Content uploaded by Lorenzo Greco

Author content

All content in this area was uploaded by Lorenzo Greco on Jul 21, 2018

Content may be subject to copyright.

Proceedings of the IASS Symposium 2018

Creativity in Structural Design

July 16-20, 2018, MIT, Boston, USA

Caitlin Mueller, Sigrid Adriaenssens (eds.)

Copyright © 2018 by Lorenzo Greco

Published by the International Association for Shell and Spatial Structures (IASS) with permission.

Machine Learning and Optimization techniques for Steel

Connections

Lorenzo GRECO*

*www.parametricism.co.uk

London

lorenzogreco@gmail.com

Abstract

Most part of their time, engineers around the globe are asked to design over and over again the same or

very similar structures, without just taking what has already been done or learning from the past.

Arguably the same structural elements with given acting forces and constraints have been designed

thousands of times and the same can be said for architectural finishing, MEP, and in principle to entire

buildings which could be informed from previous similar ones. Also, traditional methods for

optimizing structures require a large amount of resources and time, whereas an AI-based approach can

draw from previous knowledge [7, 8]. The more such an approach were used, the more the data points

collected and therefore the more efficient it would become. This paper tries to take a step further in the

realm of structural optimization by having a fresh look at machine learning strategies to address one of

the above-mentioned challenges: the automatic design of steel end-plates.

Keywords: machine learning, optimization, steel connections, AI, steel connections, supervised learning, structural

engineering, case study.

1. Introduction

Figure 1: Steel end-plates, (a) 2D drawing, (b) 3D view.

Engineers around the globe are asked to design, over and over again, the same or very similar

structures, without learning from the past. Arguably the same structural elements with given forces and

constraints have been designed thousands of times and the same can be said for architectural finishes,

MEP, and in principle to entire buildings, which could be informed from previous similar ones.

Repetitive tasks, inefficient workflows, and low technology penetration are some of the issues the

industry needs to address, highlighted in [1].

Optimization algorithms have long been applied to structural problems such as form-finding, cross-

section optimization, topology optimization, and the broader holistic optimization considering

Proceedings of the IASS Symposium 2018

Creativity in Structural Design

2

architectural, structural and construction aspects [2, 4]. Their drawback is that they require a large

amount of computational resources, the need to choose the right parameters, constraints, domain,

design space, and skilled personnel.

A machine learning-based approach can draw from previous knowledge. The more such an approach is

used, the more data points collected and therefore the more accurate would become. Machine learning

strategies have progressed over the past decade, thanks to ever increasing data and faster computer

processing speed, which has led to more people investigating novel applications [3].

This paper takes a step further in the realm of structural optimization, by taking a fresh look at

machine learning strategies to ease the daily tasks of structural engineers, providing a framework for

automatic real-time design of steel connections.

Several Machine Learning algorithms have been trained from a data set of optimized steel connections,

the most accurate and robust one is picked, and then its effectiveness is tested against a real world case

study. Discrepancies between the mathematical optimum and what actually has been designed are

highlighted to understand what causes this difference. It is also shown that the workflow described is

much quicker and reliable than finding an optimal solution for each connection. The framework shows

its robustness on different data sets and can easily be integrated in structural engineers’ workflow.

Machine Learning can give useful insights into cost sensitivity thanks to the statistical correlation

between inputs and outputs, which can in turn be used to run automatized checks for their design.

2. Machine Learning strategies

Machine learning strategies are mainly divided into supervised and unsupervised learning (and semi-

supervised which is a mix of the two). The first one is what happens with a labelled set of data,

meaning when both inputs and outputs are known. This is the case if we have data of patients and we

know for each patient if he is ill or not. Unsupervised learning is when we only know the patients’ data

and we ask the algorithm to split the data into two groups - ill or healthy - without hints. Some of the

most common techniques used in ML for supervised learning are Random Forest, SVM and

regression, while for unsupervised learning one is K-nearest neighbours. They have a very long history

behind with benchmarks and documentation and are still used as benchmark cases.

Let’s have a more detailed look at k-nearest neighbours, which is the one that was eventually chosen.

This is a technique used for both classification and regression, where the inputs consists in n closest

data point and the output is either the class for classification or in the case of regression the value

which is then interpolated. The distance metric can be the Eulerian or any other specified one,

interpolation is done weighting the distance. This algorithm is inherently sensitive to localities in data

which can be improved by using metric learning.

