Search results for: generalized linear model

Authors: J. Hey, D. A. Howey, R. Martinez-Botas, M. Lamperth

Abstract:

This paper presents the development of a hybrid thermal model for the EVO Electric AFM 140 Axial Flux Permanent Magnet (AFPM) machine as used in hybrid and electric vehicles. The adopted approach is based on a hybrid lumped parameter and finite difference method. The proposed method divides each motor component into regular elements which are connected together in a thermal resistance network representing all the physical connections in all three dimensions. The element shape and size are chosen according to the component geometry to ensure consistency. The fluid domain is lumped into one region with averaged heat transfer parameters connecting it to the solid domain. Some model parameters are obtained from Computation Fluid Dynamic (CFD) simulation and empirical data. The hybrid thermal model is described by a set of coupled linear first order differential equations which is discretised and solved iteratively to obtain the temperature profile. The computation involved is low and thus the model is suitable for transient temperature predictions. The maximum error in temperature prediction is 3.4% and the mean error is consistently lower than the mean error due to uncertainty in measurements. The details of the model development, temperature predictions and suggestions for design improvements are presented in this paper.

Keywords: Electric vehicle, hybrid thermal model, transient temperature prediction, Axial Flux Permanent Magnet machine.

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Authors: Changchun Shen, Shouming Zhong

Abstract:

This paper investigates the problem of absolute stability and robust stability of a class of Lur-e systems with neutral type and time-varying delays. By using Lyapunov direct method and linear matrix inequality technique, new delay-dependent stability criteria are obtained and formulated in terms of linear matrix inequalities (LMIs) which are easy to check the stability of the considered systems. To obtain less conservative stability conditions, an operator is defined to construct the Lyapunov functional. Also, the free weighting matrices approach combining a matrix inequality technique is used to reduce the entailed conservativeness. Numerical examples are given to indicate significant improvements over some existing results.

Keywords: Lur'e system, linear matrix inequalities, Lyapunov, stability.

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Authors: Swarniv Chandra, Basudev Ghosh

Abstract:

Using the quantum hydrodynamic (QHD) model for quantum plasma at finite temperature the modulational instability of electron plasma waves is investigated by deriving a nonlinear Schrodinger equation. It was found that the electron degeneracy parameter significantly affects the linear and nonlinear properties of electron plasma waves in quantum plasma.

Keywords: Amplitude Modulation, Electron Plasma Waves, Finite Temperature Model, Modulational Instability, Quantum Plasma.

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Authors: António L. Topa

Abstract:

A complete spectral representation for the electromagnetic field of planar multilayered waveguides inhomogeneously filled with omega media is presented. The problem of guided electromagnetic propagation is reduced to an eigenvalue equation related to a 2 ´ 2 matrix differential operator. Using the concept of adjoint waveguide, general bi-orthogonality relations for the hybrid modes (either from the discrete or from the continuous spectrum) are derived. For the special case of homogeneous layers the linear operator formalism is reduced to a simple 2 ´ 2 coupling matrix eigenvalue problem. Finally, as an example of application, the surface and the radiation modes of a grounded omega slab waveguide are analyzed.

Keywords: Metamaterials, linear operators, omega media, layered waveguide, orthogonality relations

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Authors: Jui-Sheng Lin, Yi-Sung Yang, Meei-Ling Hung, Teh-Lu Liao, Jun-Juh Yan

Abstract:

The global chaos synchronization for a class of time-delayed power systems is investigated via observer-based approach. By employing the concepts of quadratic stability theory and generalized system model, a new sufficient criterion for constructing an observer is deduced. In contrast to the previous works, this paper proposes a theoretical and systematic design procedure to realize chaos synchronization for master-slave power systems. Finally, an illustrative example is given to show the applicability of the obtained scheme.

Keywords: Chaos, Synchronization, Quadratic stability theory, Observer

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Authors: Paras Ram, Vikas Kumar

Abstract:

An attempt has been made to study the effect of rotation on incompressible, electrically non-conducting ferrofluid in porous medium on Axi-symmetric steady flow over a rotating disk excluding thermal effects. Here, we solved the boundary layer equations with boundary conditions using Neuringer-Rosensweig model considering the z-axis as the axis of rotation. The non linear boundary layer equations involved in the problem are transformed to the non linear coupled ordinary differential equations by Karman's transformation and solved by power series approximations. Besides numerically calculating the velocity components and pressure for different values of porosity parameter with the variation of Karman's parameter we have also calculated the displacement thickness of boundary layer, the total volume flowing outward the z-axis and angle between wall and ferrofluid. The results for all above variables are obtained numerically and discussed graphically.

