State Variable Model Research Articles

Impact of COVID-19 Type Events on the Economy and Climate Under the Stochastic DICE Model

The classical DICE model is a widely accepted integrated assessment model for the joint modeling of economic and climate systems, where all model state variables evolve over time deterministically. We reformulate and solve the DICE model as an optimal control dynamic programming problem with six state variables (related to the carbon concentration, temperature, and economic capital) evolving over time deterministically and affected by two controls (carbon emission mitigation rate and consumption). We then extend the model by adding a discrete stochastic shock variable to model the economy in the stressed and normal regimes as a jump process caused by events such as the COVID-19 pandemic. These shocks reduce the world gross output leading to a reduction in both the world net output and carbon emission. The extended model is solved under several scenarios as an optimal stochastic control problem, assuming that the shock events occur randomly on average once every 100 years and last for 5 years. The results show that, if the world gross output recovers in full after each event, the impact of the COVID-19 events on the temperature and carbon concentration will be immaterial even in the case of a conservative 10% drop in the annual gross output over a 5-year period. The impact becomes noticeable, although still extremely small (long-term temperature drops by 0.1°C), in a presence of persistent shocks of a 5% output drop propagating to the subsequent time periods through the recursively reduced productivity. If the deterministic DICE model policy is applied in a presence of stochastic shocks (i.e. when this policy is suboptimal), then the drop in temperature is larger (approximately 0.25°C), that is, the lower economic activities owing to shocks imply that more ambitious mitigation targets are now feasible at lower costs.

Modular Approach for Odometry Localization Method for Vehicles with Increased Maneuverability.

Localization and navigation not only serve to provide positioning and route guidance information for users, but also are important inputs for vehicle control. This paper investigates the possibility of using odometry to estimate the position and orientation of a vehicle with a wheel individual steering system in omnidirectional parking maneuvers. Vehicle models and sensors have been identified for this application. Several odometry versions are designed using a modular approach, which was developed in this paper to help users to design state estimators. Different odometry versions have been implemented and validated both in the simulation environment and in real driving tests. The evaluated results show that the versions using more models and using state variables in models provide both more accurate and more robust estimation.

Informing Mechanical Model Development Using Lower-Dimensional Descriptions of Lattice Distortion

This paper describes a method combining in situ X-ray diffraction data and dimensionality reduction (local linear embedding) to inform the development of state variable plasticity models. The method is applied to developing a state variable plasticity model for pure nickel deformed in uniaxial tension in the small strain regime. Prior to model development, connections between state variables representing evolution of mobile dislocations and the lower-dimensional representations of the data are established. Correlations between lower-dimensional representation of data and state variable evolution motivate the introduction of new evolution equation terms to increase alignment between experiment and model. These terms capture dislocation interactions leading to hardening transients prior to steady-state plastic flow. The discussion focuses on interpreting these new evolution terms and outstanding issues associated with linking lower-dimensional representations of data to state variable evolution modeled with ordinary differential equations.

A high-precision and high-order error model for airborne distributed POS transfer alignment

Distributed position and orientation systems (DPOSs) can provide abundant time-spatial information for interferometric synthetic aperture radar (InSAR) in airborne earth observation systems. However, some key error terms have not been taken into consideration in the traditional low-order error model, which suppresses the performance of the slave POS and further cannot meet the compensation precision of InSAR. To improve the compensation precision, a precise high-order error model with 45 dimensions was derived. Not only does it take into account the influence of scale factor errors and installation errors of the gyro and accelerometer, but it also makes use of random constants and a first-order Markov process model to describe the gyro drift and accelerometer bias. In addition, the flexure angle and its angular rate were added to the state variables of the transfer alignment model. Based on the model, a measurement equation for attitude errors that considers flexure was deduced. Then, a transfer alignment model based on the matching algorithm including position-velocity-attitude was designed. Finally, the proposed model was validated by simulated and real tests, and the experimental results show that its performance is obviously better than that of the traditional model.

