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DOE OSTI2022

Kinetic theory of particle-in-cell simulation plasma and the ensemble averaging technique

Abstract We derive the kinetic theory of fluctuations in physically and numerically stable particle-in-cell (PIC) simulations of electrostatic plasmas. The starting point is the single-time correlation at the start of the simulation between the statistical fluctuations of the weighted densities of macroparticle centers in the plasma particle phase-space. The fluctuations are associated with different initial conditions, typically due to the random initial conditions (in velocity space) of the macroparticles/simulation plasma, assigned according to their initial distribution of probability. The single-time correlations at all time steps and in each spatial grid cell are then determined from the Laplace–Fourier transforms of the discretized Klimontovich-like equation for the macroparticles and Maxwell’s equations for the fields, as computed by modern PIC codes. We recover the expressions for the electrostatic field and the plasma particle density fluctuation autocorrelation spectra as well as the kinetic equations describing the average evolution of PIC-simulated plasma particles, first derived by Langdon (1970b Proc. 4th Conf. Numerical Simulation of Plasmas ) using a test macroparticle approach perturbing a discretized Vlasovian plasma and then averaging the obtained physical quantity over the initial macroparticle velocity distribution. We generalize and extend these results to the modern algorithms in PIC codes using arbitrary macroparticle weights. Analytical estimates of statistical fluctuation amplitudes are derived as a function of the plasma simulation parameters, using the central limit theorem in the limit of a large number of macroparticles per cell. The theory is then used to analyze the ensemble averaging technique of PIC simulations where statistical averages are performed over ensembles of PIC simulations, modeling the same plasma physics problem but using different statistical realizations of the initial distribution functions of the macroparticles. This method is illustrated by linear Landau damping uncovering (from noise, which is usually considered numerical) the physical fluctuations driven by a single small amplitude electrostatic wave perturbing a PIC simulation plasma in equilibrium.

fluctuations correlations↗

DOE OSTI2020

Duty-Cycle Predictive Control of Quasi-Z-Source Modular Cascaded Converter Based Photovoltaic Power System

A duty-cycle predictive control is proposed for dc grid integration of front-end isolated quasi-Z-source modular cascaded converter (qZS-MCC) photovoltaic (PV) power system. The post-stage qZS half-bridge dc-dc converter deals with PV maximum power point tracking, dc grid integration, and dc-link voltage balance; whereas, the front-end isolation converters operate at a constant duty cycle of 50%. Thus, it saves control hardware resources while overcoming challenges from PV-panel voltage variations and dc-bus voltage limit. The proposed control uses the derived circuit model to predict the global active-state duty cycle for grid-connected current control and predict the shoot-through duty cycles for dc-link voltage balance, achieving a fast and accurate tracking target. The proposed control method has advantages of: i) eliminating weighting factors that exist in conventional model predictive control (MPC), ii) no sophisticated loop parameters design that exists in proportional-integral (PI) control, iii) operating at constant switching frequency that is different from the conventional MPC with variable switching frequency. Simulation and experimental tests are carried out to verify the effectiveness of the proposed control method and compare with the PI-based control system.

42 ENGINEERING↗

DOE OSTI2019

Adaptive Voltage Regulation for Solar Power Inverters on Distribution Systems

The most recent version of IEEE 1547 has incorporated four reactive power control modes, including constant power factor, voltage-reactive power (Volt-Var), active power-reactive power and constant reactive power. These modes are specified to be mutually exclusive, and they don’t include every smart inverter function proposed by industry collaboration. In earlier work, we found that Volt-Var settings could be optimized but were sensitive to changes in the normal grid voltage. This sensitivity can be mitigated by combining Volt-Var with dynamic reactive current (DRC), but neither DRC nor combined modes appear in IEEE 1547. One problem with Volt-Var is the default dead-band; it mitigates the sensitivity to setpoint, but also limits the effectiveness in managing voltage fluctuations. There has been continued interest in tuning smart inverter functions locally, and in combining central with local control, but this process still requires extensive simulations. The goal is to find a default inverter setting that will effectively mitigate voltage fluctuations even as grid conditions change. It must be compatible with the current version of IEEE 1547. It should also be compatible with advanced control methods when available. Otherwise, it should not require communications, detailed engineering studies or field commissioning of custom settings. This would facilitate the integration of distributed solar in larger amounts. Adaptive voltage regulation (AVR) is a Volt-Var implementation, but with “autonomously adjusting” setpoint as described below Table 8 in IEEE 1547. Through simulation of a test system in OpenDSS, it was shown that AVR having a high gain and a time constant of 300 seconds could work well in any location. This mode and setting should be considered for a new universal default setting on smart inverters.

