Modeling Of Large-scale Systems Research Articles

Domain Decomposition for Data-Driven Reduced Modeling of Large-Scale Systems

This paper focuses on the construction of accurate and predictive data-driven reduced models of large-scale numerical simulations with complex dynamics and sparse training datasets. In these settings, standard, single-domain approaches may be too inaccurate or may overfit and hence generalize poorly. Moreover, processing large-scale datasets typically requires significant memory and computing resources, which can render single-domain approaches computationally prohibitive. To address these challenges, we introduce a domain-decomposition formulation into the construction of a data-driven reduced model. In doing so, the basis functions used in the reduced model approximation become localized in space, which can increase the accuracy of the domain-decomposed approximation of the complex dynamics. The decomposition furthermore reduces the memory and computing requirements to process the underlying large-scale training dataset. We demonstrate the effectiveness and scalability of our approach in a large-scale three-dimensional unsteady rotating-detonation rocket engine simulation scenario with more than 75 million degrees of freedom and a sparse training dataset. Our results show that compared to the single-domain approach, the domain-decomposed version reduces both the training and prediction errors for pressure by up to 13% and up to 5% for other key quantities, such as temperature, and fuel, and oxidizer mass fractions. Lastly, our approach decreases the memory requirements for processing by almost a factor of four, which in turn reduces the computing requirements as well.

Subgrid scale modeling of droplet bag breakup in VOF simulations

The mesh-dependency of the breakup of liquid films, including their breakup length scales and resulting drop size distributions, has long been an obstacle inhibiting the computational modeling of large-scale spray systems. With the aim of overcoming this barrier, this work presents a framework for the prediction and modeling of subgrid-thickness liquid film formation and breakup within two-phase simulations using the volume of fluid method. A two-plane interface reconstruction is used to capture the development of liquid films as their thickness decreases below the mesh size. The breakup of the film is predicted with a semi-analytical model that incorporates the film geometry captured through the two-plane reconstruction. The framework is validated against experiments of the bag breakup of a liquid drop at We=13.8 through the comparison of the resulting drop size and velocity distributions. The generated distributions show good agreement with experimental results for drop resolutions as low as 25.6 cells across the initial diameter. The presented framework enables these drop breakup simulations to be performed at a computational cost three orders of magnitude lower than the cost of simulations utilizing adaptive mesh refinement.

An integrated intelligent intersection management and control system design

While a fair amount of study has been done recently on integrated management and control models for large-scale traffic systems, there is comparatively little information available regarding the design of management and control systems for small-scale intersections. This study aims to create the structural diagram of a management system for intersections and control technologies. It does this by designing three distinct systems: congestion prediction, traffic signal timing, and congestion flow dredging. This study searches the current state of common technology and chooses the intersection integrated management system by means of comparison. Fuzzy TOPSIS algorithm and ADP adaptive dynamic programming are chosen as the calculation techniques of signal lamp timing, while BP neural network and ATT-GCN network are chosen as the key algorithms of congestion prediction after thorough investigation. In the end, conventional traffic management techniques like forbidding left turns are used to direct cars that haven't arrived at the busy crossroads beforehand. This paper aims to select the best model for an intersection management system currently available from the common technologies. The idealized management system and its structure diagram are designed in a straightforward manner, and they will serve as a guide for future road and vehicular intersection design.

Timed Automata-Based Strategy for Controlling Drone Access to Critical Zones: A UPPAAL Modeling Approach

