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Inductive Aerodynamics

Samuel Wilkinson1, Sean Hanna2, Lars Hesselgren3, Volker Mueller4

1,2University College London, UK, 3PLP/Architecture, UK, 4Bentley Systems, US

1smlwilkinson@gmail.com, 2s.hanna@ucl.ac.uk, 3lhesselgren@plparchitecture,

4volker.mueller@bentley.com

Abstract. A novel approach is presented to predict wind pressure on tall buildings for

early-stage generative design exploration and optimisation. The method provides

instantaneous surface pressure data, reducing performance feedback time whilst

maintaining accuracy. This is achieved through the use of a machine learning algorithm

trained on procedurally generated towers and steady-state CFD simulation to evaluate the

training set of models. Local shape features are then calculated for every vertex in each

model, and a regression function is generated as a mapping between this shape

description and wind pressure. We present a background literature review, general

approach, and results for a number of cases of increasing complexity.

Keywords. Machine learning; CFD; tall buildings; wind loads; procedural modelling.

Introduction

It is generally recognised that architects currently require performance information to

guide their decisions almost from the inception of a project. In fact, there is a

mentality present of simply trying to collect as much data as possible with the

intention of synthesising it into a situated design response. This presents a problem,

especially for computational fluid dynamic (CFD) wind simulation, whereby the time

required to assess the performance is obstructive to the fast and iterative nature of

current parametric design softwares. This is possibly due to the tendency for

architectural software tools to originate in engineering fields, without due

consideration of speed-accuracy tradeoffs to adjust for the application requirements

(Chittka et al., 2009; Lu et al., 1991). In other words, they are typically too accurate

and slow for the fast pace of modern conceptual design, massing or form decisions.

Developing a method that can give real-time performance feedback about a form

allows for intuitive play of the kind we are used to with physical models.

Wind engineering has traditionally been within the remit of engineers or

specialists, with numerical simulation (CFD) considered a supportive tool to physical

boundary layer wind tunnel (BLWT) testing. For instance, in the computational wind

engineering (CWE) literature there is substantial caution around numerical analysis,

namely for Reynolds-averaged Navier-Stokes (RANS) and to a lesser extent large-

eddy simulations (LES) (Stathopoulos, 1997; Bitsuamlak, 2006; Dagnew et al., 2009;

Menicovich et al., 2002). However, architects are increasingly getting involved with

analysis, where concerns over accuracy are less paramount since demand is typically

for relative scenario comparison or general flow behaviour (Lomax et al., 2001;

Malkawi et al., 2005; Chronis et al., 2012).

The tall building typology has been identified as a focal area here for a number of

reasons. Firstly, as height increases so too do the wind forces (along with seismic and

gravitational) which has consequences on facade panelisation and structural

efficiency, amongst others. We can construct a simple motivational argument to say

that increased external wind force requires more opposing force, i.e. more structure,

more materials, larger cores, less let-able floor space, less revenue etc. Therefore there

is a need to consider the aerodynamic form of these buildings as they increase in

height. Secondly, the trend for tall buildings is to build them as high as (contextually,

economically and structurally) possible, necessitating cutting-edge design and

construction technologies (CTBUH, 2012). Thirdly, tall building form lends itself well

to parametric design as there is often a high degree of vertical logic that can be

expressed neatly with mathematical expressions (this generalisation is at least more

true than for shorter buildings). Given this, it is possible to easily generate a

procedural, or generic, tall building model that, with a relatively small number of

parameters, can represent a large number of potential designs. This becomes useful

when the objective is to sample the typological space of potential buildings, which

will be discussed in the methodology.

We present a novel approach to predict wind pressure on tall building models for

early-stage generative design exploration and optimisation (exploration as the non-

discrete parametric equivalent of tinkering, and optimisation as the single- or multi-

objective directed design space search requiring iterative testing and evaluation). The

method provides fast surface pressure data with the conventional visualisation,

reducing performance feedback time whilst maintaining verisimilitude.

This is achieved through the use of a machine learning algorithm, trained on a pre-

computed set of CFD simulation data. ANSYS CFX 13.0, a commonly used solver in

engineering practice, was used for steady-state RANS with a k-E turbulence model.