McDermott, Thomas E.↗

DOE OSTI2024

Robust Restoration From Cyber-Physical Attacks in Active Distribution Grids With Grid-Edge IBRs

The inverter-based resources (IBRs) have enabled the integration of renewable energy at the grid edge with enhanced control capabilities to support the reliable operation of power grids. Different control frameworks, such as hierarchical or distributed architecture, have been proposed with the expansion of cyber networks for real-time monitoring and control. This evolution of critical infrastructure into cyber-physical systems also brings more vulnerabilities for the broadened attack surfaces, and significantly increases the possibility of physical system failures or outages caused by cyberattacks. Among tremendous efforts in the defense-in-depth approach, it remains challenging to provide prompt detection and accurate location of attack entry points or paths. Therefore, the prevailing restoration framework may struggle to fully consider the cyber-physical interdependence, successfully isolate the compromised cyber and physical components, and safely recover the systems without the potential risks leading to secondary outages. This paper is motivated to develop a cyber-physical restoration framework for distribution grids to recover from cyber attacks by harnessing grid-edge IBRs. The framework is first built on the operational guidelines of IBRs considering the compromised cyber layer. Then, an ambiguity set is established to represent the uncertainty of attack scenarios and their possibility levels. Next, a distributionally robust optimization model is developed to provide the optimal load restoration strategy across all scenarios. The effectiveness of the proposed model is demonstrated through various use cases on the modified IEEE 13-node and 123-node test systems. Finally, simulation results demonstrate the effectiveness and advancement of developed post-attack restoration strategies.

Cybersecurity↗

DOE OSTI2024

Advanced Laboratory and Field Arrays (ALFA)/Lab Collaboration Project (LCP) for Marine Energy (Final Scientific/Technical Report)

The objective of the Advanced Laboratory and Field Arrays (ALFA) project was to reduce the Levelized Cost of Energy (LCOE) of Marine and Hydrokinetic (MHK) energy by leveraging research, development, and testing capabilities at Oregon State University, University of Washington, and the University of Alaska, Fairbanks. ALFA is a project within the Pacific Marine Energy Center (PMEC; formerly NNMREC), a multi-institution entity with a diverse funding base that focuses on research and development for marine renewables. The ALFA project aimed to accelerate the development of next-generation arrays of wave energy conversion (WEC) and tidal energy conversion (TEC) devices through a suite of field-focused R&D activities spanning a broad range of strategic opportunity areas identified in the Funding Opportunity Announcement: • Device and/or array operation and maintenance (O&M) logistics development; • High-fidelity resource characterization and/or modeling technique development and validation; • Array-specific component technology development (e.g. moorings and foundations, transmission, and other offshore grid components); • Array performance testing and evaluation; and • Novel cost-effective environmental monitoring techniques and instrumentation testing and evaluation. The objective of the Lab Collaboration Project (LCP) was to accelerate the development of next-generation marine energy conversion systems. The LCP aimed to achieve these project objectives in collaboration with the national laboratories by: • Developing concept generation and assessment tools; • Improving access to existing testing resources; • Validating collision risk models between fish and turbines; and • Advancing analysis and simulation capabilities for wave-WEC interactions and PTO analysis in nonlinear ocean waves. The ALFA portion of the project was comprised of six overarching technical tasks: • Task 1: Debris Modeling, Detection and Mitigation; • Task 2: Autonomous Monitoring & Intervention; • Task 3: Resource Characterization for Extreme Conditions; • Task 4: Robust Models for Design of Offshore Anchoring and Mooring Systems; • Task 5: Performance Enhancement for Marine Energy Converter (MEC) Arrays; and • Task 6: Evaluating Sampling Techniques for MHK Biological Monitoring. The LCP was divided into four overarching technical tasks: • Task 7: Project Management and Reporting • Task 8: Novel Design and Assessment Methodologies for Wave Energy Converter Design (Wave- SPARC) • Task 9: Testing Access for Commercial Marine Renewable Energy Technology Developers • Task 10: Quantifying Collision Risk for Fish and Turbines • Task 11: Nonlinear Ocean Waves and PTO Control Strategy Each ALFA/LCP task listed above functioned as a separate and discreet project. A final Technical Report was written for each individual task and these reports were uploaded to OSTI, after receiving DOE approval. The following document is a compilation of each of these final, approved reports arranged as individual chapters.

