Oct 6, 2008 - School of Civil, Environmental and Mining Engineering, University of ... briefly examines the areas of geotechnical engineering to which ANNs ...
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The 12 International Conference of International Association for Computer Methods and Advances in Geomechanics (IACMAG) 1-6 October, 2008 Goa, India
Future Challenges for Artificial Neural Network Modelling in Geotechnical Engineering M. B. Jaksa, H. R. Maier School of Civil, Environmental and Mining Engineering, University of Adelaide, Adelaide, Australia
M. A. Shahin Department of Civil Engineering, Curtin University of Technology, Perth, Australia Keywords: artificial neural networks, artificial intelligence ABSTRACT: Artificial neural networks (ANNs) are a form of artificial intelligence and, since the mid-1990s, ANNbased models have been successfully applied to virtually every problem in geotechnical engineering. This paper briefly examines the areas of geotechnical engineering to which ANNs have been applied, provides a brief overview of the operation of ANN models, and highlights and discusses four important issues which require further attention in the future. These are model robustness, transparency and knowledge extraction, extrapolation, and uncertainty. For ANN models to be more effective and useful in the future, it is essential that further work be undertaken in these four areas, particularly in the context of geotechnical engineering.
1 Introduction Since the early 1990s, artificial neural networks (ANNs) have been applied to almost every problem in geotechnical engineering, including: blasting (Lu, 2005); dams (Kim and Kim, 2007); earth retaining structures (Goh et al., 1995; Kung et al., 2007); environmental geotechnics (Shang et al., 2004); ground anchors (Shahin and Jaksa, 2004; 2005a; 2005b; 2006); liquefaction (Goh, 1994b; 1996a; Agrawal et al., 1997; Ali and Najjar, 1998; Najjar and Ali, 1998; Ural and Saka, 1998; Juang and Chen, 1999; Goh, 2002; Javadi et al., 2006; Young-Su and Byung-Tak, 2006; Goh and Goh, 2007); pile foundations (Goh, 1994a; 1995b; 1996b; Chan et al., 1995; Lee and Lee, 1996; Teh et al., 1997; Abu-Kiefa, 1998; Nawari et al., 1999; Rahman et al., 2001; Hanna et al., 2004; Goh et al., 2005; Das and Basudhar, 2006); rock mechanics (Gokceoglu et al., 2004); site characterisation (Zhou and Wu, 1994; Basheer et al., 1996; Najjar and Basheer, 1996a; Rizzo et al., 1996); shallow foundations (Sivakugan et al., 1998; Shahin et al., 2002a; 2002b; 2003a; 2003b; 2003c; 2004a; 2005a; 2005b; Provenzano et al., 2004; Padmini et al., 2007; Rezania and Javadi, 2007; Samui, 2007); slope stability (Ni et al., 1996; Ferentinou and Sakellariou, 2007; Zhao, 2007); soil properties and behaviour (Ellis et al., 1992; Agrawal et al., 1994; Gribb and Gribb, 1994; Penumadu et al., 1994; Basheer and Najjar, 1995; Cal, 1995; Ellis et al., 1995; Goh, 1995a; 1995c; Najjar and Basheer, 1996b; Najjar et al., 1996a; 1996b; Romero and Pamukcu, 1996; Penumadu and Jean-Lou, 1997; Basheer and Najjar, 1998; Ghaboussi and Sidarta, 1998; Sidarta and Ghaboussi, 1998; Tutumluer and Seyhan, 1998; Zhu et al., 1998a; 1998b; Najjar et al., 1999; Penumadu and Zhao, 1999; Kurup and Dudani, 2002; Habibagahi and Bamdad, 2003; Lee et al., 2003; Shahin and Indraratna, 2006; Erzin, 2007; Hung and Ni, 2007; Najjar and Huang, 2007); and tunnels and underground openings (Lee and Sterling, 1992; Moon et al., 1995; Shi et al., 1998; Shi, 2000; Yoo and Kim, 2007). The interested reader is referred to Shahin et al. (2001) where the pre-2001 papers are reviewed in some detail. As geotechnical engineering deals with materials which, by their very nature, can exhibit extreme variability, ANNs are particularly amenable to modelling the complex behaviour of these materials and have generally demonstrated superior predictive performance when compared with traditional methods. The aim of this paper is to highlight and discuss a number of important issues associated with the development of ANN models which require further attention in the future.
