Large-scale Dynamical Systems Research Articles

Optimization-based disjoint and overlapping epsilon decompositions of large-scale dynamical systems via graph theory

To address the complexity challenge of a large-scale system, the decomposition into smaller subsystems is very crucial and demanding for distributed estimation and control purposes. This paper proposes novel optimization-based approaches to decompose a large-scale system into subsystems that are either weakly coupled or weakly coupled with overlapping components. To achieve this goal, first, the epsilon decomposition of large-scale systems is examined. Then, optimization frameworks are presented for disjoint and overlapping decompositions utilizing bipartite graphs. Next, the proposed decomposition algorithms are represented for particular cases of large-scale systems using directed graphs. In contrast to the existing user-based techniques, the proposed optimization-based methods can reach the solution rapidly and systematically. At last, the capability and efficiency of the proposed algorithms are investigated by conducting simulations on three case studies, which include a practical distillation column, a modified benchmark model, and the IEEE 118-bus power system.

Optimization-based Disjoint and Overlapping Epsilon Decompositions of Large-scale Dynamical Systems via Graph Theory

To address the complexity challenge of a large-scale system, the decomposition into smaller subsystems is very crucial and demanding for distributed estimation and control purposes. This paper proposes novel optimization-based approaches to decompose a large-scale system into subsystems that are either weakly coupled or weakly coupled with overlapping components. To achieve this goal, first, the epsilon decomposition of large-scale systems is examined. Then, optimization frameworks are presented for disjoint and overlapping decompositions utilizing bipartite graphs. Next, the proposed decomposition algorithms are represented for particular cases of large-scale systems using directed graphs. In contrast to the existing user-based techniques, the proposed optimization-based methods can reach the solution rapidly and systematically. At last, the capability and efficiency of the proposed algorithms are investigated by conducting simulations on three case studies, which include a practical distillation column, a modified benchmark model, and the IEEE 118-bus power system.

Energetic spectral-element time marching methods for phase-field nonlinear gradient systems

We propose two efficient energetic spectral-element methods in time for marching nonlinear gradient systems with the phase-field Allen–Cahn equation as an example: one fully implicit nonlinear method and one semi-implicit linear method. Different from other spectral methods in time using spectral Petrov-Galerkin or weighted Galerkin approximations, the presented implicit method employs an energetic variational Galerkin form that can maintain the mass conservation and energy dissipation property of the continuous dynamical system. Another advantage of this method is its superconvergence. A high-order extrapolation is adopted for the nonlinear term to get the semi-implicit method. The semi-implicit method does not have superconvergence, but can be improved by a few Picard-like iterations to recover the superconvergence of the implicit method. Numerical experiments verify that the method using Legendre elements of degree three outperforms the 4th-order implicit-explicit backward differentiation formula and the 4th-order exponential time difference Runge-Kutta method, which were known to have best performances in solving phase-field equations. In addition to the standard Allen–Cahn equation, we also apply the method to a conservative Allen–Cahn equation, in which the conservation of discrete total mass is verified. The applications of the proposed methods are not limited to phase-field Allen–Cahn equations. They are suitable for solving general, large-scale nonlinear dynamical systems.

A moment-based Kalman filtering approach for estimation in ensemble systems.

A persistent challenge in tasks involving large-scale dynamical systems, such as state estimation and error reduction, revolves around processing the collected measurements. Frequently, these data suffer from the curse of dimensionality, leading to increased computational demands in data processing methodologies. Recent scholarly investigations have underscored the utility of delineating collective states and dynamics via moment-based representations. These representations serve as a form of sufficient statistics for encapsulating collective characteristics, while simultaneously permitting the retrieval of individual data points. In this paper, we reshape the Kalman filter methodology, aiming its application in the moment domain of an ensemble system and developing the basis for moment ensemble noise filtering. The moment system is defined with respect to the normalized Legendre polynomials, and it is shown that its orthogonal basis structure introduces unique benefits for the application of Kalman filter for both i.i.d. and universal Gaussian disturbances. The proposed method thrives from the reduction in problem dimension, which is unbounded within the state-space representation, and can achieve significantly smaller values when converted to the truncated moment-space. Furthermore, the robustness of moment data toward outliers and localized inaccuracies is an additional positive aspect of this approach. The methodology is applied for an ensemble of harmonic oscillators and units following aircraft dynamics, with results showcasing a reduction in both cumulative absolute error and covariance with reduced calculation cost due to the realization of operations within the moment framework conceived.

