In this work, a model order reduction (MOR) technique for a linear multivariable system is proposed using invasive weed optimization (IWO). This technique is applied with the combined advantages of ...retaining the dominant poles and the error minimization. The state space matrices of the reduced order system are chosen such that the dominant eigenvalues of the full order system are unchanged. The other system parameters are chosen using the invasive weed optimization with objective function to minimize the mean squared errors between the outputs of the full order system and the outputs of the reduced order model when the inputs are unit step. The proposed algorithm has been applied successfully, a 10th order Multiple-Input–Multiple-Output (MIMO) linear model for a practical power system was reduced to a 3rd order and compared with recently published work.
A new kind of optimization technique, namely, continuous genetic algorithm, is presented in this paper for numerically approximating the solutions of Troesch’s and Bratu’s problems. The underlying ...idea of the method is to convert the two differential problems into discrete versions by replacing each of the second derivatives by an appropriate difference quotient approximation. The new method has the following characteristics. First, it should not resort to more advanced mathematical tools; that is, the algorithm should be simple to understand and implement and should be thus easily accepted in the mathematical and physical application fields. Second, the algorithm is of global nature in terms of the solutions obtained as well as its ability to solve other mathematical and physical problems. Third, the proposed methodology has an implicit parallel nature which points to its implementation on parallel machines. The algorithm is tested on different versions of Troesch’s and Bratu’s problems. Experimental results show that the proposed algorithm is effective, straightforward, and simple.
In this paper, the continuous genetic algorithm is applied for the solution of singular two-point boundary value problems, where smooth solution curves are used throughout the evolution of the ...algorithm to obtain the required nodal values. The proposed technique might be considered as a variation of the finite difference method in the sense that each of the derivatives is replaced by an appropriate difference quotient approximation. This novel approach possesses main advantages; it can be applied without any limitation on the nature of the problem, the type of singularity, and the number of mesh points. Numerical examples are included to demonstrate the accuracy, applicability, and generality of the presented technique. The results reveal that the algorithm is very effective, straightforward, and simple.
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Finding an accurate model to present the hysteresis nonlinearities behavior of the smart actuator has attracted the attention of the researchers in recent years, since an accurate model has an ...essential role in the position control application of these actuators. Different models have been developed to describe the hysteresis nonlinearities, the generalized Prandtl-Ishlinskii (GPI) model is one of the most popular used models. This model uses the play operators represented by the threshold values and weights integrated with the odd envelope functions to characterize the hysteresis nonlinearities of smart actuators. The contribution of this paper proposes three different approaches using the Real-Coded Genetic Algorithm (RCGA) for the parameters identification of the Generalized Prandtl-Ishlinskii (GPI) model. In Approach 1, the thresholds and the values of the weights are calculated based on the proposed formulas with the unknown parameters to be identified using RCGA. In Approach 2, the thresholds values are calculated based on the proposed formula with the unknown parameters to be identified using RCGA and the values of the weights are identified directly using RCGA. In Approach 3, the thresholds and the values of the weights are identified directly using RCGA. Also, RCGA was used to identify the values of the coefficients of the envelope functions for all approaches. All approaches are tested through four different examples. Two examples are simulated examples that have linear and tangent hyperbolic envelope functions. Moreover, the other two examples represent experimental data obtained for a piezoelectric actuator and a shape alloy memory (SMA) actuator. The simulation results are carried through by the statistical and convergence analysis of the proposed approaches. The comparison and analysis show that three different approaches can be employed for modeling hysteresis nonlinearities with minimum differences between them.
In this paper, continuous genetic algorithm is introduced as an efficient solver for systems of second-order boundary value problems where smooth solution curves are used throughout the evolution of ...the algorithm to obtain the required nodal values of the unknown variables. The solution methodology is based on representing each derivative in the system of differential equations by its finite difference approximation. After that, the overall residue for all nodes in the given system of differential equations is formulated. The solution to the system of differential equations is then converted into the problem of minimizing the overall residue or maximizing the fitness function based on the nodal values generated from the genetic operators. Three numerical test problems including linear and nonlinear systems were analyzed to illustrate the procedure and confirm the performance of the proposed method. In addition to that, a convergence and sensitivity analysis to genetic operators and control parameters of the algorithm has been carried out. The numerical results show that the proposed algorithm is a robust and accurate procedure for solving systems of second-order boundary value problems. Furthermore, the obtained accuracy for the solutions using CGA is much better than the results obtained using some modern methods.
A robust computational technique for model order reduction (MOR) of multi-time-scale discrete systems (single input single output (SISO) and multi-input multioutput (MIMO)) is presented in this ...paper. This work is motivated by the singular perturbation of multi-time-scale systems where some specific dynamics may not have significant influence on the overall system behavior. The new approach is proposed using genetic algorithms (GA) with the advantage of obtaining a reduced order model, maintaining the exact dominant dynamics in the reduced order, and minimizing the steady state error. The reduction process is performed by obtaining an upper triangular transformed matrix of the system state matrix defined in state space representation along with the elements of B, C, and D matrices. The GA computational procedure is based on maximizing the fitness function corresponding to the response deviation between the full and reduced order models. The proposed computational intelligence MOR method is compared to recently published work on MOR techniques where simulation results show the potential and advantages of the new approach.
This paper presents a new technique for model order reduction (MOR) that is based on an artificial neural network (ANN) prediction. The ANN-based MOR can be applied for different scale systems with ...substructure preservation. In the proposed technique, the ANN is implemented for predicting the unknown elements of the reduced order model. Prediction of the ANN architecture is based on minimizing the cost function obtained by the difference between the actual and desired system behaviour. The ANN prediction process is pursued while maintaining the full order substructure in the reduced model. The proposed ANN-based model order reduction method is compared to recently published work on MOR techniques. Simulation results verify the validity of the new MOR technique.
In this article, a new analytical method has been devised to solve higher-order initial value problems for ordinary differential equations. This method was implemented to construct a series solution ...for higher-order initial value problems in the form of a rapidly convergent series with easily computable components using symbolic computation software. The proposed method is based on the Taylor series expansion which constructs an analytical solution in the form of a polynomial and reproduces the exact solution when the solution is polynomial. This technique is applied to a few test examples to illustrate the accuracy, efficiency, and applicability of the method. The results reveal that the method is very effective, straightforward, and simple.
A new substructure preservation Sylvester-based model order reduction technique with application to power systems is presented in this article. The new approach is intended for ...multiple-input-multiple-output linear time invariant systems, given in the form of state-space realization with the objective of obtaining a proper reduced-order model (complexity reduction), preserving the dominant eigenvalues of the full-order model as a subset in the reduced model, and maintaining a minimum steady-state error. The proposed reduction method is performed based on transforming the system state matrix into a special form, taking into account the dominant eigenvalues, while the rest of the model transformation is derived utilizing the Sylvester equation formula. Once the system is transformed, the reduced-order model is obtained by truncating the less dominant eigenvalues using the singular perturbation technique. To evaluate the potential of the new approach, results of the proposed technique are compared to some of the well-known methods for model order reduction and relatively recently published work. Results comparison shows the superiority of the new method especially in terms of time convergence.
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