Keywords: Ferrofluid, magnetic field porous medium, rotating disk.

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Authors: A. K. Al-Othman, H. A. Al-Mekhaizim

Abstract:

Multilevel inverters supplied from equal and constant dc sources almost don-t exist in practical applications. The variation of the dc sources affects the values of the switching angles required for each specific harmonic profile, as well as increases the difficulty of the harmonic elimination-s equations. This paper presents an extremely fast optimal solution of harmonic elimination of multilevel inverters with non-equal dc sources using Tanaka's fuzzy linear regression formulation. A set of mathematical equations describing the general output waveform of the multilevel inverter with nonequal dc sources is formulated. Fuzzy linear regression is then employed to compute the optimal solution set of switching angles.

Keywords: Multilevel converters, harmonics, pulse widthmodulation (PWM), optimal control.

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Authors: D. Vijayakumar, R. K. Nema

Abstract:

Over Current Relays (OCRs) and Directional Over Current Relays (DOCRs) are widely used for the radial protection and ring sub transmission protection systems and for distribution systems. All previous work formulates the DOCR coordination problem either as a Non-Linear Programming (NLP) for TDS and Ip or as a Linear Programming (LP) for TDS using recently a social behavior (Particle Swarm Optimization techniques) introduced to the work. In this paper, a Modified Particle Swarm Optimization (MPSO) technique is discussed for the optimal settings of DOCRs in power systems as a Non-Linear Programming problem for finding Ip values of the relays and for finding the TDS setting as a linear programming problem. The calculation of the Time Dial Setting (TDS) and the pickup current (Ip) setting of the relays is the core of the coordination study. PSO technique is considered as realistic and powerful solution schemes to obtain the global or quasi global optimum in optimization problem.

Keywords: Directional over current relays, Optimization techniques, Particle swarm optimization, Power system protection.

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Authors: Xinhui Wang, Xiuyong Ding

Abstract:

This paper addresses the controller synthesis problem of discrete-time switched positive systems with bounded time-varying delays. Based on the switched copositive Lyapunov function approach, some necessary and sufficient conditions for the existence of state-feedback controller are presented as a set of linear programming and linear matrix inequality problems, hence easy to be verified. Another advantage is that the state-feedback law is independent on time-varying delays and initial conditions. A numerical example is provided to illustrate the effectiveness and feasibility of the developed controller.

Keywords: Switched copositive Lyapunov functions, positive linear systems, switched systems, time-varying delays, stabilization.

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Authors: Amit Kumar, Manjot Kaur

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In this paper, the fuzzy linear programming formulation of fuzzy maximal flow problems are proposed and on the basis of the proposed formulation a method is proposed to find the fuzzy optimal solution of fuzzy maximal flow problems. In the proposed method all the parameters are represented by triangular fuzzy numbers. By using the proposed method the fuzzy optimal solution of fuzzy maximal flow problems can be easily obtained. To illustrate the proposed method a numerical example is solved and the obtained results are discussed.

Keywords: Fuzzy linear programming, Fuzzy maximal flow problem, Ranking function, Triangular fuzzy number

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Authors: A. Hung, K. Mithraratne, M. Sagar, P. Hunter

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A biophysically based multilayer continuum model of the facial soft tissue composite has been developed for simulating wrinkle formation. The deformed state of the soft tissue block was determined by solving large deformation mechanics equations using the Galerkin finite element method. The proposed soft tissue model is composed of four layers with distinct mechanical properties. These include stratum corneum, epidermal-dermal layer (living epidermis and dermis), subcutaneous tissue and the underlying muscle. All the layers were treated as non-linear, isotropic Mooney Rivlin materials. Contraction of muscle fibres was approximated using a steady-state relationship between the fibre extension ratio, intracellular calcium concentration and active stress in the fibre direction. Several variations of the model parameters (stiffness and thickness of epidermal-dermal layer, thickness of subcutaneous tissue layer) have been considered.

Keywords: Bio-physically based, soft tissue mechanics, facialtissue composite, wrinkling.

