Bryan Eisenhower

Uncertainty and sensitivity decomposition of building energy models

As building energy modelling becomes more sophisticated, the amount of user input and the number of parameters used to define the models continue to grow. There are numerous sources of uncertainty in these parameters, especially when the modelling process is being performed before construction and commissioning. Past efforts to perform sensitivity and uncertainty analysis have focused on tens of parameters, while in this work, we increase the size of analysis by two orders of magnitude (by studying the influence of about 1000 parameters). We extend traditional sensitivity analysis in order to decompose the pathway as uncertainty flows through the dynamics, which identifies which internal or intermediate processes transmit the most uncertainty to the final output. We present these results as a method that is applicable to many different modelling tools, and demonstrate its applicability on an example EnergyPlus model.

Passive Control of Limit Cycle Oscillations in a Thermoacoustic System Using Asymmetry

In this paper we investigate oscillations of a dynamical system containing passive dynamics driven by a positive feedback and how spatial characteristics (i.e., symmetry) affect the amplitude and stability of its nominal limit cycling response. The physical motivation of this problem is thermoacoustic dynamics in a gas turbine combustor. The spatial domain is periodic (passive annular acoustics) which are driven by heat released from a combustion process, and with sufficient driving through this nonlinear feedback a limit cycle is produced which is exhibited by a traveling acoustic wave around this annulus. We show that this response can be controlled passively by spatial perturbation in the symmetry of acoustic parameters. We find the critical parameter values that affect this oscillation, study the bifurcation properties, and subsequently use harmonic balance and temporal averaging to characterize periodic solutions and their stability. In all of these cases, we carry a parameter associated with the spatial symmetry of the acoustics and investigate how this symmetry affects the system response. The contribution of this paper is a unique analysis of a particular physical phenomena, as well as illustrating the equivalence of different nonlinear analysis tools for this analysis. DOI: 10.1115/1.2745399

A mechanism for energy transfer leading to conformation change in networked nonlinear systems

Understanding mechanisms for conformation change in large networks of biological oscillators leads to comprehension of robustness notions in generic large interconnected dynamical systems. Biological systems are known to be extremely robust to most environmental perturbation while in certain situations they embrace external influence to carry out a particular task. In light of this, the connection with networked or distributed control systems becomes clear. In this paper, we study the dynamical properties of energy transfer through a macromolecule undergoing conformation change. We use a series of dynamical systems tools to identify energy pathways in the system that enable conformation change. We find that during internal resonance, a certain funneling structure appears which channels energy in a manner that enables this conformation change to occur.

Uncertainty in the energy dynamics of commercial office buildings

Whole-building energy models take information about the structure of a building, its equipment (electrical loads, lights, conditioning equipment, etc.), and disturbances (people, weather) and predict its year long comfort and energy performance. Both commercial and freely available tools are available for performing these time-domain simulations, which are used for design trade studies and more frequently to check for energy consumption and comfort compliance. These models require hundreds of assumptions as input when it comes to parameterizing the building model. Previous studies have investigated how predictions are influenced by these assumptions and which of the parameters are critical to year-long calculations. In this paper we extend this approach to investigate how parametric uncertainty influences uncertainty in the energy dynamics within a building. We provide a case study that investigates an office building by extracting dynamic information out of an EnergyPlus model, and supplies this information to an automatically generated analytical thermal network model. We conclude with a control-oriented frequency-based robustness assessment as well as a study of how uncertainty influences the network structure of the building by investigating the spectral gap of its graph Laplacian.

Actuation requirements in high dimensional oscillator systems

Understanding actuation needs for re- conformation processes in high dimensional multi-stable systems is key to efficient nonlinear control design. Many solitary systems exhibit multiple equilibria and control of these systems when networked with others becomes a challenging task. In this paper we study a networked model in which each single entity contains multiple equilibria and a operational objective is to transition the entire coupled system from one equilibrium to another. We show that after a series of coordinate transformations, the structure of the system and mechanisms for internal resonance leading to this behavior become clear. We also characterize the amount of energy needed for such conformation change (the activation energy) both through numerical simulation and perturbation techniques. We find that unlike traditional transition state theories, the activation energy is a function of the spatial structure of such energy (it is not a constant number). We find that a reduced order model which results from averaging accurately predicts this activation energy in a very concise way.

Extracting Dynamic Information From Whole-Building Energy Models

Whole-building energy models are used in practice to predict energy and comfort for an entire building given its architectural and built state, external stimuli from weather, and internal behavior of both the equipment and occupants of the building. There exists both open source and commercial software for simulating such cases for an entire year at sub-hourly reporting intervals. Unfortunately, the dynamics of the building are masked in assumptions included in the numerical routines that are often intertwined within the thermal physics. Because of this, control-oriented analysis is limited to performing exhaustive time-based simulations. In this paper, we describe a method to analytically extract the dynamics from a whole-building energy simulator for the purpose of control and dynamical systems analysis. In this way, the function of the energy simulator is only a user interface and a means to organize information inherent in the dynamics (capacitances, interaction between elements of the building, etc.). We provide a test case on a medium office building and illustrate some of its control-oriented dynamic properties using EnergyPlus as the simulator.Copyright

Computational Modeling and Analysis of Multiple Steady States in Vapor Compression Systems

In this paper, we present a well-posed two-point boundary value problem framework for computing, via continuation, the steady states of interconnected vapor compression systems. We illustrate the ease and utility of our approach by employing the path following software AUTO to compute steady solutions of an experimental air-to-water heat pump that uses CO 2 as a refrigerant. We validate some of the computational solutions against the experimental data and carry out continuation and bifurcation analysis in external parameters of practical interest. The results of these computations show that multiple and qualitatively distinct distributed steady-state solutions can arise for the problem, and that our approach provides for a simpler alternative to the much harder problem of dynamic simulation.

Modeling and analysis of bistable behavior in a transcritical heat pump

Effective marketing motivates this control study to understand the multiplicity of stable solutions in a transcritical heat pump where in prototype units two steady states exist (very efficient, and inefficient). Control oriented modelling, originating from first principles highlights the state-dependent heat transfer coefficient in the evaporator dynamics as a contributing cause to this bistable phenomena. Specifically, the bilinear nature of the controlled gas cooler and its coupling to the dynamic nonlinearity in the evaporator induces a system-wide bifurcation in the equilibrium conditions. Model results are presented to illustrate this, along with steady-state and dynamic data to confirm the accuracy of the model.