The learning technique is grouped with artificial neural networks (ANN), support

vector machines (SVM), and random forest (RF) decision trees, in that there is a

training set of cases from which generalised rules are generated (Duffy, 1997). The

term machine learning stems from the fields of computer science (Mitchell, 1997) and

artificial intelligence (Samuel, 1959), but in statistics is referred to as regression and

in engineering as function approximation or surrogate modelling. Once trained, this

enables us to provide a new test case and make a prediction of the outcome. Inductive

reasoning, epistemologically, means constructing generalisations from specific

information, as opposed to deductive reasoning where small details are construed

from generalisations. The fundamental outcome of this learning approach is therefore

a continuous output response allowing interpolation and extrapolation between cases

that have not been explicitly simulated. In doing so, we are essentially moving the

simulation time from the front-end to the back-end of the process where more time is

available for pre-computation.

The following section provides a review of relevant literature in the generative,

performative design of tall buildings, wind modelling methods, speed-accuracy

tradeoffs, incorporation of learning in design, concluding with a problem-solution

hypothetical argument positioned in this state of current literature. The subsequent

structure of this paper will describe the methodological approach in general terms,

and results are presented from a series of experimental case studies of increasing

complexity from trivial to practical. The conclusions, further work and the paper as a

whole are positioned within the scope of ongoing research.

Literature Review

Tall Buildings

Tamura et al. (2009, 2010) and Tanaka et al. (2012) acknowledge the increase in tall

building complexity beyond the traditional extruded rectilinear form. We are now

seeing more unconventional free-style forms derived from the architect's use of more

advanced modelling software. These new complicated sectional shapes that may vary

with height, can actually provide better aerodynamic performance by disrupting, or

'confusing', vortex shedding and thus reducing crosswind response. Benefits can also

be found in more subtle manipulations such as corner chamfering or cutting, and by

creating voids, or porous regions, near the edges.

Despite rapid advances over the past century, this emerging generation of

skyscrapers poses new challenges for wind engineering. Irwin (2009) discusses a

number of these, such as the impact that aerodynamics have on construction cost.

Since the structure itself is a large proportion of the cost, and as for tall buildings the

wind is the governing lateral load, there are significant benefits to be had from

reducing wind loads. This also has the effect of reducing lateral motions that can

potentially cause occupant discomfort. He also suggests that shape aerodynamics

must be proactively considered, and iteratively optimised, early on in the design. With

the new generation of super-tall towers over 600m it is simply not possible to ignore

the wind performance. He quotes a designer of the Burj Khalif, saying “we

practically designed the tower in the wind tunnel”, and were therefore able to produce

an extremely efficient aerodynamic shape that enabled the height with reasonable

structural systems and costs, and without any damping system.

The increase in the use of parametric CAD softwares has seen a rise in the last

decade namely with the release of Bentley GenerativeComponents and Rhino

Grasshopper, plus more generally with the increased adoption of scripting. These

allow the user to create parametrically associative relationships related to geometry.

The extension of this idea is to use rules to define the parameters, or where these rules

can be related to the performance of a model component the geometry is directed by

some evaluative metric. Certain metrics can be calculated quickly without problem,

but if the calculation takes time it becomes obstructive to the modelling process. We

adopt the premise that it is better to have a broader range of lower resolution data

rather than a limited amount of exact data.

Speed-Accuracy Tradeoffs

Speed-accuracy tradeoffs (SATs) show that response accuracy generally increases

with response time, i.e. taking more time to make a decision results in a better

decision. Biological examples have been noted by Chittka et al. (2009), who explains

that “when it takes a long time to solve a difficult task, and the potential costs of

errors are low, the best solution from the perspective of an animal might be to guess

the solution quickly, a strategy that is likely to result in low decision accuracy.” The

two extremes can be called impulsive and reflective. This provides a neat analogy for

performance analysis in design where it is necessary to consider what the application

of the simulation tool is, and the consequent risks, before deciding a suitable accuracy.

Crucially though, and in conjunction with this reasoning, Burns (2005)

demonstrates that making more decisions with more mistakes (fast and inaccurate)

results in better overall performance (with bees, more nectar collected) than the more

fastidious (slow and accurate). Defining accuracy as the proportion of choices that are

correct, this highlights that accuracy should not be confined to the immediate task, i.e.

simulation accuracy, but to the larger one of improving building performance (see

Figure 1).

Response time is critical for performance-driven design and SATs must be

considered when developing early stage tools for when large-scale decisions are

made. Performance information is often scarce at this stage and iterative decisions

must be made quickly, necessitating fast response times in sync with the project

cycles. The development of CFD models have been focused over the past decades on

improving accuracy, and computational time is optimised by specific software

vendors after-the-fact, with little thought given to the accuracy required by the user. In

contrast, recent developments in computer graphics have started with the desired

accuracy (believable) and speed (real-time) in mind, with successful results.