Formation Control of Autonomous Underwater Vehicles Using an Improved Nonlinear Backstepping Method

The characteristics of autonomous underwater vehicles include nonlinearity, strong coupling, multiple inputs and multiple outputs, uncertainty, strong disturbance, underdrive, and multiple constraints. Autonomous underwater vehicle cluster systems are associated with large-scale complex dynamic systems through local perception or network communication, which have the structural characteristics of “complex dynamic + association topology + interaction rules”. To solve the problem of formation trajectory tracking of underactuated autonomous underwater vehicles, a controller was designed on the basis of an improved nonlinear backstepping algorithm, cascade system theory, and the Lyapunov direct method. In this design, the formation is determined from the actual trajectory of the leader autonomous underwater vehicle. The formation control rate is determined using the backstepping method and Lyapunov theory. Nonlinear disturbance observers were added to ensure that the trajectory error of the formation control could be quickly reduced in a real case with interference. The stability and effectiveness of this method were verified through simulation experiments. The robustness of the control algorithm was verified using two simulation cases, and the simulation results show that the proposed control method can maintain the expected formation.

Wishful Thinking about Consciousness

We contrast three very distinct mathematical approaches to the hard problem of consciousness: quantum consciousness, integrated information theory, and the very large-scale dynamical systems simulation of a network of networks. We highlight their features and their associated hypotheses, and we discuss how they are aligned or in conflict. We suggest some challenges to these theories, in considering how they might apply to the human brain as it develops both cognitive and conscious sophistication, from infancy to adulthood. We indicate how an evolutionary perspective challenges the distinct approaches to aver performance advantages and physiological surrogates for consciousness.

A new method for model reduction and controller design of large-scale dynamical systems

A new method for model reduction and controller design of large-scale dynamical systems

Preserving Lagrangian structure in data-driven reduced-order modeling of large-scale dynamical systems

This work presents a nonintrusive physics-preserving method to learn reduced-order models (ROMs) of Lagrangian systems, which includes nonlinear wave equations. Existing intrusive projection-based model reduction approaches construct structure-preserving Lagrangian ROMs by projecting the Euler–Lagrange equations of the full-order model (FOM) onto a linear subspace. This Galerkin projection step requires complete knowledge about the Lagrangian operators in the FOM and full access to manipulate the computer code. In contrast, the proposed Lagrangian operator inference approach embeds the mechanics into the operator inference framework to develop a data-driven model reduction method that preserves the underlying Lagrangian structure. The proposed approach exploits knowledge of the governing equations (but not their discretization) to define the form and parametrization of a Lagrangian ROM which can then be learned from projected snapshot data. The method does not require access to FOM operators or computer code. The numerical results demonstrate Lagrangian operator inference on an Euler–Bernoulli beam model, the sine-Gordon (nonlinear) wave equation, and a large-scale discretization of a soft robot fishtail with 779,232 degrees of freedom. The learned Lagrangian ROMs generalize well, as they can accurately predict the physical solutions both far outside the training time interval, as well as for unseen initial conditions.