13 HYDRO ENERGY↗

NASA NTRS2013

Verification and Validation Studies for the LAVA CFD Solver

The verification and validation of the Launch Ascent and Vehicle Aerodynamics (LAVA) computational fluid dynamics (CFD) solver is presented. A modern strategy for verification and validation is described incorporating verification tests, validation benchmarks, continuous integration and version control methods for automated testing in a collaborative development environment. The purpose of the approach is to integrate the verification and validation process into the development of the solver and improve productivity. This paper uses the Method of Manufactured Solutions (MMS) for the verification of 2D Euler equations, 3D Navier-Stokes equations as well as turbulence models. A method for systematic refinement of unstructured grids is also presented. Verification using inviscid vortex propagation and flow over a flat plate is highlighted. Simulation results using laminar and turbulent flow past a NACA 0012 airfoil and ONERA M6 wing are validated against experimental and numerical data.

Validation↗

DOE OSTI2017

Uncertainty and Sensitivity Analysis of TREAT Transient Test #15

The U.S. Department of Energy (DOE) is preparing for the resumption of transient testing using the Transient Reactor Test Facility (TREAT) located at the Idaho National Laboratory (INL). In order to support the analysis of TREAT operation and experiment planning, the MAMMOTH reactor physics team has recently begun development of uncertainty and sensitivity analysis for the TREAT core simulated via MAMMOTH. MAMMOTH is a high-fidelity three-dimensional transient multi-physics code developed at INL under the DOE-NE Advanced Modeling and Simulation program (NEAMS) [1]. This research is part of the development presenting some initial uncertainty and sensitivity analysis of TREAT Transient Test #15 [2]. In this summary, we employ the Sobol sampling strategy implemented in RAVEN [3] to efficiently perform the sensitivity and uncertainty analysis. The idea is using Sobol functional decomposition with generalized polynomial chaos (gPC) expansions to estimate the responses of interest [4]. The gPC coefficients are then computed via the spectral projection method with sparse grid approach. In addition, this strategy includes evaluation of the second or higher order sensitivity indices, allowing the study of interactions between several input variables. The principal focus of this analysis is to quantify the uncertainties in the total power and maximum fuel temperatures with respect to uncertainties in the initial transient conditions, such as rated power, fuel temperature, graphite fuel density and control rod boron concentration. In addition, both the first order and second order time-dependent sensitivity indices are computed and analyzed. The results show that the interactions between initial control rod boron concentration and the rated power will contribute at most 1% to the total uncertainty of the power peak.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS2017

Global Gridded Crop Model Evaluation: Benchmarking, Skills, Deficiencies and Implications.

Crop models are increasingly used to simulate crop yields at the global scale, but so far there is no general framework on how to assess model performance. Here we evaluate the simulation results of 14 global gridded crop modeling groups that have contributed historic crop yield simulations for maize, wheat, rice and soybean to the Global Gridded Crop Model Intercomparison (GGCMI) of the Agricultural Model Intercomparison and Improvement Project (AgMIP). Simulation results are compared to reference data at global, national and grid cell scales and we evaluate model performance with respect to time series correlation, spatial correlation and mean bias. We find that global gridded crop models (GGCMs) show mixed skill in reproducing time series correlations or spatial patterns at the different spatial scales. Generally, maize, wheat and soybean simulations of many GGCMs are capable of reproducing larger parts of observed temporal variability (time series correlation coefficients (r) of up to 0.888 for maize, 0.673 for wheat and 0.643 for soybean at the global scale) but rice yield variability cannot be well reproduced by most models. Yield variability can be well reproduced for most major producing countries by many GGCMs and for all countries by at least some. A comparison with gridded yield data and a statistical analysis of the effects of weather variability on yield variability shows that the ensemble of GGCMs can explain more of the yield variability than an ensemble of regression models for maize and soybean, but not for wheat and rice. We identify future research needs in global gridded crop modeling and for all individual crop modeling groups. In the absence of a purely observation-based benchmark for model evaluation, we propose that the best performing crop model per crop and region establishes the benchmark for all others, and modelers are encouraged to investigate how crop model performance can be increased. We make our evaluation system accessible to all crop modelers so that other modeling groups can also test their model performance against the reference data and the GGCMI benchmark.