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Authors: S. N. Deepa, G. Sugumaran

Abstract:

This paper proposes a new algebraic scheme to design a PID controller for higher order linear time invariant continuous systems. Modified PSO (MPSO) based model order formulation techniques have applied to obtain the effective formulated second order system. A controller is tuned to meet the desired performance specification by using pole-zero cancellation method. Proposed PID controller is attached with both higher order system and formulated second order system. The closed loop response is observed for stabilization process and compared with general PSO based formulated second order system. The proposed method is illustrated through numerical example from literature.

Keywords: Higher order systems, model order formulation, modified particle swarm optimization, PID controller, pole-zero cancellation.

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Authors: Jean-Christophe Sibel, Sylvain Reynal, David Declercq

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In the context of channel coding, the Generalized Belief Propagation (GBP) is an iterative algorithm used to recover the transmission bits sent through a noisy channel. To ensure a reliable transmission, we apply a map on the bits, that is called a code. This code induces artificial correlations between the bits to send, and it can be modeled by a graph whose nodes are the bits and the edges are the correlations. This graph, called Tanner graph, is used for most of the decoding algorithms like Belief Propagation or Gallager-B. The GBP is based on a non unic transformation of the Tanner graph into a so called region-graph. A clear advantage of the GBP over the other algorithms is the freedom in the construction of this graph. In this article, we explain a particular construction for specific graph topologies that involves relevant performance of the GBP. Moreover, we investigate the behavior of the GBP considered as a dynamic system in order to understand the way it evolves in terms of the time and in terms of the noise power of the channel. To this end we make use of classical measures and we introduce a new measure called the hyperspheres method that enables to know the size of the attractors.

Keywords: iterative decoder, LDPC, region-graph, chaos.

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Authors: Jörg Linde, Ekaterina Buyko, Robert Altwasser, Udo Hahn, Reinhard Guthke

Abstract:

Reverse engineering of full-genomic interaction networks based on compendia of expression data has been successfully applied for a number of model organisms. This study adapts these approaches for an important non-model organism: The major human fungal pathogen Candida albicans. During the infection process, the pathogen can adapt to a wide range of environmental niches and reversibly changes its growth form. Given the importance of these processes, it is important to know how they are regulated. This study presents a reverse engineering strategy able to infer fullgenomic interaction networks for C. albicans based on a linear regression, utilizing the sparseness criterion (LASSO). To overcome the limited amount of expression data and small number of known interactions, we utilize different prior-knowledge sources guiding the network inference to a knowledge driven solution. Since, no database of known interactions for C. albicans exists, we use a textmining system which utilizes full-text research papers to identify known regulatory interactions. By comparing with these known regulatory interactions, we find an optimal value for global modelling parameters weighting the influence of the sparseness criterion and the prior-knowledge. Furthermore, we show that soft integration of prior-knowledge additionally improves the performance. Finally, we compare the performance of our approach to state of the art network inference approaches.

Keywords: Pathogen, network inference, text-mining, Candida albicans, LASSO, mutual information, reverse engineering, linear regression, modelling.

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Authors: T. Sanches, K. Bousson

Abstract:

As part of the development of a 4D autopilot system for unmanned aerial vehicles (UAVs), i.e. a time-dependent robust trajectory generation and control algorithm, this work addresses the problem of optimal path control based on the flight sensors data output that may be unreliable due to noise on data acquisition and/or transmission under certain circumstances. Although several filtering methods, such as the Kalman-Bucy filter or the Linear Quadratic Gaussian/Loop Transfer Recover Control (LQG/LTR), are available, the utter complexity of the control system, together with the robustness and reliability required of such a system on a UAV for airworthiness certifiable autonomous flight, required the development of a proper robust filter for a nonlinear system, as a way of further mitigate errors propagation to the control system and improve its ,performance. As such, a nonlinear algorithm based upon the LQG/LTR, is validated through computational simulation testing, is proposed on this paper.

Keywords: Autonomous flight, LQG/LTR, nonlinear state estimator, robust flight control and stability.

