This paper presents a new method of detecting multi-periodicities in a seasonal time series. Conventional methods such as the average power spectrum or the autocorrelation function plot have been used in detecting mul...This paper presents a new method of detecting multi-periodicities in a seasonal time series. Conventional methods such as the average power spectrum or the autocorrelation function plot have been used in detecting multiple periodicities. However, there are numerous cases where those methods either fail, or lead to incorrectly detected periods. This, in turn in applications, produces improper models and results in larger forecasting errors. There is a strong need for a new approach to detecting multi-periodicities. This paper tends to fill this gap by proposing a new method which relies on a mathematical instrument, called the Average Power Function of Noise (APFN) of a time series. APFN has a prominent property that it has a strict local minimum at each period of the time series. This characteristic helps one in detecting periods in time series. Unlike the power spectrum method where it is assumed that the time series is composed of sinusoidal functions of different frequencies, in APFN it is assumed that the time series is periodic, the unique and a much weaker assumption. Therefore, this new instrument is expected to be more powerful in multi-periodicity detection than both the autocorrelation function plot and the average power spectrum. Properties of APFN and applications of the new method in periodicity detection and in forecasting are presented.展开更多
The paper presents results of reliability analysis made for lignite fired 370 MW rated power units installed in the Belchatow Power Plant (Poland). The concept of standardized power unit and the method of a histogram ...The paper presents results of reliability analysis made for lignite fired 370 MW rated power units installed in the Belchatow Power Plant (Poland). The concept of standardized power unit and the method of a histogram with a set number of observations in each class were applied in a study. The study includes analysis of probability distributions of operation times and repair times for the main power unit components. Empirical probability distribution functions have been identified and their parameters estimated in the study. The final forecast includes an estimation of such reliability measures like expected operation time, expected failure rate, average repair time and expected annual failure duration.展开更多
Finite time blow up of the solutions to Boussinesq equation with linear restoring force and combined power nonlinearities is studied. Sufficient conditions on the initial data for nonexistence of global solutions are ...Finite time blow up of the solutions to Boussinesq equation with linear restoring force and combined power nonlinearities is studied. Sufficient conditions on the initial data for nonexistence of global solutions are derived. The results are valid for initial data with arbitrary high positive energy. The proofs are based on the concave method and new sign preserving functionals.展开更多
文摘This paper presents a new method of detecting multi-periodicities in a seasonal time series. Conventional methods such as the average power spectrum or the autocorrelation function plot have been used in detecting multiple periodicities. However, there are numerous cases where those methods either fail, or lead to incorrectly detected periods. This, in turn in applications, produces improper models and results in larger forecasting errors. There is a strong need for a new approach to detecting multi-periodicities. This paper tends to fill this gap by proposing a new method which relies on a mathematical instrument, called the Average Power Function of Noise (APFN) of a time series. APFN has a prominent property that it has a strict local minimum at each period of the time series. This characteristic helps one in detecting periods in time series. Unlike the power spectrum method where it is assumed that the time series is composed of sinusoidal functions of different frequencies, in APFN it is assumed that the time series is periodic, the unique and a much weaker assumption. Therefore, this new instrument is expected to be more powerful in multi-periodicity detection than both the autocorrelation function plot and the average power spectrum. Properties of APFN and applications of the new method in periodicity detection and in forecasting are presented.
文摘The paper presents results of reliability analysis made for lignite fired 370 MW rated power units installed in the Belchatow Power Plant (Poland). The concept of standardized power unit and the method of a histogram with a set number of observations in each class were applied in a study. The study includes analysis of probability distributions of operation times and repair times for the main power unit components. Empirical probability distribution functions have been identified and their parameters estimated in the study. The final forecast includes an estimation of such reliability measures like expected operation time, expected failure rate, average repair time and expected annual failure duration.
基金partially supported by Grant No.DFNI I-02/9 of the Bulgarian Science Fund
文摘Finite time blow up of the solutions to Boussinesq equation with linear restoring force and combined power nonlinearities is studied. Sufficient conditions on the initial data for nonexistence of global solutions are derived. The results are valid for initial data with arbitrary high positive energy. The proofs are based on the concave method and new sign preserving functionals.
