Multi-timescale Dynamics Research Articles

Multi-timescale modeling and order reduction towards stability analysis of isolated microgrids

Microgrids incorporate a significant proportion of renewable energy sources and power electronic converters in the energy conversion process, creating a sustainable and clean energy infrastructure. However, the multi-timescale dynamics of microgrids are interactively coupled under a nonlinear structure, which makes it difficult to gain insight into the instability mechanisms without a high-fidelity reduced-order model that preserves the main dynamic behaviors of the system. For the isolated AC microgrid dominated by voltage source inverters (VSI), a detailed state-space model of the system, including the inverter, network, and load, is first developed. Based on this model, the eigenvalue analysis is carried out, and a participation factor analysis tool is also utilized to identify the relevant dynamics that have a strong impact on the system's dominant mode. Furthermore, to simplify the system modeling process without losing essential dynamic interactions, a novel multi-timescale coupled reduced-order model is proposed using a transfer function-based order reduction method, which retains the open-loop gain characteristics to preserve the critical couplings between fast inner loop dynamics and slow droop control dynamics. Finally, the accuracy of the reduced-order model is verified by comparing it with the detailed model and the conventional singular perturbation reduced-order model through eigenvalue distribution and time-domain simulation analysis.

Multi-timescale neural dynamics for multisensory integration.

Carrying out any everyday task, be it driving in traffic, conversing with friends or playing basketball, requires rapid selection, integration and segregation of stimuli from different sensory modalities. At present, even the most advanced artificial intelligence-based systems are unable to replicate the multisensory processes that the human brain routinely performs, but how neural circuits in the brain carry out these processes is still not well understood. In this Perspective, we discuss recent findings that shed fresh light on the oscillatory neural mechanisms thatmediate multisensory integration (MI), including power modulations, phase resetting, phase-amplitude coupling and dynamic functional connectivity. We then consider studies that also suggest multi-timescale dynamics in intrinsic ongoing neural activity and during stimulus-driven bottom-up and cognitive top-down neural network processing in the context of MI. We propose a new concept of MI that emphasizes the critical role of neural dynamics at multiple timescales within and across brain networks, enabling the simultaneous integration, segregation, hierarchical structuring and selection of information in different time windows. To highlight predictions from our multi-timescale concept of MI, real-world scenarios in which multi-timescale processes may coordinate MI in a flexible and adaptive manner are considered.

Temporal dendritic heterogeneity incorporated with spiking neural networks for learning multi-timescale dynamics

It is widely believed the brain-inspired spiking neural networks have the capability of processing temporal information owing to their dynamic attributes. However, how to understand what kind of mechanisms contributing to the learning ability and exploit the rich dynamic properties of spiking neural networks to satisfactorily solve complex temporal computing tasks in practice still remains to be explored. In this article, we identify the importance of capturing the multi-timescale components, based on which a multi-compartment spiking neural model with temporal dendritic heterogeneity, is proposed. The model enables multi-timescale dynamics by automatically learning heterogeneous timing factors on different dendritic branches. Two breakthroughs are made through extensive experiments: the working mechanism of the proposed model is revealed via an elaborated temporal spiking XOR problem to analyze the temporal feature integration at different levels; comprehensive performance benefits of the model over ordinary spiking neural networks are achieved on several temporal computing benchmarks for speech recognition, visual recognition, electroencephalogram signal recognition, and robot place recognition, which shows the best-reported accuracy and model compactness, promising robustness and generalization, and high execution efficiency on neuromorphic hardware. This work moves neuromorphic computing a significant step toward real-world applications by appropriately exploiting biological observations.

Modeling Multi-Timescale Dynamics for Airport Surface Congestion and Recovery

Modeling Multi-Timescale Dynamics for Airport Surface Congestion and Recovery

Multi-level data-predictive control for linear multi-timescale processes with stability guarantee

Multi-timescale dynamics are common in chemical processes. These processes are often difficult to model and pose challenges in control system design. In this paper, we propose a data-based control approach for linear multi-timescale systems using a system behavioural framework. A data resampling method coupled with a novel data predictive control (DPC) design with multi-level optimisation horizons is developed to handle different timescales. To deal with the dynamics of different timescales, the optimisation horizons with small to large time intervals are used to predict and optimise control actions from near to distant future. Computational complexity wise, the multi-level structure allows horizon length to expand exponentially with optimisation steps. A trajectory-based dissipativity condition is also developed to ensure stability of the proposed DPC, while achieving disturbance rejection and tracking control. An example of controlling a multi-timescale reactive distillation column is presented to illustrate the proposed approach.