Controlling access to critical zones by drones is crucial for ensuring safety and efficient operations in various applications. In this research, we propose a strategy for controlling the access of a set of drones to a critical zone using timed automata and UPPAAL. UPPAAL is a model checker and simulator for real-time systems, which allows for the modeling, simulation, and verification of timed automata. Our system consists of six drones, a controller, and a buffer, all modeled as timed automata. We present a formal model capturing the behavior and interactions of these components, considering the constraints of allowing only one drone in the critical zone at a time. Timed automata are a powerful formalism for modeling and analyzing real-time systems, as they can capture the temporal aspects of system behavior. The advantages of using timed automata include the ability to model time-critical systems, analyze safety and liveness properties, and verify the correctness of the system. We design a strategy that involves signaling the approaching drones, preventing collisions, and ensuring orderly access to the critical zone. We utilize UPPAAL for simulating and verifying the system, including the evaluation of properties such as validation properties, safety properties, liveness properties, and absence of deadlocks. However, a limitation of timed automata is that they can become complex and difficult to model for large-scale systems, and the analysis can be computationally expensive as the number of components and behaviors increases. Through simulations and formal verification, we demonstrate the effectiveness and correctness of our proposed strategy. The results highlight the ability of timed automata and UPPAAL to provide reliable and rigorous analysis of drone access control systems. Our research contributes to the development of robust and safe strategies for managing drone operations in critical zones.

Stability Analysis for Large-Scale Multi-Agent Molecular Communication Systems.

Molecular communication (MC) is recently featured as a novel communication tool to connect individual biological nanorobots. It is expected that a large number of nanorobots can form large multi-agent MC systems through MC to accomplish complex and large-scale tasks that cannot be achieved by a single nanorobot. However, most previous models for MC systems assume a unidirectional diffusion communication channel and cannot capture the feedback between each nanorobot, which is important for multi-agent MC systems. In this paper, we introduce a system theoretic model for large-scale multi-agent MC systems using transfer functions, and then propose a method to analyze the stability for multi-agent MC systems. The proposed method decomposes the multi-agent MC system into multiple single-input and single-output (SISO) systems, which facilitates the application of simple analysis technique for SISO systems to the large-scale multi-agent MC system. Finally, we demonstrate the proposed method by analyzing the stability of a specific large-scale multi-agent MC system and clarify a parameter region to synchronize the states of nanorobots, which is important to make cooperative behaviors at a population level.

A comprehensive framework for stochastic calibration and sensitivity analysis of large-scale groundwater models

Abstract. We introduce a comprehensive and robust theoretical framework and operational workflow that can be employed to enhance our understanding, modeling and management capability of complex heterogeneous large-scale groundwater systems. Our framework encapsulates key components such as the three-dimensional nature of groundwater flows, river–aquifer interactions, probabilistic reconstruction of three-dimensional spatial distributions of geomaterials and associated properties across the subsurface, multi-objective optimization for model parameter estimation through stochastic calibration, and informed global sensitivity analysis (GSA). By integrating these components, we effectively consider the inherent uncertainty associated with subsurface system characterizations as well as their interactions with surface waterbodies. The approach enables us to identify parameters impacting diverse system responses. By employing a coevolutionary optimization algorithm, we ensure efficient model parameterization, facilitating simultaneous and informed optimization of the defined objective functions. Additionally, estimation of parameter uncertainty naturally leads to quantification of uncertainty in system responses. The methodology is designed to increase our knowledge of the dynamics of large-scale groundwater systems. It also has the potential to guide future data acquisition campaigns through an informed global sensitivity analysis. We demonstrate the effectiveness of our proposed methodology by applying it to the largest groundwater system in Italy. We address the challenges posed by the characterization of the heterogeneous spatial distribution of subsurface attributes across large-scale three-dimensional domains upon incorporating a recent probabilistic hydrogeological reconstruction specific to the study case. The system considered faces multiple challenges, including groundwater contamination, seawater intrusion, and water scarcity. Our study offers a promising modeling strategy applicable to large-scale subsurface systems and valuable insights into groundwater flow patterns that can then inform effective system management.

Anomaly detection model for large-scale industrial systems using transfer entropy and graph attention network

Abstract Multivariate time series (MTS) anomaly detection is vital for ensuring the safety and reliability of large-scale industrial systems. However, existing deep learning methods often overlook complex interrelationships between different time series and the study of anomalies has been limited to detection. To address this, we propose an MTS anomaly detection model based on transfer entropy (TE) and graph attention network (GAT). In the graph construction module, by combining modified TE with automatic structure learning, we extract intricate relationships between features. In the prediction module, we modify the GAT to implement the dynamic attention mechanism and non-linear interaction between different features to improve the accuracy of model prediction. Finally, our model combines the modified TE with anomaly detection task, which can be used to provide interpretability for the detected anomalies using the constructed causal graph. Experimental results on both real and public datasets show that our approach outperforms the mainstream methods, in particular, achieving optimal results in terms of F1 scores and recall.