Advanced Bayesian approaches for state-space models with a case study on soil carbon sequestration

Sequestering carbon into the soil can mitigate the atmospheric concentration of greenhouse gases, improving crop productivity and yield financial gains for farmers through the sale of carbon credits. In this work, we develop and evaluate advanced Bayesian methods for modelling soil carbon sequestration and quantifying uncertainty around predictions that are needed to fit more complex soil carbon models, such as multiple-pool soil carbon dynamic models. This paper demonstrates efficient computational methods using a one-pool model of the soil carbon dynamics previously used to predict soil carbon stock change under different agricultural practices applied at Tarlee, South Australia. We focus on methods that can improve the speed of computation when estimating parameters and model state variables in a statistically defensible way. This paper also serves as a tutorial on advanced Bayesian methods for fitting complex state-space models, which will be of interest to soil scientists and other environmental scientists more generally.

System of Multigrid Nonlinear Least-squares Four-dimensional Variational Data Assimilation for Numerical Weather Prediction (SNAP): System Formulation and Preliminary Evaluation

A new forecasting system—the System of Multigrid Nonlinear Least-squares Four-dimensional Variational (NLS-4DVar) Data Assimilation for Numerical Weather Prediction (SNAP)—was established by building upon the multigrid NLS-4DVar data assimilation scheme, the operational Gridpoint Statistical Interpolation (GSI)-based data-processing and observation operators, and the widely used Weather Research and Forecasting numerical model. Drawing upon lessons learned from the superiority of the operational GSI analysis system, for its various observation operators and the ability to assimilate multiple-source observations, SNAP adopts GSI-based data-processing and observation operator modules to compute the observation innovations. The multigrid NLS-4DVar assimilation framework is used for the analysis, which can adequately correct errors from large to small scales and accelerate iteration solutions. The analysis variables are model state variables, rather than the control variables adopted in the conventional 4DVar system. Currently, we have achieved the assimilation of conventional observations, and we will continue to improve the assimilation of radar and satellite observations in the future. SNAP was evaluated by case evaluation experiments and one-week cycling assimilation experiments. In the case evaluation experiments, two six-hour time windows were established for assimilation experiments and precipitation forecasts were verified against hourly precipitation observations from more than 2400 national observation sites. This showed that SNAP can absorb observations and improve the initial field, thereby improving the precipitation forecast. In the one-week cycling assimilation experiments, six-hourly assimilation cycles were run in one week. SNAP produced slightly lower forecast RMSEs than the GSI 4DEnVar (Four-dimensional Ensemble Variational) as a whole and the threat scores of precipitation forecasts initialized from the analysis of SNAP were higher than those obtained from the analysis of GSI 4DEnVar.

The Added Value of Different Data Types for Calibrating and Testing a Hydrologic Model in a Small Catchment.

This study investigated the added value of different data for calibrating a runoff model for small basins. The analysis was performed in the 66 ha Hydrological Open Air Laboratory, in Austria. An Hydrologiska Byråns Vattenbalansavdelning (HBV) type, spatially lumped hydrologic model was parameterized following two approaches. First, the model was calibrated using only runoff data. Second, a step‐by‐step approach was followed, where the modules of the model (snow, soil moisture, and runoff generation) were calibrated using measurements of runoff and model state variables and output fluxes. These measurements comprised laser‐based measurements of precipitation, satellite and camera observations of snow, ultrasonic measurements of snow depth, eddy covariance measurements of evapotranspiration, time domain transmissometry‐based soil moisture measurements, time‐lapse photography of overland flow, and groundwater level measurements by piezometers. The two model parameterizations were evaluated on annual, seasonal, and daily time scales, in terms of how well they simulated snow, soil moisture, evapotranspiration, overland flow, storage change in the saturated zone, and runoff. Using the proposed step‐by‐step approach, the relative runoff volume errors in the calibration and validation periods were 0.00 and −0.01, the monthly Pearson correlation coefficients were 0.92 and 0.82, and the daily logarithmic Nash Sutcliffe efficiencies were 0.59 and 0.18, respectively. By using different sources of data besides runoff, the overall process consistency improved, compared to the case when only runoff was used for calibration. Soil moisture and evapotranspiration observations had the largest influence on simulated runoff, while the parameterization of the snow and runoff generation modules had a smaller influence.