Efficient multi-timescale dynamics of precessing black-hole binaries

Efficient multi-timescale dynamics of precessing black-hole binaries

Multi-timescale dynamics of extreme river flood and storm surge interactions in relation with large-scale atmospheric circulation: Case of the Seine estuary

The present work investigates the multi-timescale dynamics of extreme fluvial-surge interactions (EFS) in a river-tide environment, in the case of the Seine estuary. This environment is considered an excellent natural laboratory to analyze river-surge interaction because of its time-varying flow and the available water-level records provided by tide gauges along the estuary. A spectral approach has been used to investigate the multi-timescale changes in EFS, governed by fluvial and marine contributions, in relation to the historical events of flood-storm concomitance and the large-scale atmospheric circulation. The spectral components of EFS, calculated at five stations along the estuary, highlighted a series of variability modes varying from the inter-month (∼3–6 months) to the inter-annual (∼2-, ∼3-5- and ∼6-8-years) scales and exhibiting, respectively, 55% and 20% of the total variability. The contribution of marine and fluvial effects in the EFS varies along the estuary and according to the timescale from seasons, when the interaction is governed by tidal deformation, to years. The connection of the historical flood-storm events with the EFS signal changes in their spectral signature according to their severity as well as the energetic physical drivers acting in each event: events with high return period are manifested at larger scales while events with low return period are limited to small scales.Finally, the examination of the physical relationships between the EFS and the global climate mechanisms has demonstrated the key role of the Sea Level Pressure (SLP) and the North Atlantic Oscillation (NAO) acting, respectively, in anti-phase at ∼1-2-yr and in phase at scales larger than 3-yr. The signature of the climate drivers operates differently according to the timescale; they are identified within the ∼80% of the inter-annual EFS. This signature is more significative since the 2000s when the increase in the NAO generates a rise in EFS variability. ∼20% of EFS would be related to the non-linear effects of the timescale interactions and other local mechanisms operating at such scales.This finding highlights the non-stationarity of the multi-timescale dynamics of marine storms and fluvial floods, and the relevance of the climate connection use for assessing the compound multi-hazard events at large-scales.

Small-signal synchronization stability of grid-forming converter influenced by multi time-scale control interaction

The grid-forming (GFM) converters that simulate the dynamics of synchronous generators (SGs) and actively participate in grid voltage and frequency regulation are increasingly employed as grid interfaces for renewable energy generation. Its synchronization stability with AC grid is also increasingly concerned in recent years. In this paper, the small-signal synchronization stability of GFM converters with virtual synchronous generator (VSG) control is investigated, with the influence of multi time-scale control interaction considered especially. First, based on multi time-scale dynamics analysis, an analogized Heffron–Phillips model is developed to physically depict the small-signal synchronization dynamics of VSG. The multi time-scale control interaction introduces an additional input torque to the equivalent motion of VSG’s synchronization behavior. Based on damping torque analysis, the synchronization stability is depended by the inherent damping component of VSG’s virtual rotor motion and the additional damping component introduced by multi time-scale control interaction. Qualitative and quantitative analysis reveal that the additional damping is negative and deteriorates the synchronization stability. When the negative additional damping is greater than the positive inherent damping, small-signal synchronization instability occurs due to insufficient damping. Finally, the influence factors including control parameters and grid strength are discussed.

Towards More Realistic Human Motion Prediction With Attention to Motion Coordination

Joint relation modeling is a curial component in human motion prediction. Most existing methods rely on skeletal-based graphs to build the joint relations, where local interactive relations between joint pairs are well learned. However, the motion coordination, a global joint relation reflecting the simultaneous cooperation of all joints, is usually weakened because it is learned from part to whole progressively and asynchronously. Thus, the final predicted motions usually appear unrealistic. To tackle this issue, we learn a medium, called coordination attractor (CA), from the spatiotemporal features of motion to characterize the global motion features, which is subsequently used to build new relative joint relations. Through the CA, all joints are related simultaneously, and thus the motion coordination of all joints can be better learned. Based on this, we further propose a novel joint relation modeling module, Comprehensive Joint Relation Extractor (CJRE), to combine this motion coordination with the local interactions between joint pairs in a unified manner. Additionally, we also present a Multi-timescale Dynamics Extractor (MTDE) to extract enriched dynamics from the raw position information for effective prediction. Extensive experiments show that the proposed framework outperforms state-of-the-art methods in both short- and long-term predictions on H3.6M, CMU-Mocap, and 3DPW.