Physics to system-level modeling of silicon-organic-hybrid nanophotonic devices

The continuous growth in data volume has sparked interest in silicon-organic-hybrid (SOH) nanophotonic devices integrated into silicon photonic integrated circuits (PICs). SOH devices offer improved speed and energy efficiency compared to silicon photonics devices. However, a comprehensive and accurate modeling methodology of SOH devices, such as modulators corroborating experimental results, is lacking. While some preliminary modeling approaches for SOH devices exist, their reliance on theoretical and numerical methodologies, along with a lack of compatibility with electronic design automation (EDA), hinders their seamless and rapid integration with silicon PICs. Here, we develop a phenomenological, building-block-based SOH PICs simulation methodology that spans from the physics to the system level, offering high accuracy, comprehensiveness, and EDA-style compatibility. Our model is also readily integrable and scalable, lending itself to the design of large-scale silicon PICs. Our proposed modeling methodology is agnostic and compatible with any photonics-electronics co-simulation software. We validate this methodology by comparing the characteristics of experimentally demonstrated SOH microring modulators (MRMs) and Mach Zehnder modulators with those obtained through simulation, demonstrating its ability to model various modulator topologies. We also show our methodology's ease and speed in modeling large-scale systems. As an illustrative example, we use our methodology to design and study a 3-channel SOH MRM-based wavelength-division (de)multiplexer, a widely used component in various applications, including neuromorphic computing, data center interconnects, communications, sensing, and switching networks. Our modeling approach is also compatible with other materials exhibiting the Pockels and Kerr effects. To our knowledge, this represents the first comprehensive physics-to-system-level EDA-compatible simulation methodology for SOH modulators.

The potential role of airborne and floating wind in the North Sea region

Abstract Novel wind technologies, in particular airborne wind energy (AWE) and floating offshore wind turbines, have the potential to unlock untapped wind resources and contribute to power system stability in unique ways. So far, the techno-economic potential of both technologies has only been investigated at a small scale, whereas the most significant benefits will likely play out on a system scale. Given the urgency of the energy transition, the possible contribution of these novel technologies should be addressed. Therefore, we investigate the main system-level trade-offs in integrating AWE systems and floating wind turbines into a highly renewable future energy system. To do so, we develop a modelling workflow that integrates wind resource assessment and future cost and performance estimations into a large-scale energy system model, which finds cost-optimal system designs that are operationally feasible with hourly temporal resolution across ten countries in the North Sea region. Acknowledging the uncertainty on AWE systems’ future costs and performance and floating wind turbines, we examine a broad range of cost and technology development scenarios and identify which insights are consistent across different possible futures. We find that onshore AWE outperforms conventional onshore wind regarding system-wide benefits due to higher wind resource availability and distinctive hourly generation profiles, which are sometimes complementary to conventional onshore turbines. The achievable power density per ground surface area is the main limiting factor in large-scale onshore AWE deployment. Offshore AWE, in contrast, provides system benefits similar to those of offshore wind alternatives. Therefore, deployment is primarily driven by cost competitiveness. Floating wind turbines achieve higher performance than conventional wind turbines, so they can cost more and remain competitive. AWE, in particular, might be able to play a significant role in a climate-neutral European energy supply and thus warrants further study.

