The focus of this study is to find the appropriateness of the Levenberg–Marquardt (LM) neural network (NN) training algorithm for recognition of odor patterns associated with an electronic nose (e-nose). Multiple time-patterns represent step response of the array of sensors to the odorants. The experiments are performed on four representative classes of odorants: coffees, fragrances, hog farm air, and cola beverages. The odor recognition system is composed of a Karhunen–Loeve (KL) based pre-processing unit, and a feedforward neural network with the LM training algorithm. The parameters of the pre-processing unit and the neural network are fine-tuned using a genetic algorithm. Back-propagation algorithm with adaptive learning rate is selected as a standard neural network training method, for the purpose of comparison. The results of the experiments indicate that the LM algorithm provides high correct recognition ratios. In addition, the results confirm that the LM method outperforms the back-propagation (BP) method with adaptive learning rate, for the classes of the odorants provided in this study.

Performance of the Levenberg–Marquardt neural network training method in electronic nose applications

The lightning current waveform has a major influence on the dynamic performance of ground electrodes. While high lightning current intensity improves the dynamic grounding performance due to ionization of the soil, very fast fronted pulses might worsen the performance in case of inductive behavior. The previous analysis has often been based on quasistatic approximation that is not applicable to very fast fronted pulses. To extend the analysis to fast fronted pulses in this paper, the full-wave analysis method based on the rigorous electromagnetic-field theory approach is used. In addition, realistic lightning current waveforms are applied, which reproduce the observed concave rising portion of typical recorded lightning current pulses. Based on the simulation results, new empirical formulas applicable for slow and very fast fronted lightning current pulses are proposed. The effects of the ionization of the soil are disregarded; therefore, the new formulas are applicable for a conservative estimate of the upper bound of the impulse impedance of ground electrodes.

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Impulse Efficiency of Ground Electrodes

A nonuniform transmission line approach is adopted in this paper for modeling the transient behavior of different types of grounding systems under lightning strikes in time domain by solving Telegrapher's equations based on finite-difference time-domain (FDTD) technique. Electromagnetic couplings between different parts of the grounding wires are included using effective per-unit length parameters (l, c, and g), which are space and time dependent. The present model can predict both the effective length and the transient voltage of grounding electrodes accurately, while, an uniform transmission line approach with electrode length dependent per-unit length parameters fails to predict the same. Unlike the circuit theory approach , the present model is capable of predicting accurately the surge propagation delay in the large grounding system. The simulation results for buried horizontal wires and grounding grids based on the present model are in good agreement with that of the circuit and electromagnetic field approaches , . From an engineering point of view, the model presented in this paper is sufficiently accurate, time efficient, and easy to apply.

An engineering model for transient analysis of grounding system under lightning strikes: nonuniform transmission-line approach

More precise modeling of the dynamic performance of grounding electrodes under lightning currents must include both the time-dependent nonlinear soil ionization and the frequency-dependent phenomena. These phenomena might have mutually opposing effects since the soil ionization effectively improves, while frequency-dependent inductive behavior impairs, the grounding performance. Modern approaches that take into account both phenomena are based on circuit theory that does not allow for accurate analysis of high-frequency behavior. This paper aims to further improve the understanding of the dynamic behavior of grounding electrodes under lightning currents by focusing on the following aspects: analyzing the validity domains of popular modeling approaches, based on circuit, transmission line, and electromagnetic theory; providing parametric analysis that takes into account both the propagation and soil ionization effects; analyzing simple formulas for surge characteristics; and comparing the modeling with experimental data. A model and a simple formula that combine the electromagnetic approach, suitable for high-frequency analysis, with the method that accounts for the soil ionization effects, recommended by the International Council on Large Electric Systems (CIGRE) and the IEEE Working Groups, are used for the parametric analysis. Both the model and the simple formula are verified by comparison with experimental results available in the literature.

Modeling of Grounding Electrodes Under Lightning Currents

According to the method of moment, a new method to analyze the grid fed by harmonic currents is presented. The method can be used for the condition that the grid is in at least ten-layer soil with a frequency of the injected currents up to 1 MHz. There can be more than one injected current, and the grounding conductor of the grid can be put in any form. Validation of the method is presented by comparing it with other existing methods. As an application of the presented method, breaks in the substation's grounding grid are diagnosed by the measured voltages on the surface of the ground.

Diagnosis of breaks in substation's grounding grid by using the electromagnetic method

A new method to analyze the performance of grounding systems is presented. The model is based on electric circuit theory and is solved by applying a conventional nodal analysis technique. Although the problem is treated in the frequency domain, a transient response may be obtained by means of the Fourier transform. Comparison with other methods and practical applications are presented.

Frequency-dependent grounding system calculation by means of a conventional nodal analysis technique

This paper intends to compare the performance of eight techniques, based on five different methods, used to find the electrical grounding parameters of a two-layered earth (resistivities and thickness) corresponding to a specific mathematical model. Parameter estimation is carried out in such a way as to obtain an optimum fitting between the set of resistivity values measured in the field by means of Wenner's Method, and those calculated from the mathematical model using such parameters. Firstly, the paper presents a review of the mathematical basis of five optimization methods used for the implementation of the different techniques subject to comparison. Secondly, the paper defines the implementation of the algorithms for the eight techniques. Three of them are of first order gradient type, one more of second order (Newton-method), the fifth one is based on the Levenberg-Marquardt method, the sixth one on the generalized inverse method, the seventh one on a quasi-Newton method and the last one on a mixed Newton-generalized inverse method. Algorithms are applied to six test cases and comparison of the results is shown. Furthermore, new algorithms to improve existing procedures are presented. >

A comparison among eight different techniques to achieve an optimum estimation of electrical grounding parameters in two-layered earth

The method presented makes it possible to achieve the absolute minimum of the objective function, without constraints, by checking the value of the first order gradient component; when the first order gradient technique is unable to achieve a significant improvement in terms of decreasing the value of the objective function, then a Newton-Raphson based second order technique is used. As the objective function, a classic least squares fitting function is used. Results obtained are presented and compared to those of other methods. The characteristics of computer implementation and the average execution time are indicated. The iterative process does not require the guessing of any special starting point, and achieving the absolute minimum (gradient components less than a predetermined value) is guaranteed provided that the earth can be modeled as a two-layer earth. >

A second order gradient technique for an improved estimation of soil parameters in a two-layer earth

Profile of Voltage Distributions Around a Grounding Electrode in a Two-Layer Earth with Concrete Foundations

The author has collected a set of algorithms implemented by digital computer (with results) in order to find: an optimal estimation of soil parameters using as data a set of measurements of resistivity taken by the F. Wenner method; a previous design of the grounding electrode; an accurate determination of both the intensity distribution factors which the electrode will be obliged to diffuse and the resistance of earth; an accurate calculus of potentials on soil and, as a consequence, the step and touch voltages; and an oriented rectification of the initial design that searches for agreement between calculated values and maximum permissible values. It is also found that is is possible to show the tridimensional evolution and bidimensional evolution of the potential in a preselected way. >

J.L. del Alamo

Papers

Frequency-dependent grounding system calculation by means of a conventional nodal analysis technique

A comparison among eight different techniques to achieve an optimum estimation of electrical grounding parameters in two-layered earth

A second order gradient technique for an improved estimation of soil parameters in a two-layer earth

Profile of Voltage Distributions Around a Grounding Electrode in a Two-Layer Earth with Concrete Foundations

A powerful tool for grounding design in high voltage substations