Convergent algorithms for frequency weighted L2 model reduction

This paper is concerned with computing an L₂-optimal reduced-order model for a given stable multivariable linear system in the presence of input and output frequency weightings. By parametrizing a class of reduced-order models in terms of an orthogonal projection and using manifold techniques as tools, both continuous and iterative algorithms are derived and their convergence properties are established. As an application, we show that an L₂ optimal reduced-order filter in the closed-loop sense can be computed using these algorithms.     

Robust stability and stabilization of discrete singular systems: an equivalent characterization

This note deals with the problems of robust stability and stabilization for uncertain discrete-time singular systems. The parameter uncertainties are assumed to be time-invariant and norm-bounded appearing in both the state and input matrices. A new necessary and sufficient condition for a discrete-time singular system to be regular, causal and stable is proposed in terms of a strict linear matrix inequality (LMI). Based on this, the concepts of generalized quadratic stability and generalized quadratic stabilization for uncertain discrete-time singular systems are introduced. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are obtained in terms of a strict LMI and a set of matrix inequalities, respectively. With these conditions, the problems of robust stability and robust stabilization are solved. An explicit expression of a desired state feedback controller is also given, which involves no matrix decomposition. Finally, an illustrative example is provided to demonstrate the applicability of the proposed approach.     

Designing learning objects that afford learners the experience of important variations in Chinese characters

Effective teaching should focus the attention of learners to its essential aspects. It follows that instructional software can be designed in such a way that allows learners to experience the important variations in the critical aspects of the content to be learned. This paper reports on the experience of designing such special kinds of instructional learning objects for the learning of Chinese characters. The design of these learning objects takes into consideration not only what Chinese characters are all about but also how learners commonly make errors while they learn to write the characters. Out of the analysis of these learners' errors, variations in the structural features of Chinese characters were pulled out and embodied in the design of the learning objects. Learners tinkering with the learning objects can thus implicitly develop a sense of the structural features or regularity of Chinese characters, which most importantly should prepare the learners to learn more new characters in the future. The main proposal of this paper is the notion of this variation‐affording instructional software that allows learners to attend to the essential aspects of what is to be learned. Furthermore, the idea of the learning object also differs from other instructional software in its small, self‐contained and reusable nature, such that teachers can flexibly embed the learning objects into their own teaching materials.     

Determination of phenomenological constants of shear-induced particle migration model

Particles in initially well-mixed suspensions subject to inhomogeneous shear flows will migrate and establish a particle concentration gradient and a non-Newtonian velocity profile. In this study, a phenomenological diffusive flux model coupled with flow equations was employed to describe the shear-induced particle migration in a concentrated suspension. The focus of the paper is on the determination of the two phenomenological constants in the diffusive flux model k_c and k_η. They were determined inversely by employing a least square analysis on the experimental pressure data with different capillary die ratios of length to diameter of the die. The pressures and the flow patterns of the non-Newtonian concentrated suspension were predicted in terms of these two phenomenological constants. The results indicated that particle migration should be accounted for to properly characterize the rheological behaviour of concentrated suspensions.     

Size-dependent fracture and higher order J-integral for solids characterized by strain gradient elasticity

Elastic fracture is governed by the material's strain energy released rate and depends on the applied loads and the stiffness of the structure. The effect of stiffness on fracture as a function of structural size is typically modeled using strain-based elastic fracture mechanics, but recent experimental evidence indicated that when the size of the structure is on the order of the higher order material length scale parameters, elastic strain gradients would stiffen the structure. In this paper, the higher order J-integral and energy-released rate for the analysis of fracture of strain gradient stiffened structures are developed. The effects of beam size on the fracture behaviors of strain gradient stiffened cantilevers on a substrate were analyzed using the higher order J-integral and the energy-released rate. Analyses revealed that the fracture load is elevated to more than 1.4 times of the un-stiffened case when the bending stiffness is doubled by strain gradient stiffening. Elastic fracture is shown to have an added dependence on the size of the structure when strain gradient stiffening is non-negligible.     

Phase I IASC-ASCE Structural Health Monitoring Benchmark Problem Using Simulated Data

Structural health monitoring (SHM) is a promising field with widespread application in civil engineering. Structural health monitoring has the potential to make structures safer by observing both long-term structural changes and immediate postdisaster damage. However, the many SHM studies in the literature apply different monitoring methods to different structures, making side-by-side comparison of the methods difficult. This paper details the first phase in a benchmark SHM problem organized under the auspices of the IASC–ASCE Structural Health Monitoring Task Group. The scale-model structure adopted for use in this benchmark problem is described. Then, two analytical models based on the structure—one a 12 degree of freedom (DOF) shear-building model, the other a 120-DOF model, both finite element based—are given. The damage patterns to be identified are listed as well as the types and number of sensors, magnitude of sensor noise, and so forth. MATLAB computer codes to generate the response data for the various cases are explained. The codes, as well as details of the ongoing Task Group activities, are available on the Task Group web site at 〈http://wusceel.cive.wustl.edu/asce.shm/〉.     

Lead-free multilayer piezoelectric transformer

In this article, a multilayer piezoelectric transformer based on lead-free Mn-doped 0.94(Bi(12)Na(12))TiO(3)-0.06BaTiO(3) ceramics is presented. This piezoelectric transformer, with a multilayered construction in the thickness direction, is 8.3 mm long, 8.3 mm wide, and 2.3 mm thick. It operates in the second thickness extensional vibration mode. For a temperature rise of 20 degrees C, the transformer has an output power of >0.3 W. With a matching load resistance of 10 Omega, its maximum efficiency approaches 81.5%, and the maximum voltage gain is 0.14. It has potential to be used in low voltage power supply units such as low power adapter and other electronic circuits.     

Observer design and stabilization for linear neutral delay systems

This paper focuses on the state observer design problem as well as the observer-based stabilization problem for linear neutral delay systems. The purpose of the former problem is to design an observer that guarantees the asymptotic stability of the estimation error dynamics. The existence condition for such an observer is established. The latter problem, which is the main problem studied in this paper, aims at designing an observer-based feedback controller, such that the closed-loop system is asymptotically stabilized. It is shown that the desired controller can be easily designed if there are solutions to several linear matrix inequalities. Finally, two simulation examples are given to demonstrate the validity and effectiveness of the proposed approach.