Modeling combined-cycle power plants in a detailed electricity market model

The efficiency and flexibility of combined-cycle gas turbines (CCGT) are gaining importance in view of more decarbonized energy systems. Therefore, an adequate representation of CCGTs in large-scale energy system models is required. When modeling large-scale energy systems, a trade-off between detailed representation of the technical restrictions and reasonable computing times emerges because of limited computing capacities.We present an approach that accounts for the operational dependencies between the gas and steam turbines of a CCGT but remains applicable in large-scale market models. Duct burners and bypasses that enable the solo operation of steam or gas turbines are also modeled. We implement our approach using the well-established Joint Market Model and apply it in a case study of the German electricity system in 2040.Our modeling approach captures more detailed operation modes, while increases in computation time remain limited. Thus, the approach is advantageous when turbine-wise modeling and analysis of CCGTs is required, e.g. for a detailed analysis of start-ups and operations. The results show no substantial differences between the aggregated market results of five cases investigated. The consideration of bypasses and duct burners yet leads to higher contribution margins for individual CCGTs – with stronger effects observed for more efficient groups.

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.

Representing Hourly Energy Prices in a Large-Scale Monthly Water System Model

Water system management models represent different purposes, such as water supply, flood control, recreation, and hydropower. When building large-scale system models to represent these diverse objectives, their most appropriate time steps for each purpose often do not coincide. A monthly time step is usually sufficient for water supply modeling, but it can be too coarse for flood control, hydropower, and energy operations, where hourly time steps are preferred. Large-scale water management and planning models mostly employ monthly time steps, but using monthly average energy prices underestimates hydropower revenue and overestimates pumping energy cost because these plants tend to operate during times with above- or below-average energy prices within any month. The approach developed here uses hourly varying prices depending on the percent of monthly operating hours. This paper examines an approach that approximately incorporates hourly energy price variations for hydropower and pumping into large-scale monthly time-step water system model operations without affecting water delivery results. Results from including hourly varying energy prices in a large-scale monthly water supply model of California (CALVIN) are presented. CALVIN is a hydroeconomic linear programming optimization model that allocates water to agricultural and urban users with an objective to minimize total scarcity costs, operating costs, and hydropower revenue loss. Thirteen hydropower plants are modeled with hourly varying prices, and their revenue increased by 25 to 58% compared to revenue calculated with monthly average constant energy prices. Hydropower revenue improvements are greater in critically dry years. For pumping plants modeled with hourly varying prices, the energy use cost decreased by 10 to 59%. This study improves system representation and results for large-scale modeling.

Economic Model-Predictive Control of Building Heating Systems Using Backbone Energy System Modelling Framework

Accessing the demand-side management potential of the residential heating sector requires sophisticated control capable of predicting buildings’ response to changes in heating and cooling power, e.g., model-predictive control. However, while studies exploring its impacts both for individual buildings as well as energy markets exist, building-level control in large-scale energy system models has not been properly examined. In this work, we demonstrate the feasibility of the open-source energy system modelling framework Backbone for simplified model-predictive control of buildings, helping address the above-mentioned research gap. Hourly rolling horizon optimisations were performed to minimise the costs of flexible heating and cooling electricity consumption for a modern Finnish detached house and an apartment block with ground-to-water heat pump systems for the years 2015–2022. Compared to a baseline using a constant electricity price signal, optimisation with hourly spot electricity market prices resulted in 3.1–17.5% yearly cost savings depending on the simulated year, agreeing with comparable literature. Furthermore, the length of the optimisation horizon was not found to have a significant impact on the results beyond 36 h. Overall, the simplified model-predictive control was observed to behave rationally, lending credence to the integration of simplified building models within large-scale energy system modelling frameworks.

Model reduction for second-order systems with inhomogeneous initial conditions

In this paper, we consider the problem of finding surrogate models for large-scale second-order linear time-invariant systems with inhomogeneous initial conditions. For this class of systems, the superposition principle allows us to decompose the system behavior into three independent components. The first behavior corresponds to the transfer between the input and output having zero initial conditions. In contrast, the other two correspond to the transfer between the initial position or the initial velocity and the output when no input is applied. Based on this superposition of systems, our goal is to propose model reduction schemes that allow to preserve the second-order structure in the surrogate models. To this aim, we introduce tailored second-order Gramians for each system component and compute them numerically, solving Lyapunov equations. As a consequence, two methodologies are proposed. The first one consists in reducing each of the components independently using a suitable balanced truncation procedure. The sum of these reduced systems provides an approximation of the original system. This methodology allows flexibility on the order of the reduced-order model. The second proposed methodology consists in extracting the dominant subspaces from the sum of Gramians to build the projection matrices leading to a surrogate model. Additionally, we discuss error bounds for the overall output approximation. Finally, the proposed methods are illustrated by means of benchmark problems.

