scholarly journals Comparison Between Heidler Function And The Pulse Function For Modeling The Lightning Return-Stroke Current

2021 ◽  
Author(s):  
Khaled Elrodesly
Keyword(s):  
Curve Fitting ◽  
Measured Data ◽  
Current Waveform ◽  
Return Stroke ◽  
Lightning Current ◽  
Optimal Value ◽  
Analytical Parameter ◽  
Estimation System ◽  
Current Derivative ◽  
Best Fit

In the past, many functions were considered for simulating the lightning return-stroke current. Some of these functions were found to have problems related to their discontinuities or the discontinuities of their derivatives at onset time. Such problems appear in the double exponential function and its modifications. However, other functions like the Pulse function and Heidler function do not suffer from such problems. One of the main objectives of this work is to simulate the lightning return-stroke current full wave, including the decay part, using either Heidler function or the Pulse function. This work is not only necessary for the evaluation and development of lightning return-stroke modeling, but also for the calculation of the lightning current waveform parameters. Although the lightning return-stroke current, measured at the CN Tower, is simulated using the Pulse function and Heidler function, the simulation of the CN Tower lightning current derivative signal is considered using the derivative of the Pulse and Heidler functions. First, we build a modeling environment for each function, which can be described as parameter estimation system. This system, which represents an automated approach for estimating the analytical parameters of a given function, is capable to best fit the function with the measured data. Using these analytical parameters transforms the discrete data into a continuous signal, from which the current waveform parameters can be estimated. This analytical parameters estimation system is recognized as a curve fitting system. For curve fitting technique, the initial value of each analytical parameter and its feasible region, where the optimal value of this analytical parameter is located, must be specified. The more accurate the initial point is the easier and faster the optimal value can be estimated. On choosing the best approach of the initial condition, which gives the nearest location to the optimal point, applying the estimation system and achieving the analytical model that fits the CN Tower measured current derivative, the current waveform parameters can be easily studied. In order to be sure that the analytical parameter extraction system gives the best fit of a function, it needs to be evaluated. Instead of going through the measured data, we first use artificial digital data as a productive way to evaluate the system. Also, a comparison between both the Pulse and Heidler functions is performed. The described fitting process is applied on 15 flashes, containing 31 return strokes. The calculated current waveform parameters were used to form statistics to determine the probability distribution of the value of each parameter, including the range and the 50% probability level, which is fundamental in building lightning protection systems.

scholarly journals Comparison Between Heidler Function And The Pulse Function For Modeling The Lightning Return-Stroke Current

2021 ◽  
Author(s):  
Khaled Elrodesly
Keyword(s):  
Curve Fitting ◽  
Measured Data ◽  
Current Waveform ◽  
Return Stroke ◽  
Lightning Current ◽  
Optimal Value ◽  
Analytical Parameter ◽  
Estimation System ◽  
Current Derivative ◽  
Best Fit

In the past, many functions were considered for simulating the lightning return-stroke current. Some of these functions were found to have problems related to their discontinuities or the discontinuities of their derivatives at onset time. Such problems appear in the double exponential function and its modifications. However, other functions like the Pulse function and Heidler function do not suffer from such problems. One of the main objectives of this work is to simulate the lightning return-stroke current full wave, including the decay part, using either Heidler function or the Pulse function. This work is not only necessary for the evaluation and development of lightning return-stroke modeling, but also for the calculation of the lightning current waveform parameters. Although the lightning return-stroke current, measured at the CN Tower, is simulated using the Pulse function and Heidler function, the simulation of the CN Tower lightning current derivative signal is considered using the derivative of the Pulse and Heidler functions. First, we build a modeling environment for each function, which can be described as parameter estimation system. This system, which represents an automated approach for estimating the analytical parameters of a given function, is capable to best fit the function with the measured data. Using these analytical parameters transforms the discrete data into a continuous signal, from which the current waveform parameters can be estimated. This analytical parameters estimation system is recognized as a curve fitting system. For curve fitting technique, the initial value of each analytical parameter and its feasible region, where the optimal value of this analytical parameter is located, must be specified. The more accurate the initial point is the easier and faster the optimal value can be estimated. On choosing the best approach of the initial condition, which gives the nearest location to the optimal point, applying the estimation system and achieving the analytical model that fits the CN Tower measured current derivative, the current waveform parameters can be easily studied. In order to be sure that the analytical parameter extraction system gives the best fit of a function, it needs to be evaluated. Instead of going through the measured data, we first use artificial digital data as a productive way to evaluate the system. Also, a comparison between both the Pulse and Heidler functions is performed. The described fitting process is applied on 15 flashes, containing 31 return strokes. The calculated current waveform parameters were used to form statistics to determine the probability distribution of the value of each parameter, including the range and the 50% probability level, which is fundamental in building lightning protection systems.

