Analysis Of Large-scale Systems Research Articles

The role of symmetry in the post-buckling behaviour of structures.

Symmetry plays an integral role in the post-buckling analysis of elastic structures. We show that the post-buckling response of engineering systems with given symmetry properties can be described using a preselected set of buckling modes. Therefore, the main original contribution of this paper is to prove the existence of these influential buckling modes and reveal some insights about them. From an engineering point of view, this study leads to the possibility of reducing computational effort in the analysis of large-scale systems. Firstly, symmetry groups for nonlinear elastic structural problems are discussed. Then, we invoke Curie's principle and describe the relationship between these groups and related pre-buckling and linear buckling deformation patterns. Then, for structural systems belonging to a given symmetry group, we re-invoke Curie's principle for describing the relationship between linear buckling modes and post-buckled deformation of the structure. Subsequently, we furnish a simplified asymptotic description which is obtained by projecting the equilibrium equations onto the subset of the most representative modes. As examples, classic bifurcation problems including isotropic and composite laminate panels under compression loading are investigated. Finally, the accuracy and computational advantages given by this new approach are discussed.

A Generalized Fluid Model of Ride-Hailing Systems

This paper proposes a macroscopic fluid modeling framework to assist with strategic decision making of a platform for operating a large-scale on-demand app-based ride-hailing system. The framework captures the spatiotemporal characteristics of a ride-hailing system, and is flexible in representing control policies that a platform is implementing. It thus enables the analysis of a large-scale ride-hailing system with observable market responses and facilitates the optimization of the control polices. As a demonstration of the proposed framework, we customize it for a ride-hailing system operated by Didi Chuxing in a large city of China, and conduct an empirical study of the system. In doing so, we calibrate the model with a high degree of granularity using empirical data, and then investigate optimal pricing strategies to achieve various managerial objectives of the platform. To our best knowledge, the proposed model is the first of its kind that offers a tractable way to support the analysis and optimization of large-scale ride-hailing systems. The empirical study also provides one of the first testbeds for examining various operations strategies for ride-hailing services.

Data-driven surrogate models for LTI systems via saddle-point dynamics

For the analysis, simulation, and controller design of large-scale systems, a surrogate model with small complexity is mostly required. A standard approach to determine such a model is given by modelling the system and applying model-order-reduction techniques. Contrary, we propose a data-driven approach, where the surrogate model of the input-output behaviour of an LTI system is determined from data without modelling the system beforehand. Moreover, we provide a guaranteed bound on the maximal error between the system and the surrogate model in case of noise-free measurements. We analyse the stability and convergence of the presented schemes and apply them on a benchmark system from the model-order-reduction literature.

Minimal Driver Nodes for Structural Controllability of Large-Scale Dynamical Systems: Node Classification

This article considers the problem of minimal control inputs to affect the system states such that the resulting system is structurally controllable. This problem and the dual problem of minimal observability are claimed to have no polynomial-order exact solution and, therefore, are NP-hard. Here, adopting a graph-theoretic approach, this problem is solved for general nonlinear (and also structure-invariant) systems, and a P-order solution is proposed. In this direction, the dynamical system is modeled as a directed graph, called system digraph , and two types of graph components are introduced, which are tightly related to structural controllability. Two types of nodes, which are required to be affected (or driven) by an input, called driver nodes , are defined, and minimal number of these driver nodes are obtained. Polynomial-order complexity of the given algorithms to solve the problem ensures applicability of the solution for analysis of large-scale dynamical systems. The structural results in this article are significant as compared with the existing literature, which offer approximate and computationally less-efficient, e.g. Gramian-based, solutions for the problem, while this article provides an exact solution with the lower computational complexity and applicable for controllability analysis of nonlinear systems.

Dilution and propagation of provenance trends in sand and mud: Geochemistry and detrital zircon geochronology of modern sediment from central California (U.S.A.)