Oculomotor plant and neural dynamics suggest gaze control requires integration on distributed timescales.

A fundamental principle of biological motor control is that the neural commands driving movement must conform to the response properties of the motor plants they control. In the oculomotor system, characterizations of oculomotor plant dynamics traditionally supported models in which the plant responds to neural drive to extraocular muscles on exclusively short, subsecond timescales. These models predict that the stabilization of gaze during fixations between saccades requires neural drive that approximates eye position on longer timescales and is generated through the temporal integration of brief eye velocity-encoding signals that cause saccades. However, recent measurements of oculomotor plant behaviour have revealed responses on longer timescales. Furthermore, measurements of firing patterns in the oculomotor integrator have revealed a more complex encoding of eye movement dynamics. Yet, the link between these observations has remained unclear. Here we use measurements from the larval zebrafish to link dynamics in the oculomotor plant to dynamics in the neural integrator. The oculomotor plant in both anaesthetized and awake larval zebrafish was characterized by a broad distribution of response timescales, including those much longer than 1s. Analysis of the firing patterns of oculomotor integrator neurons, which exhibited a broadly distributed range of decay time constants, demonstrates the sufficiency of this activity for stabilizing gaze given an oculomotor plant with distributed response timescales. This work suggests that leaky integration on multiple, distributed timescales by the oculomotor integrator reflects an inverse model for generating oculomotor commands, and that multi-timescale dynamics may be a general feature of motor circuitry. KEY POINTS: Recent observations of oculomotor plant response properties and neural activity across the oculomotor system have called into question classical formulations of both the oculomotor plant and the oculomotor integrator. Here we use measurements from new and published experiments in the larval zebrafish together with modelling to reconcile recent oculomotor plant observations with oculomotor integrator function. We developed computational techniques to characterize oculomotor plant responses over several seconds in awake animals, demonstrating that long timescale responses seen in anaesthetized animals extend to the awake state. Analysis of firing patterns of oculomotor integrator neurons demonstrates the sufficiency of this activity for stabilizing gaze given an oculomotor plant with multiple, distributed response timescales. Our results support a formulation of gaze stabilization by the oculomotor system in which commands for stabilizing gaze are generated through integration on multiple, distributed timescales.

Enhanced Social Cognitive Theory Dynamic Modeling and Simulation Towards Improving the Estimation of "Just-In-Time" States.

Insufficient physical activity (PA) is commonplace in society, in spite of its significant impact on personal health and well-being. Improved interventions are clearly needed. One of the challenges faced in behavioral interventions is a lack of understanding of multi-timescale dynamics. In this paper we rely on a dynamical model of Social Cognitive Theory (SCT) to gain insights regarding a control-oriented experimental design for a behavioral intervention to improve PA. The intervention (Just Walk JITAI) is designed with the aim to better understand and estimate ideal times for intervention and support based on the concept of "just-in-time" states. An innovative input signal design strategy is used to study the just-in-time state dynamics through the use of decision rules based on conditions of need, opportunity and receptivity. Model simulations featuring within-day effects are used to assess input signal effectiveness. Scenarios for adherent and non-adherent participants are presented, with the proposed experimental design showing significant potential for reducing notification burden while providing informative data to support future system identification and control design efforts.

Model Predictive Control of a Tandem-Rotor Helicopter With a Nonuniformly Spaced Prediction Horizon

This paper considers model predictive control of a tandem-rotor helicopter. The error is formulated using the matrix Lie group SE2(3). A reference trajectory to a target is calculated using a quartic guidance law, leveraging the differentially flat properties of the system, and refined using a finite-horizon linear quadratic regulator. The nonlinear system is linearized about the reference trajectory enabling the formulation of a quadratic program with control input, attitude keep-in zone, and attitude error constraints. A non-uniformly spaced prediction horizon is leveraged to capture the multi-timescale dynamics while keeping the problem size tractable. Monte-Carlo simulations demonstrate robustness of the proposed control structure to initial conditions, model uncertainty, and environmental disturbances.