A Memory-Efficient Neural Ordinary Differential Equation Framework Based on High-Level Adjoint Differentiation

Neural ordinary differential equations (neural ODEs) have emerged as a novel network architecture that bridges dynamical systems and deep learning. However, the gradient obtained with the continuous adjoint method in the vanilla neural ODE is not reverse-accurate. Other approaches suffer either from an excessive memory requirement due to deep computational graphs or from limited choices for the time integration scheme, hampering their application to large-scale complex dynamical systems. To achieve accurate gradients without compromising memory efficiency and flexibility, we present a new neural ODE framework, PNODE, based on high-level discrete adjoint algorithmic differentiation. By leveraging discrete adjoint time integrators and advanced checkpointing strategies tailored for these integrators, PNODE can provide a balance between memory and computational costs, while computing the gradients consistently and accurately. We provide an open-source implementation based on PyTorch and PETSc, one of the most commonly used portable, scalable scientific computing libraries. We demonstrate the performance through extensive numerical experiments on image classification and continuous normalizing flow problems. We show that PNODE achieves the highest memory efficiency when compared with other reverse-accurate methods. On the image classification problems, PNODE is up to two times faster than the vanilla neural ODE and up to 2.3 times faster than the best existing reverse-accurate method. We also show that PNODE enables the use of the implicit time integration methods that are needed for stiff dynamical systems.

A Compositional Dissipativity Approach for Data-Driven Safety Verification of Large-Scale Dynamical Systems

This work is concerned with a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">compositional data-driven approach</i> for formal safety verification of large-scale continuous-time dynamical systems with unknown models. The proposed framework enjoys the interconnection matrix and joint dissipativity-type properties of subsystems, described by the notion of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">stochastic storage certificates</i> . In the first part of the paper, we cast the required conditions for constructing storage certificates as a robust optimization program (ROP). Since the proposed ROP is not tractable due to the unknown model appearing in one of its constraints, we propose a scenario optimization program (SOP) corresponding to the original ROP by collecting finite numbers of data from trajectories of each subsystem. By establishing a probabilistic relation between the optimal value of SOP and that of ROP, we construct a storage certificate for each unknown subsystem based on the number of data and a required level of confidence. We accordingly propose a compositional technique based on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dissipativity reasoning</i> to construct <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">stochastic barrier certificates</i> of interconnected systems based on storage certificates of individual subsystems. By leveraging the acquired barrier certificate, we quantify a lower bound on the probability that an interconnected system never reaches a certain unsafe region in finite time horizons with an a-priori guaranteed confidence. We also propose an auxiliary compositional approach without requiring any compositionality condition but at the cost of providing a potentially conservative safety guarantee. In the second part of the paper, we propose our approaches for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">deterministic</i> continuous-time systems with unknown dynamics. We verify our results over an unknown room temperature network containing 100 rooms.

Performance enhancement of large-scale linear dynamic MIMO systems using GWO-PID controller

The multi-input multi-output (MIMO) technique is becoming grown and integrated into wireless wideband communication. MIMO techniques suffer from a large-scale linear dynamic problem, it will be easy to adjust the proportional-integral-derivative (PID) of a continuous system, unlike the nonlinear model. This work displays the tuning of the PID controller for MIMO systems utilizing a statistical grey wolf optimization (GWO) and evaluated by objective function as integral time absolute error (ITAE). The instantaneous adjusting characteristic GWO approach is the criterion that distinguishes such a combination-proposed strategy from that existing in the traditional PID approach. The GWO algorithm searching-based methodology is used to determine the adequate gain factors of the PID controller. The suggested approach guarantees stability as the initial scheme for a steady state condition. A combination of ITAE combined with the GWO reduction method is adopted to reduce the steady-state transient time responses between the higher-order initial scheme and the unit amplitude response. Simulation outcomes are illustrated using MATLAB software to show the capability of adopting the GWO scheme for PID controlling.

