7.3 Verifying the strain results from DIANA
7.4.6 Discussion
Based on the findings here it seems possible to make well-performing models that can predict the trend of strains due to the long-term effects with high accuracy. As long as the trend in a signal does not have a sudden change, as for node 1143, it is enough to obtain strain measurements for three years. The models can only predict trends that have already happened, not trends that come later. A challenge with this is that the nature of the strain signals at the points of interest needs to be known to know whether three years of training is sufficient or not. It is also interesting to note that the performance of the models for node 18 is increasing with increasing lengths on the training signal, while for
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node 3 and node 6 the model performance is more shifting. In further work, more research should be done to discover the reasons behind this. It could be interesting to investigate the effect of the network structure and see if it is possible to reduce the length of the training signal.
The models show some potential to eliminate strains due to temperature when a constant temperature is used to predict strains, although it depends on the point of the beam. For node 3 and node 6 the models manage to eliminate the strains from the temperature effect quite well. At these nodes, the strain due to temperature is small compared to the strain from loading, creep and shrinkage. When the strains due to temperature and the strains due to loading, creep and shrinkage are about the same magnitude, such as for node 18, the model has a harder time of damping the daily strain variation due to temperature.
Hence, it can seem like a model’s ability to eliminate strains due to temperature effects is dependent on the magnitude of strains due to temperature effects in the total strain signal used for training. For node 1143 the magnitude of strains due to temperature effects are also relatively large similarly to node 18, but for this node, the model is unable to eliminate the effects of the temperature. The performance of the model for node 1143 is lower than for the other models. This means that the model has a lower generalization, that will say that the model’s ability to follow other trends than the ones it was trained on is not so good at node 1143. Thus, the model performance is important for the model to be able to eliminate the strains due to temperature effects.
The attempts at separating the contributions of creep and shrinkage from the strain signals gave bad results. Maybe further investigations on this point can improve the results or another method for separating the signal should be used.
Another aspect that could be of interest for further work is the possibility to include properties for the concrete quality, creep and shrinkage in one structure when training the model, and then use this model for other similar structures without having to obtain a lot of data for training. This would increase the complexity of the models. Further investigations should also be done to try and remove the daily strain variations due to temperature, and to see how the moment of loading affects both the model performance but also the ability to remove the strains.
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8 Related work
Artificial neural network for predicting drying shrinkage of concrete [31]
Study [31] looks at the possibility of using artificial neural network ANN for predicting the drying shrinkage in concrete. The ANN used in the study is a multi-layer perceptron with backpropagation. Mean squared error is used as the optimization scheme. Experimental data from shrinkage tests were taken from the RILEM database to compare results from the neural network model with results from the material models for calculating shrinkage in concrete that are used today.
The structure of the network that performed best in the study consisted of 11 inputs, two hidden layers with 8 and 4 neurons respectively, and 1 output which is the drying shrinkage. The inputs that were used are the volume/surface exposed to air, relative humidity, age at the start of drying, age of onset of shrinkage measurement, cement type, cement content, water content, the total quantity of aggregates, sand/total aggregate, average compressive strength and modulus of elasticity at 28 days.
From the correlation values in table 8.1 it can be seen that the model based on ANN called NNMPS had the best correlation to the experimental data compared to several different material models used for calculating drying shrinkage.
Table 8.1: Correlation coefficients for shrinkage from experimental data compared with various material models and shrinkage calculated with ANN, called the NNMPS model [31].
Models
ATKANTA model 0.8993 0.8088
S.B3 model 0.8887 0.7898
Artificial neural network for predicting creep of concrete [32]
A similar study to [31] was conducted to look at the possibility of using artificial neural network ANN for predicting creep in concrete [32]. Again, a multi-layer perceptron with back propagation was used, with the mean squared error as the optimization scheme.
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The structure of the network that performed the best in the study consisted of 12 inputs, two hidden layers with 8 neurons each and 1 output which is the drying creep. The inputs used were volume/surface exposed to air, relative humidity, age at start of drying, age at start of loading, age of onset of creep measurement, cement type, cement content, water content, total quantity of aggregates, fine aggregate/total aggregate, average compressive strength at 28 days and modulus of elasticity at loading.
