Higher-Order Stabilized Perturbation for Recursive Eigen-Decomposition Estimation

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Paul Mucchielli ◽  
Basuraj Bhowmik ◽  
Budhaditya Hazra ◽  
Vikram Pakrashi
Keyword(s):  
Real Time ◽  
Degrees Of Freedom ◽  
Higher Order ◽  
Mode Shapes ◽  
Accurate Estimation ◽  
Perturbation Approach ◽  
Mode Identification ◽  
First Order ◽  
Ill Conditioned Matrices ◽  
Eigen Decomposition

Abstract Eigen-decomposition remains one of the most invaluable tools for signal processing algorithms. Although traditional algorithms based on QR decomposition, Jacobi rotations and block Lanczos tridiagonalization have been proposed to decompose a matrix into its eigenspace, associated computational expense typically hinders their implementation in a real-time framework. In this paper, we study recursive eigen perturbation (EP) of the symmetric eigenvalue problem of higher order (greater than one). Through a higher order perturbation approach, we improve the recently established first-order eigen perturbation (FOP) technique by creating a stabilization process for adapting to ill-conditioned matrices with close eigenvalues. Six algorithms were investigated in this regard: first-order, second-order, third-order, and their stabilized versions. The developed methods were validated and assessed on multiple structural health monitoring (SHM) problems. These were first tested on a five degrees-of-freedom (DOF) linear building model for accurate estimation of mode shapes in an automated framework. The separation of closely spaced modes was then demonstrated on a 3DOF + tuned mass damper (TMD) problem. Practical utility of the methods was probed on the Phase-I ASCE-SHM benchmark problem. The results obtained for real-time mode identification establishes the robustness of the proposed methods for a range of engineering applications.

scholarly journals A higher order perfectly matched layer formulation for finite-difference time-domain seismic wave modeling

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. T1-T16 ◽  
Author(s):  
David P. Connolly ◽  
Antonios Giannopoulos ◽  
Michael C. Forde
Keyword(s):  
Finite Difference ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Degrees Of Freedom ◽  
Higher Order ◽  
Staggered Grid ◽  
First Order ◽  
Enhanced Absorption ◽  
Absorption Performance ◽  
Difference Time

We have developed a higher order perfectly matched layer (PML) formulation to improve the absorption performance for finite-difference time-domain seismic modeling. First, we outlined a new unsplit “correction” approach, which allowed for traditional, first-order PMLs to be added directly to existing codes in a straightforward manner. Then, using this framework, we constructed a PML formulation that can be used to construct higher order PMLs of arbitrary order. The greater number of degrees of freedom associated with the higher order PML allow for enhanced flexibility of the PML stretching functions, thus potentially facilitating enhanced absorption performance. We found that the new approach can offer increased elastodynamic absorption, particularly for evanescent waves. We also discovered that the extra degrees of freedom associated with the higher order PML required careful optimization if enhanced absorption was to be achieved. Furthermore, these extra degrees of freedom increased the computational requirements in comparison with first-order schemes. We reached our formulations using one compact equation thus increasing the ease of implementation. Additionally, the formulations are based on a recursive integration approach that reduce PML memory requirements, and do not require special consideration for corner regions. We tested the new formulations to determine their ability to absorb body waves and surface waves. We also tested standard staggered grid stencils and rotated staggered grid stencils.

First order error-adapted eigen perturbation for real-time modal identification of vibrating structures

2020 ◽  
pp. 1-25
Author(s):  
Satyam Panda ◽  
Tapas Tripura ◽  
Budhaditya Hazra
Keyword(s):  
Real Time ◽  
Covariance Matrix ◽  
Passive Control ◽  
Perturbation Technique ◽  
Modal Identification ◽  
Eigenvalue Decomposition ◽  
Mode Shapes ◽  
Computationally Efficient ◽  
Order Error ◽  
First Order

Abstract A new computationally efficient error adaptive first-order eigen-perturbation technique for real-time modal identification of linear vibrating systems is proposed. The existence of error terms in the approximation of the eigenvalue problem of response covariance matrix, in a perturbative framework often hinders the convergence of response-only modal identification. In the proposed method, the error in first-order eigen-perturbation is incorporated using a feedback, formulated by exploiting the generalized eigenvalue decomposition of the real-time covariance matrix of streaming response data. Since the incorporation of the higher-order perturbation terms in the total perturbation is mathematically challenging, the proposed feedback approach provides a computationally efficient framework yet in a more elegant manner. A new criterion for the quality of updated eigenspace is proposed in the present work utilizing the concept of diagonal dominance. Numerical case studies and validation using a standard ASCE benchmark problem have shown applicability of the proposed approach in faster estimation of real-time modal properties and anomaly identification with minimal number of initially required batch data. The applicability of the proposed approach towards real-time under-determined modal identification problems is demonstrated using a real-time decentralized framework. The advantage of rapidly converging online mode-shapes is demonstrated using a passive vibration control problem, where a multi-tuned-mass-damper (MTMD) for a multi-degree of freedom system is tuned online. An extension for online retuning of the detuned MTMD system further demonstrates the fidelity of the proposed algorithm in online passive control.

