Detection of Noise Signal in the Additive Mixture Based on the Second-Order Cumulant

In order to determine the technical condition of energetic objects with the objective of ensuring their operational reliability, durability and safety, systems of noise diagnostics, which are based on the analysis of acoustic diagnostic signals. A promising area of noise diagnostics are cumulant methods, based on cumulant analysis, which involves the use of cumulants and cumulant coefficients. In known literature no characteristics of detection of a signal within an interference-containing additive mixture with the use of a second-order cumulant (variance) can be found. That is why the objective of the paper is to study the use of cumulant method on the basis of point estimations of variance for a sample of momentary values for detection of an acoustic signal against the background of noise interference. The research was carried out by way of modeling the additive mixture of signal and interference using the MATLAB® software package. Interference is a model of a noise acoustic signal, which accompanies the operation of properly functional equipment. Signal is a model of an acoustic signal which is created with the occurrence of a malfunction. Signal and interference are independent random variables, so the property of additivity of cumulants was used – the variance of a mixture equals the sum of variances of signal and interference. The decision about the presence of a signal was made on the basis of testing two statistical hypotheses. The null hypothesis – the signal is absent, variance equals to the variance of the interference. The first hypothesis – the signal is present, variance equals to the variance of the mixture. Additional parameters: probability of a Type I error 0,01, probability of correct determination 0,99. The relative error of estimation determined the minimal sample size. These values allowed for the calculation of the threshold value, upon the exceeding of which by the variance estimation, the decision on the presence of signal is made. For each sample, assessments of variance were made. Experimental probability of correct determination is calculated as a total number of decisions taken regarding the presence of a signal, divided by the number of realizations, and corresponds to the value of the specified probability of correct determination. Its relative error was calculated in order to control the validity of the results. Also, kernel density estimation of the probability of the variance assessment for the case of a signal with normal distribution. As shown by the graphs, the assessments have a distribution that is close to normal. The conducted study proves that a variance -based cumulant method allows to detect a signal against the background of noise interference. The necessary sample size, which shows the number of the necessary momentary values, is given in the paper. That is to say that with the help of the frequency of an analogue digital converter the needed duration of the recording of a real for assessment of its variance can be obtained, and the decision on the presence or absence of a signal is to be made on the basis of the specified threshold values. The results of the study can be added to the known sample sizes and threshold values for the coefficients of asymmetry and excess with different distributions. Application of the described method requires additional testing on real acoustic signals and has the areas of use in systems of noise diagnostics.

A probabilistic approach for optimal capacitor planning in distribution systems with wind generators

This thesis proposes a probabilistic approach based on the Cumulant method for optimal capacitor planning in distribution systems with high penetration of wind generators. To account for the problem uncertainties, the probabilistic behaviour of load forecasts and wind generators are modeled using Probability Density Functions. Once the probabilistic framework is defined, an optimization problem can be formulated to minimize the total costs of the capacitors and of the annual energy losses. The optimization problem is then solved by using the Logarithm Barrier Interior Point Method, which provides a linear relationship between the cumulants of load and wind variables and the cumulants of the system parameters and solution cost. The Cumulant method offers a generous advantage in speed, while maintaining acceptable accuracy, as compared to the traditional Monte Carlo Simulation method. The proposed method is tested on a 7-bus and on a 33-bus systems, and the results are reported and discussed.

A probabilistic approach for optimal capacitor planning in distribution systems with wind generators

This thesis proposes a probabilistic approach based on the Cumulant method for optimal capacitor planning in distribution systems with high penetration of wind generators. To account for the problem uncertainties, the probabilistic behaviour of load forecasts and wind generators are modeled using Probability Density Functions. Once the probabilistic framework is defined, an optimization problem can be formulated to minimize the total costs of the capacitors and of the annual energy losses. The optimization problem is then solved by using the Logarithm Barrier Interior Point Method, which provides a linear relationship between the cumulants of load and wind variables and the cumulants of the system parameters and solution cost. The Cumulant method offers a generous advantage in speed, while maintaining acceptable accuracy, as compared to the traditional Monte Carlo Simulation method. The proposed method is tested on a 7-bus and on a 33-bus systems, and the results are reported and discussed.

Исследование фазовых переходов и термодинамических свойств модели Поттса с C-=SUB=-q-=/SUB=-=4 на гексагональной решетке с взаимодействиями вторых ближайших соседей

Magnetic structures of the ground state, phase transitions and thermodynamic properties of the 2D ferromagnetic Potts model with the number of spin states q = 4 on a hexagonal lattice with next-nearest neighbors interactions are investigated by the Monte Carlo method based on the Wang-Landau algorithm. It is shown that taking into account the antiferromagnetic interactions of the next-nearest neighbors leads to the appearance of frustration and a violation of magnetic ordering. The orders of the phase transitions are investigated using the Binder fourth-order cumulant method and histogram analysis of data. It is established that a first-order transition is observed in the model being investigated.

Фазовые переходы и термодинамические свойства модели Поттса с числом состояний спина q=4 на решетке кагоме

Phase transitions and thermodynamic properties of the 2D ferromagnetic Potts model with the number of spin states q = 4 on a kagome lattice are investigated by the Mote Carlo method based on the Wang-Landau algorithm. The orders of the phase transitions are investigated using the Binder fourth-order cumulant method and histogram analysis of data. It is established that a first-order transition is observed in the model being investigated.