Again, the correlation between the creep predicted with the neural network and the experimental creep data from the RILEM database was better than the correlation between several material models used to calculate creep deformations with today.
An apt material model for drying shrinkage and specific creep of HPC using artificial neural network [33]
Study [33] looked into the possibility of using neural networks for predictions of creep and shrinkage in high-performance concrete (HPC). The challenge with HPC is that the material models describing creep and shrinkage are based on normal concrete, so when the same models are used for calculating creep and shrinkage in HPC, the results vary greatly from actual creep and shrinkage deformations in structures with HPC.
A feed-forward backpropagation network using the Levenberg-Marquardt algorithm in MATLAB was used. The structures of the network used for predicting shrinkage had 12 inputs, 1 hidden layer with 7 neurons and 1 output. The structure of the network used for predicting creep had 12 inputs, 1 hidden layer with 5 neurons and 1 output. The performance of the networks was evaluated using correlation coefficient, root means square error and mean absolute percentage error.
The mean absolute error values found when using the existing material models for calculations of shrinkage in HPC are laying between 20-50%, which shows that the existing models are not very suitable for calculating shrinkage in HPC. With the ANN model, the results showed better correlations between the calculations and the experimental data with a mean absolute error of about 5-12%.
Similar results were found for the creep calculations, where one of the existing material models resulted in mean absolute errors ranging from 6-53% and another model ranged from 56-89%, while the ANN model ranged from 2-14%.
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An Integrated Machine Learning Algorithm for Separating the Long-Term Deflection Data of Prestressed Concrete Bridges [34]
Study [34] uses several different techniques in order to separate the deflection signal from a prestressed concrete bridge into different deflection components such as the live load effect, temperature effect and structural deflection. The different deflection components have different recurrence periods, and this was used to separate the signal. First, a Butterworth filter was used to separate the live load effect, which has a high frequency, from the long-term deflection which has a low frequency. Afterward ensemble empirical mode decomposition (EEMD) and principal component analysis (PCA) were used to process the data so that a fast-independent component analysis (FastICA) algorithm could be used to find the independent deflection components.
The study found that the deflection components could be separated with good accuracy for signals containing 10% noise or less. The correlation coefficients for the different deflection components when the source signal contained 10% noise was above 0.8 while when the signal contained 5% noise all the correlation coefficients were more than 0.9.
Remarks
All these studies [31] [32] [33] show that there is potential in using neural networks for prediction of creep and shrinkage in concrete. The models that are used for calculating these effects today are only approximations often based on empirical data and they also might overestimate the effect of creep and shrinkage for design purposes. The studies show that it is possible to create models with machine learning that are able to predict the effects of creep and shrinkage with higher accuracy than the methods that are used today for calculating these effects. This is useful in cases where it is of importance to know the exact deflection of a structure, such as when constructing cantilever bridges.
As the deflection depends on the long-term effects creep and shrinkage, and the methods used for calculating these effects are not accurate the calculation of deflection also becomes inaccurate. When it is possible to separate a measured deflection signal in a structure it becomes possible to get the accurate contributions of deflection due to different effects, as done in study [34].
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9 Conclusion
Concrete structures experience strains due to loading, long-term effects and temperature effects. As the material models used for calculating the effect of creep and shrinkage today are only approximate methods, these models do not give the accurate strains that can be measured in structures. This has been confirmed in several studies, among them [22] [23]
[24]. The matter of calculating the creep in concrete structures also becomes harder by the fact that concrete behaves nonlinearly when it starts cracking. As the tensile strength in concrete is generally small, cracking of concrete is usually inevitable and also something that is desirable as concrete has a brittle fracture mechanism while steel used to reinforce concrete structures has a ductile fracture mechanism.
Creep and shrinkage effects in concrete structures are complex problems which make it hard to describe the effects with formulas. The fact that the structural stiffness for concrete is dependent on temperature also affects the creep. As machine learning can be very useful for complex problems where a lot of data is available, this thesis has looked at how machine learning can be used to make models with better descriptions of the effect of creep, shrinkage and temperature in concrete. An introduction to machine learning is presented, including some basic information about different learning algorithms, generalization and optimisation of a model, deep learning and neural networks.