scholarly journals Higher-order patterns of aquatic species spread through the global shipping network

2019 ◽  
Author(s):  
Mandana Saebi ◽  
Jian Xu ◽  
Erin K. Grey ◽  
David M. Lodge ◽  
Nitesh Chawla
Keyword(s):  
Ballast Water ◽  
Cost Effective ◽  
The United States ◽  
Higher Order ◽  
Accurate Estimation ◽  
Targeted Prevention ◽  
Indigenous Species ◽  
First Order ◽  
Non Indigenous Species ◽  
Higher Order Networks

AbstractThe introduction and establishment of non-indigenous species (NIS) through global ship movements is a significant threat to marine ecosystems and economies. While ballast-vectored invasions have been partly addressed by some national policies and an international agreement regulating the concentrations of organisms in ballast water, biofouling-vectored invasions remain a large risk. Development of additional realistic and cost-effective ship-borne NIS policies requires an accurate estimation of NIS spread risk from both ballast water and biofouling. In this paper, we demonstrate that first-order Markov assumptions limit accurate modeling of NIS spread risks through the global shipping network. In contrast, we show that higher-order patterns overcome this limitation by revealing indirect pathways of NIS transfer. We accomplish this by developing Species Flow Higher-Order Networks (SF-HON), which we developed independently for ballast and biofouling, for comparison with first-order Markovian models of ballast and biofouling. We evaluated SF-HON predictions using the largest available datasets of invasive species for Europe and the United States. We show that not only does SF-HON yield more accurate NIS spread risk predictions than first-order models and existing higher-order models, but also that there are important differences in NIS spread via the ballast and biofouling vectors. Our work provides information that policymakers can use to develop more efficient and targeted prevention strategies for ship-borne NIS spread management, especially as management of biofouling is of increasing concern.

Designing of IMC-PID Controller for Higher-order Process Based on Model Reduction Method and Fractional Coefficient Filter with Real-time Verification

2019 ◽  
Vol 15 (3) ◽  
Author(s):  
Ujjwal Manikya Nath ◽  
Chanchal Dey ◽  
Rajani K. Mudi
Keyword(s):  
Model Reduction ◽  
Real Time ◽  
Pid Controller ◽  
Performance Enhancement ◽  
Higher Order ◽  
Process Models ◽  
Reduction Scheme ◽  
Level Control ◽  
First Order ◽  
Improved Model

AbstractAn improved model reduction scheme is proposed here for higher-order processes and subsequently an enhanced IMC-PID controller is designed based on the obtained reduced model. In the proposed scheme, higher-order processes are estimated as first-order-plus-dead-time (FOPDT) model. Designed IMC controller includes a filter having two separate time constants with fractional order coefficients. Efficacy of the proposed model reduction scheme is verified in terms of closed loop performance evaluation for higher-order minimum and non-minimum phase process models in comparison with improved SIMC (iSIMC) controller (Grimholt. Optimal PI and PID control of first-order plus delay processes and evaluation of the original and improved SIMC rules. J Process Control. 2018;70:36–46). Overall performance enhancement for the proposed method is demonstrated through simulation study as well as real-time experimentation on a level control loop.

Macroscopic and kinetic modelling of rarefied polyatomic gases

2016 ◽  
Vol 806 ◽  
pp. 437-505 ◽  
Author(s):  
Behnam Rahimi ◽  
Henning Struchtrup
Keyword(s):  
Kinetic Model ◽  
Degrees Of Freedom ◽  
Kinetic Modelling ◽  
Higher Order ◽  
Macroscopic Model ◽  
Order Effects ◽  
Moment Equations ◽  
Polyatomic Gases ◽  
First Order ◽  
Order Set

