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Multiscale modeling frameworks for
architecture - Designing the unseen and
invisible with PCM
Author names [AU]:
Billie Faircloth, Ryan Welch, Martin Tamke, Paul Nicholas, Phil
Ayres, Yuliya Sinke, Mette Ramsgaard Thomsen.
Abstract:
Multiscale design and analysis models promise a robust,
multi-method, multi-disciplinary approach, but at present, have
limited application during the architectural design process. To explore
the use of multiscale models in architecture, we develop a calibrated
modeling and simulation platform for the design and analysis of a
prototypical envelope made of phase change materials (PCM). The
model is mechanistic in nature, incorporates material-scale, and
precinct scale-attributes, and supports the design of two and three
dimensional PCM geometries informed by heat transfer phenomena.
PCM behavior, in solid and liquid states, dominates the visual and
numerical evaluation of the multiscale model. Model calibration is
demonstrated using real-time data gathered from the prototype. Model
extensibility is demonstrated when it is used by designers to predict
the behavior of alternate envelope options. Given the dominance of
PCM behavior in this multiscale model, multiple linear regression is
applied to data collected from the physical prototype in order to
demonstrate an alternate method for predicting the melting and
solidification of PCM.
1. Introduction
Our work begins with the following observation: Architects miss the interrelatedness between
scales and methods when we operate within the confines of our profession’s modeling
practices. When modelers expand the boundary of the system they are studying, first by
extending modeling authorship to other disciplines, then by adjusting the scales accounted for
in their models, and finally by engaging a full definition of time, they may discover the
potential for trans-disciplinary, trans-scalar, and trans-temporal practices.
An architect often operates at the scale and resolution attributed to a single building, and
engages modeling practices to fully describe a building’s dimensions, material assemblies
and systems. With similar focus, a climatologist operates at the scale and resolution of one
single planet or region thereof, and for a given climate model, even the world’s largest
mega-city is not discernable in the resulting pattern of surface air temperatures. Resolution
silos are endemic to all professions’ modeling practices – from materials engineers and
physicists to urban ecologists. They are practical in one sense, as they uphold accepted
methods, system boundaries, and permit results to be reviewed and communicated internally
to their profession. However, in another sense, resolution silos signify entrenchment, and
inhibit the finding of phenomenal feedback loops between different scales of resolution, and
by extension, disciplinary modeling practices that could influence design decision making.
Should we pursue design practices that engage not only architecture but also materials, urban
ecology, regional-, and global-climate - practices where our disciplinary models recognize the
‘handshakes’ between scales and resolutions that make actionable these very real feedback
loops?
These questions are explored through a collaborative experiment conducted by
KieranTimberlake (KT, Philadelphia) and the Center for Information Technology in
Architecture (CITA, Copenhagen). We develop a modeling and simulation platform for a
geo-located building envelope system whose geometry and surface texture are informed by
regional and local climate, weather, and vegetation; and by the more enduring behavior of
selected materials attributes, and surrounding built context. The envelope system is chiefly
composed of bulk organic phase change paraffins; is an open, non-isolated thermodynamic
system, and is thus exposed to the transient behavior of its environment. To establish
dependencies across scales, we investigate the visual characteristics of melting and
solidification correlated to heat transfer across the envelope. The scope of our study is
situated in the domain of, and dependent upon the methods of several disciplines including
architecture, visual arts, physics, materials engineering, and ecology.
This paper contextualizes the experiment within the state-of-the-art; describes the data model
schema in-depth; demonstrates the model’s calibration, verification, and validation; and
demonstrates the model’s use by the transdisciplinary team. It also provides a critical review
of the results in association with the opportunities and limits of modeling material behavior,
as well as the challenges of establishing handshakes and feedback loops across different
scales and resolutions to support a focused design exercise at a conventional architectural
scale.
2. Background
2.1 Multiscale Models
The thermodynamics of architecture are normally modeled using heat-transfer equations for
conduction, convection and radiation that are selectively incorporated into two and
three-dimensional modeling platforms, and may be used to predict whole building energy use
(building energy models or BEMs), or to identify condensation planes in exterior walls 25.