Experimental characterization and constitutive modeling of an aluminum 7085-T711 alloy under large deformations at varying strain rates, stress states, and temperatures

The strain rate, stress state, and temperature dependent mechanical behavior of a hot rolled aluminum 7085-T711 alloy is experimentally observed and subsequently modeled using a continuum Internal State Variable (ISV) plasticity-damage constitutive model. Structure-property relationships for the alloy are quantified using a series of microstructural analyses and mechanical property experiments. The calibrated ISV model for the Al 7085-T711 alloy is implemented in an implicit finite element code (Abaqus) to simulate the deformation of notch Bridgman tension specimens at a variety of stress states and temperatures. The ISV model accurately captures the material's elastoplastic behavior by predicting the stress state difference between tension, compression, and torsion and temperature dependent microstructure evolution under large deformations.

Using an ensemble Kalman filter method to calibrate parameters of a prediction model for chemical transport from soil to surface runoff.

Water pollution from surface runoff is an important non-point pollution source, which has been a great threat to our environment. The model proposed by Gao et al. (2004) is of great significance to solve the non-point source pollution problem, which is a numerical advection-diffusion equation (ADE) model for chemical transport from soil to surface runoff. The ensemble Kalman filter (EnKF), the data assimilation (DA) method, is easy to be implemented and widely used in hydrology field. In this study, we use the EnKF method to update model state variables such as chemical concentrations in surface runoff and calibrate model parameters such as water transfer rate in Gao et al. (2004) under different study cases, while other model parameters are assumed to be known. The observations are generated from the simulation results based on synthetic real parameters. The objective of this study was to extend the application of the EnKF to the ADE-based prediction model of chemical transport from soil to surface runoff. The results of the predicted chemical concentration in the surface runoff with EnKF are greatly improved than those without EnKF in comparison with the observations, and the updated parameters are close to the real parameters. We explored feasibility of the EnKF method from six factors, including the initial parameter estimate, the ensemble size, the influence of multi-parameters, the assimilation time interval, the infiltration boundary conditions, and the relationship between the standard deviations of the observation error and initial parameter. Different study strategies are proposed for different factors. For assimilation time interval, the key observation can reduce the assimilation frequency. With the situation of much larger observation error covariance than the prediction covariance, we analyzed influences of the standard deviation of the observation error and initial parameter on the feasibility of the EnKF method. According to the study results, it is concluded that the EnKF is efficient to update the parameter for the ADE-based prediction model of chemical transport from soil to surface runoff.

A hygro-thermo-mechanical constitutive model for hygrothermally activated shape memory polymers under finite deformations

With regard to the application of shape memory polymers (SMPs) in smart structures, it is difficult to accurately predict their shape memory effects (SMEs) triggered by various external environments. Therefore, developing constitutive models for SMPs in multi-field environments is crucial. In this paper, a hygro-thermo-mechanical finite deformation constitutive model incorporated with structural relaxation and moisture diffusion is proposed for hygrothermally activated amorphous SMPs. One of the main novelties is that for the first time an internal state variable modeling approach is used in the model to describe the structural relaxation of hygrothermally activated SMPs in the vicinity of the glass transition. The other novelty is that the theory of moisture diffusion is applied to split the absorbed moisture into the mobile (free) and bound phases, and their respective effects on the hygro-thermo-mechanical behavior are also considered in the model. Comparisons between the model results and the test data for both, thermally activated and moisture-activated SMEs, present a good agreement.

Study on inversion control for integrated helicopter/engine system with variable rotor speed based on state variable model

Abstract In order to realize the fast response control for turboshaft engine with variable rotor speed, a dynamic inversion (DI) control method based on state variable model of turboshaft engine is proposed. Meanwhile, in order to expand the application of dynamic inversion controller, the linear parameter varying (LPV) model of turboshaft engine is applied, which constitutes the LPV/DI controller together. The simulation results shows that compared with the conventional PID controller, the LPV/DI controller can effectively reduce the overshoot/droop of the power turbine speed to less than 1% under different flight conditions. The control effect is remarkable and the robust performance is superior.

Study on inversion control for integrated helicopter/engine system with variable rotor speed based on state variable model

Abstract In order to realize the fast response control for turboshaft engine with variable rotor speed, a dynamic inversion (DI) control method based on state variable model of turboshaft engine is proposed. Meanwhile, in order to expand the application of dynamic inversion controller, the linear parameter varying (LPV) model of turboshaft engine is applied, which constitutes the LPV/DI controller together. The simulation results shows that compared with the conventional PID controller, the LPV/DI controller can effectively reduce the overshoot/droop of the power turbine speed to less than 1% under different flight conditions. The control effect is remarkable and the robust performance is superior.