Daylong Mobile Audio Recordings Reveal Multitimescale Dynamics in Infants’ Vocal Productions and Auditory Experiences

The sounds of human infancy—baby babbling, adult talking, lullaby singing, and more—fluctuate over time. Infant-friendly wearable audio recorders can now capture very large quantities of these sounds throughout infants’ everyday lives at home. Here, we review recent discoveries about how infants’ soundscapes are organized over the course of a day. Analyses designed to detect patterns in infants’ daylong audio at multiple timescales have revealed that everyday vocalizations are clustered hierarchically in time, that vocal explorations are consistent with foraging dynamics, and that some musical tunes occur for much longer cumulative durations than others. This approach focusing on the multiscale distributions of sounds heard and produced by infants is providing new, fundamental insights on human communication development from a complex-systems perspective.

Order reduction method for high-order dynamic analysis of heterogeneous integrated energy systems

The dynamics of heterogeneous integrated energy systems (HIES) coupling of electricity, gas, and heating/cooling subsystems is with high-order characteristics. The complex dynamics, including electromagnetic transients, electromechanical transients, hydraulic and thermal dynamics, exist in different system devices and interacts with others in different time scales. To deal with the difficulty of analysing the multi-time scale dynamics, this paper proposes an order reduction method (ORM) to map high-order modes into a lower dimensional space. Firstly, the complex model of HIES is partitioned and modelled by individuals, and the dynamic characteristics of each unit is revealed. Then modal synthesis is used to obtain feature modes of the system. Similar dynamics of individuals are synthesized whereas different modes are classified in order. When exploring dynamic process of a certain variable, the relevant modes are extracted from the synthesis model, with other modes handled as parametric or algebraic equations. Simulation studies are conducted to investigate dynamic characteristics of a test HIES using the proposed ORM. The results indicate that the proposed method is capable of simulating high-order dynamics of the test system. Furthermore, it has advantages in both computation accuracy and time, compared with equal-step method and conventional subsystem multi-step simulation method.

Tertiary regulation of cascaded run‐of‐the‐river hydropower in the islanded renewable power system considering multi‐timescale dynamics

To enable power supply in rural areas and to exploit clean energy, fully renewable power systems consisting of cascaded run-of-the-river hydropower and volatile energies such as pv and wind are built around the world. In islanded operation mode, the primary and secondary frequency control, i.e., hydro governors and automatic generation control (AGC), are responsible for the frequency stability. However, due to limited water storage capacity of run-of-the-river hydropower and river dynamics constraints, without coordination between the cascaded plants, the traditional AGC with fixed participation factors cannot fully exploit the adjustability of cascaded hydropower. When imbalances between the volatile energy and load occur, load shedding can be inevitable. To address this issue, this paper proposes a coordinated tertiary control approach by jointly considering power system dynamics and the river dynamics that couples the cascaded hydropower plants. The timescales of the power system and river dynamics are very different. To unify the multi-timescale dynamics to establish a model predictive controller that coordinates the cascaded plants, the relation between AGC parameters and turbine discharge over a time interval is approximated by a data-based second-order polynomial surrogate model. The cascaded plants are coordinated by optimising AGC participation factors in a receding-horizon manner, and load shedding is minimised. Simulation of a real-life system with real-time pv data collected on site shows the proposed method significantly reduces load loss under pv volatility.

Convolutional Multitimescale Echo State Network.

As efficient recurrent neural network (RNN) models, echo state networks (ESNs) have attracted widespread attention and been applied in many application domains in the last decade. Although they have achieved great success in modeling time series, a single ESN may have difficulty in capturing the multitimescale structures that naturally exist in temporal data. In this paper, we propose the convolutional multitimescale ESN (ConvMESN), which is a novel training-efficient model for capturing multitimescale structures and multiscale temporal dependencies of temporal data. In particular, a multitimescale memory encoder is constructed with a multireservoir structure, in which different reservoirs have recurrent connections with different skip lengths (or time spans). By collecting all past echo states in each reservoir, this multireservoir structure encodes the history of a time series as nonlinear multitimescale echo state representations (MESRs). Our visualization analysis verifies that the MESRs provide better discriminative features for time series. Finally, multiscale temporal dependencies of MESRs are learned by a convolutional layer. By leveraging the multitimescale reservoirs followed by a convolutional learner, the ConvMESN has not only efficient memory encoding ability for temporal data with multitimescale structures but also strong learning ability for complex temporal dependencies. Furthermore, the training-free reservoirs and the single convolutional layer provide high-computational efficiency for the ConvMESN to model complex temporal data. Extensive experiments on 18 multivariate time series (MTS) benchmark datasets and 3 skeleton-based action recognition datasets demonstrate that the ConvMESN captures multitimescale dynamics and outperforms existing methods.