Integrated, multi-method provenance studies of siliciclastic sedimentary deposits are increasingly used to reconstruct the history of source-to-sink transport, paleogeography, and tectonics. Invariably, analysis of large-scale depositional systems must confront issues regarding how to best sample the system and adequately cope with the details of sediment mixing. Potential biases including variations in grain size, sediment flux, and mineral concentration may cause provenance tracking tools to misrepresent the contributions of source-areas that contribute to large drainage networks. We have acquired U-Pb detrital zircon data from modern sand and whole-rock geochemistry from mud sampled from the Sacramento-San Joaquin drainage of central California to elucidate conditions that can skew provenance trends along the course of a major river system. This drainage network is fed by headwaters that tap the Mesozoic pluton-dominated southern Sierra Nevada, the Paleozoic-Mesozoic wallrock and volcanic-dominated northern Sierra Nevada, the ultramafic-dominated eastern Klamath Mountains, and the intermediate to mafic Cascades volcanic arc. Analysis of the results indicates that detrital zircon provenance trends effectively record source variations for the southern, granite-dominated portion of the drainage network where contrasts in lithology and inferred zircon fertility are relatively minor. In these circumstances, mixture modeling of U-Pb detrital zircon data calibrated with a measure of zircon fertility approximates relative sediment flux contributed by individual drainages. Alternatively, in the northern parts of the system, source regions underlain by ultramafic and/or volcanic rocks are poorly represented, or entirely missing, in downstream detrital zircon records. In some cases, mud geochemistry data more faithfully represent sediment provenance trends. Sampling performed at the confluence of the Sacramento, American, Mokelumne, and San Joaquin Rivers within the Sacramento-San Joaquin Delta region yields a detrital zircon age distribution that is indistinguishable from that of an independently established database of Sierra Nevada batholith crystallization ages. However, when the combined river flows along a recently established passage to the Pacific through the San Francisco Bay region, dredged sediment is found to be significantly contaminated by locally eroded material from the Franciscan Complex and other rocks that crop out within the Coast Ranges. Large variation of Zr concentrations measured throughout the Bay area document that significant hydrodynamic fractionation impacts sediment delivery through this segment of the system. The more Sierra Nevada-like detrital zircon age distribution yielded by a piston-core sample from the continental slope may be explained by either early-stage unroofing of the Coast Ranges or more efficient sand delivery from the delta to the Pacific by a free-flowing river driven by a low stand in sea level.

On Mean Field Games for Agents With Langevin Dynamics

Mean field games (MFG) have emerged as a viable tool in the analysis of large-scale self-organizing networked systems. In particular, MFGs provide a game-theoretic optimal control interpretation of the emergent behavior of noncooperative agents. The purpose of this paper is to study MFG models in which individual agents obey multidimensional nonlinear Langevin dynamics, and analyze the closed-loop stability of fixed points of the corresponding coupled forward-backward partial differential equation (PDE) systems. In such MFG models, the detailed balance property of the reversible diffusions underlies the perturbation dynamics of the forward–backward system. We use our approach to analyze closed-loop stability of two specific models. Explicit control design constraints, which guarantee stability, are obtained for a population distribution model and a mean consensus model. We also show that static state feedback using the steady-state controller can be employed to locally stabilize an MFG equilibrium.

A new version of the Riccati transfer matrix method for multibody systems consisting of chain and branch bodies

Computational speed and stability are two important aspects in the dynamics analysis of large-scale complex multibody systems. In order to improve both in the context of the multibody system transfer matrix method, a new version of the Riccati transfer matrix method is presented. Based on the new version of the general transfer matrix method for multibody system simulation, recursive formulae are developed which not only retain all advantages of the transfer matrix method, but also reduce the truncation error. As a result, the computational speed, accuracy and efficiency are improved. Numerical computation results obtained by the proposed method and an ordinary multibody system formulation show good agreement. The successful computation for a spatial branch system with more than 100000 degrees of freedom validates that the proposed method is also working for huge systems.