Existing modeling platforms often require low-resolution abstractions of single building
geometry, removal of vegated building context, and representation of heat balance in wall
assemblies through conduction transfer functions, which are poorly suited to modeling
non-linear capacitive systems, such as thermal energy storage. In contrast, a multiscale,
multi-domain modeling platform for building energy modeling might restore building
context, account for vegetation, its species and seasonal dynamics, 3-dimensional geometry,
and 2-dimensional surface texture, and specific meso-scale, or micro-scale material attributes.
Several examples of multiscale models from other disciplines provide insight into the
motivation for and organization of such models: At the global and regional scale, climate
models aim to predict earth’s future climate trends, and identify the potential interplay
between factors that impact the earth’s climate system. These models have developed over
decades via the contribution of many teams, and are composed of a series of sub-models and
parameterizations that combine to produce results.2 At the urban scale CityGML, an
international standard for the representation and exchange of semantic 3D city and landscape
models, bridges domain boundaries by providing a core model with entities which are
relevant to many disciplines, and annotated with domain specific information 3. Within
CityGML semantic, geometric, topological, and appearance-related information can be
represented in up to five levels-of-detail of increasing thematic differentiation, geometric
accuracy and structural complexity. At the materials scale, multiscale models have been used
for designing scaffold structures for bone tissue regeneration 4 5. Bone adaptation is modeled
as a two-scale material distribution problem. At the macroscale, the model takes into account
the mechanical behavior of bone, while the microscale domain captures some of the
biologically based features of bone tissue growth. Materials engineers also apply multiscale
techniques to the mechanical properties of intermediate-sized solid state materials 6. These
models couple the effects described by three different levels of description: continuum
mechanics to model macroscopic conditions close to equilibrium, molecular dynamics to
thermal fluctuations and material decohesions, and quantum mechanics to model the tip of a
propagating crack.
At present, multiscale models have limited application in architecture. There are, however, a
small number of experimental projects such as Stressed Skins 7 and A Bridge Too Far 8 ,
which describe multiscale modeling frameworks for structural systems, panel elements and
metal materials. In both projects, the macro scale encompasses the resolution of global design
goals, overall geometric configurations, and a full-scale understanding of structural
performance. The meso scale considers the project at an assembly and sub-assembly level,
and is concerned with material behaviors tied to geometric transformation, detailing and
component-level tectonic expression. The micro scale is concerned with relevant material
characteristics at the most discretized level, and is informed through testing and modeling by
collaborating materials scientists. The multiscale modeling approach is then comprised of
mesh-based information transfer techniques which enable the information generated at each
of these markers to flow up and down across models and modeling scales.
From these examples we learn that multiscale, multi-domain models can characterize
underlying phenomena that span a large and hierarchically organised sequence of scales 1.
Rather than attempting to simplify these problems so that they can be represented within a
single framework or boundary, multiscale models utilise different frameworks for different
aspects of the problem and couple them together. The opportunities, efficiencies and different
domain couplings achievable through this modeling practice, are applied to many different
subjects and phenomena, with a rich array of approaches and applications.
2.2 PCM Behavior and Applications
Because of our team’s interest in applying a multiscale approach to architectural
thermodynamics, we began by identifying materials that exhibit an observable and visible
reaction to heat flow. These are a class of materials that visibly change color, shape or state
through thermal stimulus, and include thermochromic pigments as inks or dyes, shape
memory polymer resins, and phase change materials as organic paraffins 9. Our experiment is
based in phase change phenomena, and demonstrates the use, modeling and simulation of
liquid organic paraffin phase change materials (PCMs).
PCMs change state from solid to liquid at a specified temperature. They visually manifest as
opaque in the solid state, and transparent in the liquid state. When PCMs solidify and melt
they maintain their specified phase transition temperature, and absorb or release relatively
large amounts of energy to do so. PCMs are pre-formulated with transition temperatures, and
are described in technical literature by their transition temperature which can be anywhere
from -10 ℃ to 90 ℃. Technical data sheets also provide the phase transition curve, which is
routinely measured under steady-state conditions, and can be useful when considering the
application of PCMs in a particular climate or application. Working methods, and custom
encapsulation instructions for liquid PCM are generally not available.
