. This study then proposes a method to compare numerical simulations with measurements of all these harmonics. A signal analysis tool is developed to extract the system harmonics’ frequency responses from the temporal signal of a swept sine experiment. An evolutionary updating algorithm (Covariance Matrix Adaptation Evolution Strategy), coupled with highly selective filters is used to identify both fundamental frequency and harmonic amplitudes in the temporal signal, at every moment. This tool enables to extract the harmonic amplitudes of the output signal as well as the input signal. The input of the Harmonic Balance Method can then be either an ideal mono-harmonic signal or a multi-harmonic experimental signal. Finally, the present work focuses on the comparison of experimental and simulated results. From experimental output harmonics and numerical simulations, it is shown that it is possible to distinguish the nonlinearities of the clamped–clamped beam and the effect of the non-ideal input signal.     

Stochastic resonance in a linear static system driven by correlated multiplicative and additive noises

In this work, we investigate the signal transmission in a linear static system driven by correlated multiplicative and additive noises. When the input signal is periodic, we depict the stochastic resonance (SR) phenomenon by employing the signal-to-noise ratio (SNR) theory; while the input signal is aperiodic, we describe the SR phenomenon by using the input–output cross correlation theory. And the exact analytic expressions of the output SNR and the normalized time averaged cross covariance between input and output are obtained. The results show: under the condition of negative correlated noises, SR arises; while with positive correlated or uncorrelated noises, there is no SR. This result may extend the SR theory to a common linear static system.     

Stability of bilinear time-delay systems

In this paper, the stability of the differential bilinear time-delaysystems is first studied. We consider time-varying bilineartime-delay systems with output feedback. The input or controlu(t)is not only a signal but also an input with output feedback.The analysis is given by using norm-transformation methods.     

Computing functions by approximating the input

In computing real-valued functions, it is ordinarily assumed that the input to the function is known, and it is the output that we need to approximate. In this work, we take the opposite approach: we show how to compute the values of some transcendental functions by approximating the input to these functions, and obtaining exact answers for their output. Our approach assumes only the most rudimentary knowledge of algebra and trigonometry, and makes no use of calculus.     

Three-Dimensional Delaunay Mesh Generation

We propose an algorithm to compute a conforming Delaunay mesh of a bounded domain in specified by a piecewise linear complex. Arbitrarily small input angles are allowed, and the input complex is not required to be a manifold. Our algorithm encloses the input edges with a small buffer zone, a union of balls whose sizes are proportional to the local feature sizes at their centers. In the output mesh, the radius-edge ratio of the tetrahedra outside the buffer zone is bounded by a constant independent of the domain, while that of the tetrahedra inside the buffer zone is bounded by a constant depending on the smallest input angle. Furthermore, the output mesh is graded. Our work is the first that provides quality guarantees for Delaunay meshes in the presence of small input angles.     

Assessment of China transit and economic efficiencies in a modified value-chains DEA model

This study incorporates the concepts of undesirable intermediate, intermediate input, uncontrollable input, and undesirable output to the value-chains model (Chen and Zhu, 2004), thereby creating a modified value-chains model to compute transit and economic efficiencies in 30 regions of China. The modified value-chains model forms a more general formulation to the value-added chains in the utilization of the above concepts; it also provides an optimal intermediate measure which differs from the independent two-stage measure.     

Input‐to‐Output Linearization of Explicit Control Systems with Constrained Measurements

Many design methods for non‐linear control problems require the measurement of the whole state of the plant. This contribution deals with a refinement of the well established exact input‐to‐output linearization such that the control laws depend only on a predefined set of measurements. More precisely, we derive the determining equations for all static control laws, such that the input‐to‐output map from the new input to the new output is linear and such that the constraints concerning the measurements are met.     

Quantitative analysis of continuous weighted marked graphs

This paper deals with the computation of the asymptotic firing rate vector and the stationary marking of continuous weighted marked graphs under infinite servers semantics. The continuous weighted marked graphs are a particular class of continuous Petri net where each place has exactly one input and one output transition. First, we give an explicit formula to compute the asymptotic firing rate vector of transitions using the structure of the given net. Then, under the assumption that there exists only one critical circuit in the strongly connected continuous neutral weighted marked graphs, an original approach to compute the vector of stationary marking is presented. Finally, an application to a flexible manufacturing system is given.     