wheat↗

DOE OSTI2018

Optimal scheduling of isolated microgrid with an electric vehicle battery swapping station in multi-stakeholder scenarios: A bi-level programming approach via real-time pricing

In order to coordinate the scheduling problem between an isolated microgrid (IMG) and electric vehicle battery swapping stations (BSSs) in multi-stakeholder scenarios, a new bi-level optimal scheduling model is proposed for promoting the participation of BSSs in regulating the IMG economic operation. In this model, the upper-level sub-problem is formulated to minimize the IMG net costs, while the lower-level aims to maximize the profits of the BSS under real-time pricing environments determined by demand responses in the upper-level decision. To solve the model, a hybrid algorithm, called JAYA-BBA, is put forward by combining a real/integer-coded JAYA algorithm and the branch and bound algorithm (BBA), in which the JAYA and BBA are respectively employed to address the upper- and lower- level sub-problems, and the bi-level model is eventually solved through alternate iterations between the two levels. The simulation results on a microgrid test system verify the effectiveness and superiority of the presented approach.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2024

When should PIC simulations be applied to atmospheric pressure plasmas? Impact of correlation heating

Abstract Molecular dynamics simulations are used to test when the particle-in-cell (PIC) method applies to atmospheric pressure plasmas. It is found that PIC applies only when the plasma density and macroparticle weight are sufficiently small because of two effects associated with correlation heating. The first is the physical effect of disorder-induced heating (DIH). This occurs if the plasma density is large enough that a species (typically ions) is strongly correlated in the sense that the Coulomb coupling parameter exceeds one. In this situation, DIH causes ions to rapidly heat following ionization. PIC is not well suited to capture DIH because doing so requires using a macroparticle weight of one and a grid that well resolves the physical interparticle spacing. These criteria render PIC intractable for macroscale domains. The second effect is a numerical error due to artificial correlation heating (ACH). ACH is like DIH in that it is caused by the Coulomb repulsion between particles, but differs in that it is a numerical effect caused by a macroparticle weight larger than one. Like DIH, it is associated with strong correlations. However, here the macroparticle coupling strength is found to scale as Γ w 2 / 3 , where Γ is the physical coupling strength and w is the macroparticle weight. So even if the physical coupling strength of a species is small, as is expected for electrons in atmospheric pressure plasmas, a sufficiently large macroparticle weight can cause the macroparticles to be strongly coupled and therefore heat due to ACH. Furthermore, it is shown that simulations in reduced dimensions exacerbate these issues.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1998

Tropical Oceanic Precipitation Processes over Warm Pool: 2D and 3D Cloud Resolving Model Simulations

Rainfall is a key link in the hydrologic cycle as well as the primary heat source for the atmosphere, The vertical distribution of convective latent-heat release modulates the large-scale circulations of the tropics, Furthermore, changes in the moisture distribution at middle and upper levels of the troposphere can affect cloud distributions and cloud liquid water and ice contents. How the incoming solar and outgoing longwave radiation respond to these changes in clouds is a major factor in assessing climate change. Present large-scale weather and climate models simulate cloud processes only crudely, reducing confidence in their predictions on both global and regional scales. One of the most promising methods to test physical parameterizations used in General Circulation Models (GCMS) and climate models is to use field observations together with Cloud Resolving Models (CRMs). The CRMs use more sophisticated and physically realistic parameterizations of cloud microphysical processes, and allow for their complex interactions with solar and infrared radiative transfer processes. The CRMs can reasonably well resolve the evolution, structure, and life cycles of individual clouds and cloud systems, The major objective of this paper is to investigate the latent heating, moisture and momenti,im budgets associated with several convective systems developed during the TOGA COARE IFA - westerly wind burst event (late December, 1992). The tool for this study is the Goddard Cumulus Ensemble (CCE) model which includes a 3-class ice-phase microphysical scheme, The model domain contains 256 x 256 grid points (using 2 km resolution) in the horizontal and 38 grid points (to a depth of 22 km depth) in the vertical, The 2D domain has 1024 grid points. The simulations are performed over a 7 day time period. We will examine (1) the precipitation processes (i.e., condensation/evaporation) and their interaction with warm pool; (2) the heating and moisture budgets in the convective and stratiform regions; (3) the cloud (upward-downward) mass fluxes in convective and stratiform regions; (4) characteristics of clouds (such as cloud size, updraft intensity and cloud lifetime) and the comparison of clouds with Radar observations. Differences and similarities in organization of convection between simulated 2D and 3D cloud systems. Preliminary results indicated that there is major differences between 2D and 3D simulated stratiform rainfall amount and convective updraft and downdraft mass fluxes.