PCMs are used predominantly in architecture for thermal energy storage, with several
applications focused on high performance building envelope systems, including masonry
rainscreen and curtain wall systems 10 11. PCMs are further integrated into roof, wall and
floor assemblies through building materials, such as plasterboard embedded with spherical
PCM microencapsulants 12 10. Applications for PCMs range widely from passive actuators for
air-vents which leverage the rate of expansion/contraction during solidification/melting, to
thermally activated concrete, where a relatively small volume of dispersed material
significantly changes the concrete’s heat storage capacity 13 14.
2.3 Modeling and Simulating PCM Behavior
PCM-based roof, wall and floor applications have been studied for several decades using
numerical models paired with physical, in-situ, instrumented prototypes 15–17. However, PCM
behavior during phase change remains difficult to predict, difficult to model, and thus persists
as a rich area of research with multiple experimental approaches from the fields of building
science, thermodynamics and materials engineering 18,19.
The chief modeling challenge is attributed to the inherent non-linear behavior at the
melting/solidification front, which is the boundary between liquid and solid PCM, where the
displacement rate is controlled by the latent heat lost or absorbed 20. Several different
approaches to the modeling and simulation of PCM phase change behavior were tested before
the enthalpy method was found to be the most suitable 21,22, 23. Though not entirely precise,
this method is increasingly used, and literature documents the simulation of PCM behavior in
geometries such as: spherical, cylindrical, packed bed, finned geometry, porous and fibrous
materials and slurry 20. Increasingly PCM studies rely solely on simulation, however, there is
low confidence in simulated results, as they are often not reproducible in an experimental
setup 15,24.
General conclusions about PCM behavior are often extrapolated from numerical and
experimental studies, which risk inappropriate or ineffective applications 20. The rate of
convection within encapsulated PCMs is, for instance, strongly sensitive to the geometry and
the size of the enclosure, as well as the viscosity and thermal conductivity of the material
itself 19. Thermal conductivity of the encapsulating material, the PCM solid–liquid density
and its conductivity influence the thermal behavior in important and counter-intuitive ways 24.
This interdependence of the behaviors is even more complex, when solar radiation, ambient
temperature or even seasonal differences are taken into account. The heat influx of solar is for
instance expected to be faster than by convection from the ambient air 14. The larger the
surface area to volume quotient, the more the influence of ambient air temperature. To
capture this complexity, inherent to the behavior and interaction of a PCM material with its
environment, in current state of the art simulation requires an immense effort.
Our motivation, however, differs from the scientific literature insofar as we are not interested
in conducting controlled experiments that isolate PCMs from external forces in order to build
a detailed understanding of their mesoscopic melting behavior. Rather, we are interested in
investigating how a broader set of environmental conditions, that occur at other scales, can be
brought to bear on these systems while still permitting models of them to have a sufficient
level of fidelity to allow designers to control temporal melting and solidification behavior
through a combination of form-making, material selection, siting and context.
3.0 Informal Experiments on Heat Flow in the Built
Environment
In order to identify the data model schema for our multiscale model, and the potential range
of scales incorporated therein, the team engaged a series of informal experiments and
workshops in Copenhagen, Denmark on the subject of heat flow and heat dissipation
phenomena in the built environment.
3.1 Heat Flow at the Precinct Scale and Experiments with Microclimates
The first experiment aimed to compute thermal difference at the urban/precinct scale in order
to determine the boundary of various microclimates according to surrounding building
materials, ground cover and vegetation. It also sought to reveal the degree to which designers
incorrectly draw these boundaries when they focus exclusively on building envelopes. Sixty
temperature sensors and fifteen temperature/rH sensors were used to perform a series of
interrelated measurements. The initial measurement required distributing sensors in a ∼300m
x 300m grid, whereas a subsequent measurement increased sensor density by distributing the
same 75 sensors in a ∼120m x 30m grid. The final measurement increased sensor density
again by further localizing 75 sensors into 5 smaller ∼3m x 3m grids. This concatenated series
of measurements exposed micro-climates, thermal gradients, and hence, zones of exchange
between warmer and cooler surfaces at increasingly smaller scales within in the same urban
region. Context features, such as trees and site walls, ground cover, surface color and texture
became increasingly relevant delimiters of thermal difference.
Figure 1:
An array of temperature and rH sensors distributed through a campus open space to expose
thermal difference across a seemingly homogeneous space. Copenhagen, DK.