scholarly journals De-noising the CN Tower lightning current signal using short term Fourier transform-based spectral substraction

2021 ◽  
Author(s):  
Mohammed Jahirul Islam
Keyword(s):  
Fourier Transform ◽  
Spectral Subtraction ◽  
Current Signal ◽  
Current Waveform ◽  
Transmission Tower ◽  
Subtraction Method ◽  
Short Term ◽  
Lightning Current ◽  
Spectral Subtraction Method ◽  
Current Derivative

The CN Tower is a transmission tower and it is not unexpected that recorded lightning current signals be corrupted by noise. The existence of noise may affect the calculation of current waveform parameters (current peak, 10-90% risetime to current peak, maximum steepness, and pulse width at half value of current peak). But accurate statistics of current waveform parameters are required to design systems for the protection of structures and devices, especially those with electrical and electronic components, exposed to hazards of lightning. Since more electrical devices are used nowadays, lightning protection becomes more important. So to determine accurate statistics of current waveform parameters, the interfering noise must be removed. In this thesis we describe a technique for de-noising the CN Tower lightning current by modifying its Fourier Transform (FT) where a simulated current waveform (Heidler function) is used to represent the lightning current signal.The limitations of Discrete Fourier Transform (DFT) for removal of non-stationary noise signals, including the noise connected with CN Tower lightning current signals and its properties are discussed. The Short Term Fourier Transform (STFT) is explored to analyze non-stationary signals and to deal with the limitations of DFT. Last of all, an STFT-based Spectral Subtraction method is developed to denoise the CN Tower lightning current signal. In order to evaluate the Spectral Subtraction method, a simulated current derivative waveform ( obtained by differentiating Heidler function) is artificially distorted by a noise signal measured at the CN Tower in the absence of lightning. The Spectral Subtraction method is then used to de-noise the distorted waveform. The de-noised waveform proved to be very close to the original simulated waveform. A signal-peak to noise-peak ratio (SPNPR) of the CN Tower lightning current signal is defined and calculated before and after the de-noising process. For example, for a typical measured current derivative signal, the SPNPR before de-noising is 7.27, and after de-noising it becomes 151.30. Similarly for its current waveform (obtained by numerical integration) the SPNPR before de-noising is 20,16 and it becomes 361.39 after de-noising. Statistics of current waveform parameters are obtained from the de-noised waveforms. The Spectral Subtraction method is also applied for de-noising the electric and magnetic field waveforms generated by lightning to the CN Tower which enables the calculation of their waveform parameters.

scholarly journals Enhancement of CN Tower lightning current derivative signals using a modified power spectral subtraction method

2021 ◽  
Author(s):  
Huma Mehmud
Keyword(s):  
Current Data ◽  
Spectral Subtraction ◽  
Transmission Tower ◽  
Subtraction Method ◽  
Return Stroke ◽  
Derivative Function ◽  
Lightning Current ◽  
Power Spectral ◽  
Spectral Subtraction Method ◽  
Current Derivative