A Redesign Decision Model for Large-Scale Complex Sustainment-Dominated Systems

This article presents a fuzzy, multiattribute decision-making method to assist managers in making more informed technology refresh planning decisions; especially when evaluating large-scale complex sustainment-dominated systems. These types of systems have inherently long operational lives, thereby incurring multiple technology design refreshes throughout their extensive lifecycles. Strategically planning for these technology refreshes presents a significant engineering, business, and logistical challenge. Existing refresh planning models are limited as they do not consider a systems’ view when forming recommendations, which can lead to suboptimal decisions. The mathematical models developed in this article are the foundation of the fuzzy, multiattribute decision-making method that allows engineering managers to use a systems’ thinking approach to evaluate competing technology refresh options. When applied to multidisciplinary projects, the fuzzy, multiattribute decision-making method evaluates several competing and complementary redesign drivers, leading to more informed systems refresh recommendations.

Global Temperature Projections from a Statistical Energy Balance Model Using Multiple Sources of Historical Data

Abstract This paper estimates a two-component energy balance model as a linear state-space system (EBM-SS model) using historical data. It is a joint model for the temperature in the mixed layer, the temperature in the deep ocean layer, and radiative forcing. The EBM-SS model allows for the modeling of nonstationarity in forcing and the incorporation of multiple data sources for the unobserved processes. We estimate the EBM-SS model using historical datasets at the global level for the period 1955–2020 by maximum likelihood. We show in the empirical estimation and in simulations that using multiple data sources for the unobserved processes reduces parameter estimation uncertainty. When fitting the EBM-SS model to six observational global mean surface temperature (GMST) anomaly series, the GMST projections under representative concentration pathway scenarios are comparable to those from Coupled Model Intercomparison Project models. The results show that a simple statistical climate model estimated on the historical period can produce GMST projections compatible with output from large-scale Earth system models. Significance Statement We develop a statistical model to understand Earth’s energy balance and how it impacts temperature across the planet’s surface and deep oceans. Unlike previous approaches, ours is fully statistical. This means that we use maximum likelihood to calculate the estimates and evaluate the level of uncertainty in the model’s parameters. By applying the model to historical data from 1955 to 2020, we are able to make predictions about the average global surface temperature that are consistent with those from the Coupled Model Intercomparison Project. Our findings support current predictions about global temperatures using a straightforward statistical climate model, grounded in historical data.

(Invited) An Industrial Perspective on Electrochemistry and the Energy Transition

As wind and solar become an increasingly larger share of primary energy, the use of electrochemical storage and conversions is growing. Traditionally, carbon-based fuels such as oil, coal and natural gas have been globally traded and served as energy storage media for the power and transportation sectors. With the growth of lower-carbon energy technologies, particularly wind and solar power, effective use of renewable electrons requires high-performing, cost-effective solutions for storage and distribution services that are analogous to traditional fuels. Electrochemical energy storage technologies are increasingly used for a range of applications from kW to GW scales, with this deployment momentum built from improved performance and declining costs.This talk will address where multiple types of storage exist in the historical & current energy system, their scales, and the roles of storage in the emerging energy transition from the perspective of an international energy company. Our energy storage and conversion research & development over the past decade will also be discussed, with a focus on current and emerging electrochemical systems designed for use in mobility, the power sector, and industry. Systems of active research include metal anodes used with high voltage cathodes and high energy density stationary batteries. This work has been driven by business challenges, with a range of modeling approaches used to generate insights that complement theory & experiment. Techniques include large-scale energy system modeling, modeling of power market operations, technoeconomic analyses to guide cost & performance targets of new technologies, and new ways to capture and predict physical phenomena that underpin device life and performance. Finally, commercial operation examples of energy storage operation will be provided, along with challenges still to be resolved through improved system understanding across scales.