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Authors: Kulin Dave, Kapil Mohan

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Earthquakes are considered to be the most destructive rapid-onset disasters human beings are exposed to. The amount of loss it brings in is sufficient to take careful considerations for designing of structures and facilities. Seismic Hazard Analysis is one such tool which can be used for earthquake resistant design. Ground Response Analysis is one of the most crucial and decisive steps for seismic hazard analysis. Rapar district of Kutch, Gujarat falls in Zone 5 of earthquake zone map of India and thus has high seismicity because of which it is selected for analysis. In total 8 bore-log data were studied at different locations in and around Rapar district. Different soil engineering properties were analyzed and relevant empirical correlations were used to calculate maximum shear modulus (Gmax) and shear wave velocity (Vs) for the soil layers. The soil was modeled using Pressure-Dependent Modified Kodner Zelasko (MKZ) model and the reference curve used for fitting was Seed and Idriss (1970) for sand and Darendeli (2001) for clay. Both Equivalent linear (EL), as well as Non-linear (NL) ground response analysis, has been carried out with Masing Hysteretic Re/Unloading formulation for comparison. Commercially available DEEPSOIL v. 7.0 software is used for this analysis. In this study an attempt is made to quantify ground response regarding generated acceleration time-history at top of the soil column, Response spectra calculation at 5 % damping and Fourier amplitude spectrum calculation. Moreover, the variation of Peak Ground Acceleration (PGA), Maximum Displacement, Maximum Strain (in %), Maximum Stress Ratio, Mobilized Shear Stress with depth is also calculated. From the study, PGA values estimated in rocky strata are nearly same as bedrock motion and marginal amplification is observed in sandy silt and silty clays by both analyses. The NL analysis gives conservative results of maximum displacement as compared to EL analysis. Maximum strain predicted by both studies is very close to each other. And overall NL analysis is more efficient and realistic because it follows the actual hyperbolic stress-strain relationship, considers stiffness degradation and mobilizes stresses generated due to pore water pressure.

Keywords: DEEPSOIL v 7.0, Ground Response Analysis, Pressure-Dependent Modified KodnerZelasko (MKZ) model, Response Spectra, Shear wave velocity.

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Authors: Mehdi Ghayoumi

Abstract:

We have applied new accelerated algorithm for linear discriminate analysis (LDA) in face recognition with support vector machine. The new algorithm has the advantage of optimal selection of the step size. The gradient descent method and new algorithm has been implemented in software and evaluated on the Yale face database B. The eigenfaces of these approaches have been used to training a KNN. Recognition rate with new algorithm is compared with gradient.

Keywords: lda, adaptive, svm, face recognition.

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Authors: Junaid Rashid, Waqar Mehmood, Muhammad Wasif Nisar

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This survey paper shows the recent state of model comparison as it’s applies to Model Driven engineering. In Model Driven Engineering to calculate the difference between the models is a very important and challenging task. There are number of tasks involved in model differencing that firstly starts with identifying and matching the elements of the model. In this paper, we discuss how model matching is accomplished, the strategies, techniques and the types of the model. We also discuss the future direction. We found out that many of the latest model comparison strategies are geared near enabling Meta model and similarity based matching. Therefore model versioning is the most dominant application of the model comparison. Recently to work on comparison for versioning has begun to deteriorate, giving way to different applications. Ultimately there is wide change among the tools in the measure of client exertion needed to perform model comparisons, as some require more push to encourage more sweeping statement and expressive force.

Keywords: Model comparison, model clone detection, model versioning, EMF Model, model diff.

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Authors: Job H. Domingo, Carolina Bancayrin-Baguio

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The Sphere Method is a flexible interior point algorithm for linear programming problems. This was developed mainly by Professor Katta G. Murty. It consists of two steps, the centering step and the descent step. The centering step is the most expensive part of the algorithm. In this centering step we proposed some improvements such as introducing two or more initial feasible solutions as we solve for the more favorable new solution by objective value while working with the rigorous updates of the feasible region along with some ideas integrated in the descent step. An illustration is given confirming the advantage of using the proposed procedure.

Keywords: Interior point, linear programming, sphere method, initial feasible solution, feasible region, centering and descent steps, optimal solution.

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Authors: Weifeng Wang, Xilong Chen, Xianwei Zeng

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The cable tower of Liede Bridge is a double-column curved-lever arched-beam portal framed structure. Being novel and unique in structure, its cable tower differs in complexity from traditional ones. This paper analyzes the ultimate load capacity of cable tower by adopting the finite element calculations and model tests which indicate that constitutive relations applied here give a better simulation of actual failure process of prestressed reinforced concrete. In vertical load, horizontal load and overloading tests, the stepped loading of the tower model is of linear relationship, and the test data has good repeatability. All suggests that the cable tower has good bearing capacity, rational design and high emergency capacity.