Lightning current measurements are possible using instrumental tall structures or rocket-triggered lightning. The CN Tower has been a source of lightning current data for the past 15 years. A major portion of research on the natural lightning is focused on developing lightning protection systems, and in order to do so, an accurate knowledge of the characteristics of lightning, including the return-stroke current, is required. The CN Tower is a transmission tower and it is expected that the recorded lightning current signals be corrupted with different kinds of noise. This makes it difficult to extract the return-stroke current waveform parameters (peak, 10-90% rise-time to peak, maximum steepness, pulse width etc.) from the measured waveforms. In this project, an over-subtraction and residual noise reduction based power spectral subtraction method has been developed in order to de-noise the lighting return-stroke current derivative signals measured at the CN Tower. In order to evaluate the proposed de-noising technique, the derivative of Heidler function is used to model the measured return-stroke current derivative signal. The measured current derivative signal is simulated using the Heidler derivative model after artificially corrupting it with noise signals measured at the CN Tower in the absence of lightning. A modified spectral substraction method (MSS) is proposed and applied to the de- noise the simulated current derivative signal and the resultant waveform is compared with the Heidler derivative model, which enabled accurate evaluation of the proposed method. The result of the evaluation show a substantial improvement in the signal peak-to-noisepeak ratio(SPNPR) of up to 32 dB depending on the level of vthe noise signal, which is added to the Heidler derivative function. Furthermore, 95.7%-98.5% recovery of the peak of the original Heidler derivative function was obtained. For further evaluation of the new MSS method, the conventional spectral subtraction (SS) method is applied for de-noising the same simulated current derivative signals, which produced a substantially lower SPNPR of up to 16 dB with a peak recovery of 93.3%- 97.5% of the original Heidler derivative model. The poposed method is successfully used to substantially remove the noise from the lightning current derivative signals measured at the CN Tower.

scholarly journals Enhancement of CN Tower lightning current derivative signals using a modified power spectral subtraction method

2021 ◽  
Author(s):  
Huma Mehmud
Keyword(s):  
Current Data ◽  
Spectral Subtraction ◽  
Transmission Tower ◽  
Subtraction Method ◽  
Return Stroke ◽  
Derivative Function ◽  
Lightning Current ◽  
Power Spectral ◽  
Spectral Subtraction Method ◽  
Current Derivative

Lightning current measurements are possible using instrumental tall structures or rocket-triggered lightning. The CN Tower has been a source of lightning current data for the past 15 years. A major portion of research on the natural lightning is focused on developing lightning protection systems, and in order to do so, an accurate knowledge of the characteristics of lightning, including the return-stroke current, is required. The CN Tower is a transmission tower and it is expected that the recorded lightning current signals be corrupted with different kinds of noise. This makes it difficult to extract the return-stroke current waveform parameters (peak, 10-90% rise-time to peak, maximum steepness, pulse width etc.) from the measured waveforms. In this project, an over-subtraction and residual noise reduction based power spectral subtraction method has been developed in order to de-noise the lighting return-stroke current derivative signals measured at the CN Tower. In order to evaluate the proposed de-noising technique, the derivative of Heidler function is used to model the measured return-stroke current derivative signal. The measured current derivative signal is simulated using the Heidler derivative model after artificially corrupting it with noise signals measured at the CN Tower in the absence of lightning. A modified spectral substraction method (MSS) is proposed and applied to the de- noise the simulated current derivative signal and the resultant waveform is compared with the Heidler derivative model, which enabled accurate evaluation of the proposed method. The result of the evaluation show a substantial improvement in the signal peak-to-noisepeak ratio(SPNPR) of up to 32 dB depending on the level of vthe noise signal, which is added to the Heidler derivative function. Furthermore, 95.7%-98.5% recovery of the peak of the original Heidler derivative function was obtained. For further evaluation of the new MSS method, the conventional spectral subtraction (SS) method is applied for de-noising the same simulated current derivative signals, which produced a substantially lower SPNPR of up to 16 dB with a peak recovery of 93.3%- 97.5% of the original Heidler derivative model. The poposed method is successfully used to substantially remove the noise from the lightning current derivative signals measured at the CN Tower.

scholarly journals Modelling of tall-structure lightning return-stroke current using the Electromagnetic Transients Program