In this paper all the algorithms come from scikit-learn, an open source Python package [6].

2. Filling the database

The AEC industry lacks shared databases of built projects and thorough explanation of

parameters. Companies usually don’t collect data on their project and the idea of using

previous experience to programmatically gain insights or predicting results is generally not

embraced. The hassle of gathering the large amount of data required from calculation sheets,

FE models and pdfs, brought the author to create a database filled with optimized joints under

different conditions. The parameters for the simplified run were:

N, Compression force [0..4..200] [kN]

Vy, Vertical shear [0..10..500] [kN]

Mx, Bending moment around the major axis [0..6..300] [kNm]

The reader is reminded that [a..k..b] stands for an array starting from a to b with step k, which

brings to (3*3)*50*50*50=1125000 entries. Combinations have been done for different

Proceedings of the IASS Symposium 2018

Creativity in Structural Design

3

beams and columns, but after the initial analysis it was found that profiles do not have a large

impact on the bolt design, as expected. This is because profiles have an impact by restricting

the available space to arrange bolts and to a smaller extent their radius.

The database is created using a script to find the optimal head plate connection given the loads

and beam cross-section. This scripts iterates through different options by changing:

Plate thickness [5..5..40] [mm]

Rows count (subject to geometrical limits) [2..1..10]

Bolt phi [16..2..30] [mm]

Bolt strength [8.8, 9.8, 10.9]

The best combination satisfying EC3 checks is found for each load condition. These variables

are assumed being strictly ordered such that Thickness > Bolt Strength > Phi > Rows count so

for example a connection having 10mm thickness and 2 Φ 16 8.8 is considered worse than a

plate 5mm thick with 10 Φ 30 10.9. This assumption derives from empirical data and

experience. The checks involve shear resistance of bolts and traction due to moment, and

punching, tear and compression on the plate side. This is an excerpt of the table populated

with the above method.

Table 1: Score Extract from the data set, showing the parameters taken into consideration for the

analysis and machine learning application.

N [kN]

Vy [kN]

Mx [kNm]

Rows

Φ

Grade

t [mm]

UF

0

0

0

0

2

16

8.8

5

0.00

1

10

0

0

2

16

8.8

5

0.02

2. Choosing the right algorithm

Usually ML needs a prepass of data cleaning, but in this case since the database was generated

programmatically, only minor flaws were present and were removed using simple filters. In this

section it is shown how the algorithm has been chosen and its settings. This was done in two steps: the

first one is explained in Par. 2, whilst the second one was done using Autodesk Robot’s embedded

steel joint analyzer. This was not used in the first place because the time needed to calculate a single

joint is significantly higher therefore generating a million data points would have required ages. In this

paragraph it will be shown how robust the algorithm is on such problem even with a small data set,

hence it was possible to generate a better one using Robot, consisting of a thousand points.

2.1 Simplified Method

The simplified method included a full check of shear capacity and an approximation of the bending

capacity. This was done because one Robot check takes relatively too long to compute and in order to

generate thousands of them would have taken days. Histograms of the data set:

Figure 2: Analysis of the data set generated programmatically with the custom EC3 designer. (a)

Forces, (b) Geometry, (c) Correlation matrix. The number of bolts is highly correlated with shear and slightly to

bending moment.

Proceedings of the IASS Symposium 2018

Creativity in Structural Design

4

The above chart shows the correlation between variables. It’s apparent that cross-sections dimensions

are highly correlated between themselves which is because out of the shelf profiles have being used for

training. It also appears that bolts’ diameter and row number strongly depends from shear and to a

lesser extent to bending moment.

Choosing the right algorithm is key for a robust workflow, therefore it is expected to give reliable

predictions within the domain of interest. The following algorithms have been tested and

benchmarked:

Ridge

RidgeCV

KNeighbors (Regressor)

Linear Regression

Elastic Net

Partial Least Squares regression

Multi-layer Perceptron

These techniques and many others are common in ML problems [5].

Figure 3: Sensitivity analysis to choose the right ML algorithm. (a) This chart shows the error rate

given a ratio of training set [0.05 to 0.95], for some algorithms, (b) Here is shown the error rate for a

K-Neighbour regressor against the share of data set trained, for varying number of neighbours.