Keywords: Cable tower of Liede Bridge, ultimate load capacity, model test, nonlinear finite element method

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Authors: A. Pereira, S. Haffner, L. V. Gasperin

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This paper presents two simplified models to determine nodal voltages in power distribution networks. These models allow estimating the impact of the installation of reactive power compensations equipments like fixed or switched capacitor banks. The procedure used to develop the models is similar to the procedure used to develop linear power flow models of transmission lines, which have been widely used in optimization problems of operation planning and system expansion. The steady state non-linear load flow equations are approximated by linear equations relating the voltage amplitude and currents. The approximations of the linear equations are based on the high relationship between line resistance and line reactance (ratio R/X), which is valid for power distribution networks. The performance and accuracy of the models are evaluated through comparisons with the exact results obtained from the solution of the load flow using two test networks: a hypothetical network with 23 nodes and a real network with 217 nodes.

Keywords: Distribution network models, distribution systems, optimization, power system planning.

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Authors: Changqiao Wu, Guoqing Ding, Xin Chen

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In this paper, ways of modeling dynamic measurement systems are discussed. Specially, for linear system with single-input single-output, it could be modeled with shallow neural network. Then, gradient based optimization algorithms are used for searching the proper coefficients. Besides, method with normal equation and second order gradient descent are proposed to accelerate the modeling process, and ways of better gradient estimation are discussed. It shows that the mathematical essence of the learning objective is maximum likelihood with noises under Gaussian distribution. For conventional gradient descent, the mini-batch learning and gradient with momentum contribute to faster convergence and enhance model ability. Lastly, experimental results proved the effectiveness of second order gradient descent algorithm, and indicated that optimization with normal equation was the most suitable for linear dynamic models.

Keywords: Dynamic system modeling, neural network, normal equation, second order gradient descent.

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Authors: Mogari I. Rapoo, Diteboho Xaba

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This paper examines the forecasting performance of Autoregressive Integrated Moving Average (ARIMA) and Artificial Neural Networks (ANN) models with the published exchange rate obtained from South African Reserve Bank (SARB). ARIMA is one of the popular linear models in time series forecasting for the past decades. ARIMA and ANN models are often compared and literature revealed mixed results in terms of forecasting performance. The study used the MSE and MAE to measure the forecasting performance of the models. The empirical results obtained reveal the superiority of ARIMA model over ANN model. The findings further resolve and clarify the contradiction reported in literature over the superiority of ARIMA and ANN models.

Keywords: ARIMA, artificial neural networks models, error metrics, exchange rates.

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Authors: Mohamed Abdallah, Mostafa Warith, Roberto Narbaitz, Emil Petriu, Kevin Kennedy

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Heterogeneity of solid waste characteristics as well as the complex processes taking place within the landfill ecosystem motivated the implementation of soft computing methodologies such as artificial neural networks (ANN), fuzzy logic (FL), and their combination. The present work uses a hybrid ANN-FL model that employs knowledge-based FL to describe the process qualitatively and implements the learning algorithm of ANN to optimize model parameters. The model was developed to simulate and predict the landfill gas production at a given time based on operational parameters. The experimental data used were compiled from lab-scale experiment that involved various operating scenarios. The developed model was validated and statistically analyzed using F-test, linear regression between actual and predicted data, and mean squared error measures. Overall, the simulated landfill gas production rates demonstrated reasonable agreement with actual data. The discussion focused on the effect of the size of training datasets and number of training epochs.

Keywords: Adaptive neural fuzzy inference system (ANFIS), gas production, landfill

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Authors: P.-W. Tsai, C.-Y. Chen, C.-W. Chen

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In this paper, the stability analysis of a GA-Based adaptive fuzzy sliding model controller for a nonlinear system is discussed. First, a nonlinear plant is well-approximated and described with a reference model and a fuzzy model, both involving FLC rules. Then, FLC rules and the consequent parameter are decided on via an Evolved Bat Algorithm (EBA). After this, we guarantee a new tracking performance inequality for the control system. The tracking problem is characterized to solve an eigenvalue problem (EVP). Next, an adaptive fuzzy sliding model controller (AFSMC) is proposed to stabilize the system so as to achieve good control performance. Lyapunov’s direct method can be used to ensure the stability of the nonlinear system. It is shown that the stability analysis can reduce nonlinear systems into a linear matrix inequality (LMI) problem. Finally, a numerical simulation is provided to demonstrate the control methodology.

