Abstract: A mixed method for model order reduction is
presented in this paper. The denominator polynomial is derived by
matching both Markov parameters and time moments, whereas
numerator polynomial derivation and error minimization is done
using Genetic Algorithm. The efficiency of the proposed method can
be investigated in terms of closeness of the response of reduced order
model with respect to that of higher order original model and a
comparison of the integral square error as well.
Abstract: In this paper, model order reduction method is used
for approximation in linear and nonlinearity aspects in some
experimental data. This method can be used for obtaining offline
reduced model for approximation of experimental data and can
produce and follow the data and order of system and also it can
match to experimental data in some frequency ratios. In this study,
the method is compared in different experimental data and influence
of choosing of order of the model reduction for obtaining the best and
sufficient matching condition for following the data is investigated in
format of imaginary and reality part of the frequency response curve
and finally the effect and important parameter of number of order
reduction in nonlinear experimental data is explained further.
Abstract: The author presented a method for model order reduction of large-scale time-invariant systems in time domain. In this approach, two modified Hankel matrices are suggested for getting reduced order models. The proposed method is simple, efficient and retains stability feature of the original high order system. The viability of the method is illustrated through the examples taken from literature.
Abstract: One of the main objectives of order reduction is to
design a controller of lower order which can effectively control the
original high order system so that the overall system is of lower
order and easy to understand. In this paper, a simple method is
presented for controller design of a higher order discrete system.
First the original higher order discrete system in reduced to a lower
order model. Then a Proportional Integral Derivative (PID)
controller is designed for lower order model. An error minimization
technique is employed for both order reduction and controller
design. For the error minimization purpose, Differential Evolution
(DE) optimization algorithm has been employed. DE method is
based on the minimization of the Integral Squared Error (ISE)
between the desired response and actual response pertaining to a
unit step input. Finally the designed PID controller is connected to
the original higher order discrete system to get the desired
specification. The validity of the proposed method is illustrated
through a numerical example.
Abstract: Accurate modeling of high speed RLC interconnects
has become a necessity to address signal integrity issues in current
VLSI design. To accurately model a dispersive system of interconnects
at higher frequencies; a full-wave analysis is required.
However, conventional circuit simulation of interconnects with full
wave models is extremely CPU expensive. We present an algorithm
for reducing large VLSI circuits to much smaller ones with similar
input-output behavior. A key feature of our method, called Frequency
Shift Technique, is that it is capable of reducing linear time-varying
systems. This enables it to capture frequency-translation and sampling
behavior, important in communication subsystems such as mixers,
RF components and switched-capacitor filters. Reduction is obtained
by projecting the original system described by linear differential
equations into a lower dimension. Experiments have been carried out
using Cadence Design Simulator cwhich indicates that the proposed
technique achieves more % reduction with less CPU time than the
other model order reduction techniques existing in literature. We
also present applications to RF circuit subsystems, obtaining size
reductions and evaluation speedups of orders of magnitude with
insignificant loss of accuracy.
Abstract: This paper features the modeling and design of a
Robust Decentralized Fast Output Sampling (RDFOS) Feedback
control technique for the active vibration control of a smart flexible
multimodel Euler-Bernoulli cantilever beams for a multivariable
(MIMO) case by retaining the first 6 vibratory modes. The beam
structure is modeled in state space form using the concept of
piezoelectric theory, the Euler-Bernoulli beam theory and the Finite
Element Method (FEM) technique by dividing the beam into 4 finite
elements and placing the piezoelectric sensor / actuator at two finite
element locations (positions 2 and 4) as collocated pairs, i.e., as
surface mounted sensor / actuator, thus giving rise to a multivariable
model of the smart structure plant with two inputs and two outputs.
Five such multivariable models are obtained by varying the
dimensions (aspect ratios) of the aluminium beam. Using model
order reduction technique, the reduced order model of the higher
order system is obtained based on dominant Eigen value retention
and the Davison technique. RDFOS feedback controllers are
designed for the above 5 multivariable-multimodel plant. The closed
loop responses with the RDFOS feedback gain and the magnitudes of
the control input are obtained and the performance of the proposed
multimodel smart structure system is evaluated for vibration control.
Abstract: Rounding of coefficients is a common practice in
hardware implementation of digital filters. Where some coefficients
are very close to zero or one, as assumed in this paper, this rounding
action also leads to some computation reduction. Furthermore, if the
discarded coefficient is of high order, a reduced order filter is
obtained, otherwise the order does not change but computation is
reduced. In this paper, the Least Squares approximation to rounded
(or discarded) coefficient FIR filter is investigated. The result also
succinctly extended to general type of FIR filters.