Figure 1

(Left) SAT for various task difficulties and skills; (Right) Notional positions of different modelling methods on SAT.

In the design context, CFD can typically be used for a number of purposes:

analysis of internal air movement, pollution dispersion, noise propagation, pedestrian

comfort in urban environments or tall building aerodynamics. As mentioned

previously, it is the last that is the focal application here, especially for early design

stages. There is a paradox here, in that the most complex flow types (bluff bodies) and

therefore most computationally intensive, need to be modelled in a scenario where

fast results are required. The numerical method must be as accurate and fast as

possible. In fact, the conclusion is reached that the fastest method has poor accuracy

and the slowest the best accuracy (as would be expected, considering the speed-

accuracy tradeoffs mentioned earlier). There is general agreement between (Lomax et

al., 2001) and (Chronis et al., 2012) that the “level of accuracy of a CFD simulation

needs to be compromised with the turnaround time requirements of its application.”

Lu et al. (1991) describe the same issue in mechanical engineering where slow but

accurate simulation makes interactive decision making impossible, when only quick

estimates are desired at early stages. It is only towards the final stages of design,

“when the engineer has converged to a small region of decision space, more accurate

simulations are needed to make fine distinctions.” The problem has therefore been

present since the early 90s, but as a solution they propose integration of simulation,

optimisation and machine learning.

Inductive Learning in Design

Our approach is supported by Samarasinghe (2007), who identifies the best solution

to predicting system behaviour through observational data. This is necessary when

there is little or no understanding of the “underlying mechanisms because of complex

and non-linear interactions among various aspects of the problem.” Extracting these

complex relationships is often difficult since the systems are typically natural, and

therefore can have randomness, heterogeneity, multiple causes and effects, and noise.

Even when they are successfully extracted, they may be beyond our understanding

and are held as intractable computational functions or data structures. Hanna (2011)

tests the hypothesis that it is unnecessary to have any understanding of this underlying

system behaviour, but rather it is possible to make predictions about the system

simply by making observations. This is demonstrated by learning the structural

behaviour of system components and applying them to larger-scale scenarios.

Graening et al. (2008) propose a method that allows the extraction of

comprehensible knowledge from aerodynamic design data (jet-blades) represented by

discrete unstructured surface meshes. They use a displacement measure in order to

investigate local differences between designs and the resulting performance variation.

Knowledge, or rule, extraction from CFD data is primarily used to guide human-

centred design by improving understanding of the system's behaviour, whether it is for

jet turbine blade optimisation or architectural design. Whilst the connection between

local geometric features and surface pressure has been extended and changed here,

and used for a different application, this work is a close precedent.

Problem Hypothesis

It is argued here that approximations of CFD simulations can be made with machine

learning regression, using geometric shape descriptors as the learning features. The

entire evaluation process can be broadly split into five key work areas: i) procedural

geometry generation; ii) batch simulation; iii) shape feature generation; iv) machine

learning training; v) prediction and visualisation. Feature generation is essentially the

core of the process since the solution depends heavily on geometric description so as

to define surface pressure as a function of it. We hypothesise that surface pressure

distribution arising from wind flow around tall buildings can be learnt and predicted

with an accuracy appropriate to early stage design (feedback from practice indicates

<20% error) using shape feature description. It can be shown that it is possible to

combine, with an acceptable error, methods that have the separate contradictory

objectives of predictive accuracy and speed.

Methodology

Data Set Generation: Procedural Modelling

The parametric model was created in Bentley GenerativeComponents. The goal was to

create a generalised tower model, with the two properties of minimising the number

of parameters used whilst maximising the design representation potential, i.e. the

number of possible buildings it could create. This is important when considering

optimisation or exploratory design space searches to avoid the curse of

dimensionality. This means that as the number of variables increases, the design space

increases exponentially by nD, where n is the number of samples taken per parameter

and D is the number of parameters, or dimensionality. There is therefore clearly a

compromise to be made between model efficiency and represent-ability.

Figure 2

(Left) Examples of evaluated procedural models in the training set on Case 4; (Right) Mesh feature extraction.