3.2 Heat Flow at the Body Scale and Experiments with Small Thermodynamic
Systems
The second experiment aimed to directly design, form, measure and adjust small, open,
non-isolated thermodynamic systems with a ∼1000 in3 interior. Using foam materials,
prototypes were built in series over several days to meet multiple, often conflicting thermal
goals. The experiment revealed that within a relatively small volume, perturbed on its interior
by a cup of boiling water, and on its exterior by diurnal changes of temperature, relative
humidity, wind speed/direction and precipitation, thermal gradients arise, are manipulable,
can be differentiated, and sustained through varying approaches to construction logic26.
Considering both the first and second experiment, thermal difference was experienced across
relatively large and small spatial scales; heat flow configured according to context features;
and heat dissipated at differing time scales. To move the development of the modeling and
simulation platform forward, it was presumed to incorporate descriptive geometry,
heat-transfer physics, and associated methods of modeling and computation.
Figure 2; Small-scale, informal experiments forming, measuring and adjusting open,
non-isolated systems made of foam boards. Copenhagen, DK.
3.3 Heat Flow at the Material Scale and Experiments with PCMs
The thermal behavior of materials, including thermal energy storage, figure prominently in
both of the aforementioned informal experiments. Heat transfer phenomena, however,
remained unseen and invisible, apparent through methods such as graphing the change of
surface temperature over time. Given the tacit knowledge gap apparent in the technical
literature on PCMs, a third set of experiments selected material PCM attributes and behaviors
to characterize through small-scale, physical prototypes. The focus of these experiments was
on the thermal behavior of PCMs under transient, rather than steady-state conditions as a
proxy for building envelope behavior. Phase change attributes selected for further study
included change of volume, color, melting and solidifying processes and associated optical
properties.
One experiment sought to understand the expansion of PCM, and included the monitoring of
the movement of pistons in syringes filled with PCM under changing temperatures. Another
sought to understand the malleability of the solid-liquid phase transition front using metal
washers at select areas to increase the rate of conduction. And, another focused on the form
of the encapsulating material itself, and sought to discern optical qualities through varied
surface geometries and topologies (Figure3) These informal studies yielded behavioral
observations, verified or refuted assumptions, and informed the team’s capacity to design
with the behavior of PCM. They also permitted visual observation, and documentation of the
phase transition process, and the measurement of a prototype’s temperature at transition
(Figure 4, 5). Based upon this set of experiments the team confirmed that it was possible to
use the phase transition behavior of PCM as a visual proxy for observed, measured and
simulated heat transfer, and that their behavior coupled with the ambient environment (Figure
6) could be abstracted at the appropriate scale of resolution in a modeling platform.
Figure 3: Initial design hypothesis on different strategies for the formation of envelopes for
PCM
Figure 4: Small scale experiments investigating volume change, crystallization and influence
of vessel geometry on the transition of PCM.
Figure 5: Small-scale probes, exploring material, behaviour, effects and manufacturing
Figure 6: Prototyping with PCM E20D in rapidly vacuum formed skins.
4. Modeling and Simulation Platform
4.1 Overview
We develop a multiscale modeling and simulation platform for the prediction and
manipulation of PCM behavior in the presence of transient environmental conditions where
context features, at small and large scales, are model features. Our approach uses a full-scale
physical prototype coupled to a high-resolution, geometrically explicit heat transfer model
using sensors to provide continuous measurement of melting and solidification.
There are two key stages to this approach: The first is the development of a mechanistic
model based on a defined model data schema, where data collected through the continuous
measurement of physical prototype are used as a means of verification, calibration and
validation of simulated behavior against predefined geometries. This effort is understood as
constructing a model of
the behaviors under scrutiny. The second stage extends the
mechanistic model into a predictive model allowing performance simulation of proposed
geometries and orientations. This is understood as constructing a model for
supporting
generative design. Within this second stage we develop and test the efficacy of machine
learning in making more refined predictions based on recent histories of observed data. This
approach permits a team composed of designers, sculptors, materials engineers, and building
scientists - the majority of whom have no training in heat transfer calculations - to engage the
prototyping, modeling and simulation process; feedback via calibration, verification, and
validation routines to reorganize and redesign the facade system.