Abstract: In this paper, a new model order reduction
phenomenon is introduced at the design stage of linear phase digital
IIR filter. The complexity of a system can be reduced by adopting the
model order reduction method in their design. In this paper a mixed
method of model order reduction is proposed for linear IIR filter. The
proposed method employs the advantages of factor division technique
to derive the reduced order denominator polynomial and the reduced
order numerator is obtained based on the resultant denominator
polynomial. The order reduction technique is used to reduce the delay
units at the design stage of IIR filter. The validity of the proposed
method is illustrated with design example in frequency domain and
stability is also examined with help of nyquist plot.
Abstract: A dead leg is a typical subsea production system
component. CFD is required to model heat transfer within the dead
leg. Unfortunately its solution is time demanding and thus not
suitable for fast prediction or repeated simulations. Therefore there is
a need to create a thermal FEA model, mimicking the heat flows and
temperatures seen in CFD cool down simulations.
This paper describes the conventional way of tuning and a new
automated way using parametric model order reduction (PMOR)
together with an optimization algorithm. The tuned FE analyses
replicate the steady state CFD parameters within a maximum error in
heat flow of 6 % and 3 % using manual and PMOR method
respectively. During cool down, the relative error of the tuned FEA
models with respect to temperature is below 5% comparing to the
CFD. In addition, the PMOR method obtained the correct FEA setup
five times faster than the manually tuned FEA.
Abstract: Order reduction of linear-time invariant systems employing two methods; one using the advantages of Routh approximation and other by an evolutionary technique is presented in this paper. In Routh approximation method the denominator of the reduced order model is obtained using Routh approximation while the numerator of the reduced order model is determined using the indirect approach of retaining the time moments and/or Markov parameters of original system. By this method the reduced order model guarantees stability if the original high order model is stable. In the second method Particle Swarm Optimization (PSO) is employed to reduce the higher order model. PSO method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Both the methods are illustrated through numerical examples.
Abstract: In this paper a mixed method by combining an evolutionary and a conventional technique is proposed for reduction of Single Input Single Output (SISO) continuous systems into Reduced Order Model (ROM). In the conventional technique, the mixed advantages of Mihailov stability criterion and continued Fraction Expansions (CFE) technique is employed where the reduced denominator polynomial is derived using Mihailov stability criterion and the numerator is obtained by matching the quotients of the Cauer second form of Continued fraction expansions. Then, retaining the numerator polynomial, the denominator polynomial is recalculated by an evolutionary technique. In the evolutionary method, the recently proposed Differential Evolution (DE) optimization technique is employed. DE method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. The proposed method is illustrated through a numerical example and compared with ROM where both numerator and denominator polynomials are obtained by conventional method to show its superiority.
Abstract: Recently, genetic algorithms (GA) and particle swarm optimization (PSO) technique have attracted considerable attention among various modern heuristic optimization techniques. The GA has been popular in academia and the industry mainly because of its intuitiveness, ease of implementation, and the ability to effectively solve highly non-linear, mixed integer optimization problems that are typical of complex engineering systems. PSO technique is a relatively recent heuristic search method whose mechanics are inspired by the swarming or collaborative behavior of biological populations. In this paper both PSO and GA optimization are employed for finding stable reduced order models of single-input- single-output large-scale linear systems. Both the techniques guarantee stability of reduced order model if the original high order model is stable. PSO method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Both the methods are illustrated through numerical example from literature and the results are compared with recently published conventional model reduction technique.
Abstract: A subsea hydrocarbon production system can undergo planned and unplanned shutdowns during the life of the field. The thermal FEA is used to simulate the cool down to verify the insulation design of the subsea equipment, but it is also used to derive an acceptable insulation design for the cold spots. The driving factors of subsea analyses require fast responding and accurate models of the equipment cool down. This paper presents cool down analysis carried out by a Krylov subspace reduction method, and compares this approach to the commonly used FEA solvers. The model considered represents a typical component of a subsea production system, a closed valve on a dead leg. The results from the Krylov reduction method exhibits the least error and requires the shortest computational time to reach the solution. These findings make the Krylov model order reduction method very suitable for the above mentioned subsea applications.
Abstract: A computationally simple approach of model order
reduction for single input single output (SISO) and linear timeinvariant
discrete systems modeled in frequency domain is proposed
in this paper. Denominator of the reduced order model is determined
using fuzzy C-means clustering while the numerator parameters are
found by matching time moments and Markov parameters of high
order system.