A kinetic model and corresponding high-order macroscopic model for the accurate description of rarefied polyatomic gas flows are introduced. The different energy exchange processes are accounted for with a two term collision model. The proposed kinetic model, which is an extension of the S-model, predicts correct relaxation of higher moments and delivers the accurate Prandtl ($Pr$) number. Also, the model has a proven linear H-theorem. The order of magnitude method is applied to the primary moment equations to acquire the optimized moment definitions and the final scaled set of Grad’s 36 moment equations for polyatomic gases. At the first order, a modification of the Navier–Stokes–Fourier (NSF) equations is obtained. At third order of accuracy, a set of 19 regularized partial differential equations (R19) is obtained. Furthermore, the terms associated with the internal degrees of freedom yield various intermediate orders of accuracy, a total of 13 different orders. Thereafter, boundary conditions for the proposed macroscopic model are introduced. The unsteady heat conduction of a gas at rest is studied numerically and analytically as an example of a boundary value problem. The results for different gases are given and effects of Knudsen numbers, degrees of freedom, accommodation coefficients and temperature-dependent properties are investigated. For some cases, the higher-order effects are very dominant and the widely used first-order set of the NSF equations fails to accurately capture the gas behaviour and should be replaced by the proposed higher-order set of equations.

scholarly journals Perturbation approach to metal surface oxidation considering volume variation

2017 ◽  
Vol 9 (1) ◽  
pp. 168781401667678 ◽  
Author(s):  
Yaohong Suo ◽  
Zhonghua Zhang ◽  
Xiaoxiang Yang
Keyword(s):  
Oxide Layer ◽  
Metal Surface ◽  
Moving Boundary ◽  
Classical Model ◽  
Surface Oxidation ◽  
Higher Order ◽  
Perturbation Approach ◽  
Perturbation Scheme ◽  
First Order ◽  
Parabolic Law

In this article, kinetics equation of the metal surface oxidation is presented using the perturbation approach. A moving boundary is converted into a fixed one by Landau transformation. The perturbation results show that (1) the solution of the zeroth-order stands for the quasi-steady state and that of the first-order is instantaneous and (2) the reaction rate, diffusion coefficient, and the thickness of the initial oxide layer have important effects on the oxidation kinetics. If the chemical reaction is supposed to be instantaneous, our results are reduced to the classical parabolic law, no matter whether there exists the initial oxide layer or not. Moreover, the kinetic coefficient of the parabolic law is analytically presented. The proposed perturbation scheme can be easily extended to the higher order, and the higher order solution will provide a method to correct the error offered by the classical model.

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

Challenging the Multidimensional Conception of Perceived Person-Environment Fit

2020 ◽  
pp. 1-9
Author(s):  
Julian M. Etzel ◽  
Gabriel Nagy
Keyword(s):  
Higher Education ◽  
University Students ◽  
Educational Outcomes ◽  
Factor Model ◽  
Higher Order ◽  
Substantial Proportion ◽  
Unique Variance ◽  
First Order ◽  
Person Environment Fit ◽  
Order Factor

Abstract. In the current study, we examined the viability of a multidimensional conception of perceived person-environment (P-E) fit in higher education. We introduce an optimized 12-item measure that distinguishes between four content dimensions of perceived P-E fit: interest-contents (I-C) fit, needs-supplies (N-S) fit, demands-abilities (D-A) fit, and values-culture (V-C) fit. The central aim of our study was to examine whether the relationships between different P-E fit dimensions and educational outcomes can be accounted for by a higher-order factor that captures the shared features of the four fit dimensions. Relying on a large sample of university students in Germany, we found that students distinguish between the proposed fit dimensions. The respective first-order factors shared a substantial proportion of variance and conformed to a higher-order factor model. Using a newly developed factor extension procedure, we found that the relationships between the first-order factors and most outcomes were not fully accounted for by the higher-order factor. Rather, with the exception of V-C fit, all specific P-E fit factors that represent the first-order factors’ unique variance showed reliable and theoretically plausible relationships with different outcomes. These findings support the viability of a multidimensional conceptualization of P-E fit and the validity of our adapted instrument.

Computational Models for Multilayered Composite Shells with Application to Tires

1996 ◽  
Vol 24 (1) ◽  
pp. 11-38 ◽  
Author(s):  
G. M. Kulikov
Keyword(s):  
Type Theory ◽  
Computational Models ◽  
Geometrical Nonlinearity ◽  
Higher Order ◽  
Stress Strain ◽  
Strain Fields ◽  
First Order ◽  
Timoshenko Type ◽  
Joint Influence ◽  
Discrete Layer

Abstract This paper focuses on four tire computational models based on two-dimensional shear deformation theories, namely, the first-order Timoshenko-type theory, the higher-order Timoshenko-type theory, the first-order discrete-layer theory, and the higher-order discrete-layer theory. The joint influence of anisotropy, geometrical nonlinearity, and laminated material response on the tire stress-strain fields is examined. The comparative analysis of stresses and strains of the cord-rubber tire on the basis of these four shell computational models is given. Results show that neglecting the effect of anisotropy leads to an incorrect description of the stress-strain fields even in bias-ply tires.

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