Stochastic model of the gearbox pair vibration

The model of vibration signal of gearbox pair in the form of periodically correlated non-stationary random process is considered. It is shown that hidden periodicities in biperiodic correlated random process mean and covariance function, characterizing the vibrations of gearbox pair can be detected using the component and least square methods. Seven particular cases of the bi-rhythmic hidden periodicity for different modulation modes are analyzed.

Comparative analysis of methods for calculating the mode of a stationary random process

The paper considers methods for calculating the mode of a stationary random process when solving the problem of processing measurement results under conditions of a priori uncertainty. The results of the conducted studies allowed us to conclude that the most effective method for calculating the mode for a given sample is the proposed method, which allows to increase the accuracy of its calculation by at least 8 times, compared to methods based on the construction of histograms. It should be noted that the proposed method allows to provide an estimate with an error of at least 5% for samples with a number of measurements of about 5 value.

A novel method for gear gravimetric wear prediction based on improved particle swarm optimization and non-stationary random process probability distribution fitting

Purpose Stimulated by previous reference, which proposed making straight line of regression to test gear gravimetric wear loss sequence distribution, this paper aims to propose using straight line of regression to fit gear gravimetric wear loss sequence based on stationary random process suppose. Faced to that the stationary random sequence suppose had not been proved by previous reference, and that prediction did not present high precision, this paper proposes a method of fitting non-stationary random process probability distribution function. Design/methodology/approach Firstly, this paper proposes using weighted sum of Gauss items to fit zero-step approximate probability density. Secondly, for the beginning, this paper uses the method with few Gauss items under low precision. With the amount of points increasing, this paper uses more Gauss items under higher precision, and some Gauss items and some former points are deleted under precision condition. Thirdly, for particle swarm optimization with constraint problem, this paper proposed improved method, and the stop condition is under precision condition. Findings In experiment data analysis section, gear wear loss prediction is done by the method proposed by this paper. Compared with the method based on the stationary random sequence suppose by prediction relative error, the method proposed by this paper lowers the relative error whose absolute values are more than 5%, except when the current point sequence number is 2, and retains the relative error, whose absolute values are lower than 5%, still lower than 5%. Originality/value Finally, the method proposed by this paper based on non-stationary random sequence suppose is proved to be the better method in gear gravimetric wear loss prediction.

A Probabilistic Analysis Of Operation Of A Flat Steel Frame Under Seismic Action

The seismic action is non-stationary random process. Calculation in the probabilistic setting makes it possible to most accurately assess the response of the system during an earthquake. In the work, the reliability of a flat steel frame under seismic action was estimated by the method of statistical tests when considering seismic action in the form of a non-stationary random process. The design cross-sections of the frame were adopted based on the results of the calculation of the seismic action of the design earthquake level in accordance with current design standards. When performing the probabilistic calculation, a deterministic solution implemented in the software package was used. The solution is based on direct integration of the equations of motion using explicit schemes. A method has been developed for determining the actual value of safety coefficient of load-bearing capacity of the frame. Considering the safety factor of the frame under seismic action as a random variable, a corresponding histogram is constructed using the criterion of non-collapse. Using the Pearson criterion, the closest theoretical distribution law to the obtained empirical distribution is determined. According to the theoretical laws produced, the assessment of the actual safety factor of the bearing capacity and the coefficients taking into account possible damage to buildings and structures with a given security. In addition, the probability of plastic deformations exceeding the value of 0.05 in the structural elements in case of accidental seismic impact of the maximum calculated earthquake level was established by statistical tests. The method is used to determine the seismic stability of structures with a given security, which makes it possible to provide the required level of reliability for all buildings and structures designed in seismic areas.

Convergence of the sequence of the Pearson statistics values to the normalized square of the Bessel process

It is shown that, with suitable time change, the finite-dimensional distributions of the process formed by successive values of the Pearson statistics for an expanding sample converge to finite-dimensional distributions of the stationary random process, namely, the normalized square of the Bessel process. The results obtained earlier on the limit joint distributions of the Pearson statistics are used to derive explicit formulas for the density of joint distributions of the Bessel process.