Parameter Estimation of Acoustic Wave Equations Using Hidden Physics Models

In this article, we present one numerical approach to infer the model parameters and state variables of acoustic wave equations. The method we consider is based on the recently proposed method-the so-called hidden physics model. With placing Gaussian process (GP) prior on the state variables, the structure and model parameters of acoustic wave equations are encoded into the kernel function of a multioutput GP. The purpose of this article includes: 1) testing the applicability of hidden physics model to infer the velocity, density, and state variables of the acoustic wave equation, which is important for many applications in geophysics; 2) adapting the method to handle for both homogeneous and heterogeneous media that are of practical interest; and 3) exploring efficient sequential sampling methods to improve the sampling efficiency. We suggest that the expected-improvement-based sequential sampling method would be effective for most practical problems related to acoustic wave propagation. Besides, we demonstrate the performance of the proposed scheme via several benchmark problems.

Differential flatness theory-based control and filtering for a mobile manipulator

The article proposes a differential flatness theory based control and filtering method for the model of a mobile manipulator. This is a difficult control and robotics problem due to the system’s strong nonlinearities and due to its underactuation. Using the Euler-Lagrange approach, the dynamic model of the mobile manipulator is obtained. This is proven to be a differentially flat one, thus confirming that it can be transformed into an input-output linearized form. Through a change of state and control inputs variables the dynamic model of the manipulator is finally written into the linear canonical (Brunovsky) form. For the latter representation of the system’s dynamics the solution of both the control and filtering problems becomes possible. The global asymptotic stability properties of the control loop are proven. Moreover, a differential flatness theory-based state estimator, under the name of Derivative-free nonlinear Kalman Filter, is developed. This comprises (i) the standard Kalman Filter recursion on the linearized equivalent model of the mobile manipulator and (ii) an inverse transformation, relying on the differential flatness properties of the system which allows for estimating the state variables of the initial nonlinear model. Finally, by redesigning the aforementioned Kalman Filter as a disturbance observer one can achieve estimation and compensation of the disturbance inputs that affect the model of the mobile manipulator.

State-dependent mortality can enhance behavioral unpredictability

BackgroundAlthough behavioral unpredictability is widely described within-individual variability in behavior, its adaptive significance is little understood. Using a dynamic state variable model, this study investigated the conditions under which behavioral unpredictability (a component of within-individual variability) in foraging behavior is advantageous. The model considers a situation in which a forager forages for a fixed period, represented by discrete time steps. The outcome of foraging may change the level of a state (e.g., size and fat storage) of the forager at each time step, and variability in the foraging outcome is assumed to be positively correlated with behavioral unpredictability. The probability of death at each time step is influenced by the state at the same time step. Reproduction occurs after all the foraging steps and is influenced by the state level of a forager at the time of reproduction. According to the expected utility hypothesis, the relationship (e.g., curvature) between the state and fitness will determine the role of behavioral unpredictability. In the model, the relationship was obtained by using the backward iteration method for each foraging time step.ResultsState-dependent mortality adds curvature to the relationship between the state and fitness, which makes the effect of behavioral unpredictability on fitness either positive or negative. This conclusion holds for any state-dependent mortality (i.e., as long as mortality is not independent of the state factor). Given that state-dependent mortality is commonly described, conditions that benefit behavioral unpredictability are likely also common.ConclusionsWhen mortality depends on a state that is influenced by behavior, conditions that favor behavioral unpredictability may become common. How behavioral unpredictability influences the variability of behavioral outcomes is as important as how it influences the expectation of behavioral outcomes when studying the adaptive significance of behavioral unpredictability.

Transient strain age hardening of Al–Mg alloys

The static strain aging response of an Al–Mg alloy is investigated by means of tensile pre-deformation followed by annealing. The mechanical response following re-testing in tension reveals a lower flow stress and raised work hardening rate at yield. The enhanced work hardening rate is shown to be transient, the behaviour returning to that of the non-aged material at high flow stress. In order to decouple the various effects arising from solute segregation and dislocation loss via recovery, a simplified version of the two internal state variable model originally proposed by Kubin and Estrin is introduced. It is proposed that the response, yield strength and work hardening rate, following pre-deformation and annealing can be ascribed to the combined effects of the loss of mobile dislocations and a transient hardening that is interpreted to come from dislocations that have had solute segregated to them.