2021 ◽  
Author(s):  
Mohammadsadegh Rahimian Emam
Keyword(s):  
Velocity Profile ◽  
Electromagnetic Transients ◽  
Simulation Function ◽  
Return Stroke ◽  
Lightning Current ◽  
Lightning Channel ◽  
Section Model ◽  
Tall Structure ◽  
Current Derivative

The main aim of this PhD work is to advance tall-structure lightning return-stroke current modelling. The Alternative Transients Program (ATP), a version of the Electromagnetic Transients program (EMTP), is used to model the lightning current distribution within a tall structure and the attached lightning channel. The tall structure, namely the CN Tower, is modeled as three or five transmission line sections connected in series. The lightning channel is represented by a transmission line with a continuously expanding length. The presented model takes into account reflections within the tower and within the lightning channel. Locations of reflections, current reflection coefficients and the parameters of the current simulation function are calculated based on the time analysis of the current derivative signal, measured at the tower. The decay parameters of the simulation function are first determined by curve fitting the decaying part of the current obtained from measurement. The other parameters are determined by curve fitting the measured initial current derivative impulse with the derivative of the simulation function, before the arrival of reflections. The simulation results substantially succeeded in reproducing the fine structure of the measured current derivative signal. The model allows for the computation of the lightning current at any point along the current path (the tower and the attached channel), which is required for the calculation of the associated electromagnetic field. Using the three-section model of the tower, the presented return-stroke current model enables the determination of a discrete return-stroke velocity profile, demonstrating that the velocity generally decays with time. Furthermore, based on the five-section model, the proposed approach enables taking into account the existence of upward-connecting leaders, which allowed, for the first time, the determination of upward-connecting leader lengths and return-stroke velocity variation profiles with more details. The return-stroke velocity profile is found to initially increase rapidly with time, reaching a peak, and then decrease less rapidly. The proposed model is also experimentally verified based on the comparison between the computed and measured electromagnetic fields. The simulated electric and magnetic field waveforms are found to reproduce important details of the measured fields, including initial split peaks that appear due to channel-front reflections in the presence of upward-connecting leaders.

scholarly journals De-noising the CN Tower lightning current signal using short term Fourier transform-based spectral substraction

2021 ◽  
Author(s):  
Mohammed Jahirul Islam
Keyword(s):  
Fourier Transform ◽  
Spectral Subtraction ◽  
Current Signal ◽  
Current Waveform ◽  
Transmission Tower ◽  
Subtraction Method ◽  
Short Term ◽  
Lightning Current ◽  
Spectral Subtraction Method ◽  
Current Derivative

The CN Tower is a transmission tower and it is not unexpected that recorded lightning current signals be corrupted by noise. The existence of noise may affect the calculation of current waveform parameters (current peak, 10-90% risetime to current peak, maximum steepness, and pulse width at half value of current peak). But accurate statistics of current waveform parameters are required to design systems for the protection of structures and devices, especially those with electrical and electronic components, exposed to hazards of lightning. Since more electrical devices are used nowadays, lightning protection becomes more important. So to determine accurate statistics of current waveform parameters, the interfering noise must be removed. In this thesis we describe a technique for de-noising the CN Tower lightning current by modifying its Fourier Transform (FT) where a simulated current waveform (Heidler function) is used to represent the lightning current signal.The limitations of Discrete Fourier Transform (DFT) for removal of non-stationary noise signals, including the noise connected with CN Tower lightning current signals and its properties are discussed. The Short Term Fourier Transform (STFT) is explored to analyze non-stationary signals and to deal with the limitations of DFT. Last of all, an STFT-based Spectral Subtraction method is developed to denoise the CN Tower lightning current signal. In order to evaluate the Spectral Subtraction method, a simulated current derivative waveform ( obtained by differentiating Heidler function) is artificially distorted by a noise signal measured at the CN Tower in the absence of lightning. The Spectral Subtraction method is then used to de-noise the distorted waveform. The de-noised waveform proved to be very close to the original simulated waveform. A signal-peak to noise-peak ratio (SPNPR) of the CN Tower lightning current signal is defined and calculated before and after the de-noising process. For example, for a typical measured current derivative signal, the SPNPR before de-noising is 7.27, and after de-noising it becomes 151.30. Similarly for its current waveform (obtained by numerical integration) the SPNPR before de-noising is 20,16 and it becomes 361.39 after de-noising. Statistics of current waveform parameters are obtained from the de-noised waveforms. The Spectral Subtraction method is also applied for de-noising the electric and magnetic field waveforms generated by lightning to the CN Tower which enables the calculation of their waveform parameters.

