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We compare a recently proposed generalized eigensystem approach and a new modified generalized eigensystem approach to more widely used truncated singular value decomposition and zero‐order Tikhonov regularization for solving multidimensional elliptic inverse problems. As a test case, we use a finite element representation of a homogeneous eccentric spheres model of the inverse problem of electrocardiography. Special attention is paid to numerical issues of accuracy, convergence, and robustness. While the new generalized eigensystem methods are substantially more demanding computationally, they exhibit improved accuracy and convergence compared with widely used methods and offer substantially better robustness.

The purpose of this paper is to apply the quantum “eigenlogic” formulation to behavioural analysis. Agents, represented by Braitenberg vehicles, are investigated in the context of the quantum robot paradigm. The agents are processed through quantum logical gates with fuzzy and multivalued inputs; this permits to enlarge the behavioural possibilities and the associated decisions for these simple vehicles.

In eigenlogic, the eigenvalues of the observables are the truth values and the associated eigenvectors are the logical interpretations of the propositional system. Logical observables belong to families of commuting observables for binary logic and many-valued logic. By extension, a fuzzy logic interpretation is proposed by using vectors outside the eigensystem of the logical connective observables. The fuzzy membership function is calculated by the quantum mean value (Born rule) of the logical projection operators and is associated to a quantum probability. The methodology of this paper is based on quantum measurement theory.

Fuzziness arises naturally when considering systems described by state vectors not in the considered logical eigensystem. These states correspond to incompatible and complementary systems outside the realm of classical logic. Considering these states allows the detection of new Braitenberg vehicle behaviours related to identified emotions; these are linked to quantum-like effects.

The method does not deal at this stage with first-order logic and is limited to different families of commuting logical observables. An extension to families of logical non-commuting operators associated to predicate quantifiers could profit of the “quantum advantage” due to effects such as superposition, parallelism, non-commutativity and entanglement. This direction of research has a variety of applications, including robotics.

The goal of this research is to show the multiplicity of behaviours obtained by using fuzzy logic along with quantum logical gates in the control of simple Braitenberg vehicle agents. By changing and combining different quantum control gates, one can tune small changes in the vehicle’s behaviour and hence get specific features around the main basic robot’s emotions.

New mathematical formulation for propositional logic based on linear algebra. This methodology demonstrates the potentiality of this formalism for behavioural agent models (quantum robots).

The application of reduced order models (ROMs) in the aerodynamic/aeroelastic analysis of long-span bridges, unlike the aeronautical structures, has not been extensively studied. ROMs are computationally efficient techniques, which have been widely used for predicting unsteady aerodynamic response of airfoils and wings. This paper aims to discuss the application of a reduced order computational fluid dynamics (CFD) model based on the eigensystem realization algorithm (ERA) in the aeroelastic analysis of the Great Belt Bridge (GBB).

The aerodynamic impulse response of the GBB section is used to construct the aerodynamic ROM, and then the aerodynamic ROM is coupled with the reduced DOF model of the system to construct the aeroelastic ROM. Aerodynamic coefficients and flutter derivatives are evaluated and compared to those of the advanced discrete vortex method-based CFD code.

Results demonstrate reasonable prediction power and high computational efficiency of the technique that can serve for preliminary aeroelastic analysis and design of long-span bridges, optimization and control purposes.

The application of a system identification tool like ERA into the aeroelastic analysis of long-span bridges is performed for the first time in this work. Authors have developed their earlier work on the aerodynamic analysis of long-span bridges, published in the Journal of Bridge Engineering, by coupling the aerodynamic forces with reduced DOF of structural system. The high computational efficiency of the technique enables bridge designers to perform preliminary aeroelastic analysis of long-span bridges in less than a minute.

A quantitative method for the estimation of the discrete transition matrix is developed for the periodic time‐varying system of state differential equations governing electrical synchronous machine behaviour. The approach allows the eigensystem of this transition matrix to be calculated to an arbitrary accuracy without significant added computational burden by using modal structural properties of the state‐space equations.

The purpose of this paper is to present an on-orbit frequency identification method for spacecraft directly using attitude maneuver data. Natural frequency of flexible solar arrays plays an important role in attitude control design of spacecraft with solar arrays, and its precision will directly affect the accuracy of attitude maneuver. However, when the flexibility of the solar arrays is large, because of air damping, gravity effect etc., the frequency obtained by ground test shows great error compared with the on-orbit real value. One solution to this problem is to conduct on-orbit identification during which proper identification methods are used to obtain the parameters of interest based on the real on-orbit data of spacecraft.

The observer/Kalman filter identification and eigensystem realization algorithm are used as identification methods, and the attitude maneuver controller is designed using the rigid-body dynamics method.

