Data Assimilation in a Nonlinear Time-Delayed Dynamical System with Lagrangian Optimization

An efficient data-driven multiscale stochastic reduced order modeling framework for complex systems

Self-excited thermoacoustic oscillations seriously threaten the operation of combustion equipment. Various active and passive control methods for self-excited thermoacoustic oscillations have been proposed, while most existing methods are complex and difficult to implement. A new passive control method was expected to be proposed in the present study. The thermoacoustic oscillations occurring in asymmetrical two-dimensional combustion systems were investigated numerically. The control effects of the asymmetrical fuel-air feed conditions on thermoacoustic oscillations were examined. In addition, experimental tests were performed to further examine the control effects. The results showed that the oscillations would be encouraged in an asymmetrical combustion system if an appropriate standing wave was formed. The asymmetrical fuel-air feed conditions could affect the waveform and consequently influence the occurrence of thermoacoustic oscillations. The oscillations could be eliminated by adjusting the length or the inlet boundary condition for half of the fuel-air feed channels, and the combustion chamber did not need to be retrofitted. The passive control method was simple and easy to implement for eliminating thermoacoustic oscillations.

Addressing climate change through carbon capture and storage (CCS) technologies necessitates advanced computational methodologies for subsurface CO2 storage monitoring. This study focuses on the Illinois Basin Decatur Project (IBDP), a CCS demonstration pilot aimed at CO2 injection into a deep saline reservoir. We introduce a novel framework combining Dynamic Mode Decomposition (DMD), a data-driven model reduction technique, with direct data assimilation to streamline the calibration of CO2 plume evolution models. This approach enhances rapid tracking and overcomes the computational challenges of traditional high-fidelity numerical reservoir simulations known as the full-order model (FOM). Using DMD, we analyzed five distinct FOM simulation cases of the IBDP with varied permeability in the Mt. Simon section to develop reduced-order models (ROMs). These ROMs utilize three state variables: reservoir pressure, CO2 plume saturation, and bottom-hole pressure (BHP) from a CO2 injection well alongside multi-level pressures from a monitoring well derived from the FOM and the actual field data respectively. Initial FOM simulation cases assessed the impact of permeability multipliers on pressure responses. We then transformed these into ROMs using DMD, preserving essential dynamics. Linear interpolation between permeabilities and DMD outputs—modes and eigenvalues—established relationships for rapid BHP prediction under different scenarios. Employing a Kalman filter, we optimized a global permeability multiplier, using the ROMs, to align measured and simulated BHP values, ensuring model calibration. The final calibrated FOM was further decomposed to a DMD-based ROM, enabling quick, accurate predictions, significantly reducing computational time from hours to minutes. Utilizing an ROM derived through DMD, we achieved an order of 160 reduction in computational time (from 8 hours to just 3 minutes) for a 3-year historical CO2 injection period modeled with 547,000 cells of the FOM. The ROM demonstrated remarkable fidelity, with a mean absolute error of 1.46 psi for pressure and 3.7e-05 for CO2 plume saturation, effectively capturing the dynamics of the full-order model. This substantial decrease in computational time illustrates an advantageous trade-off between speed and accuracy, optimizing the potential for long-term forecasting and monitoring of CO2 sequestration. Incorporating the IBDP as a case study, this research contributes a significant advancement to reservoir simulation practices, offering a potent, efficient tool for CCS monitoring. By integrating DMD for ROM construction with precise data assimilation-based calibration, the study provides a comprehensive solution for swift and accurate subsurface CO2 plume tracking, essential for the successful implementation of CCS projects and the broader effort to mitigate climate change impacts.

Wind tunnel test, Computational Fluid Dynamics (CFD) simulation, and Proper Orthogonal Decomposition (POD) based Reduced Order Model (ROM) are used for wind load prediction on a LNG carrier in this project. In order to train the model for high accurate predictions and provide wind load prediction for vessel operations with high confidence level, extended Kalman Filter (EKF) based data assimilation model is developed to fuse the experimental data and the ROM predicted data. Effects of sensor locations and sensor numbers on the data fusing are studied. Study results indicate that the single point data assimilation can help with sensor positioning and outlier data detection. Based on the standard errors at the sensor points, prediction accuracy with sorted multipoint data assimilation is higher than that with single point data assimilation.