A novel intercooled series expansion refrigeration/liquefaction cycle using pinch technology

This paper introduces pinch technology into the analysis of large-scale cryogenic processes. This study develops temperature-enthalpy diagrams for different cryogenic cycles based on pinch technology. This enables a better understanding of the development of cryogenic systems to analyze the matching relationships among different components. It is found that the expander has the other functions that parallel or cascade expanders can influence the temperature matched characteristics of the cold and hot streams as well as the irreversibility of heat transfer in cryogenic systems. Based on an analysis of pinch technology, a novel intercooled series expansion refrigeration/liquefaction cycle is proposed and analyzed. In the intercooled series expansion refrigerator/liquefier, the expander and heat exchanger are connected in serial. This paper provides an analysis and design ideas for large-scale cryogenic systems.

Small-Signal Stability Analysis of Large-Scale Power Systems in Response to Variability of Offshore Wind Power Plants

This paper presents a methodology for a small-signal stability analysis of large-scale power systems in response to variability of offshore wind power plants. This study considers the variability of wind power as the source of disturbance introduced to the system. To accomplish this goal, a singular value decomposition-total least squares extended Prony analysis is used to assess the small-signal voltage stability. In addition, a swing-based frequency response metric is used to assess the small-signal frequency stability. The case study here considers the integration of a 1000-MW offshore wind power plant, operating in Lake Erie, into the FirstEnergy/PJM service territory. This study uses a realistic model of the 63 000-bus test system that represents the U.S. Eastern Interconnection. The results verify the utility and practicality of this methodology for the integration studies of offshore wind power plants.

Efficient and Robust Dynamic Simulation of Power Systems With Holomorphic Embedding

Dynamic simulation is vitally important in power system analysis, but traditional approaches based on numerical integration over small time steps are time-consuming. Also, the Newton-Raphson method suffers from difficulty in convergence when solving nonlinear algebraic equations. This paper proposes a novel dynamic simulation approach based on holomorphic embedding. By obtaining a high-order approximation of system dynamics, it achieves a much larger time step and thus enhances the computational efficiency significantly. In addition, the new approach avoids non-convergence issues in solving algebraic equations, which improves robustness. The approach includes flexible modeling of synchronous generators and controllers, and we propose a method for modeling generator coordinate transformations. The approach is tested on the IEEE 39-bus, 10-generator system and a Polish 2383-bus, 327-generator system. The results demonstrate promising computational efficiency and satisfactory numerical robustness for the analysis of large-scale power systems.

Accurate Performance Analysis of Coded Large-Scale Multiuser MIMO Systems with MMSE Receivers

In this paper, we estimate the uplink performance of large-scale multi-user multiple-input multiple-output (MIMO) networks. By applying minimum-mean-square-error (MMSE) detection, a novel statistical distribution of the signal-to-interference-plus-noise ratio (SINR) for any user is derived, for path loss, shadowing and Rayleigh fading. Suppose that the channel state information is perfectly known at the base station. Then, we derive the analytical expressions for the pairwise error probability (PEP) of the massive multiuser MMSE–MIMO systems, based on which we further obtain the upper bound of the bit error rate (BER). The analytical results are validated successfully through simulations for all cases.

Deadlock detection-oriented unfolding of unbounded Petri nets

The state-space explosion obstructs Petri nets for large-scale system analysis. Net unfolding techniques have drawn considerable attention to solve this problem. However, existing techniques are not suitable for deadlock detection of unbounded Petri nets. To address this issue, this paper presents a deadlock detection-oriented unfolding (D2U) technique toward unbounded nets. D2U has the following advantages over traditional methods of solving deadlock detection problems: (1) Each configuration-corresponding cyclic or acyclic transition sequence in D2U is firable from the initial marking; (2) D2U can completely decide the existence of deadlocks when some conditions are met; and (3) D2U contains no spurious markings, unlike traditional unfolding techniques of unbounded Petri nets. The construction method and applications of D2U to deadlock detection of unbounded nets are presented.