4.2 Physical Prototype and Test Bed
The full-scale prototype (Figure 7), located in the courtyard of the Royal Danish Academy of
Fine Arts, served as a test-bed where the complex behavior of PCMs could be examined for
selected encapsulation geometries under diurnal and seasonal conditions. The test bed siting
offered additional context features translatable into the modeling platform such as the
surrounding three story buildings and deciduous vegetation (oak).
The testbed consisted of twenty-three rhomboid-shaped PCM panels mounted vertically to a
frame measuring 1200 mm x 2000 mm x 2500 mm. Commercially available PCM from
Rubitherm® was selected by the team as the basis for the experiment. Each panel was
textured with one of five pattern types, all variations on a bidirectional sinusoidal or egg crate
pattern, in order to establish a range of potential material behaviors in-situ. Pattern variations
included spacing (frequency), depth (amplitude), and direction of peak (up, down, left, right),
resulting in differences in direct solar exposure and shelf-shading per time of day, as well as
more or less PCM per panel. Overall, these five panel types formed the basis for observing
rates of phase change and the visual cycling between transparency and opacity.
The panel encapsulation material was thermoformed PETG, which provided good visibility
(high transparency) and workability (forming and plastic welding). Liquid PCM was poured
into an encapsulating shell composed a thermoformed and non-thermoformed panel. Prior to
pouring, 10 of the 23 panels are wired with temperature sensors measuring internal
temperature, at 5 minute intervals.
Figure 7: Full Scale test bed with installed monitoring devices
A range data types were collected for six months, March through August 2017, which
permitted observation of diurnal and seasonal PCM behavior in relationship to geometry. In
this instance sources of data vary, and include:
●40 PCM panel temperature sensors, 4 each, internal to 10 sensored panels
●9 ambient temperature sensors, internal to the testbed itself
●A regional airport-based (KPH) weather station
●A local site-based weather station
●24/7 video monitoring of phase change
The data were captured locally and stored in cloud based platforms for further analysis and
used for calibration, validation and verification of the modeling and simulation platform.
4.3 Mechanistic Model Structure and Hierarchy
The modeling and simulation platform attempts to predict the behavior of the PCM testbed
under varying environmental conditions and calibrate predictions against observed behavior.
As an interactive tool, it allows exploration of various geometric forms and siting to guide
design iteration; imputation of various material properties to aid in PCM selection; and use of
historical or projected weather data to correlate findings with observations and make
predictions about future behavior. Based on the project goal of engaging in rapid geometry
iteration, Rhinoceros3D/Grasshopper was selected as a suitable design environment.
Grasshopper’s extensible framework also permitted the development of new components to
capture the simulation inputs, execution, and results visualization within a single design
environment. These components roughly divide into six modules: Climate, Context, Sensor,
Material, Geometry, Simulation, and Results (Figure 8).
Figure 8: Grasshopper components of mechanistic model
Climate
The climate module describes the ambient environmental conditions surrounding the physical
model, in terms of dry bulb temperature, wind speed, diffuse horizontal radiation, direct
normal radiation, and solar angle. For projective simulations, these data are sourced from the
typical meteorological year data of the local airport, while for simulations of current or recent
conditions, these data reference the local weather station adjacent to the apparatus and the
regional airport or imputation of any gaps in the data collected on site. Both sources are
accessed via Weather Underground 27,28. Hourly solar angles are determined based on site
latitude and longitude using NOAA’s calculation methodology and used as input for shading
and incident radiation calculations 29. In order to obtain diffuse and direct components of the
total horizontal radiation measured by the on-site weather station, the local sky conditions
from the regional airport were applied using the methodology established by Dervishi and
Mahdavi 30. As the run-time simulation requires sub-hourly inputs, these quantities are
linearly interpolated from available data and flagged according to best available source.
Context
The context module represents the geometry of neighboring structures and vegetation that
would potentially shade the physical model from direct or diffuse radiation, thereby reducing
the rate of PCM melting. Permanent structures are modeled as coarse mesh objects in
Rhinoceros3D using point-cloud survey data and defined as ordinary context objects with a
fixed transmissivity, typically of 0.0. Trees that experience seasonal changes in leaf density
are modeled from point-cloud data as simplified convex hulls of the canopy volume and
assigned a transmissivity schedule based on the expected gap fraction over the course of the
year. For linden trees on the selected project site, this was defined as 1.0 during the leaf-off
season (Oct-Mar) and 0.12 during the leaf-on season (Apr-Sep) 31. Taken together, the
climate and context modules constitute the inputs to the exterior boundary condition of the
PCM.
