• KSII Transactions on Internet and Information Systems (TIIS)
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• v.17 no.12
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• pp.3242-3265
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• 2023

Ensuring reliability of a machinery system involve the prediction of remaining useful life (RUL). In most RUL prediction approaches, noise is always considered for removal. Nevertheless, noise could be properly utilized to enhance the prediction capabilities. In this paper, we proposed a novel RUL prediction approach based on noise injection and a Kalman filter ensemble of modified bagging predictors. Firstly, we proposed a new method to insert Gaussian noises into both observation and feature spaces of an original training dataset, named GN-DAFC. Secondly, we developed a modified bagging method based on Kalman filter averaging, named KBAG. Then, we developed a new ensemble method which is a Kalman filter ensemble of KBAGs, named DKBAG. Finally, we proposed a novel RUL prediction approach GN-DAFC-DKBAG in which the optimal noise-injected training dataset was determined by a GN-DAFC-based searching strategy and then inputted to a DKBAG model. Our approach is validated on the NASA C-MAPSS dataset of aero-engines. Experimental results show that our approach achieves significantly better performance than a traditional Kalman filter ensemble of single learning models (KESLM) and the original DKBAG approaches. We also found that the optimal noise-injected data could improve the prediction performance of both KESLM and DKBAG. We further compare our approach with two advanced ensemble approaches, and the results indicate that the former also has better performance than the latters. Thus, our approach of combining optimal noise injection and DKBAG provides an effective solution for RUL estimation of machinery systems.

• Journal of Positioning, Navigation, and Timing
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• v.9 no.3
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• pp.261-272
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• 2020

A Kalman filter algorithm is used for the generation of an ensemble timescale with three hydrogen masers maintained in KRISS. Allan deviation curves of three pairs of clocks were obtained by a three-cornered hat method and were used as reference curves for determination of parameters of the Kalman filter-based timescale. The ensemble timescale equation of a 3-clock system was established, and the clocks' phases estimated by the Kalman filter were used as the prediction time of each clock in the equation. The weight of each clock was determined inversely proportional to the Allan variance calculated with the clocks' phases. The Allan deviation of the weighted mean was 1.2×10^-16 at the averaging time of 57,600 s. However when we made fine adjustments of the clocks' weight, the minimum Allan deviation of 2×10^-17 was obtained. To find out the reason of the great improvement in the frequency stability, additional researches are in progress theoretically and experimentally.

• Journal of Positioning, Navigation, and Timing
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• v.10 no.3
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• pp.197-206
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• 2021

We compared two typical ensemble time scale algorithms; AT1 and Kalman filter. Four commercial atomic clocks composed of two hydrogen masers and two cesium atomic clocks provided measurement data to the algorithms. The allocation of relative weights to the clocks is important to generate a stable ensemble time. A 30 day-average-weight model, which was obtained from the average Allan variance of each clock, was applied to the AT1 algorithm. For the reduced Kalman filter (Kred) algorithm, we gave the same weights to the two hydrogen masers. We also compared the frequency stabilities of the outcome from the algorithms when the frequency offsets and/or the frequency drift offsets estimated by the algorithms were corrected or not corrected by the KRISS-made primary frequency standard, KRISS-F1. We found that the Kred algorithm is more effective to generate a stable ensemble time scale in the long-term, and the algorithm also generates much enhanced short-term stability when the frequency offset is used for the calculation of the Allan deviation instead of the phase offset.

• Transactions of the Korean Society of Automotive Engineers
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• v.20 no.6
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• pp.126-131
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• 2012

Tire force is one of important parameters which determine vehicle dynamics. However, it is hard to measure tire force directly through sensors. Not only the sensor is expensive but also installation of sensors on harsh environments is difficult. Therefore, estimation algorithms based on vehicle dynamic models are introduced to estimate the tire forces indirectly. In this paper, an estimation system for estimating lateral force and states is suggested. The state-space equation is constructed based on the 3-DOF bicycle model. Extended Kalman Filter, Unscented Kalman Filter and Ensemble Kalman Filter are used for estimating states on the nonlinear system. Performance of each algorithm is evaluated in terms of RMSE (Root Mean Square Error) and maximum error.

• Atmosphere
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• v.20 no.3
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• pp.287-306
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• 2010

An ensemble Kalman filter (EnKF) with Weather Research and Forecasting (WRF) Model is applied for Typhoon Wukong (200610) to investigate the performance of ensemble forecasts depending on experimental configurations of the EnKF. In addition, the ensemble sensitivity analysis is applied to the forecast and analysis ensembles generated in EnKF, to investigate the possibility of using the ensemble sensitivity analysis as the adaptive observation guidance. Various experimental configurations are tested by changing model error, ensemble size, assimilation time window, covariance relaxation, and covariance localization in EnKF. First of all, experiments using different physical parameterization scheme for each ensemble member show less root mean square error compared to those using single physics for all the forecast ensemble members, which implies that considering the model error is beneficial to get better forecasts. A larger number of ensembles are also beneficial than a smaller number of ensembles. For the assimilation time window, the experiment using less frequent window shows better results than that using more frequent window, which is associated with the availability of observational data in this study. Therefore, incorporating model error, larger ensemble size, and less frequent assimilation window into the EnKF is beneficial to get better prediction of Typhoon Wukong (200610). The covariance relaxation and localization are relatively less beneficial to the forecasts compared to those factors mentioned above. The ensemble sensitivity analysis shows that the sensitive regions for adaptive observations can be determined by the sensitivity of the forecast measure of interest to the initial ensembles. In addition, the sensitivities calculated by the ensemble sensitivity analysis can be explained by dynamical relationships established among wind, temperature, and pressure.