Tao, W.- K.↗

DOE OSTI2024

A Shock Stabilization of the HLLC Riemann Solver for the Carbuncle Instability

The HLLC approximate Riemann solver improves upon the HLL Riemann solver by resolving contact discontinuities. This is a particularly desirable property for multi-material codes in which problems usually contain material interfaces. However, the HLLC solver is known to suffer from the carbuncle phenomenon, a numerical instability most apparent at grid-aligned shocks in multi-dimensional simulations. Many problems of interest, including high energy-density physics applications, require the accurate resolution of both material interfaces and hydrodynamic shocks. A variety of methods have been developed to cure this instability, with varying degrees of complexity. The objective of this work is to describe a simple approach to modify the HLLC Riemann solver and prevent the carbuncle instability. Here, the method is then demonstrated for assorted two-dimensional test problems known to exhibit the shock instability. The performance of the new solver is compared with that of the standard HLL and HLLC Riemann solvers.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

A Model-Reference Adaptive Direct-Power Control Scheme for Grid-Interactive Inverters

This paper develops an adaptive direct power control scheme for grid-interactive inverters while the control parameters are adaptively adjusted as the grid and filter parameters vary under different conditions. To demonstrate the efficacy and robustness of the adaptive operation, the performance of the adaptive controller is compared with a typical direct power controller by estimating the filter and grid impedances using a model reference parameter estimation technique with small signal injection. The simulation results verify that the developed methodology can track the reference power setpoints under output circuit parameter uncertainties while the typical design leads to instability. To improve the performance of the adaptive technique and eliminate the need for filter parameter estimation, a Lyapunov stability criterion-based model-reference adaptive direct power controller is designed to track the filter impedance. The developed method was tested using MATLAB/Simulink software to demonstrate the effectiveness of the proposed method. The results verify that adaptively tuning the control parameter can still maintain stable operation if the control gains are poorly selected while applying the classical method leads to abnormal operation or instability.

Gursoy, Mehmetcan↗

DOE OSTI2025

BOPTest As a Platform for Building Controls and Grid-Interactive Buildings Workforce Training

Building automation and controls are becoming increasingly complex with the emergence of Grid Integrated Efficient Buildings (GEBs) as well as new highly efficient sequences of operation and data-driven control schemes. However, there remains a significant gap in hands-on training opportunities for building operators and technicians to gain practical experience with advanced control systems in a low-risk environment. This paper presents BOPTEST (Building Optimization Performance Test) as a suitable platform for workforce training in building controls and GEB technologies. BOPTEST provides a suite of standardized building simulation test cases with a REST API, real-time control interfaces through BACnet, semantic models connecting users to building data, and built-in calculation of control metrics and performance indicators. The platform enables trainees to interact with virtual buildings using industry-standard protocols while learning how to implement and innovate control strategies. The training platform is designed to offer a structured and interactive learning experience for building engineers, helping them effectively develop, learn, and retain skills in fault identification, troubleshooting, and correction. The workflow is divided into three main phases: 1) Setup, 2) Exercise, and 3) Review, each comprising specific activities performed by either the instructor or the student. Initial pilot training sessions have yielded positive feedback from instructors and participants and demonstrates that BOPTEST effectively fills an industry need for a low-risk training resource via simulation of real building control systems, allowing trainees to gain practical experience before working in the field. The platform's ability to provide immediate performance feedback while maintaining familiar industry interfaces makes it particularly suitable for workforce development programs. This work provides a replicable model for leveraging building simulation in control education and training.