scholarly journals Lightning Return-Stroke Transmission Line Modelling Based on the Derivative of Heidler Function and CN Tower Data

2021 ◽  
Author(s):  
Mariusz Milewski
Keyword(s):  
Transmission Line ◽  
Telecommunication Networks ◽  
Stroke Model ◽  
Return Stroke ◽  
Measured Current ◽  
Lightning Current ◽  
Current Parameter ◽  
Measured Field ◽  
Current Characteristics ◽  
Current Derivative

One of the most important parameters in a lightning flash that is of interest to researchers is the lightning return-stroke current as it causes most of the destructions and disturbances in electrical and telecommunication networks. In most cases, the lightning return-stroke current can not be directly measured and current characteristics are determined from measured electric and magnetic fields through the use of lightning return-stroke models. The main objective of this work is the development of a lightning return-stroke model for an elevated object. Also, an important objective is the correlation of the wavefront parameters (peak, maximum rate of rise and risetime) of the return-stroke current with the wavefront parameters of its associated lightning electromagnetic pulse (LEMP), measured 2 km north of the tower. The developed field-current parameter relationships for CN Tower lightning return strokes are compared with those obtained from measurements conducted at the Peissenberg Tower in Germany. A 3-section transmission line (TL) model of the CN Tower, along with the derivative of the modified Heidler function, is used to simulate the measured current derivative signal. Then, the spatial-temporal distribution of the lightning current along the CN Tower and the lightning channel, during the lightning return-stroke phase, is determined. The presented model simulates the measured current derivative signal instead of the current as has been used by other researchers. The use of the derivative of the modified Heidler function to simulate the lightning current derivative proved to be superior than simulating the lightning current. For the quantitative assessment of the proposed model, a comparison between the simulated field, obtained through the usage of Maxwell’s equations and the simulated current, and the measured field is performed. The developed 3-section TL model based on the measured current derivative and the derivative of the modified Heidler function produced a simulated magnetic field that is much closer to the measured field in comparison with previous models. The developed field-current parameter relationships as well as the experimentally verified lightning return-stroke model can contribute to solving the inverse-source problem, one of the most challenging problems in lightning research, where the lightning current characteristics are estimated based on the characteristics of the measured LEMP.

scholarly journals Modelling of tall-structure lightning return-stroke current using the Electromagnetic Transients Program

2021 ◽  
Author(s):  
Mohammadsadegh Rahimian Emam
Keyword(s):  
Velocity Profile ◽  
Electromagnetic Transients ◽  
Simulation Function ◽  
Return Stroke ◽  
Lightning Current ◽  
Lightning Channel ◽  
Section Model ◽  
Tall Structure ◽  
Current Derivative

The main aim of this PhD work is to advance tall-structure lightning return-stroke current modelling. The Alternative Transients Program (ATP), a version of the Electromagnetic Transients program (EMTP), is used to model the lightning current distribution within a tall structure and the attached lightning channel. The tall structure, namely the CN Tower, is modeled as three or five transmission line sections connected in series. The lightning channel is represented by a transmission line with a continuously expanding length. The presented model takes into account reflections within the tower and within the lightning channel. Locations of reflections, current reflection coefficients and the parameters of the current simulation function are calculated based on the time analysis of the current derivative signal, measured at the tower. The decay parameters of the simulation function are first determined by curve fitting the decaying part of the current obtained from measurement. The other parameters are determined by curve fitting the measured initial current derivative impulse with the derivative of the simulation function, before the arrival of reflections. The simulation results substantially succeeded in reproducing the fine structure of the measured current derivative signal. The model allows for the computation of the lightning current at any point along the current path (the tower and the attached channel), which is required for the calculation of the associated electromagnetic field. Using the three-section model of the tower, the presented return-stroke current model enables the determination of a discrete return-stroke velocity profile, demonstrating that the velocity generally decays with time. Furthermore, based on the five-section model, the proposed approach enables taking into account the existence of upward-connecting leaders, which allowed, for the first time, the determination of upward-connecting leader lengths and return-stroke velocity variation profiles with more details. The return-stroke velocity profile is found to initially increase rapidly with time, reaching a peak, and then decrease less rapidly. The proposed model is also experimentally verified based on the comparison between the computed and measured electromagnetic fields. The simulated electric and magnetic field waveforms are found to reproduce important details of the measured fields, including initial split peaks that appear due to channel-front reflections in the presence of upward-connecting leaders.

