Large-scale Dynamic Model Research Articles

Order Reduction in Linear Dynamical Systems by Using Improved Balanced Realization Technique

In this article, a new model order reduction scheme is proposed for the simplification of large-scale linear dynamical models. The proposed technique is based on the balanced realization method, in which the steady-state gain problem of the balanced truncation is circumvented. In this method, the denominator coefficients of the reduced system are evaluated by using the balanced realization, and the numerator coefficients are obtained by using a simple mathematical procedure as given in the literature. The proposed technique has been illustrated through some standard large-scale systems. This method gives the least performance error indices compared to some other existing system reduction methods. The time response of the approximated system, evaluated by the proposed method, is also shown which is the excellent matching of the response of the actual model when compared to the responses of other existing techniques.

A hybrid bacterial foraging and modified particle swarm optimization for model order reduction

This paper study the model reduction procedures used for the reduction of large-scale dynamic models into a smaller one through some sort of differential and algebraic equations. A confirmed relevance between these two models exists, and it shows same characteristics under study. These reduction procedures are generally utilized for mitigating computational complexity, facilitating system analysis, and thence reducing time and costs. This paper comes out with a study showing the impact of the consolidation between the Bacterial-Foraging (BF) and Modified particle swarm optimization (MPSO) for the reduced order model (ROM). The proposed hybrid algorithm (BF-MPSO) is comprehensively compared with the BF and MPSO algorithms; a comparison is also made with selected existing techniques.

Satellite-based large-scale vegetation dynamics in ecological restoration programmes of Northern China

ABSTRACTIn the past, large-scale terrestrial vegetation dynamics have been used to evaluate the efficiency of national ecological restoration programmes in northern China. However, complete documentation and timely updates of vegetation dynamics in the Ecological Restoration Programmes Regions (ERPRs) of northern China are rare. Furthermore, the main challenges in analysing large-scale vegetation changes in ERPRs are so far not entirely clear. We chose four ERPR study areas (the Beijing–Tianjin Sand Source Region (BTSSR), the Loess Plateau (LP), and the north-east (NE), and the north-west (NW) of the Three-North Shelterbelt Forest Project (TNSFP)), avoiding the overlap of administrative regions. We used long-term Normalised Different Vegetation Index (NDVI) data to investigate the trends of vegetation activities in these four ERPRs of northern China between 1982 and 2011. A persistent and widespread increase of the growing season NDVI was found in this time span, with 58.54% increase in NE, 89.84% in LP, 54.59% in BTSSR, and 76.13% in NW. The observed increase of NDVI indicates the success of Chinese restoration programmes, which have helped to improve ecological conditions after 2000. However, a comparison of long-term vegetation changes between before and after implementation of restoration programmes is insufficient for assessing the programmes’ efficiency. Large-scale Dynamic Global Vegetation Models (DGVMs) are promising tools for future evaluation of the benefits of ecological restoration programmes.

Large-scale dynamic modeling of task-fMRI signals via subspace system identification

Objective. We analyze task-based fMRI time series to produce large-scale dynamical models that are capable of approximating the observed signal with good accuracy. Approach. We extend subspace system identification methods for deterministic and stochastic state-space models with external inputs. The dynamic behavior of the generated models is characterized using control-theoretic analysis tools. To validate their effectiveness, we perform a probabilistic inversion of the identified input–output relationships via joint state-input maximum likelihood estimation. Our experimental setup explores a large dataset generated using state-of-the-art acquisition and pre-processing methods from the Human Connectome Project. Main results. We analyze both anatomically parcellated and spatially dense time series, and propose an efficient algorithm to address the high-dimensional optimization problem resulting from the latter. Our results enable the quantification of input–output transfer functions between each task condition and each region of the cortex, as exemplified by a motor task. Further, the identified models produce impulse response functions between task conditions and cortical regions that are compatible with typical hemodynamic response functions. We then extend subspace methods to account for multi-subject experimental configurations, identifying models that capture common dynamical characteristics across subjects. Finally, we show that system inversion via maximum-likelihood allows the time-of-occurrence of the task stimuli to be estimated from the observed outputs. Significance. The ability to produce dynamical input–output models might have an impact in the expanding field of neurofeedback. In particular, the models we produce allow the partial quantification of the effect of external task-related inputs on the metabolic response of the brain, conditioned on its current state. Such a notion provides a basis for leveraging control-theoretic approaches to neuromodulation and self-regulation in therapeutic applications.