Paul, Lazlo↗

DOE OSTI2021

LANL Institutional Computing Highlight: Local Time-Stepping in Global to Regional Ocean Modeling (Annual Report) [Slides]

Multi-resolution global ocean simulations are possible with the Model for Prediction Across Scales-Ocean (MPAS-Ocean), although the model is currently constrained to a uniform time step. The time step is determined by the size of the smallest cell in the grid, according to the CFL condition. To overcome this issue, a local time stepping (LTS) scheme has been designed for MPAS-Ocean. We have made progress on implementing the LTS scheme, as well as quantitative results and performance tests.

58 GEOSCIENCES↗

DOE OSTI2025

Optimized V1G and V2G Electric Vehicle Fleet Management and Grid Transaction at Marine Corps Air Station Miramar in San Diego, CA

The overall technical goal of the project was to demonstrate an all-electric bi-directional non-tactical fleet at Marine Corps Air Station (MCAS) Miramar that was integrated and controlled with other distributed energy resources (DERs) (i.e., PV, stationary battery, and building loads) to provide resilience to critical electric loads in the event of grid outages, to minimize charging costs, and to provide economic energy resources to electricity markets. In this project, the specific, technical objectives were: 1. Demonstrate that bi-directional electric vehicles can provide critical complementary services to fixed storage batteries in microgrid applications while performing function as non-tactical vehicles. 2. Demonstrate participation of bi-directional (V2G) and unidirectional (V1G) PEVs for demand management and minimization of charging costs. 3. Demonstrate integration of multiple DERs for grid service participation. US Marine Corps Air Station (MCAS) Miramar in San Diego was the site of this electric vehicle-to-microgrid-utility grid test and demonstration project. Existing microgrid assets in this study included (1) a public works building; (2) a 30-kW rooftop photovoltaic (PV) system and (3) a separate 250 kW carport PV system. In this project, six bi-directional V2G vans were located at the MCAS Miramar’s showcase building-scale microgrid to develop and test technical capabilities that V2G can provide in microgrid applications (e.g., cost reduction and resiliency). These resources provided aggregated demand management and simulated participation in current retail DR programs. The vehicles used in this demonstration were selected because they provided functionality that MCAS Miramar needed, 15 passenger transport and facilities work cargo carrying capacity, and bi-directional charging capability that the research project required. All vehicles in this study were manufactured and distributed by VIA Motors, Inc. There were six vehicles total and each was VIA’s VTRUX eREV V2G model, a modified General Motors Chevrolet 2500 2WD van. Three of the vans were configured as passenger vans and the other three were configured as cargo vans. Each van had an on-board bi-direcrtional inverter/charger, Bel Power Solutions model 350INVCHGT150-120-240-8G nominally rated at +/-15 kW. The VIA van’s charging connector follows the J1772 charging protocol. The bi-directional EVSEs demonstrated in this study were manufactured by Coritech, Inc. Each VGI-80-AC charging station enabled enhanced V2G charging capability to a Clipper Creek CS-100 charging module. The enhanced capabilities included ethernet communication following the SEP2.0 protocol with a distributed energy resource function set and an operator screen displaying real-time SOC, voltage, and current. The VGI-80-AC charging stations are classified as level 2 with a maximum current output of 80 A or effectively 19 kW. The VIA van’s onboard charger limited the charging and discharging power to 15 kW in each direction. A control computer was installed in the EWOC and connected to an existing monitor. The V2G control communication network was a completely stand-alone closed system that did not have any connection to any other networks on the base. A cybersecure remote communication connection was created with a cellular modem, firewall hardware, and a virtual private network configuration.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

BOPTEST as a Platform for Building Controls and Grid-Interactive Buildings Workforce Training

Paul, Lazlo↗

NASA NTRS1985

An Eigensystem Realization Algorithm (ERA) for modal parameter identification and model reduction

A method, called the Eigensystem Realization Algorithm (ERA), is developed for modal parameter identification and model reduction of dynamic systems from test data. A new approach is introduced in conjunction with the singular value decomposition technique to derive the basic formulation of minimum order realization which is an extended version of the Ho-Kalman algorithm. The basic formulation is then transformed into modal space for modal parameter identification. Two accuracy indicators are developed to quantitatively identify the system modes and noise modes. For illustration of the algorithm, examples are shown using simulation data and experimental data for a rectangular grid structure.

Juang, J. N.↗