Eccentricity-Induced Seismic Behavior of Curved Bridges Based on Controllability

The difficulty in curved bridge design lies in the eccentricity. Eccentricities break the regularity and make it difficult to resist horizontal loads. However, relatively stable and robust performance can still be achieved through properly aligned eccentricity. This paper used the controllability-related concepts, the controllability Grammians and Hankel singular values (HSVs), to study the impact of eccentricities on the seismic performance of curved bridges. An analytical model was expressed by second order differential equations with rigid deck assumption. Six eccentricity cases: three different radii (resulting in different center of mass (CM)), three different bearing arrangements (resulting in different center of stiffness (CS)), and variable earthquake directions (resulting in different moment arms) were strategized for research. Analyses showed that effects of eccentricities (offsets of CS from CM) can be extensively interpreted by controllability indices. Proper eccentricity may “reach” and thus “control” the responses better and decrease the coupling effects, counteract the unfavorable excitation effects, and make the bridge less sensitive to excitation changes. In this sense, regularity or stability could be somewhat re-established through design. Time history analyses confirmed the results.

Truncated model reduction methods for linear time-invariant systems via eigenvalue computation

This paper provides three model reduction methods for linear time-invariant systems in the view of the Riemannian Newton method and the Jacobi-Davidson method. First, the computation of Hankel singular values is converted into the linear eigenproblem by the similarity transformation. The Riemannian Newton method is used to establish the model reduction method. Besides, we introduce the Jacobi-Davidson method with the block version for the linear eigenproblem and present the corresponding model reduction method, which can be seen as an acceleration of the former method. Both the resulting reduced systems can be equivalent to the reduced system originating from a balancing transformation. Then, the computation of Hankel singular values is transformed into the generalized eigenproblem. The Jacobi-Davidson method is employed to establish the model reduction method, which can also lead to the reduced system equivalent to that resulting from a balancing transformation. This method can also be regarded as an acceleration of a Riemannian Newton method. Moreover, the application for model reduction of nonlinear systems with inhomogeneous conditions is also investigated.

Active Integrated Devices PDN Balanced Truncation Reduction Method

For EMC simulation, the vector fitting model is transformed into time domain state equation model. Then the system is balanced. Then the reduced model can be obtained by removing the states corresponding to the small HSV (Hankel Singular Values). The order of the reduced model is determined by the singular curvature spectrum. Finally, balanced truncation model reduction method is used on a sample chip PDN (Power Distribution Network) and compared with the performance of the AWE (Asymptotic Waveform Evaluation) method. Simulation results show that the proposed method can operate in a wide frequency range and has smaller error and faster speed.

Schur Decomposition Model Reduction Algorithm of Discrete-Time Singular Dynamical Systems

In this paper, a model reduction for discrete-time singular dynamical systems is investigated. First, by transforming the original systems, the singular systems of impulse models are decomposed into the casual subsystems and the non-casual subsystems, and the reduction problem becomes merely a simplification of the non-casual subsystems reduction. Based on the Schur decomposition and apply Matlab to reorder the Schur forms, the degree of the systems state controllability and observability is scaled by Hankel singular values, and the results show that the controllability and observability of the states which are corresponding to the smaller Hankel singular values are weaker. Based on it, a new model reduction algorithm of discrete-time singular systems is given. Finally, a numerical simulation illustrates the effectiveness of the proposed algorithm.

An Alternative Approach to the Balanced Model Truncation Algorithm for Acoustic Minimum-Phase Inverse Filters Order Reduction

We propose an alternative approach to the Balanced Model Truncation method (standard method). This approach reduces substantially the order of minimum-phase inverse filters for equalizing room acoustics. This method is based on a property of the filter z transform function, which modifies the corresponding FIR coefficients before the application of the standard technique to the modified FIR coefficients filter version. In the standard technique, the Hankel singular values plot is the chief guide for a user for the selection of a reduced filter order. Results for minimum-phase inverse filter corresponding to partial equalization of measured acoustic impulse response show the superiority of the proposed method over the standard technique, in terms of reduced filters order selection.