Sensor
The sensor module connects the mechanistic model to an array of Maxim 1-wire temperature
sensors that report in 5-minute intervals to KieranTimberlake’s Pointelist network 32. These
sensors are deployed in a 3 x 3 grid along the interior face of the PCM envelope and
represents the inputs to the interior boundary condition of the PCM in the neighborhood of
each panel. A second array of calibration sensors is embedded within the PCM medium of
each panel type at locations expected to have differential melting behavior due to location,
solar orientation, or thickness of material. The data collected by these sensors is calibrated
against the predicted behavior at corresponding locations. Numerical variances are captured
to aid in automated refinement of material and simulation properties using Grasshopper’s
evolutionary solver and depicted graphically as time-series line graphs to aid in identifying
systematic differences in predicted and actual behavior.
Material
The material module attempts to capture the thermodynamic properties of the phase change
materials considered for the study 33 and includes the heat of fusion, melting point range, and
liquid- and solid-state properties of density, heat capacity, thermal conductivity, and albedo.
To reduce the complexity of the run-time simulation, the enthalpy vs temperature profile is
presumed to be piecewise linear for the three phase regimes, and hysteresis has been
disregarded. Based on the published literature for the PCMs under consideration 29, the error
introduced by this simplification is well within the published accuracy of the sensors. This
has the added advantage of reducing the degrees of freedom for material calibration for
materials whose published thermodynamic properties may not be comprehensive. Solid- and
liquid-state albedo are not typically reported for such materials, so these quantities have been
determined through calibration.
Geometry
The geometry module translates the bounding surfaces of the encapsulated PCM form into a
series of finite elements and boundary conditions. The bounding surfaces may be modeled as
NURBs surfaces, and a bounding region and resolution selected for analysis. Based on the
selected region and resolution, a flattened triangulated mesh is automatically generated in the
principal plan of the PCM panel and projected onto the top and bottom surfaces to establish
mesh boundary conditions of consistent resolution and topology. This allows one to decouple
the arbitrary resolution of form generation from the selected resolution for analysis so that the
models sensitivity to finite element size can be calibrated separately. Each mesh face of the
exterior boundary takes input from the climate and context modules and pre-computes its
direct and diffuse shading coefficients for each hour of the year. As these inputs depend only
on quantities known in advance (orientation, context geometry, and solar angle) this frees the
run-time simulation from the burden of running expensive occlusion calculations.
From the set of interior and exterior boundary elements the geometry module generates a 3D
finite element mesh represented by a series of triangular extrusions that extend through the
depth of the panel and whose thickness is based on the selected resolution. In order to
maintain consistent mesh resolution where panel depth varies, some of the mesh faces may
collapse to form 4-face and 5-face triangular polyhedra. Neighbor-neighbor relations are
automatically generated so that at any point during the simulation, the heat flow between
neighboring elements may be computed and cached at each time step based on the local
temperature gradient and the area of their common face (Figure 9). This geometry remains
fixed during the simulation, as described in the Fixed Grid Method of 23. Hence, this approach
can be seen as a 3D generalization of the conduction finite difference method typically
applied to modeling PCM in building energy applications 34.
.
Figure 9: Exploded isometric view of instantaneous heat flow between neighboring finite
elements.
An important feature of PCM materials is that the diffusion rate of a local temperature
gradient cannot be calculated in a single step because the phase change regime introduces
non-linear behavior. Instead, the complete set of heat flows must be calculated at each
time-step and subsequently applied to each element, which - depending on its current phase -
may be variously applied to modifying its temperature, phase, or both. Hence storing the heat
flows independently permits parallelization of the run-time computation.
Simulation
The simulation module allows the user to select a date and time range and finite element
mesh to predict behavior of a panel or to calibrate its phase change behavior against sensor
data collected over the selected time period. This module may be initiated through a UI
dialog or may be run automatically in a headless mode to permit automated calibration of
material properties over multiple simulations. In both cases, a splash screen displays
simulation progress and run-time metrics. These include boundary conditions (interior and
exterior temperature, wind speed and direction, direct and diffuse solar radiation, data
source); features of the finite element model (minimum, average, and maximum values for
temperature and phase); and calibration metrics (variance between measured and predicted
values at each calibration sensor location) (Figure 10).