Record-breaking marine heatwave in northern Yellow Sea during summer 2018: Characteristics, drivers and ecological impact

Globally, marine heatwaves (MHWs) are becoming more common, more intense, and longer-lasting. They could have a large ecological and societal impact when compounded by low oxygen concentrations or high acidity. Here, using a high-resolution satellite product and reanalysis datasets, we investigated the characteristics of the MHW at northern Yellow Sea (NYS) during mid-summer 2018 and the driving mechanisms of large-scale atmospheric circulations. Results showed that the MHW in mid-summer 2018 (lasting from 26 July to 18 August 2018) had been the most intense since 1982, reaching an anomaly peak of 5.15 °C. For the 2018 MHW, the onset rate was 0.49 °C/day, indicating that the reaction window was relatively short and hard to take mitigation measures, while the decline rate was 0.19 °C/day, meaning the coping window was long and easy to push an already stressed system. The synergy of the two large-scale dynamic systems, i.e., the northward-shifted western north Pacific subtropical high (WNPSH) and the northeastward-expanded South Asia high (SAH), was likely responsible for establishment and maintenance of the hot-weather conditions. These high-pressure systems could result in stronger descending motion, less cloud cover, more solar radiation, and smaller wind speeds which in combination aggravated the MHW. We further found that the unprecedented MHW was actually also impacted by terrestrial heatwave. From 14 July to 15 August 2018, Northeast China was affected by an exceptionally long and intense atmospheric heat wave (AHW). The AHW had impacted on the MHW through warm advection transportation and may significantly contribute to the record-breaking intensity of the MHW, in addition to the impact of abnormal atmospheric circulations. Finally, we showed that a mass mortality of sea cucumbers in the study region during mid-summer 2018 was highly likely caused by the MHW through severe heat stress.

Dynamic behavior of outburst two-phase flow in a coal mine T-shaped roadway: The formation of impact airflow and its disaster-causing effect

The study of the dynamic disaster mechanism of coal and gas outburst two-phase flow is crucial for improving disaster reduction and rescue ability of coal mine outburst accidents. An outburst test in a T-shaped roadway was conducted using a self-developed large-scale outburst dynamic disaster test system. We investigated the release characteristics of main energy sources in coal seam, and obtained the dynamic characteristics of outburst two-phase flow in a roadway. Additionally, we established a formation model for outburst impact flow and a model for its flow in a bifurcated structure. The results indicate that the outburst process exhibits pulse characteristics, and the rapid destruction process of coal seam and the blocking state of gas flow are the main causes of the pulse phenomenon. The outburst energy is released in stages, and the elastic potential energy is released in the vertical direction before the horizontal direction. In a straight roadway, the impact force oscillates along the roadway. With an increase in the solid–gas ratio, the two-phase flow impact force gradually increases, and the disaster range extends from the middle of the roadway to the coal seam. In the area near the coal seam, the disaster caused by the two-phase flow impact is characterized by intermittent recovery. In a bifurcated roadway, the effect of impact airflow on impact dynamic disaster is much higher than that of two-phase flow, and the impact force tends to weaken with increasing solid-gas ratio. The impact force is asymmetrically distributed; it is higher on the left of the bifurcated roadway. With an increase in the solid-gas ratio, the static pressure rapidly decreases, and the bifurcated structure accelerates the attenuation of static pressure. Moreover, secondary acceleration is observed when the shock wave moves along the T-shaped roadway, indicating that the bifurcated structure increases the shock wave velocity.

Efficient Sensor Node Selection for Observability Gramian Optimization.

Optimization approaches that determine sensitive sensor nodes in a large-scale, linear time-invariant, and discrete-time dynamical system are examined under the assumption of independent and identically distributed measurement noise. This study offers two novel selection algorithms, namely an approximate convex relaxation method with the Newton method and a gradient greedy method, and confirms the performance of the selection methods, including a convex relaxation method with semidefinite programming (SDP) and a pure greedy optimization method proposed in the previous studies. The matrix determinant of the observability Gramian was employed for the evaluations of the sensor subsets, while its gradient and Hessian were derived for the proposed methods. In the demonstration using numerical and real-world examples, the proposed approximate greedy method showed superiority in the run time when the sensor numbers were roughly the same as the dimensions of the latent system. The relaxation method with SDP is confirmed to be the most reasonable approach for a system with randomly generated matrices of higher dimensions. However, the degradation of the optimization results was also confirmed in the case of real-world datasets, while the pure greedy selection obtained the most stable optimization results.