Multi-time scale dynamics of mixed depolarization block bursting

Two-coupled excitatory neurons model containing both calcium-activated non-specific cationic and persistent sodium current in the pre-Botzinger complex (pre-BotC) is studied. A new type of mixed burst similar to a depolarization block bursting (DB-bursting) is observed in the model of pre-BotC neurons. The multi-time scale dynamics, one- and two-parameter bifurcation analysis, are used to study the types of mixed burst and their transition mechanisms. The results show that the periodic fluctuation of calcium concentration has a great influence on the generation of mixed bursting. The change of time scale caused by fluctuation of calcium concentration and the relative position of bifurcation curves have great influence on patterns of bursting.

Relaxation and mixed mode oscillations in a shape memory alloy oscillator driven by parametric and external excitations

Abstract This paper performs analytical investigations on symmetric jump phenomena reflecting multi-timescale dynamics in a nonlinear shape memory alloy oscillator with parametric and external cosinoidal excitations by means of geometrical singular perturbation theory (GSPT). The conditions concerning the existence of homoclinic and heteroclinic chaos subjected to periodic perturbations are studied in mathematical models by applying Melnikov method. Then we treat the excitation item as the slow variable acting on the bifurcation structure of the fast subsystem and present explicit algebraic expressions of the critical manifold of this subsystem for the investigation of fast-slow motions in the whole system. The study reveals the dynamical features of the relaxation oscillations formed by the alternative stable states on the different branches. In addition, the range of parametric excitation amplitude and stiffness values of the system plays an important role in the singularities and shaping the oscillation patterns. We determine numerically how the parameter values affect the manifold of the fast subsystem during the active fast transitions. Using the fast-slow analysis, one can provide the correct analytical predictions of the region of parameter space where the periodic orbits that alternate between epochs of fast and slow motions occur. Numerical simulations are also carried out to illustrate the validity of our study.

Bursting oscillations in Sprott B system with multi-frequency slow excitations: two novel “Hopf/Hopf”-hysteresis-induced bursting and complex AMB rhythms

Bursting oscillations in systems with multi-frequency slow excitations reflect multi-timescale dynamics. As there exist many kinds of multiple periodic excitations in actual dynamical systems, the analysis of dynamical behavior of such systems has received much attention. In this article, we first investigate the bursting in Sprott B system with a single excitation. We show that Hopf bifurcation delay may exhibit due to the effect of slow passage through the supercritical Hopf bifurcation. Interestingly, such delay behavior leads to a pinched “Hopf/Hopf”-hysteresis bursting when delay time is long enough. Then, we focus on the effects of the additional excitation $${\beta _2}{\mathrm{cos(}}{\omega _2}{\mathrm{t)}}$$ on the zero-crossing pinched “Hopf/Hopf”-hysteresis bursting. We find that, under the effects of $${\beta _2}{\mathrm{cos(}}{\omega _2}{\mathrm{t)}}$$ , “Hopf/Hopf”-bifurcation-delay-induced hysteresis behaviors may exhibit very interesting dynamical characteristics. In particular, each equilibrium branch may become the one with twists and turns. Then, the novel bursting pattern, turnover-of-zero-crossing pinched-“Hopf/Hopf”-hysteresis-induced bursting, is disclosed accordingly. In addition, we show that the equilibrium branches may cross each other spirally, leading to multiple intersection points under certain parameter conditions. There are two Hopf bifurcation points perching separately upon either side of the intersection points. This creates multiple delay-induced hysteresis behavior, and the other novel bursting pattern, cascaded pinched “Hopf/Hopf”-hysteresis bursting, is thus created. Finally, we investigate the complex amplitude-modulated bursting (CAMB) rhythms in Sprott B system with multi-frequency slow excitations.

Nonlinear control of high duty counter-current heat exchangers using reduced order model

In this study, nonlinear control of high duty counter-current heat exchanger is considered. The dynamics of this system can be captured by first order hyperbolic partial differential equations (PDEs), which are stiff due to the high rate of heat transfer. The potential of multi-time scale dynamics is discussed, and model reduction is performed using singular perturbations to obtain non-stiff PDE models which are valid in each time scale. Three controllers are designed and compared in the simulation case study: input/output linearizing controllers on the basis of original model and reduced order model, and a proportional-integral controller. The nonlinear controller designed using the reduced order model showed a superior performance compared to the others, especially in the presence of large modeling errors and disturbances.