Mitigating self-excited flame pulsating and thermoacoustic oscillations using perforated liners

Four-dimensional variational (4D-Var) data assimilation (DA) experiments using Global Positioning System (GPS)-derived precipitable water vapor (PWV) were conducted for the tropical cyclone (TC) Nargis in 2008. In order to analyze the initial field at 1200 UTC 30 April 2008, 12, 24, 36, and 48 h sequential DA experiments with 3 h assimilation windows were performed. The initial fields made by these DA experiments were applied to subsequent forecast experiments using a nonhydrostatic model (NHM) with a horizontal resolution of 10 km. NHM predictions using initial fields produced by DA experiments that used only ordinary observational data (without GPS PWV) exhibited a large variation of predicted maximum TC intensity (958 to 983 hPa) for each experiment. In these experiments, a longer assimilation period did not necessarily result in better prediction. The DA of GPS PWV yielded a smaller variation of predicted maximum TC intensity (964 to 974 hPa), and a longer assimilation period tended to bring deeper depression of TC central pressure. Overall, TC intensities determined by DA experiments with GPS data were closer to the best track produced by the Regional Specialized Meteorological Centre (RSMC) New Delhi than the DA experiments without GPS data. The 48 h DA without GPS PWV resulted in the weakest prediction of TC development with the deepest TC central pressure of 983 hPa, while 48 h DA with GPS PWV successfully predicted rapid TC development with the deepest pressure of 967 hPa. One cause of the incomplete development of Nargis in the 48 h DA experiment without GPS PWV was insufficient observations in the Bay of Bengal, especially in the first 12 h. Underestimation of precipitation was conspicuous in the first 12 h of the DA. Implementation of GPS PWV into the DA contributed to increasing the precipitation and changed the fields of pressure and wind in the bay. In the first several hours, modifications of the fields of pressure and wind around the Andaman Islands were conspicuous. These affected areas extended with time and created a more favorable environment for TC development.

Stratospheric dynamics are strongly affected by the absorption/emission of radiation in the Earth’s atmosphere and Rossby waves that propagate upward from the troposphere, perturbing the zonal flow. Reduced order models of stratospheric wave–zonal interactions, which parameterize these effects, have been used to study interannual variability in stratospheric zonal winds and sudden stratospheric warming (SSW) events. These models are most sensitive to two main parameters: Λ, forcing the mean radiative zonal wind gradient, and h, a perturbation parameter representing the effect of Rossby waves. We take one such reduced order model with 20 years of ECMWF atmospheric reanalysis data and estimate Λ and h using both a particle filter and an ensemble smoother to investigate if the highly-simplified model can accurately reproduce the averaged reanalysis data and which parameter properties may be required to do so. We find that by allowing additional complexity via an unparameterized Λ(t), the model output can closely match the reanalysis data while maintaining behavior consistent with the dynamical properties of the reduced-order model. Furthermore, our analysis shows physical signatures in the parameter estimates around known SSW events. This work provides a data-driven examination of these important parameters representing fundamental stratospheric processes through the lens and tractability of a reduced order model, shown to be physically representative of the relevant atmospheric dynamics.

Parameter identification of reduced-order electrochemical model simplified by spectral methods and state estimation based on square-root cubature Kalman filter

We propose a high-order stochastic-statistical moment closure model for efficient ensemble prediction of leading-order statistical moments and probability density functions in multiscale complex turbulent systems. The statistical moment equations are closed by a precise calibration of the high-order feedbacks using ensemble solutions of the consistent stochastic equations, suitable for modeling complex phenomena including non-Gaussian statistics and extreme events. To address challenges associated with closely coupled spatiotemporal scales in turbulent states and expensive large ensemble simulation for high-dimensional systems, we introduce efficient computational strategies using the random batch method (RBM). This approach significantly reduces the required ensemble size while accurately capturing essential high-order structures. Only a small batch of small-scale fluctuation modes is used for each time update of the samples, and exact convergence to the full model statistics is ensured through frequent resampling of the batches during time evolution. Furthermore, we develop a reduced-order model to handle systems with really high dimensions by linking the large number of small-scale fluctuation modes to ensemble samples of dominant leading modes. The effectiveness of the proposed models is validated by numerical experiments on the one-layer and two-layer Lorenz '96 systems, which exhibit representative chaotic features and various statistical regimes. The full and reduced-order RBM models demonstrate uniformly high skill in capturing the time evolution of crucial leading-order statistics, non-Gaussian probability distributions, while achieving significantly lower computational cost compared to direct Monte-Carlo approaches. The models provide effective tools for a wide range of real-world applications in prediction, uncertainty quantification, and data assimilation.