To investigate the possibilities of machine learning, strain results have been obtained for a generic concrete bridge. To simplify the modelling, the concrete bridge was modelled as a simply supported beam in 2D. Reinforcement and post-tensioning have been included in the model in accordance with EC2, HB N400 and R668. Strain results with the long-term effects have been obtained with DIANA while strains from the temperature effects were calculated with MATLAB. The Neural Network Time Series toolbox in MATLAB was used for training neural network models with the total strain results. Several models were trained for different points at the beam with time and temperature as inputs and strain as output.
It was seen that the models had a good generalization when trained on three years of the strain signals and managed to predict future strain signals with high accuracy. The models can only predict trends they have already experienced in the training data. If the trends in the strain signal change at a point after the end of the training signal, the model gets problems with predicting future strains. For some strain signals, the performance increases with increased lengths on the training signals while for other strain signals using a shorter training signal might provide a better performing model than using a longer signal. The reason for this could be the general nature and complexity of the strain signals and further investigations should be done to gain more knowledge about this.
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An interesting discovery is that there seems to be potential of eliminating the strain due to the temperature effects by using a constant temperature as input in the model. When the constant temperature is set equal to the initial temperature used in the concrete beam model, the predicted strains match the long-term strains from DIANA well. It has also been seen that the models manage to follow the trend of the long-term strains when the constant temperature is set to a value different than the initial temperature. Further work could be done to see if these strain predictions correspond to long-term strains in the beam modelled with other initial temperatures. In general, the models eliminated the yearly strain variations due to temperature effects, but the models could not remove the daily strain variation. The magnitude of the daily strain variation seems to be affected by the ratio of strains due to temperature compared to the long-term strains.
A downside with machine learning is that it is hard to know exactly what is going on in the algorithm. The more hidden layers and neurons that are added to a neural network, the harder it becomes to know what is going on. It can therefore seem quite random whether a model performs well on data or not, and it is also important to check out many possibilities. Although some algorithms are known to give good results for certain types of problems, it can be necessary to try out several different algorithms and network structure before an optimal model is found. Despite this, machine learning seems to have great potential in many areas. Based on the findings here, it seems possible to use neural networks to predict the effect of creep and shrinkage in concrete. There are also some possibilities to take the effects of temperature into consideration and eliminate parts of these effects. Other studies [31] [32] [33] also agrees with these results, showing that machine learning has potential to generate models for prediction of the effects of creep and shrinkage that has very high accuracy. Although the method for separating different strain components attempted in this thesis did not give good results, study [34] shows that there are methods for separating deflection signals which could also be tested for separating strain signals. Further work in this area might prove other methods for separating strain signals as well.
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Appendix
Appendix A: v01_temperature_variation Appendix B: v05_EI
Appendix C: v06_Temperature_strain Appendix D: v08_MLstrain_temp
Appendix E: Derivation of the stiffness term Appendix F: Stresses distribution, DIANA
Appendix G: Additional machine learning results
Appendix A: v01_temperature_variation
% Matlab script to generate temperature data
% It is possible to define:
% - Length and sampling frequency of the generated array
% - Multiple harmonic variations can be added, each defined in terms of
% period and amplitude
%Temp.Time.dt = Temp.Time.t_end/20000; % [seconds]
Temp.Time.dt = Temp.Time.t_end/(100*365*10);
Temp.Var(var_num).T = 60*60*24*365; % Period [seconds]
Temp.Var(var_num).amp = 10; % [C]
% Temp.Var(var_num).T = 60*60*24*10; % Period [seconds]
% Temp.Var(var_num).amp = 20; % [C]
% ---- Temperature generation, TOP ---- disp('Generating data ... '); tic;
end % for var_num = 1:size(Temp.Var,2)
fprintf('\b'); disp([' DONE (',num2str(toc),'s)']);
clear var_num
% ---- Temperature, BOTTOM ---
Temp.Series.bottom = Temp.Series.top*0;
x = 0; %counting
for i= 1:length(Temp.Series.t)
if Temp.Series.t(i) < Beam.Bottom.delay
Temp.Series.bottom(i) = Temp.T_0 + Beam.Bottom.shift;
x = x + 1;
else
Temp.Series.bottom(i) = Temp.Series.top(i-x) + Beam.Bottom.shift;
Temp.Series.bottom(i) = Temp.Series.top(i-x) + Beam.Bottom.shift;