Figure 10: Simulation splash screen with calibration metrics
4.4 Machine Learning Prediction of Material Behavior
A multiple linear regression model of the observed behavior was developed as a complement
to the mechanistic model in order to determine near-term predictions of PCM behavior and
rankings of features that influence these predictions. The training data were drawn from the
weather station recordings of outside temperature and radiation, interior sensors temperature
readings, and readings from 11 sensors embedded in a single panel. At each timestep,
features vectors were created for the complete set of readings at 5-min, 20-min, and 60-min
prior, and prediction vectors were created for panel sensor readings at 5-min, 20-min, and
60-min forecasts. The model was trained using the Multiple Linear Regression model of the
SciKit learn python library using 3 days of data, and subsequently used to predict 5-min,
20-min, and 60-min running predictions over the following 7 days, for which empirical data
were also available. In this manner, the accuracy of the predictions could be assessed relative
to recordings that were outside of the original training sets.
Automated feature ranking was used to identify for each panel sensor, which data sources and
relatives time offsets had the greatest influence on 5-, 20- and 60- minute predictions. As the
varying panel depths and buoyancy effects tend to produce reproducible melting patterns, it
was anticipated that feature ranking may be able to identify sensors that are leading indicators
of melting - or solidifying - behavior.
5 Results
5.1 Verification of Mechanistic Model
Verification of the mechanistic model was conducted through qualitative visual inspection
and quantitative numerical analysis of time-series predictions, both of which utilized the
simulation interface. Visual inspection of the model was conducted in a manner similar to
design exploration, using false color mesh rendering and mesh-element scaling to provide the
designer graphic feedback of the differential melting behavior within each panel. Periods of
melting were identified and isolated to produce a series of still images depicting the melting
progress. These images were then compared to concurrent time lapse images of the panels in
situ to confirm that the melting patterns bore a resemblance to predicted behavior.
Following a first set of panel designs in which the late-phase melting behavior was dominated
by buoyant convection effects outside the scope of the mechanistic model, a second series of
panels were designed to compartmentalize fluid flow. These attempted to reveal a range of
diagonal hatch patterns mid-way through the melting of a form whose solid state appeared
undifferentiated.
Figure 11: Uniform visual composition of panels in solid state followed by transient patterns
of dashes and dots revealed during melting process.
The mechanistic model was largely successful at predicting the qualitative melting behavior,
which began where the PCM thickness was minimal and proceeded gradually to the thicker
regions where more enthalpy was required to melt the material.
Figure 12: Predicted and observed melting behavior in panels employing a diagonal hatch and dash-dot
patterns
While qualitative aspects of the melting behavior were largely successful in terms of timing,
duration, and sequence, accurate quantitative predictions of temperature profiles could not be
achieved with a high-level of accuracy. Calibration sensor readings varied from predictions
with root mean square deviations ranging between 1.4°C and 2.6°C. Deviations in the
melting regime were typically small, and the model accurately predicted the onset of
solidification. However, the model also consistently overestimated the rate of solidification,
often predicting complete solidification several hours before it was actually achieved (Figure
13). These deviations could not be overcome through GA-based optimization of material
properties and likely point to systematic errors introduced by the model’s simplified
treatment of PCM heat transfer, which neglects microscopic effects such as nucleation which
contribute to different enthalpies of melting and solidification, as suggested by 24.
Liquid phase predictions exemplified no such systematic deviation from observed
measurements, despite large statistical variations. Large swings in the measured values
during the liquid phase may be attributable to direct solar gain on the sensor itself, which is
made visible by the transparency of the PCM. Hence, a detailed calibration was not feasible
in the absence of proper shielding, given that liquid-state measurements were likely of
questionable accuracy.