Figure 2 shows the algorithms’ benchmark: on the ordinate is plotted the average error rate on 20

random subsets and on the abscissa the ratio of training set over the total data set, where 0.0 is no

training set and 1.0 means the whole data set. The graph shows that overfitting rarely occurs and with

the best algorithm being the K-Neighbours Regressor. Classification algorithms were tried as well, but

it was thought being more sensible to better investigate regression as it could prove being more handy

in developing this research further for fabricated cross-sections, plates, and welds dimensions as well.

Classifications gave good results as well and that might explain why KNeighbours are giving the best

results. In fact this design space is relatively straightforward KNeighbours successful in “bridging the

gap” between data points.

Having chosen the K-Neighbour Regressor as the algorithm for the rest of the research, a sensitivity

analysis on the number of neighbours has been done, again taking the average score on 20 random

subsets. The best neighbouring size is 3 with a proportion rate of approximately 0.5 (see next picture).

The K-Neighbour Regressor with 3 neighbours is chosen and finally an accuracy test is run on the data

set, to test the accuracy given a certain accepted error ratio (0.05, 0.1, 0.2 and 0.3). As shown in figure

6a the true positive ratio is fairly constant at around 0.98.

4.2 Detailed Method

Having seen how good the results are with the previous analysis and how not sensitive it is to small

data sets, the same analysis was run using Autodesk Robot’s embedded EC3 joint analyzer. The

parameters used for the Autodesk Robot run were:

Proceedings of the IASS Symposium 2018

Creativity in Structural Design

5

N, Compression force [0..20..200] [kN]

Vy, Vertical shear [0..25..500] [kN]

Mx, Bending moment around the major axis [0..15..300] [kNm]

Which brings to 10*10*10=1000 entries, one thousandth of the previous run. Picture 4 shows the data

set analysis as for the previous one. Comparing this chart with the previous one it can be seen how

bending moment plays the lion share in sizing the connection with vertical shear still having a good

influence on the number of bolts.

Figure 4: Analysis of the data set produced using Autodesk Robot’s connection EC3 checker. (a) Forces, (b)

Geometry, (c) Correlation matrix of the data set produced using Robot. The number of bolts is highly correlated

with moment as opposed to the previous chart where it was more dependent on shear.

The same investigation was done to find the fittest algorithm. This showed some differences, but both

show KNeighbours being the best one and again a sensitivity analysis on what number of neighbours

to pick was run which gave the same result: 3 neighbours (see figure 5). Accuracy gave results worse

than the previous one, which is in line with the other two sensitivity analysis. This can be a good

starting point to improve the ML study and explore new ways as well as optimizing the parameters for

fine-tuning.

Figure 5: The comparison leads to the same conclusion, with K-Neighbours proving to be the best fit. (a)

Sensitivity analysis as in figure fig:Sensitivity-analysis-1-1. K-Neighbours is still the best regressor, although the

error rate is sensibly higher, (b) Again, the best number of neighbours is found to be 3.

Table 1: Score metrics on the predictions shown in this paper.

Simplified Method

Detailed Method

WCP

Optimized WCP

UA

0.993

0.637

-2.134

0.061

VW

0.98

0.608

-4.261

-0.043

Proceedings of the IASS Symposium 2018

Creativity in Structural Design

6

(a) Accuracy as function of absolute error in

predicting the correct utilization factor (UF), for

a K-Neighbour Regressor trained on an

optimized dataset

(b) Accuracy as function of absolute error in

predicting the correct utilization factor (UF), for

a K-Neighbour Regressor trained on an

optimized data set, derived from Robot's

analysis

(c) Accuracy as function of absolute error in

predicting the correct utilization factor (UF).

The algorithm is tested against a real case.

(d) Accuracy as function of absolute error in

predicting the correct utilization factor (UF).

The algorithm is tested against a real case, but

with the goal of hitting the optimized algorithm

that would fit rather than the actual ones used.

Figure 6: Accuracy analysis for the prediction of optimized steel connections and the ones used in a real project.

5. Benchmark

These analyses have been benchmarked for 1000 connections and the results are presented in table 1.

These numbers scale up quickly. NL-Optimization scales exponentially with the number of

dimensions while heuristic search has not yet found sufficient practical use in the industry. Executing

ML algorithms scales better with respect to both iterations and time which makes them a perfect fit for

complex problem, provided training has been found successful.