An Adaptive Frequency Sampling Algorithm for Dynamic Condensation-Based Frequency Response Analysis

This paper proposed an efficient and adaptive frequency sampling algorithm for frequency response analysis using dynamic condensation-based reduced-order modeling. For the degree of freedom-based model reduction method, the reduced-order basis becomes a frequency-dependent matrix since the relationship between master and slave degrees of freedom stems from partial equations of a second-order dynamical system. Such frequency-dependency makes the analysis inefficient for investigating the frequency response of the system. Considering that the coverage of a local reduced-order basis at a single frequency varies depending on the frequency, a new frequency sampling algorithm was proposed with a strategy of constructing multiple local reduced-order models (ROMs) at sample frequencies. For adaptive sampling, the frequency range of a local ROM was evaluated, and a new sample was added if there was a gap between two adjacent ROMs. As a result, the accuracy of the local ROM can be estimated, and the efficiency in the online stage was greatly enhanced. The proposed method was verified by performing frequency response analysis with several numerical examples, including a large-scale structural and dynamic system.

A New Algorithm of Cubic Dynamic Uncertain Causality Graph for Speeding Up Temporal Causality Inference in Fault Diagnosis

Representing and reasoning uncertain causalities have diverse applications in fault diagnosis for industrial systems. Owing to the complicated dynamics and a multitude of uncertain factors in such systems, it is hard to implement efficient diagnostic inference when a process fault occurs. The cubic dynamic uncertain causal graph was proposed for graphically modeling and reasoning about the fault spreading behaviors in the form of causal dependencies across multivariate time series. However, in certain large-scale scenarios with multiconnected and time-varying causalities, the existing inference algorithm is incapable of dealing with the logical reasoning process in an efficient manner. We, therefore, explore the solutions to enhanced computational efficiency. Causality graph decomposition and simplification, and graphical transformation, are proposed to reduce model complexity and form a minimal causality graph. An algorithm, event-oriented early logical absorption, is also presented for logical reasoning. It is mainly intended to minimize the computational costs for compulsory absorption operations in the early stage of reasoning process. The effectiveness of the proposed algorithm is verified on the secondary loop model of nuclear power plant by utilizing the fault data derived from a nuclear power plant simulator. The results show the anticipated capability of efficient fault diagnosis of the proposed algorithm for large-scale dynamic systems.

Multidiscipline Design Optimization for Large-Scale Complex Nonlinear Dynamic System Based on Weak Coupling Interfaces

For high-tech manufacturing industries, developing large-scale complex nonlinear dynamic systems must be taken as one of the basic works, formulating problems to be solved, steering system design in a more preferable direction, and making correct strategic decisions. By using effective tools of big data mining, Dynamic Design Methodology was proposed to establish a technical platform for Multidiscipline Design Optimization such as High-Speed Rolling Stock, including three key technologies: analysis graph of full-vehicle stability properties and variation patterns, improved transaction strategy of flexible body to MBS interface, seamless collaboration with weldline fatigue damage assessments through correct Modal Stress Recovery. By applying the above methodology, a self-adaptive improved solution was formulated with optimal parameter configuration, which is one of the more favorable options for higher-speed bogies. While within a velocity (140–200) km/h at λe &lt; 0.10, car body instability’s influence on ride comfort can be easily improved by using a semi-active vibration reduction technique between inter-vehicles through outer windshields. Comprehensive evaluations show that only under rational conditions of wheel-rail matching, i.e., 0.10 ≥ λeN &gt; λemin and λemin = (0.03–0.06), can this low-cost solution achieve the three goals of low track conicity, optimal route planning, and investment benefit maximization. So, rail vehicle experts are necessary to collaborate and innovate intensively with passenger transportation and steel rail ones. Specifically, by adopting rail grinding treatment, occurrence probability is controlled at 85% and 5% for track conicity of (0.03–0.10) and (0.25–0.35). By optimizing routing planning, operating across dedicated lines of different speed grades can achieve self-cleaning of central hollow tread wear over time. According to the inherent rigid-flex coupling relationship, geometric nonlinearities of worn wheel-rail contact should be avoided as much as possible for HSR practices. Only under weak coupling interfaces in the floor frame can the structural integrity of an aluminum alloy car body be ensured.