Figure 13: Predicted (light, dashed) and observed (dark) temperature profiles
5.2 Multiple Linear Regression
The multiple linear regression model produced accurate forecasts of system behavior based
on 3 days of training data. As was expected, the 5-minute forecast yielded the most accurate
predictions with standard deviation for the 11 sensors ranging between 0.15°C and 0.23°C,
while the 20- and 60-minute forecasts yielded slightly larger deviations ranging between
0.29°C and 0.47°C and between 0.47°C and 0.76°C, respectively. What is notable about the
deviations in the longer range forecasts, is that they occur largely in the liquid state, where
the aforementioned solar effects complicate analysis. Conversely, these models proved
extremely effective at predicting the onset and duration of melting and solidification,
suggesting that they are well-suited to forecasting the visual effects of phase change, which
are the primary focus of this study.
Figure 14: Comparison of measured sensor readings (black) against 5-minute forecasts (red)
and 60-minute forecasts (yellow) over 48 hours. Note the high correlation in the
neighborhood of the 18°C melting temperature.
Feature ranking results conformed partially to expectations. The primary influences for the
overwhelming majority of sensors were their own most recent recording as well as the three
most recent recordings of solar radiation (Figure 15). Interior sensor data figured somewhat
less significantly, as did exterior ambient temperature data. Other sensors recordings, as well
as readings from the same sensor prior to the most recent reading typically featured the
lowest in feature ranking. These results suggest that while multiple linear regression models
may be capable of producing accurate near-term forecasts for PCMs in similar applications,
sensoring plans should account for solar radiation monitoring and low-resolution temperature
monitoring of interior, exterior, and PCM conditions before turning to higher-resolution
temperature monitoring.
Figure 15: Feature ranking of 5-minute forecast for each of the 11 sensors (reading top-down
by column). Features include the most recent recording from the same sensor (red); the three
most recent solar radiation readings (yellow), exterior temperature readings (blue), interior
temperature readings from multiple sensors (green), and all remaining panel sensor readings
(white).
6. Discussion/Conclusion
Multiscale architectural models that attempt to describe, predict, and design precinct-scale
and material-scale behavior inherently depend on the knowledge of multiple disciplines, and
hence multiple methods. These complexities require the profession to develop its own
methods for combining models borrowed from other disciplines and validating the
handshakes across their respective system boundaries. The model presented here incorporates
modeling methods from the fields of architectural design, urban ecology, and
thermodynamics into an integrated platform that allows designers to test hypotheses about the
melting behavior of PCMs in response to surface geometry, solar orientation, context features
such as trees and buildings, and time. By admitting a more complex heat balance model and a
broader system boundary than is typically presented in architectural-scale analysis (e.g.
building energy models), this work engages designers with dynamic systems whose study is
normally inaccessible. This has allowed our team to curate and refine visual effects across
two seasons, and develop the means to manipulate and represent temporal effects.
Multiscale models may be described as bespoke models, and in our experience, can be
limited by access to another discipline’s knowledge and modeling practice. This multiscale
model encompases scales ranging from regional and local climate to the meso scale of
visually observable melting regions in a prototypical PCM envelope. The omission of
microscopic phenomena governing nucleation sites, melting fronts, and buoyant convection,
whose effects can be readily observed, suggests that we we bracketed the model’s scales too
narrowly. This omission also suggests possible opportunities for expanding the scope and
system boundary of our model. However, the need to maintain rapid feedback loops within a
design context may place a lower bound on the resolution of such features, suggesting a
tradeoff between multiscale model accuracy and usefulness.
This design-based context contrasts with approaches to PCM modeling presented in scientific
literature because it seeks to model PCMs that are exposed to a broader set of conditions than
are typically encountered in controlled scientific experiments, in service of informing the
design and performance of an experimental architectural envelope. In contrast to much of the
literature which considers PCM’s exclusively from a thermal perspective, our architectural
motivations have supplemented thermal consideration with a focus on optical properties.
Where recent literature has focused on optical properties, with PCM used as fill between
multiple layers of glass for optically switching windows, or as operable and adjustable slats
and louvers 35, 36, which aims toward thermal equilibrium and visual homegentity. Our work,
therefore contributes methods that support the design of heterogeneous and localized zoning
of thermo-optical conditions and, critically, support informed design and definition of model
boundaries.
7. Acknowledgments
The project took place in the frame of the Velux Guest Professorship of Billie Faircloth at
CITA supported by the Villum Foundation / Denmark. We wish to thank Patrick Weiss,
Suzanne Mahoney, Erica Ehrenbard, Eric Eisele, Christopher Connock, Angelos Chronis and
Asya Ilgun for their contribution to the project.
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