6. Case Study

The study conducted so far has proved being very reliable when confronted with untrained data. The

next step has thus been applying it to a real project to assess its use for practical applications. The

project analyzed is a 7 storeys building in London. It is intended for commercial use with spans of

approximately 9 meters. For the scope of this research, 24 end-plate connections were analyzed with

the following properties:

N, Compression force [0..70] [kN]

Proceedings of the IASS Symposium 2018

Creativity in Structural Design

7

Vy, Vertical shear [50..500] [kN]

Mx, Bending moment around the major axis [0..100] [kNm]

Number of bolts: [0..100]

Plate thickness [10..20] [mm]

Bolt diameter: 20 [mm]

Bolt grade: 8.8

Figure 7: Histogram of the White City One data set. (a) Forces, (b) Geometry, (c) Correlation matrix. The

number of bolts is highly correlated with shear and slightly to bending moment. It emerges a strong correlation

between bending moment and plate thickness.

Despite the small number of connection typologies, the data is quite variegated so it should be a good

test case. Picture 6c shows the trained KNeighbours algorithm's predictions for these connections. It is

easy to see a clear discrepancy between these predictions and the joints actually used. But if the head

plates taken from the design are optimized in Robot and the result of this is tested against the ML

algorithm, we get what is shown in figure 6d, which is way closer to the training result. The EC3

design routine embedded in Robot gives us a completely different picture which is not discrepant

anymore but in line with the training results.

Figure 8: The chart shows the breakdown of utilization factor for connections used in White City One and the

forecasted optimized ones.

Fig. 8 shows that the red curve (optimized joints, chosen through ML) is always above or the same as

the blue, except a few exceptions. This means that theoretically there could have been a saving in

material.

This raises the question: where does the truth lie? One can say that since robot’s results are conform to

EC3 requirements and being more utilized are arguably cheaper, that is the right choice. But this is

based on the assumption that there are no other factors to be taken into account which maybe the

Proceedings of the IASS Symposium 2018

Creativity in Structural Design

8

engineers have learned from their experience and on that particular type of project in a particular

situation. It might also have been the case that the contractor had stricter requirements which not

necessarily concerned EC3 design. Optimization needs to have the right design space to be effective,

but it is chosen by the user as well as the parameters. A machine learning approach able to work on

data point embedding the largest number of information possible, would be able to find those patterns

that bring engineer to move away from basic requirements. On the other hand, it might also highlight

outliers in the data and flag possible issues in time or maybe spot better approaches therefore

informing regulations.

7. Conclusion and future progress

This paper has tried to shed a light on the potential AI can bring to the construction industry.

In fact, by gathering data and learning from the past, it would be possible to release engineers

from reinventing the wheel as well as learning from technical experience which can be

extrapolated from patterns in data, improvements in design based on patterns emerging from

real projects, and also incorporate it into guidelines and even codes. It would allow for

automatic statistical predictions on very large amount of data and checks also which is a key

issue in revising large projects. Having this extensive database would also ease retrofitting

and diagnose existent buildings. Complex structures requiring many iterations to solve

(gridshells, highly hyperstatic arrangements, tensegrity, reciprocal frames) will profit as well,

as much as those needing many analysis, tweaking, sensitivity analysis, optimization, etc…

Moreover, the same approach can be applied to spatial arrangement, MEP layout, architectural

finishing, detailing and so on, with the aim to be able to leverage this process to entire

buildings and infrastructures, which would reduce and improve design time while improving

its effectiveness by largely reducing human errors.

References

[1] F. Barbosa, et al, Reinventing Construction: A route to higher productivity, McKinsey Global

Institute, 2017.

[2] S. Adriaenssens, P. Block, D. Veenendaal and C. Williams (eds.), Shell Structures for

Architecture: Form Finding and Optimization, Routledge, 2014.

[3] P. Lu, S. Chen, Y. Zheng, Artificial Intelligence in Civil Engineering, Mathematical Problems in

Engineering, 2012

[4] L. Greco, M. G. Bevilacqua, P. Croce, Computational Architecture: Development, Optimization

and Design. Case study of a glass and steel roof for the Scuola Normale Superiore's courtyard,

Poster for Advances in Architectural Geometry 2014

[5] T. Hastle, R. Tibshirani, J.Friedman, The Elements of Statistical Learning. Data Mining, Inference,

and Prediction, Springer, 2001

[6] Pedregosa et al., Scikit-learn: Machine Learning in Python, JMLR 12, pp. 2825-2830, 2011

[7] P. Samul, Artificial Intelligence in Civil Engineering: AI in Civil Engineering, Lambert, 2012

[8] B. H. Topping, Optimization and Artificial Intelligence in Civil and Structural Engineering,

Springe, 1992