The geometry for the training set was generated using a procedural tall building

model with a select number of key parameters. There are in fact three separate

topologies in the procedural model with their own parameters, since it is difficult to

incorporate the entire design space with one parametric logic (Park et al., 2004;

Samareh, 1999). Using the unstructured triangulated surface mesh from these means

we are not limited by a single parametric topology in the learning phase of the method

(Graening et al., 2008). Local surface-mesh shape characteristics are used as input

features to the learning algorithm instead of the design parameters, avoiding reliance

on any one parametric model definition.

Simulation Method

An established solver, ANSYS CFX 13.0, was used throughout to run the RANS

steady-state simulations, with a k-ε turbulence model as it is regarded as the most

robust. Each simulation, depending on the complexity, requires up to 60 minutes to

converge (on a 2.66GHz i7). Solver convergence is reached when residuals fall below

a minimum of 1−6, typically at around 100 to 200 iterations. The number of cells in the

tetrahedral meshes varies between 0.8x106 and 1.5x106 depending on the geometry,

with prismatic expansion on surfaces 3 cells deep and a minimum cell size of 0.1m.

The wind was applied at an upstream inlet, with a reference speed (Ur) of 1ms−1 at a

reference height (Zr) of 10m. The most commonly used distribution of mean wind

speed with height is the 'power-law' expression:

Ux = Ur ( Zx / Zr ) α (1)

The exponent α is an empirically derived coefficient that is dependent on the

stability of the atmosphere. For neutral stability conditions it is approximately 0.143,

and is appropriate for open-surroundings such as open water or landscape. Future

work will include a wind profile that takes surrounding surface roughness, or context,

into account, as well as potential wind direction change with height.

Shape Features and Learning

This method creates a definition for the pressure at a point on the model as the

function of a local geometric description. To describe a simple example of the

process: there are N models of a cuboid with various orientations; each is evaluated,

and the pressure P is extracted at M points over each model; for every M, a shape

descriptor X is calculated, such as the vertex height, normal components, curvature,

etc; this gives a set of geometric characteristics, and a corresponding pressure value;

these sets of P(X) are used as the training data. Pressure distribution is predicted from

these geometric descriptors alone meaning the selection is critical. A sensitivity

analysis has been conducted with a variety of descriptors to determine suitable

representation, details of which are not included here. When a new case is presented,

the shape descriptors are calculated and used to make a prediction of P. The feature

definition for point pressure in R22 vector space used throughout the following is:

P ( Z, N(x,y,z), Nσ1-5(x,y,z), U(x,y,z)) (2)

For a specific model vertex, P is the surface pressure, Z is the height, N(x,y,z) are the

normal components, Nσ1-5(x,y,z) is the standard deviation σ of normal components of

cumulative mesh neighbourhood rings 1 through 5, and U(x,y,z) are the normalised

model position components. The extent of the neighbourhood curvature can be

extended beyond 5 rings, within computational resource limits. The definition in

Equation 2 gives 22 inputs and 1 output feature to train the learning algorithm for all

cases described below.

For the Orientation, Height and Topology cases, an Artificial Neural Network

(ANN) was used, with a 70:30% split of the provided data to training:validation. For

the first two cases, separate sets constituting entire models were also held back for

testing, i.e. training was at 15° and 20m intervals respectively. For the third case, there

was no extra test set but the whole was split 70:15:15% to training:validation:test.

Validation data is to check for convergence during training. For the fourth case,

training data was from the procedural tall building model and test data from another

set of real buildings. In this case, a Random Forest (RF) algorithm was used instead as

it provided better results for the more complex problem. Further work is needed with

both methods to understand their applicability to certain tasks, however it is known

that the RF is better with noisy data sets than the ANN. Training set sizes and

summary results are given in Table 1, and computation times are given in Table 2.

Results

Cuboid Orientation

The first and most simple test is the rotation of a cuboid, of width and depth 10m, and

height 50m. Simulations were run at 5° intervals from 0 to 85°, and the ANN trained

on 15° and tested at 5° intervals. The sensitivity analysis here varies the number of

training samples and measures the standard deviation, σ, of the difference between

simulation and prediction. Figure 3 (left) shows the error σ against orientation for

various set sizes (bold vertical lines are training intervals of 15°), (centre) the training

regression of the entire set, and (right) the prediction error for an orientation of 25°.

With less training data, it can be seen that error is highest around 45° when flow

bifurcations (regime change) occur, although this is negated with sufficient data.

Figure 3

(Left) Orientation vs. Error σ %; (Centre) Training set regression, R=0.99564; (Right) Prediction error (25°).