Development of traditional Chinese medicine taxonomy for Embase

A main feature of microgrid systems is their ability to operate in isolation from the main grid, i.e., islanded microgrid (IMG) operation. The power flow (PF) problem of IMGs has been shown to exhibit several distinct features compared to that of traditional distribution systems; namely: (1) having no slack bus, (2) frequency being a PF variable, and (3) generators controlled as droop units. Several studies in the literature have focused on and addressed these particularities. Still, existing IMG PF algorithms are not suitable for the analysis of large-scale IMG systems comprising thousands of buses. On the other hand, practical distribution systems and the IMGs created within such systems may in many cases comprise thousands of electric nodes. As such, the implementation of the microgrid concept in real distribution systems requires PF tools suitable for the analysis of large-scale IMGs. This paper proposes a Zbus PF algorithm for droop-controlled IMG that is particularly suited for sparse implementation. The proposed algorithm is inversion-free, does not require bus renumbering and is independent of third party sparse linear algebra libraries. The accuracy and effectiveness of the proposed algorithm is validated through several case studies considering balanced and unbalanced test systems.

Value-Set-Based Power System Robust Stability Analysis: Further Results

This paper presents some further results for multi-parameter robust stability analysis of large-scale power systems. A finite frequency test is first applied to check robust stability of the system. The parametric stability margins are then calculated to measure the degree of robust stability at different frequencies. The uncertainty's effects on stability are revealed by tracing the value set movements at the worst case frequency. The proposed approach allows the value set plot to be generated automatically, and is applicable to a substantially large number of parameters. The advantages of the approach derive from the affine uncertainty of the characteristic polynomial; for large-scale power systems, we explain that such affine uncertainty usually exists. Case studies of the 547-machine 8647-bus China system are reported, revealing that the suggested value set method appears to be a practical tool for real-world stability analysis.

Propagating Uncertainty in Power System Dynamic Simulations Using Polynomial Chaos

Quantifying the uncertainty of the renewable energy generation units and loads is critical to ensure the dynamic security of next-generation power systems. To achieve that goal, the time-consuming Monte Carlo simulations are usually used, which is not suitable for online dynamic analysis of large-scale power systems. To circumvent this difficulty, two uncertainty quantification approaches using polynomial-chaos-based methods are proposed and investigated. The first approach is the generalized polynomial chaos method that is able to reduce the computing time by three orders of magnitude compared with Monte Carlo methods while achieving the same accuracy. We find that this approach is very useful for short-term power system dynamic simulations, but it may produce unreliable results for long-term simulations. To address the weakness of that approach, we present the second method, namely the multi-element generalized-polynomial-chaos method. It is seen that this method is more accurate and more numerically stable than the generalized polynomial chaos method. Since the uncertainties of the renewable energy generation units and loads can follow very different distributions, we extend the Stieltjes’ recursive procedure that allows us to derive the orthogonal basis functions for any assumed probability distribution of the input random variables. Extensive simulations carried out on the WECC 3-machine 9-bus system and the New England 10-machine 39-bus system reveal that our proposed approaches are able to produce comparable accuracy as the Monte Carlo based method while achieving significantly improved computational efficiency for both stable and unstable power system operating conditions.

A Mixed Integer Programming Model for Evaluating the Hidden Probabilities of <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math> </inline-formula>-<inline-formula> <tex-math notation="LaTeX">${k}$ </tex-math> </inline-formula> Line Contingencies in Smart Grids

In contingency analysis of large-scale power systems, the high-order contingencies involving a relatively large number of component failures are traditionally assumed to have a very low occurrence probability. However, this may underestimate the probability of some ${N}$ - ${k}$ contingencies and thus pose risk to the reliable system operations considering that those contingencies would cause severe consequences. In this paper, we investigate the problem of hidden ${N}$ - ${k}$ contingencies and cast the problem of evaluating the hidden probability of an ${N}$ - ${k}$ contingency as a mixed integer linear programming problem. The simulation results on the IEEE 14-bus and 118-bus systems verify the effectiveness of the proposed model.