• Atmosphere
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• v.17 no.3
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• pp.217-230
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• 2007

Using the Lorenz-95 simple model, which can simulate many atmospheric characteristics, we compare the performance of ensemble strategies such as bred vectors, the bred vectors rotated (to be orthogonal to each bred member), and the Ensemble Transform Kalman Filter (ETKF). The performance metrics used are the RMSE of ensemble means, the ratio of RMS error of ensemble mean to the spread of ensemble, rank histograms to see if the ensemble member can well represent the true probability density function (pdf), and the distribution of eigen-values of the forecast ensemble, which can provide useful information on the independence of each member. In the meantime, the orthogonal bred vectors can achieve the considerable progress comparing the bred vectors in all aspects of RMSE, spread, and independence of members. When we rotate the bred vectors for orthogonalization, the improvement rate for the spread of ensemble is almost as double as that for RMS error of ensemble mean compared to the non-rotated bred vectors on a simple model. It appears that the result is consistent with the tentative test on the operational model in KMA. In conclusion, ETKF is superior to the other two methods in all terms of the assesment ways we used when it comes to ensemble prediction. But we cannot decide which perturbation strategy is better in aspect of the structure of the background error covariance. It appears that further studies on the best perturbation way for hybrid variational data assimilation to consider an error-of-the-day(EOTD) should be needed.

• Atmosphere
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• v.23 no.1
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• pp.33-37
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• 2013

In meteorology, exploitation of Kalman filter as a data assimilation system is virtually impossible due to simultaneous requirements of adjoint model and large computer resource. The other substitute of utilizing ensemble Kalman filter is only affordable by compensating an enormous usage of computing resource. Furthermore, the latter employs ensemble integration sets for evolving the background error covariance matrix by compensating the dynamical feature of the temporal evolution of weather conditions. We propose a new implementation method that works without the adjoint model by utilizing the explicit expression of the background error covariance matrix in backward evolution. It will also break a barrier in the evolution of the covariance matrix. The method may be applied with a slight modification to the real time assimilation or the retrospective analysis.

• Atmosphere
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• v.22 no.4
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• pp.415-427
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• 2012

$CO_2$ is the most important trace gas related to climate change. Therefore, understanding surface carbon sources and sinks is important when seeking to estimate the impact of $CO_2$ on the environment and climate. CarbonTracker, developed by NOAA, is an inverse modeling system that estimates surface carbon fluxes using an ensemble Kalman filter with atmospheric $CO_2$ measurements as a constraint. In this study, to investigate the capability of CarbonTracker as an analysis tool for estimating surface carbon fluxes in Asia, an experiment with a nesting domain centered in Asia is performed. In general, the results show that setting a nesting domain centered in Asia region enables detailed estimations of surface carbon fluxes in Asia. From a rank histogram, the prior ensemble spread verified at observational sites located in Asia is well represented with a relatively flat rank histogram. The posterior flux in the Eurasian Boreal and Eurasian Temperate regions is well analyzed with proper seasonal cycles and amplitudes. On the other hand, in tropical regions of Asia, the posterior flux does not differ greatly from the prior flux due to fewer $CO_2$ observations. The root mean square error of the model $CO_2$ calculated by the posterior flux is less than the model $CO_2$ calculated by the prior flux, implying that CarbonTracker based on the ensemble Kalman filter works appropriately for the Asia region.

• Smart Structures and Systems
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• v.22 no.4
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• pp.399-411
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• 2018

The difficulty in modeling complex nonlinear structures lies in the presence of significant sources of uncertainties mainly attributed to sudden changes in the structure's behavior caused by regular aging factors or extreme events. Quantifying these uncertainties and accurately representing them within the complex mathematical framework of Structural Health Monitoring (SHM) are significantly essential for system identification and damage detection purposes. This study highlights the importance of uncertainty quantification in SHM frameworks, and presents a comparative analysis between intrusive and non-intrusive techniques in quantifying uncertainties for SHM purposes through two different variations of the Kalman Filter (KF) method, the Ensemble Kalman filter (EnKF) and the Polynomial Chaos Kalman Filter (PCKF). The comparative analysis is based on a numerical example that consists of a four degrees-of-freedom (DOF) system, comprising Bouc-Wen hysteretic behavior and subjected to El-Centro earthquake excitation. The comparison is based on the ability of each technique to quantify the different sources of uncertainty for SHM purposes and to accurately approximate the system state and parameters when compared to the true state with the least computational burden. While the results show that both filters are able to locate the damage in space and time and to accurately estimate the system responses and unknown parameters, the computational cost of PCKF is shown to be less than that of EnKF for a similar level of numerical accuracy.

• Journal of Korea Water Resources Association
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• v.42 no.11
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• pp.963-972
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• 2009

The objective of this study is to evaluate an application of stochastic continuous storage function model with ensemble Kalman filter technique. The case study is performed at the upstream basin of Jibo streamflow gauge including Andong and Imha dam. Test period is for the rainy season during 2006 and 2007. Long term runoff analysis is feasible in the case of using deterministic model. Ensemble members for input data and parameters are generated using Monte Carlo simulation for the purpose of applying ensemble Kalman filter technique. The cumulative absolute errors of stochastic model to the deterministic one are improved for the amount of 17.5 %, 18.3 % and more than 40.0 % for Andong dam, Imha dam and Jibo station, respectively. The results indicate that the stochastic model improves the accuracy of the simulated discharge considerably.