Which Indicators Matter? Analyzing the Swiss Business Cycle Using a Large-Scale Mixed-Frequency Dynamic Factor Model

For policy institutions such as central banks, it is important to have a timely and accurate measure of past and current economic activity and the business cycle situation. The most prominent example for such a measure is gross domestic product (GDP). However, GDP is only released at a quarterly frequency and with a substantial delay. Furthermore, it captures elements that are not directly linked to the business cycle and the underlying momentum of the economy. In this paper, I construct a new business cycle index for the Swiss economy, which uses state-of-the-art methods, is available at a monthly frequency and can be calculated in real-time, even when some indicators are not yet available for the most recent periods. The index is based on a large and broad set of monthly and quarterly indicators. As I show, for the case of Switzerland, it is important to base a business cycle index on a broad set of indicators instead of only a small subset. This result confirms the findings of a previous study on tracking short-term economic developments in Switzerland and is in contrast with the results for other countries.

Macroeconomic Effects of an Open-ended Asset Purchase Programme

In this paper we evaluate the effectiveness of an open-ended Asset Purchase Programme (APP) for the euro area. To this purpose, we build on the large-scale New Keynesian dynamic general equilibrium model calibrated to the euro area and the rest of the world developed in Burlon et al. (2017), but, different from that contribution, we assume that the central bank does not announce the ending date of the programme, while leaving open the possibility of extending it in future periods conditionally on inflation developments. We assume that agents form their expectations about possible additional purchases beyond the horizon of the announcement by the central bank according to a rule linking them to the expected inflation gap. It is showed that the open-ended APP is more effective in immediately stimulating macroeconomic conditions than committing ex ante to an ending date. Importantly, the open-ended dimension provides a hedge against the materialization of negative euro-area aggregate demand shocks that pushes inflation away from its path towards the target. The effectiveness is further reinforced by a forward guidance on monetary policy rates.

Conditional Gaussian Systems for Multiscale Nonlinear Stochastic Systems: Prediction, State Estimation and Uncertainty Quantification.

A conditional Gaussian framework for understanding and predicting complex multiscale nonlinear stochastic systems is developed. Despite the conditional Gaussianity, such systems are nevertheless highly nonlinear and are able to capture the non-Gaussian features of nature. The special structure of the system allows closed analytical formulae for solving the conditional statistics and is thus computationally efficient. A rich gallery of examples of conditional Gaussian systems are illustrated here, which includes data-driven physics-constrained nonlinear stochastic models, stochastically coupled reaction–diffusion models in neuroscience and ecology, and large-scale dynamical models in turbulence, fluids and geophysical flows. Making use of the conditional Gaussian structure, efficient statistically accurate algorithms involving a novel hybrid strategy for different subspaces, a judicious block decomposition and statistical symmetry are developed for solving the Fokker–Planck equation in large dimensions. The conditional Gaussian framework is also applied to develop extremely cheap multiscale data assimilation schemes, such as the stochastic superparameterization, which use particle filters to capture the non-Gaussian statistics on the large-scale part whose dimension is small whereas the statistics of the small-scale part are conditional Gaussian given the large-scale part. Other topics of the conditional Gaussian systems studied here include designing new parameter estimation schemes and understanding model errors.

Labour Tax Reforms, Cross-Country Coordination and the Monetary Policy Stance in the Euro Area: A Structural Model-Based Approach

We evaluate the effects of permanently reducing labour tax rates in the euro area (EA) by simulating a large-scale open economy dynamic general equilibrium model. The model features the EA as a monetary union, split in two regions (Home and the rest of the EA - REA), the US, and the rest of the world, region-specific labour markets with search and matching frictions, and public employment. Our results are as follows. First, a permanent reduction in labour tax rates in the Home region would have stimulating effects on domestic economic activity and employment. Second, reducing labour tax rates simultaneously in both Home and REA would have additional expansionary effects on the Home region. Third, in the short run the expansionary effects on the EA economy of a EA-wide tax reduction are enhanced if the EA monetary policy is accommodative.

Control Design for Soft Robots based on Reduced Order Model

Inspired by nature, soft robots promise disruptive advances in robotics. Soft robots are naturally compliant and exhibit nonlinear behavior, which makes their study challenging. No unified framework exists to control these robots, especially when considering their dynamics. This letter proposes a methodology to study this type of robots around a stable equilibrium point. It can make the robot converge faster and with reduced oscillations to a desired equilibrium state. Using computational mechanics, a large-scale dynamic model of the robot is obtained and model reduction algorithms enable the design of a low-order controller and observer. A real robot is used to demonstrate the interest of the results.

Efficient Control Discretization Based on Turnpike Theory for Dynamic Optimization

Dynamic optimization offers a great potential for maximizing performance of continuous processes from startup to shutdown by obtaining optimal trajectories for the control variables. However, numerical procedures for dynamic optimization can become prohibitively costly upon a sufficiently fine discretization of control trajectories, especially for large-scale dynamic process models. On the other hand, a coarse discretization of control trajectories is often incapable of representing the optimal solution, thereby leading to reduced performance. In this paper, a new control discretization approach for dynamic optimization of continuous processes is proposed. It builds upon turnpike theory in optimal control and exploits the solution structure for constructing the optimal trajectories and adaptively deciding the locations of the control discretization points. As a result, the proposed approach can potentially yield the same, or even improved, optimal solution with a coarser discretization than a conventional uniform discretization approach. It is shown via case studies that using the proposed approach can reduce the cost of dynamic optimization significantly, mainly due to introducing fewer optimization variables and cheaper sensitivity calculations during integration.