Improved Well-Conditioned Model Order Reduction Method Based on Multilevel Krylov Subspaces

Reduced order models (ROMs) based on the asymptotic waveform evaluation enable fast and efficient parametric analysis of large-scale matrix systems exhibiting nonlinear dependence on certain desired parameter(s). However, they are known to be narrowband due to the inherently ill-conditioned moment generation process. While well-conditioned approaches exist that enforce the moment-matching criteria by introducing some correction terms, these are not optimal and are difficult to parallelize. This letter introduces a well-conditioned multilevel Krylov model order reduction (WMKMOR) technique which is accurate over a larger band and faster to set up than existing approaches. Also, the multiple levels of Krylov subspaces in WMKMOR are generated independently. The improvement in ROM bandwidth using this technique is demonstrated for a finite-element model of an electromagnetic scattering example.

Robust stability analysis for barrier-based equation-free multi-linear model predictive control

On-line optimization strategies such as model predictive control (MPC) have been widely used to compute control actions for a range of complex industrial systems. Barrier based MPC has recently been introduced, bringing together theory and algorithms for analysing the stability of linear models, however such models may not describe complex systems dynamics adequately. Multi-model linear MPC configurations can be used as a more reliable solution as piecewise affine (PWA) models can describe the underlying nonlinear dynamics more accurately. Additionally, model order reduction can be applied to large-scale distributed systems, to reduce their dimensionality, jeopardising however their closed-loop stability. As a result, there is a clear need for an input to output stability analysis for closed loop systems under unstructured uncertainty when multi-model barrier MPC is utilized. In this work, we combine equation-free model reduction with integral quadratic constraints (IQCs) for the stability analysis of large-scale closed-loop systems under unstructured uncertainties, including model approximation errors and nonlinearities, including MPC. An illustrative example is used to elucidate the proposed methodology.

The Nested Structure of Emergent Supply Networks

Inspired by studies in ecological networks, we look for a nested pattern in a large-scale data set describing the global automotive industry, including more than 18 000 firms, their clients, and products. Two bipartite networks are formed, namely, supplier–product distribution and supplier–manufacturer relations. Both networks are found to be significantly nested. The pattern means that suppliers produce proper subsets of what other suppliers produce and rare products are produced only by those suppliers that already produce high numbers of product types. In addition, the manufacturers that procure from few suppliers procure from those that supply to most other manufacturers in the network. Similarly, suppliers that supply to few supply to those manufacturers that procure from most others. A nested structure is more robust than a nonnested structure as disrupted suppliers can be substituted, but nestedness also means that small suppliers face more competition as their production can be redundant. Our finding is contrary to conventional wisdom that associates large diversified firms with efficiency and small specialist firms with rare products, showing that large-scale complex system analysis can lead to the discovery of important systemic characteristics, which are obscured when viewed from local points of view. We then propose a multiagent model that creates more realistic nested structures to study systemic outcomes influenced by topology.

A distributed control framework and delay-dependent stability analysis for large-scale networked control systems with non-ideal communication network

Recently, the incorporation of telecommunication technology with control systems provides the usability of remote measurement signals for the designing of networked controllers for geographically distributed large-scale systems. However, communication network introduces new difficulties such as time delays and packet dropouts to the design of networked controllers. This paper presents a new Distributed Networked Control Scheme (DNCS) and its stability analysis for stabilizing of large-scale systems with interconnected subsystems featuring both random delays and random packet dropouts in their communication links. Firstly, a general model for large scale distributed networked system consisting of subsystems is used in which the state of each subsystem has its own time varying delay and there are also delays and packet dropouts in their interconnection communication links. To compensate the influence of subsystems on each other and enhance performance and stability margin of the closed-loop system, a suitable distributed control scheme is proposed. The stability criteria are provided based on Lyapunov-Krasovskii and Linear Matrix Inequality (LMI) techniques. For this, a new type of Lyapunov-Krasovskii functional and certain slack matrices are developed to conclude some LMI-based delay-dependent theorems for designing the control law, as well as the stabilizing of the DNCS. To evaluate the proposed method, three illustrative examples are provided. To indicate the efficiency of the suggested approach, a small-gain-based approach and an observer-based consensus method are applied for comparison. Simulation results show the effectiveness of the proposed approach to enhance the performance of large-scale networked systems among a non-ideal communication network.