A Hybrid Systems-Based Hierarchical Control Architecture for Heterogeneous Field Robot Teams.

Field robot systems have recently been applied in a wide range of research fields. Further automation, development, and activation of such systems require cooperation among heterogeneous robots. Classical control theory is inefficient in managing large-scale complex dynamic systems. Therefore, a discrete-event system based on the supervisory control theory must be introduced to overcome this limitation. In this article, we propose a hybrid system-based hierarchical control architecture using a supervisory control-based high-level controller and a traditional control-based low-level controller. The hybrid system and its dynamics are modeled through a formal method, called hybrid automata, and the behavior specifications are designed to express the control objectives for cooperation. In addition, modular supervisors that are more scalable and maintainable than a centralized supervisory controller were synthesized. The proposed hybrid system and hierarchical control architecture were implemented, validated, and evaluated for performance through a physics-based simulator and field tests. The experimental results confirmed that the robot team satisfied the given specifications and presented systematic results, validating the efficiency of the proposed control architecture.

Order Reduction of Large-Scale Linear Dynamic Systems Using Balanced Truncation with Modified Cauer Continued Fraction

This article discusses a new technique to reduce the order of high-dimensional, continuous, linear time-invariant dynamic systems. The proposed approach utilizes the merits of the balanced truncation method, and modified Cauer continued fraction expansion. The reduced model denominator was retrieved via the concept of Lyapunov balancing, and state truncation and numerator coefficients were obtained by using a modified Cauer continued fraction. The proposed technique circumvents the steady-state gain discrepancy and steady-state error mismatch of the conventional balanced truncation method, and the instability issue of continued fraction expansion. The proposed method assures steady-state gain approximation, few moments, Markov parameters, stability, and other essential control features of a high-order system. The efficacy and applicability of the proposed technique are demonstrated using some typical test systems adopted from the literature. This method gives improved performance indices like minimum H∞ norm, H2 norm, a minimum ISE (integral squared error), IAE (integral absolute error), and retains approximately the full IRE (impulse response energy) of the existing system in the reduced model. The simulation findings of the proposed technique are compared with other current model reduction methods in recent literature using MATLAB.

Substructuring based parametric reduced order modelling for large-scale dynamical systems containing viscoelasticity with application to bonded assemblies

Adhesive bonding plays an increasingly important role in mechanical systems to connect different components and multi-material assemblies, and usually exhibits viscoelasticity. To accurately predict their structural dynamic behavior, finite element models are often used. When large systems are considered, these models result in high computational costs. To reduce the computational costs, substructuring combined with model order reduction can be applied. In this context, the well-known Craig-Bampton method is often used. However, due to the frequency-dependency of viscoelastic material properties, it cannot be directly applied to assemblies with adhesive joints. To enable its use for viscoelastic substructures, this work proposes several improvements to the Craig-Bampton method. Moreover, since the dynamic performance of adhesive bonded structures can strongly depend on the viscoelastic properties, the efficient assessment of different material parameters is highly desirable. Therefore, this work also extends the improved Craig-Bampton method towards parametric model order reduction in which a global reduction basis is constructed by singular value decomposition and interpolation of sampling-based local bases. Two numerical examples of adhesive bonded systems are employed to demonstrate the accuracy and computation time reduction which can be achieved with the proposed approach.