Non-Linear Regression Models with Vibration Amplitude Optimization Algorithms in a Microturbine

Abstract

Machinery condition monitoring and failure analysis is an engineering problem to pay attention to among all those being studied. Excessive vibration in a rotating system can damage the system and cannot be ignored. One option to prevent vibrations in a system is through preparation for them with a model. The accuracy of the model depends mainly on the type of model and the fitting that is attained. The non-linear model parameters can be complex to fit. Therefore, artificial intelligence is an option for performing this tuning. Within evolutionary computation, there are many optimization and tuning algorithms, the best known being genetic algorithms, but they contain many specific parameters. That is why algorithms such as the gray wolf optimizer (GWO) are alternatives for this tuning. There is a small number of mechanical applications in which the GWO algorithm has been implemented. Therefore, the GWO algorithm was used to fit non-linear regression models for vibration amplitude measurements in the radial direction in relation to the rotational frequency in a gas microturbine without considering temperature effects. RMSE and R2 were used as evaluation criteria. The results showed good agreement concerning the statistical analysis. The 2nd and 4th-order models, and the Gaussian and sinusoidal models, improved the fit. All models evaluated predicted the data with a high coefficient of determination (85–93%); the RMSE was between 0.19 and 0.22 for the worst proposed model. The proposed methodology can be used to optimize the estimated models with statistical tools.

Metaheuristic Algorithm-Based Vibration Response Model for a Gas Microturbine

“…The trajectories in Figures 5c and 6c were very similar to those observed in previous studies [27,28] in which the effect of temperature was not considered. In [27] the gray wolf optimizer (GWO) was used to fit non-linear regression models to the measurements.…”

“…The trajectories in Figures 5c and 6c were very similar to those observed in previous studies [27,28] in which the effect of temperature was not considered. In [27] the gray wolf optimizer (GWO) was used to fit non-linear regression models to the measurements. By including the effect of combustion and high temperatures in this investigation, much more variability was found in the results, and the vibration amplitude levels were up to 45% higher with maximum peaks of 12.06 µm in relation to 6.62 µm for the study referred to.…”

“…Both maximum peaks were found at the second rotational frequency, which suggests that, at the second level of nominal rotational frequency (76 Hz), a resonance could manifest itself, and no matter the temperature, the vibration will be the highest in this condition. According to [27,28], the deviation in the vibration amplitudes when the effects of temperature were not considered were from 0.2 to 0.7 µm, and when temperature was included, they were from 0.44 to 2.19 µm (see Table 2), which represented a 122.74% increase in the deviation for the mentioned low values, and a 212.85% increase in the deviation for the mentioned high values. The minimum vibration amplitude value of 1.34 µm remained practically the same as in the previous study with a difference of only 2.33%, but it did not appear at the same nominal rotational frequency, changing from the lowest (27 Hz) to the highest (127 Hz), which was attributed to the effect of temperature.…”

“…In this study, a polynomial model was identified and the degree of the polynomial was selected based on performance. However, there is a wide variety of nonlinear models that can be tested in future research, such as those analyzed in [27], where the use of logarithmic, exponential, polynomial and trigonometric models is discussed.…”

Adaptive Ascent Control of a Collaborative Object Transportation System Using Two Quadrotors

“…The monitoring of an important parameter-the vibration of their rotors-is an interesting aspect of the reliability of particularly large quadrotors. A diagnostic system using nonlinear regression models is shown in [37].…”