Quenching of limit cycle oscillations (LCO), either through mutual coupling or external forcing, has attracted wide attention in several fields of science and engineering. However, the simultaneous utilization of these coupling schemes in quenching of LCO has rarely been studied despite its practical applicability. We study the dynamics of two thermoacoustic oscillators simultaneously subjected to mutual coupling and asymmetric external forcing through experiments and theoretical modeling. We investigate the forced response of both identical and non-identical thermoacoustic oscillators for two different amplitudes of LCO. Under mutual coupling alone, identical thermoacoustic oscillators display the occurrence of partial amplitude death and amplitude death, whereas under forcing alone, asynchronous quenching of LCO is observed at non-resonant conditions. When the oscillators are simultaneously subjected to mutual coupling and asymmetric forcing, we observe a larger parametric region of oscillation quenching than when the two mechanisms are utilized individually. This enhancement in the region of oscillation quenching is due to the complementary effect of amplitude death and asynchronous quenching. However, a forced response of coupled non-identical oscillators shows that the effect of forcing is insignificant on synchronization and quenching of oscillations in the oscillator which is not directly forced. Finally, we qualitatively capture the experimental results using a reduced-order theoretical model of two coupled Rijke tubes which are coupled through dissipative and time-delay coupling and asymmetrically forced. We believe that these findings offer fresh insights into the combined effects of mutual and forced synchronization in a system of coupled nonlinear oscillators.

<p>This study investigates the effect of erroneous parameter values for state and parameter estimation using data assimilation. The numerical model chosen for this study solves the van der Pol equation, a second-order differential equation that can be used to simulate oscillatory processes, such as earthquakes. In the model, discrepancies in the parameter values can have a significant influence on the forecasted states of the model, which is even more significant if its behaviour is highly nonlinear. When observations of the state variables are assimilated to update the parameters along with the state variables, this improves the quality of the state forecasts. The results suggest that corrections in the model parameter not only recover the actual parameter values but also reduce state-variable errors after a certain time period. However, data assimilation that updates the state variables but not the parameter can lead to erroneous estimates as well as forecasts of the oscillation. Since the study is performed on a simplified nonlinear model framework, the consequences of these results for data assimilation in more realistic models remains to be investigated.</p>

Amplitude–frequency response of parametric resonance of electrostatically actuated MEMS clamped circular plate

Experiments on self-excited thermoacoustic oscillations in an air-filled closed tube

We have submitted a secular variation (SV) candidate model for the thirteenth generation of International Geomagnetic Reference Field model (IGRF-13) using a data assimilation scheme and a magnetohydrodynamic (MHD) dynamo simulation code. This is the first contribution to the IGRF community from research groups in Japan. A geomagnetic field model derived from magnetic observatory hourly means, and CHAMP and Swarm-A satellite data, has been used as input data to the assimilation scheme. We adopt an ensemble-based assimilation scheme, called four-dimensional ensemble-based variational method (4DEnVar), which linearizes outputs of MHD dynamo simulation with respect to the deviation from a dynamo state vector at an initial condition. The data vector for the assimilation consists of the poloidal scalar potential of the geomagnetic field at the core surface and flow velocity field slightly below the core surface. Dimensionless time of numerical geodynamo is adjusted to the actual time by comparison of secular variation time scales. For SV prediction, we first generate an ensemble of dynamo simulation results from a free dynamo run. We then assimilate the ensemble to the data with a 10-year assimilation window through iterations, and finally forecast future SV by the weighted sum of the future extension parts of the ensemble members. Hindcast of the method for the assimilation window from 2004.50 to 2014.25 confirms that the linear approximation holds for 10-year assimilation window with our iterative ensemble renewal method. We demonstrate that the forecast performance of our data assimilation and forecast scheme is comparable with that of IGRF-12 by comparing data misfits 4.5 years after the release epoch. For estimation of our IGRF-13SV candidate model, we set assimilation window from 2009.50 to 2019.50. We generate our final SV candidate model by linear fitting for the weighted sum of the ensemble MHD dynamo simulation members from 2019.50 to 2025.00. We derive errors of our SV candidate model by one standard deviation of SV histograms based on all the ensemble members.

Non-linearly stable reduced-order models for incompressible flow with energy-conserving finite volume methods