Robust H∞ Takagi–Sugeno fuzzy output-feedback control for differential speed steering vehicles

This paper studied the modelling and control of four-wheel independently driven electric vehicles using differential speed steering. The Takagi–Sugeno fuzzy modelling approach represents the nonlinearities of the four-wheel independently driven electric vehicle state variables in several system models. The proposed controller design is a robust Takagi–Sugeno fuzzy output-feedback control based on a fuzzy Lyapunov function approach. More precisely, the Lyapunov function is chosen to be dependent on the membership functions. Sufficient conditions for the existence of the robust Takagi–Sugeno fuzzy controller are given in terms of linear matrix inequality constraints. The designed parameters are tested by simulating the four-wheel independently driven electric vehicles under varying operating conditions. The simulation results underscore the robustness and disturbance rejection importance of the proposed controller, which is then contrasted to better highlight the improved performance of the proposed approach over a fixed robust controller design.

Modeling of flow behavior and microstructure evolution for Mg-6Gd-5Y-0.3Zr alloy during hot deformation using a unified internal state variable method

The hot deformation behavior of Mg-6Gd-5Y-0.3Zr alloy at the temperatures of 673–748K and the strain rates of 0.01–1.0s−1 were investigated by hot compression experiments. On this basis, a physically based internal state variable (ISV) model coupling the microstructural evolution was established, in which the ISVs of the model included dislocation density, grain size and volume fraction of dynamic recrystallization (DRX). Besides, the recrystallized and un-recrystallized grain sizes were considered to characterize the evolution process of microstructure. By comparing the calculated and experimental flow stresses, the model was proved to be reliable. Then the model was imported into the finite element analysis (FEA) software ABAQUS to predict the ISV evolution of Mg-6Gd-5Y-0.3Zr alloy in the hot extrusion process. The comparative analysis of the simulation and experimental results further verified the applicability of the constitutive model established in this study.

Research advances in model simulation and data assimilation of water and carbon fluxes in land surface vegetation

Accurately estimating water and carbon fluxes is of great significance for the research in land surface water and carbon cycles. However, it is very challenging. The estimation accuracy needs further improvement. Both traditional model simulation and site observation methods have advantages and disadvantages, which need to be examined in combination. Data assimilation integrates observations into models based on physics laws to obtain the optimal estimates of model state variables and parameters as much as possible, and provides an effective way for their combination. In this review, we traced the research progress for process models assimilated with multi-source observational data of land surface water carbon fluxes and analyzed the domestic and foreign research status of land surface process models focused on water carbon fluxes, data assimilation algorithms, and assimilation of land surface carbon flux data. We summaried problems in this research area, including insufficient coordination of multi-source observation data, relatively simple assimilation strategy, lacking fusion of assimilation models, and limited assimilation scale. The future development directions and trends were analyzed and prospected from five aspects, including assimilation strategy, model selection, data expansion, scale effect, and scientific calculation. This work would provide more comprehensive background information for scholars in this field, and arouse common concerns.

Impact of the Hierarchical Ensemble Filter Covariance Localization Method on EnKF Radar Data Assimilation: Observing system simulation experiments

An adaptive localization method using the hierarchical ensemble filter (HEF) technique was first applied to the ensemble Kalman filter (EnKF) radar data assimilation (DA) though observing system simulation experiments (OSSEs) for an idealized supercell storm. The HEF method calculates localization by minimizing the sampling error without defining the physical distance between observation and state variables. Four experiments using regular Gaspari and Cohn (GC) and HEF localization methods with different group sizes (group numbers of ensembles) were performed. The HEF localization experiments perform better than GC experiment, producing smaller analysis errors and larger ensemble spreads for most model state variables, and stronger wind, vertical vorticity, and cold pools. The best results are obtained when the largest group size is used in the HEF experiment. With this improved analysis, the forecast error is reduced for most variables and levels. The dynamical and thermal distributions of HEF experiments are found to better promote the development of the supercell storm which helps to improve the forecast reflectivity in terms of location, intensity, and area coverage. This suggests the potential of HEF localization for an EnKF radar DA. A larger group size for this method is expected to lead to improved analysis and forecast results compared with the regular GC localization method.