Some Pitfalls in Statistical Downscaling of Future Climate

AbstractStatistical downscaling (SD) is commonly used to provide information for the assessment of climate change impacts. Using as input the output from large-scale dynamical climate models and observation-based data products, SD aims to provide a finer grain of detail and to mitigate systematic biases. It is generally recognized as providing added value. However, one of the key assumptions of SD is that the relationships used to train the method during a historical period are unchanged in the future, in the face of climate change. The validity of this assumption is typically quite difficult to assess in the normal course of analysis, as observations of future climate are lacking. We approach this problem using a “perfect model” experimental design in which high-resolution dynamical climate model output is used as a surrogate for both past and future observations.We find that while SD in general adds considerable value, in certain well-defined circumstances it can produce highly erroneous results. Furthermore, the breakdown of SD in these contexts could not be foreshadowed during the typical course of evaluation based on only available historical data. We diagnose and explain the reasons for these failures in terms of physical, statistical, and methodological causes. These findings highlight the need for caution in the use of statistically downscaled products and the need for further research to consider other hitherto unknown pitfalls, perhaps utilizing more advanced perfect model designs than the one we have employed.

Stability Analysis of a Set of Uncertain Large-Scale Dynamical Models with Saturations

From a sparse set of large-scale Linear Time Invariant (LTI) dynamical models, a methodology to generate a low-order parameter-dependent and uncertain model, with guaranteed bounds on the approximation error is firstly obtained using advanced approximation and interpolation techniques. Secondly, the stability of the aforementioned model, represented as a Linear Fractional Representation (LFR) and subject to actuator saturation and dynamical uncertainties, is addressed through the use of an irrational multiplier-based Integral Quadratic Constraint (IQC) approach. The effectiveness of the approach is assessed on a complex set of aeroservoelastic aircraft models used in an industrial framework for control design and validation purposes.

Integration of long transmission lines in large-scale dq0 dynamic models

The dq0 transformation is increasingly used today to model distributed sources, complex loads, renewable generators, and power electronics-based devices. This paper presents a dynamic model of long transmission lines that is based entirely on dq0 quantities, and demonstrates how such a model may be integrated with emerging dq0 models of large-scale networks. The model is first developed in the frequency domain and then converted to the time domain, using a state-space representation which inputs and outputs are dq0 signals. The proposed approach may be used to evaluate the stability and dynamic behavior of power systems that include long transmission lines, taking advantage of the dq0 reference frame inherent benefits. This is demonstrated on the basis of a 7-bus network, which shows how long transmission lines influence the network dynamics and stability. The proposed models and examples are provided as a part of an open-source software.

Stability Analysis of a Set of Uncertain Large-Scale Dynamical Models With Saturations: Application to an Aircraft System

From a sparse set of large-scale linear time-invariant dynamical models, a methodology to generate a low-order parameter-dependent and uncertain model, with guaranteed bounds on the approximation error, is first obtained using advanced approximation and interpolation techniques. Second, the stability of the aforementioned model, represented as a linear fractional representation and subject to actuator saturation and dynamical uncertainties, is addressed through the use of an irrational multiplier-based integral quadratic constraint approach. The effectiveness of the approach is assessed on a complex set of aeroservoelastic aircraft models used in an industrial framework for control design and validation purposes.

Identifiability of large-scale non-linear dynamic network models applied to the ADM1-case study

In this work, both the structural and practical identifiability of the Anaerobic Digestion Model no. 1 (ADM1) is investigated, which serves as a relevant case study of large non-linear dynamic network models. The structural identifiability is investigated using the probabilistic algorithm, adapted to deal with the specifics of the case study (i.e., a large-scale non-linear dynamic system of differential and algebraic equations). The practical identifiability is analyzed using a Monte Carlo parameter estimation procedure for a ‘non-informative’ and ‘informative’ experiment, which are heuristically designed.The model structure of ADM1 has been modified by replacing parameters by parameter combinations, to provide a generally locally structurally identifiable version of ADM1. This means that in an idealized theoretical situation, the parameters can be estimated accurately. Furthermore, the generally positive structural identifiability results can be explained from the large number of interconnections between the states in the network structure. This interconnectivity, however, is also observed in the parameter estimates, making uncorrelated parameter estimations in practice difficult.