Keywords: Adaptive fuzzy sliding mode control, Lyapunov direct method, swarm intelligence, evolved bat algorithm.

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Authors: Watcharapan Sukkerd, Teeradej Wuttipornpun

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This paper aims to present non-population search algorithms called tabu search (TS), simulated annealing (SA) and variable neighborhood search (VNS) to minimize the total cost of capacitated MRP problem in multi-stage assembly flow shop with two alternative machines. There are three main steps for the algorithm. Firstly, an initial sequence of orders is constructed by a simple due date-based dispatching rule. Secondly, the sequence of orders is repeatedly improved to reduce the total cost by applying TS, SA and VNS separately. Finally, the total cost is further reduced by optimizing the start time of each operation using the linear programming (LP) model. Parameters of the algorithm are tuned by using real data from automotive companies. The result shows that VNS significantly outperforms TS, SA and the existing algorithm.

Keywords: Capacitated MRP, non-population search algorithms, linear programming, assembly flow shop.

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Authors: Yang Weiping, Zhang Zhilong, Zhang Yan, Chen Zengping

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Infrared focal plane arrays (IRFPA) sensors, due to their high sensitivity, high frame frequency and simple structure, have become the most prominently used detectors in military applications. However, they suffer from a common problem called the fixed pattern noise (FPN), which severely degrades image quality and limits the infrared imaging applications. Therefore, it is necessary to perform non-uniformity correction (NUC) on IR image. The algorithms of non-uniformity correction are classified into two main categories, the calibration-based and scene-based algorithms. There exist some shortcomings in both algorithms, hence a novel non-uniformity correction algorithm based on non-linear fit is proposed, which combines the advantages of the two algorithms. Experimental results show that the proposed algorithm acquires a good effect of NUC with a lower non-uniformity ratio.

Keywords: Non-uniformity correction, non-linear fit, two-point correction, temporal Kalman filter.

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Authors: Niloufar Ghoreishi, Ali Nekouzadeh

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The stability of the flight during maneuvering and in response to probable perturbations is one of the most essential features of an aircraft that should be analyzed and designed for. In this study, we derived the non-linear governing equations of aircraft dynamics during the climb/descend phase and simulated a model aircraft. The corresponding force and moment dimensionless coefficients of the model and their variations with elevator angle and other relevant aerodynamic parameters were measured experimentally. The short-period mode and phugoid mode response were simulated by solving the governing equations numerically and then compared with the desired stability parameters for the particular level, category, and class of the aircraft model. To meet the target stability, a controller was designed and used. This resulted in significant improvement in the stability parameters of the flight.

Keywords: Flight stability, phugoid mode, short period mode, climb phase, damping coefficient.

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Authors: Inta Volodko, Valentina Koliskina

Abstract:

Linear stability analysis of wake-shear layers in twophase shallow flows is performed in the present paper. Twodimensional shallow water equations are used in the analysis. It is assumed that the fluid contains uniformly distributed solid particles. No dynamic interaction between the carrier fluid and particles is expected in the initial moment. The stability calculations are performed for different values of the particle loading parameter and two other parameters which characterize the velocity ratio and the velocity deficit. The results show that the particle loading parameter has a stabilizing effect on the flow while the increase in the velocity ratio or in the velocity deficit destabilizes the flow.

Keywords: Linear stability, Shallow flows, Wake-shear flows.

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Authors: Takashi Kaburagi, Takamasa Komura, Yosuke Kurihara

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Absolute pitch is the ability to identify a musical note without a reference tone. Training for absolute pitch often occurs in preschool education. It is necessary to clarify how well the trainee can make use of synesthesia in order to evaluate the effect of the training. To the best of our knowledge, there are no existing methods for objectively confirming whether the subject is using synesthesia. Therefore, in this study, we present a method to distinguish the use of color-auditory synesthesia from the separate use of color and audition during absolute pitch training. This method measures blood volume in the prefrontal cortex using functional Near-infrared spectroscopy (fNIRS) and assumes that the cognitive step has two parts, a non-linear step and a linear step. For the linear step, we assume a second order ordinary differential equation. For the non-linear part, it is extremely difficult, if not impossible, to create an inverse filter of such a complex system as the brain. Therefore, we apply a method based on a self-organizing map (SOM) and are guided by the available data. The presented method was tested using 15 subjects, and the estimation accuracy is reported.

Keywords: Absolute pitch, functional near-infrared spectroscopy, prefrontal cortex, synesthesia.

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