Cuboid Height

Secondly, a parametric cuboid was created with width and depth 10m, and height

varying from 10 to 100m in 5m increments. Figure 4 (left) shows the variability when

trained on 10, 20, 30 and 45m intervals, and (right) the prediction error for a height of

25m when trained at 20m intervals.

Figure 4

(Left) dHeight vs. Error σ %; (Centre) Training set regression, R=0.9992; (Right) Prediction error (25m).

Topology

Here the number of edges was varied from 3 to 10, with 0 (circle), diameter 10m and

height 50m. Instead of keeping a complete model separate for testing as in the last two

cases, here all cases were used but only a fraction of the total data set was used. This

is varied in Figure 5 (left), with a training set ranging from 10000 to 50000.

Figure 5

(Left) No. Edges vs. Error σ %; (Centre) Training set regression, R=0.98355; (Right) Prediction error (n0).

Tall Buildings

In the final case, training data was collected from simulations of 600 procedural tall

building models, with a total of over 4x106 shape features extracted. This was down-

sampled to 105 by removing features in close proximity to reduce training time. The

test set contains 10 real tall buildings from around the world, selected for their range

of unique architectural characteristics. Figure 6 below shows predicted surface

pressure distribution in the top row, and the error distribution for the set in the bottom

row. The pressure range (-5.5 to 2.0 Pa) was taken over the entire test set, as was the

absolute error range (0 to 65.2%). The error distribution is shown in Figure 7 (right),

which fits a Gaussian normal distribution. Error percentiles: 99th = 35.7%, 95th =

20.0%, 90th = 13.0%, 75th = 6.1%. That is, 75% of the test features have an error

below 6.1%.

Figure 6

(Upper) Predicted pressure, Pa; (Lower) Error, %. Pressure range is the min. and max. of the entire set for

comparison, the error range is absolute max. error of the set (65.2%).

(Left to right) (1) Metlife Building, NYC; (2) The Shard, London; (3) Willis Tower (Sears), Chicago; (4) Euston

Tower, London; (5) Taipei 101, Taiwan; (6) Shanghai World Financial Centre; (7) Bank of China; (8) Exchange

Place, NYC; (9) Frankfurter Buro Centre, Frankfurt; (10) Washington Street, NYC.

Figure 7

(Left) Error σ % for each case; (Centre) Random Forest learning convergence; (Right) Error probability density.

Results Summary

Case Min σ Error (%) Max σ Error (%) Training Set Size

Orientation 1.2 (55°) 1.6 (10°) 110000 (15° training intervals)

Height 0.7 (10m) 2.0 (50m) 44720 (20m training intervals)

Topology 1.8 (5 Edges) 3.5 (0 Edges) 50000

Real 4.8 (Bank of China) 18.3 (Euston) 100000 (Procedural training)

Table 1

Summary of minimum and maximum error standard deviations (% over test case pressure range).

Case Train Sim. Train Feat. Gen. †Train Predict Feat. Gen. * Predict *

Orientation 21600 9060 2600 1540 < 0.1

Height 18000 2370 720 620 < 0.1

Topology 32400 4670 1060 1750 < 0.1

Real 2160000 12000 620 720 < 0.1

Table 2

Summary of time (seconds) required for each case, split into Training (one-off back-end time) and Prediction

(front-end time). Mean feature generation time is 0.085s/vertex. *Mean over all test set. †After down-sampling.

Conclusion

The results show that it is possible to achieve a relatively small prediction error

(Figure 7 and Table 1) for less time (Table 2), with the methodology and constraints

described. These prediction errors are necessary for the compromise in avoiding

considerably intensive CFD simulation. Traditionally, for every individual CFD

simulation the process can take a minimum of 1 hour, compared to our methodology

that has a total front-end prediction time of under 12 minutes (for feature generation

and prediction) and a back-end, one-off training set simulation time of 600 hours (for

the real case). Once trained, an unlimited number of predictions can then be made.

Whilst these preliminary results are outside the rigorous accuracy necessary for

final engineering analysis, they are within the boundaries acceptable for early-stage

concept design for tall buildings, where interactive response time is a significant

consideration. The prediction accuracy and response times achieved are promising for

further work given the well-known complexities of fluid behaviour.

The next stages of the work are to consider time-dependent simulations to fully

consider the approximation of turbulence, vortex shedding and gusts, as well as

interference from complex urban contexts on boundary conditions, and further

improvement to the shape feature selection and generation time.

Acknowledgements

This research was sponsored by the EPSRC, Bentley Systems and PLP Architects.

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