Automation of Strategic Data Prioritization in System Model Calibration: Sensor Placement

Model calibration is challenging for large-scale system models with a great number of variables. Existing approaches to partitioning system models and prioritizing data acquisition rely on heuristics rather than formal treatments. The sensor placement problem in physical dynamic systems points to a promising avenue for formalizing data acquisition priorities, which addresses the following question for system models: With the model at hand and pre-existing data availability on a subset of model variables, what are the (next) k model variables that would bring the largest utility to model calibration, once their data are acquired? In this study, we formalize this problem as a combinatorial optimization and adapt two solutions, the information-entropy approach and the miss-probability approach, from physical dynamic systems to system models in management sciences. Next, based on the idea of the data availability partition, we develop a third solution. The new approach can be understood from the entropy perspective and is embedded in the theoretical framework for the evaluation of side information. Our solution applies to system models of all topologies: analytical results of the optimal placement are derived for binary/multinary trees; for general (directed) tree structures, an algorithm to determine the optimal placement is devised, whose complexity is upper-bounded by [Formula: see text] for an n-variable system; for arbitrary model topologies with the presence of loops, sequential-optimal and simulated-annealing schemes are formulated. Three approaches are compared on a validating example; our solution outperforms the two alternatives. Application on a multicompartment system demonstrates the toolkit’s practical use. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0128 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0128 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Software/Code for "Automation of Strategic Data Prioritization in System Model Calibration: Sensor Placement"

Model calibration is challenging for large-scale system models with a great number of variables. Existing approaches to partitioning system models and prioritizing data acquisition rely on heuristics rather than formal treatments. The sensor placement problem in physical dynamic systems points to a promising avenue for formalizing data acquisition priorities, which addresses the following question for system models: With the model at hand and pre-existing data availability on a subset of model variables, what are the (next) k model variables that would bring the largest utility to model cali-bration, once their data are acquired? In this study, we formalize this problem as a com-binatorial optimization and adapt two solutions, the information-entropy approach and the miss-probability approach, from physical dynamic systems to system models in management sciences. Next, based on the idea of the data availability partition, we develop a third solution. The new approach can be understood from the entropy per-spective and is embedded in the theoretical framework for the evaluation of side infor-mation. Our solution applies to system models of all topologies: analytical results of the optimal placement are derived for binary/multinary trees; for general (directed) tree structures, an algorithm to determine the optimal placement is devised, whose complex-ity is upper-bounded by O(nlog2(n))for an n-variable system; for arbitrary model topolo-gies with the presence of loops, sequential-optimal and simulated-annealing schemes are formulated. Three approaches are compared on a validating example; our solution outperforms the two alternatives. Application on a multicompartment system demon-strates the toolkit’s practical use.

Nonlinear coupling vibration analyses of large-scale wind turbine system

With the development of wind energy, the unit capacity of wind turbine is becoming larger and the height of the support tower is getting higher. Limited by the transport conditions, the diameter of the tubular steel tower cannot further increase with the increase of the tower height, which results in the lower natural frequencies of the tower. The higher and more slender wind turbine towers are more sensitive to the external excitation and many tower collapses have occurred in recent years because of the interplay with the longer rotor blades. A 2 MW wind turbine system with a 120 m full steel tubular tower is taken as an example in this study to research the nonlinear coupling vibration mechanism under the normal operation case and the emergency shut-down case. An integrated model of large-scale wind turbine system including the tower, blades, hub, and nacelle is established by the open-source software FAST to study its nonlinear interaction vibration mechanism. Under the normal operation load case, the acceleration response of the steel wind turbine tower is greatly affected by the rotational frequency of the rotor. The maximum accelerations in the fore-aft and side-side directions both appear around the middle-upper height of the tower. Under the emergency shut-down load case, the maximum fore-aft acceleration response appears at the top of the tower, but the maximum side-side response still appears around the middle-upper height of the tower. The first-order vibration mode plays a dominant role in the top fore-aft acceleration and the second-order vibration mode has great contribution to the side-side acceleration under the emergency shut-down load case. The numerical results of this study can provide insight into the vibration control mechanism of the full steel tower.