scholarly journals Lightning Return-Stroke Transmission Line Modelling Based on the Derivative of Heidler Function and CN Tower Data

2021 ◽  
Author(s):  
Mariusz Milewski
Keyword(s):  
Transmission Line ◽  
Telecommunication Networks ◽  
Stroke Model ◽  
Return Stroke ◽  
Measured Current ◽  
Lightning Current ◽  
Current Parameter ◽  
Measured Field ◽  
Current Characteristics ◽  
Current Derivative

One of the most important parameters in a lightning flash that is of interest to researchers is the lightning return-stroke current as it causes most of the destructions and disturbances in electrical and telecommunication networks. In most cases, the lightning return-stroke current can not be directly measured and current characteristics are determined from measured electric and magnetic fields through the use of lightning return-stroke models. The main objective of this work is the development of a lightning return-stroke model for an elevated object. Also, an important objective is the correlation of the wavefront parameters (peak, maximum rate of rise and risetime) of the return-stroke current with the wavefront parameters of its associated lightning electromagnetic pulse (LEMP), measured 2 km north of the tower. The developed field-current parameter relationships for CN Tower lightning return strokes are compared with those obtained from measurements conducted at the Peissenberg Tower in Germany. A 3-section transmission line (TL) model of the CN Tower, along with the derivative of the modified Heidler function, is used to simulate the measured current derivative signal. Then, the spatial-temporal distribution of the lightning current along the CN Tower and the lightning channel, during the lightning return-stroke phase, is determined. The presented model simulates the measured current derivative signal instead of the current as has been used by other researchers. The use of the derivative of the modified Heidler function to simulate the lightning current derivative proved to be superior than simulating the lightning current. For the quantitative assessment of the proposed model, a comparison between the simulated field, obtained through the usage of Maxwell’s equations and the simulated current, and the measured field is performed. The developed 3-section TL model based on the measured current derivative and the derivative of the modified Heidler function produced a simulated magnetic field that is much closer to the measured field in comparison with previous models. The developed field-current parameter relationships as well as the experimentally verified lightning return-stroke model can contribute to solving the inverse-source problem, one of the most challenging problems in lightning research, where the lightning current characteristics are estimated based on the characteristics of the measured LEMP.

Research in Destruction of Concrete Bridge Expanded Joint Influenced by Temperature Difference

2015 ◽  
Vol 744-746 ◽  
pp. 803-806 ◽  
Author(s):  
Xiao Lei ◽  
Yue Yao ◽  
Shi Cao ◽  
Zhi Gang Guo
Keyword(s):  
Temperature Difference ◽  
Curve Fitting ◽  
Effective Temperature ◽  
Joint Damage ◽  
Measured Data ◽  
Concrete Bridge ◽  
Box Girder ◽  
Concrete Box Girder ◽  
Extremum Value ◽  
The Relationship

Destruction of bridge expanded joint is a serious problem for concrete bridge. Based on 5 years measured data, the temperature in the different positions of the concrete box girder was systemically analyzed to illuminate the cause of the bridge expanded joint damage. A method for predicting the extremum value of the temperature difference of concrete girder was proposed by use of the extrema analysis and curve fitting based on the temperature in the different positions of the concrete box girder. The relationship is quite useful in estimating the destruction of bridge expanded joint by effective temperature difference in concrete box-girder.

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