飞艇姿态跟踪系统的研究

研究了具有参数不确定和外部干扰的飞艇姿态跟踪控制问题．飞艇姿态运动的数学模型为一个多输入/多输出不确定非线性系统,根据该系统的特点,采用了一个基于不确定项上界的鲁棒输出跟踪控制器设计方法,应用输入/输出反馈线性化法和李雅普诺夫方法,设计了飞艇姿态鲁棒控制律,它可确保系统输出按指数规律跟踪期望输出．该控制器设计简单,易于实现．仿真结果表明:即使系统存在不确定性和外界干扰,仍可在闭环系统中实现精确的姿态控制．     

The Concept of Dividing Lines/Surfaces for the Finite Difference Element Method (FDEM)

The FDEM (Finite Difference Element Method) is a black‐box solver for the solution of nonlinear systems of elliptic and parabolic PDEs [1]. We use a FDM of arbitrary consistency order on an unstructured FEM mesh. We compute a reliable error estimate which we also use for an automatic consistency order control and mesh refinement. By dividing lines (2‐D) or dividing surfaces (3‐D) we extend this method for the uniform solution over coupled domains.     

Computation of the observer gain for extended Luenberger observers using automatic differentiation

For a given nonlinear system, the extended Luenberger observerprovides nearly exact error dynamics. In contrast to the normalform observer, the extended Luenberger observer exists evenif the associated integrability condition is violated. Up tonow, Lie derivatives and Lie brackets required by the designprocedure have been computed symbolically. Even for systemswith moderate size and complexity, one usually obtains extremelylarge expressions for the observer gain. The design of an extendedLuenberger observer based on symbolic differentiation is not feasible for complicated or large-scale systems. In this paperwe discuss a new approach to compute the observer gain. Ourapproach is based on a computation method for derivatives calledautomatic differentiation. In contrast to numeric differentiationby means of divided differences, automatic differentiationincurs no truncation errors.     

“Chaos” in superregenerative receivers

The superregenerative principle has been known since the early 1920s. The circuit is extremely simple and extremely sensitive. Today, superheterodyne receivers generally supplant superregenerative receivers in most applications because there are several undesirable characteristics: poor selectivity, reradiation, etc. Superregenerative receivers undergo a revival in recent papers for wireless systems, where low cost and very low power consumption are relevant: house/building meters (such as water, energy, gas counter), personal computer environment (keyboard, mouse), etc. Another drawback is the noise level which is higher than that of a well-designed superheterodyne receiver; without an antenna input signal, the output of the receiver hears in an earphone as a waterfall noise; this sound principally is the inherent input noise amplified and detected by the circuit; however, when the input noise is negligible with respect of an antenna input signal, we are faced to an other source of “noise” self-generated by the superregenerative working. The main objective of this paper concerns this self-generated noise coming from an exponential growing followed by a re-injection process for which the final state is a function of the phase of the input signal.     

Spurious correlation as an approximation of the mutual information between redundant outputs and an unknown input

Stochastic resonance (SR) is a counterintuitive phenomenon, observed in a wide variety of nonlinear systems, for which the addition of noise of opportune magnitude can improve signal detection. Tuning the noise for maximizing the SR effect is important both for artificial and biological systems. In the case of artificial systems, full exploitation of the SR effect opens the possibility of measuring otherwise unmeasurable signals. In biology, identification of possible SR maximization mechanisms is of great interest for explaining the low-energy high-sensitivity perception capabilities often observed in animals. SR maximization approaches presented in literature use knowledge on the input signal (or stimulus, in the case of living beings), and maximize the mutual information between the input and the output signal. The input signal, however, is unknown in many practical settings. To cope with this problem, this paper introduces an approximation of the input–output mutual information based on the spurious correlation among a set of redundant units. A proof of the approximation, as well as numerical examples of its application are given.