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The noise characteristics of the Global Navigation Satellite System (GNSS) position time series can be biased by many factors, which in turn affect the estimates of parameters in the deterministic model using a least squares method. The authors assess the effects of seasonal signals, weight matrix, intermittent offsets, and Helmert transformation parameters on the noise analyses. Different solutions are obtained using the simulated and real position time series of 647 global stations and power law noise derived from the residuals of stacking solutions are compared. Since the true noise in the position time series is not available except for the simulated data, the authors paid most attention to the noise difference caused by the variable factors. First, parameterization of seasonal signals in the time series can reduce the colored noise and cause the spectral indexes to be closer to zero (much “whiter”). Meanwhile, the additional offset parameters can also change the colored noise to be much “whiter” and more offsets parameters in the deterministic model leading to spectral indexes closer to zero. Second, the weight matrices derived from the covariance information can induce more colored noise than the unit weight matrix for both real and simulated data, and larger biases of annual amplitude of simulated data are attributed to the covariance information. Third, the Helmert transformation parameters (three translation, three rotation, and one scale) considered in the model show the largest impacts on the power law noise (medians of 0.4 mm−k/4 and 0.06 for the amplitude and spectral index, respectively). Finally, the transformation parameters and full-weight matrix used together in the stacking model can induce different patterns for the horizontal and vertical components, respectively, which are related to different dominant factors.

Accurate prediction of temporal evolution of turbulent flames represents one of the most challenging problems in the combustion community. In this work, predictive models for turbulent flame evolution were proposed based on machine learning with long short-term memory (LSTM) and convolutional neural network-long short-term memory (CNN-LSTM). Two configurations without and with mean shear are considered, i.e., turbulent freely propagating premixed combustion and turbulent boundary layer premixed combustion, respectively. The predictions of the LSTM and CNN-LSTM models were validated against the direct numerical simulation (DNS) data to assess the model performance. Particularly, the statistics of the fuel (CH4 for the freely propagating flames and H2 for the boundary layer flames) mass fraction and reaction rate were examined in detail. It was found that generally the performance of the CNN-LSTM model is better than that of the LSTM model. This is because that the CNN-LSTM model extracts both the spatial and temporal features of the flames while the LSTM model only extracts the temporal feature of the flames. The errors of the models mainly occur in regions with large scalar gradients. The correlation coefficient of the mass fraction from the DNS and that from the CNN-LSTM model is larger than 0.99 in various flames. The correlation coefficient of the reaction rate from the DNS and that from the CNN-LSTM model is larger than 0.93 in the freely propagating flames and 0.99 in the boundary layer flames. Finally, the profiles of the DNS values and predictions conditioned on axial distance were examined, and it was shown that the predictions of the CNN-LSTM model agree well with the DNS values. The LSTM model failed to accurately predict the evolution of boundary layer flames while the CNN-LSTM model could accurately predict the evolution of both freely propagating and boundary layer flames. Overall, this study shows the promising performance and the applicability of the proposed CNN-LSTM model, which will be applied to turbulent flames a posteriori in future work.

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His research interests include power industry restructuring, power system alarm processing, fault diagnosis and restoration strategies, as well as smart grids and electric vehicles.Prof. Wen is an editor of IEEE TRANSACTIONS ON POWER SYSTEMS and IEEE POWER ENGINEERING LETTERS, a subject editor on power system economics of IET Generation, Transmission and Distribution, an associate editor of the Journal of Energy Engineering (ASCE) and the Journal of Modern Power Systems and Clean Energy (Springer).