Two conclusions are drawn in this paper according to results of numerical simulations. The first one is that the attitude controller based on the rigid-body dynamics method is effective in attitude maneuver of the spacecraft. The second one is that the on-orbit parameter identification can be directly achieved by using attitude maneuver data of spacecraft without adding additional missions.

Based on the methods proposed in this paper, it is convenient to obtain the natural frequencies of the spacecraft using the data of the attitude maneuver, which may greatly reduce the cost of on-orbit identification test.

The way of obtaining natural frequencies based on attitude maneuver data of spacecraft provides high originality and value for practical application.

The purpose of this paper is to propose a novel on‐line print‐defect detecting approach.

The proposed method uses incremental principal component analysis (IPCA) to model a variety pattern with respect to the detected image itself.

The algorithm is constructed and deployed to a real‐time detecting print‐defect system, and the test results show that the system reduces false alarms dramatically.

The paper describes groundbreaking work which, for the first time in the printing industry, uses IPCA in relation to print‐defect detecting.

The purpose of this paper is to propose the generalized integral transform technique (GITT) to the solution of convection-diffusion problems with nonlinear boundary conditions by employing the corresponding nonlinear eigenvalue problem in the construction of the expansion basis.

The original nonlinear boundary condition coefficients in the problem formulation are all incorporated into the adopted eigenvalue problem, which may be itself integral transformed through a representative linear auxiliary problem, yielding a nonlinear algebraic eigenvalue problem for the associated eigenvalues and eigenvectors, to be solved along with the transformed ordinary differential system. The nonlinear eigenvalues computation may also be accomplished by rewriting the corresponding transcendental equation as an ordinary differential system for the eigenvalues, which is then simultaneously solved with the transformed potentials.

An application on one-dimensional transient diffusion with nonlinear boundary condition coefficients is selected for illustrating some important computational aspects and the convergence behavior of the proposed eigenfunction expansions. For comparison purposes, an alternative solution with a linear eigenvalue problem basis is also presented and implemented.

This novel approach can be further extended to various classes of nonlinear convection-diffusion problems, either already solved by the GITT with a linear coefficients basis, or new challenging applications with more involved nonlinearities.

An eigenvalue method is presented for solving the transient heat conduction problem with time‐dependent or time‐independent boundary conditions. The spatial domain is divided into finite elements and at each finite element node, a closed‐form expression for the temperature as a function of time can be obtained. Three test problems which have exact solutions were solved in order to examine the merits of the eigenvalue method. It was found that this method yields accurate results even with a coarse mesh. It provides exact solution in the time domain and therefore has none of the time‐step restrictions of the conventional numerical techniques. The temperature field at any given time can be obtained directly from the initial condition and no time‐marching is necessary. For problems where the steady‐state solution is known, only a few dominant eigenvalues and their corresponding eigenvectors need to be computed. These features lead to great savings in computation time, especially for problems with long time duration. Furthermore, the availability of the closed form expressions for the temperature field makes the present method very attractive for coupled problems such as solid—fluid and thermal—structure interactions.

To reduce the computational complexity per step from O(n²) to O(n) for optimization based on quadratic surrogates, where n is the number of design variables.

Applying nonlinear optimization strategies directly to complex multidisciplinary systems can be prohibitively expensive when the complexity of the simulation codes is large. Increasingly, response surface approximations (RSAs), and specifically quadratic approximations, are being integrated with nonlinear optimizers in order to reduce the CPU time required for the optimization of complex multidisciplinary systems. For evaluation by the optimizer, RSAs provide a computationally inexpensive lower fidelity representation of the system performance. The curse of dimensionality is a major drawback in the implementation of these approximations as the amount of required data grows quadratically with the number n of design variables in the problem. In this paper a novel technique to reduce the magnitude of the sampling from O(n²) to O(n) is presented.

The technique uses prior information to approximate the eigenvectors of the Hessian matrix of the RSA and only requires the eigenvalues to be computed by response surface techniques. The technique is implemented in a sequential approximate optimization algorithm and applied to engineering problems of variable size and characteristics. Results demonstrate that a reduction in the data required per step from O(n²) to O(n) points can be accomplished without significantly compromising the performance of the optimization algorithm.

A reduction in the time (number of system analyses) required per step from O(n²) to O(n) is significant, even more so as n increases. The novelty lies in how only O(n) system analyses can be used to approximate a Hessian matrix whose estimation normally requires O(n²) system analyses.

Recent advances in the fabrication technology of heterojunction semiconductor nanostructures have made possible the realization of systems with extremely small sizes. In these devices, electrons are confined along some directions and are free to move in others. Semiconductor nanostructures have become so small that we have to take into account quantum effects. The two dimensional physical model consists of Poisson’s equation for the electrostatic potential φ, coupled with an eigenvalue problem for Schrödinger’s equation. Proposes