Linear optimization of forest management for dynamic recursive model

Our study presents development of a forest management model based on LP which can be easily integrated into a large-scale dynamic recursive model and contain the instruments providing future consideration for harvesting plans under recursive limitations. We introduce a general structure and simulation algorithm of the model. The forest management algorithm was tested applying historical data of Ukrainian forests. Obtained modeling results demonstrate a correct age class transition. They prove as well adequacy of utilizing benefit losses and delay costs as regulative mechanisms for temporal allocation of forest harvesting. As far as statistic data concerning age structure of Ukrainian forests are not publicly available, FesT was validated by comparing projected forest age structure with results of Global Forest Model (G4M).The comparison shows that the projections of both models are fairly close to each other. The divergence between the results can be explained by difference in forest management modelling approach.

An integrated framework for embedding large-scale dynamic traffic assignment models in advanced traveler information systems

In recent years, increasing attention has been drawn to the development of various applications of intelligent transportation systems (ITS), which are credited with the amelioration of traffic conditions in urban and regional environments. Advanced traveler information systems (ATIS) constitute an important element of ITS by providing potential travelers with information on the network's current performance both en-route and pre-trip. In order to tackle the complexity of such systems, derived from the difficulty of providing real-time estimations of current as well as forecasts of future traffic conditions, a series of models and algorithms have been initiated. This paper proposes the development of an integrated framework for real-time ATIS and presents its application on a large-scale network, that of Thessaloniki, Greece, concluding with a discussion on development and implementation challenges as well as on the advantages and limitations of such an effort.

Fiscal devaluation in the euro area: A model-based analysis

We assess the effects of a temporary fiscal devaluation enacted in Spain on the trade balance by simulating EAGLE, a large-scale multi-country dynamic general equilibrium model of the euro area. Social contributions paid by firms are reduced by 1% of GDP for four years and are financed by increasing the consumption tax. Our main results are the following. First, in the first years following implementation the Spanish trade balance improves by around 0.6% of GDP, the (before-consumption tax) real exchange rate depreciates by 0.7% and the terms of trade deteriorate by 1.3%. Second, the trade balance improves when the temporary fiscal devaluation is also enacted in the rest of the euro area, albeit to a lower extent than in the case of unilateral (country-specific) implementation. Third, similar results are obtained if we consider the case of a smaller euro area economy, specifically Portugal. Fourth, quantitative results are robust to changes in some key parameters but crucially depend on the degree of substitutability between domestic and imported tradables.

Economic Oriented NMPC for an Extractive Distillation Column Using an Index Hybrid DAE Model Based on Fundamental Principles

Nonlinear model predictive control (NMPC) is an advanced control strategy that uses a rigorous dynamic model of the process, usually described by differential-algebraic equations (DAE), to predict its future behavior. The economic optimization of the process can be included directly in the objectives of the NMPC controller, which make it attractive for application in highly nonlinear and energy-intensive processes that are subject to fluctuating operational conditions. Currently, the implementation of NMPC controllers with large-scale dynamic models is limited by the computational difficulty of solving the associated dynamic optimization problem at each period of time. In this work, we propose an index two DAE model based on fundamental principles that uses its equivalent reduced index one model to define consistent initial conditions (index hybrid DAE) with the aim of representing the dynamics of a distillation column. We demonstrate that this model describes the same physical behavior of its equivalent index one reduced model and that it decreases significantly the computational complexity of the online optimization associated with the NMPC controller. Finally, we use the index hybrid DAE model in the economic oriented NMPC (EO-NMPC) of an extractive distillation column considering different disturbances over the inlet conditions. Also, we compare the EO-NMPC with a classic PI (proportional and integral) controller to show that the first one has a better dynamic performance and improves the economic profit of the process.

Multivariable control with grid objectives of an HVDC link embedded in a large-scale AC grid

Abstract The HVDC links are increasingly used not only to interconnect asynchronous AC systems but are also embedded into a same meshed AC power system. Thanks to its speed and flexibility, the HVDC technology is able to provide transmission system advantages as transfer capacity enhancement and power flow control. In addition, studies have shown that the way of controlling the HVDC converters impacts the stability of the AC system. This can be particularly exploited to enhance the dynamic power system performances during transients. In this paper a robust multivariable control design for HVDC link converters is proposed. It is based on the coordination of the control actions of the HVDC converters and the use of a control model which takes into account the dynamics that mostly impact stability of the neighbor zone of the HVDC link. This new methodology was used to synthesize the controller for an actual grid 1000 MW HVDC link reinforcement project called “Midi-Provence” in the southern part of the French grid. The synthesis, implementation and validation processes are presented in detail. The new controller is tested in comparison with the standard vector control. A large-scale dynamic model of the whole European power system, currently used and updated by the European TSO’s for the interconnection studies has been used with Eurostag simulation software.