2 Brief overview of artificial neural networks Whilst a comprehensive description of ANNs is beyond the scope of this paper, and is provided by several authors (e.g. Hecht-Nielsen, 1990; Maren et al., 1990; Zurada, 1992; Fausett, 1994; Ripley, 1996), in the context of this paper, it is useful to provide a brief overview. ANNs are a form of artificial intelligence which attempt to mimic, in a very simplistic fashion, the behaviour of the human brain and nervous system. Typically, the
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architecture of ANNs consists of a series of processing elements (PEs), or nodes, that are usually arranged in layers: an input layer, an output layer and one or more hidden layers, as shown in Figure 1. x
f(I j
0
x1
Ij
w j0 w j1
. . .
. .
x2
. . .
w j2 Weights
Hidden Input
w jn
Output
yj
Sum
Output path Processing Element
xn Figure 1. Typical structure and operation of an ANN model. (After Maier and Dandy, 1998). The input from each PE in the previous layer xi is multiplied by an adjustable connection weight wji. At each PE, the weighted input signals are summed and a threshold value θj is added. This combined input Ij is then passed through a non-linear transfer function f(.) to produce the output of the PE yj. The output of one PE provides the input to the PEs in the next layer. This process is summarised in Eqns (1) and (2) and illustrated in Figure 1.
Ij =
∑w
ji x i
+θ j
y j = f (I j )
summation
(1)
transfer
(2)
The propagation of information in an ANN starts at the input layer where the input data are presented. The network adjusts its weights on the presentation of a training data set and uses a learning rule to find a set of weights that will produce the input/output mapping that has the smallest possible error. This process is called ‘learning’ or ‘training.’ Once the training phase of the model has been successfully accomplished, the performance of the trained model needs to be validated using an independent testing set. The main steps involved in the development of an ANN, as suggested by Maier and Dandy (2000), are illustrated in Figure 2. Several of these steps are discussed in some depth in the following section.
Choice of model architecture
Choice of performance criteria
Connection type (e.g. feedforward, feedback) Degree of connectivity (e.g. fully connected) Number of layers Number of nodes per layer (trial & error, constructive or pruning methods)
Training Speed Processing speed during recall Prediction accuracy
Choice of data sets
Choice of stopping criteria
Number of data sets (e.g. two, three, holdout method) Method for data division
Fixed number of iterations Training error Cross-validation
Data pre-processing
Choice of optimization method Scaling Transformation to normality Removal of non-stationarities
Local first order (e.g. back-propagation) Local second order (e.g. Levenberg-Maquardt , Conjugate Gradient) Global (e.g. simulated annealing, genetic algorithm)
Choice of model inputs
Validation Choice of variables Choice of lags
Figure 2. The main steps involved in ANN model development. (After Maier and Dandy, 2000). As described above, ANNs learn from data examples presented to them and use these data to adjust their weights in an attempt to capture the relationship between the model input variables and the corresponding
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outputs. Consequently, ANNs need no prior knowledge regarding the nature of the relationship between the input and output variables. This is one of the main benefits of ANNs when compared with most empirical and statistical methods.
3 Issues requiring further attention in the future In the context of modelling environmental systems, Maier and Dandy (2000; 2001) highlighted the lack of guidance when developing ANN models and identified several issues that need to be considered. These include data transformation, the determination of appropriate model inputs and network geometry, the optimisation of connection weights and validation of model performance. These issues are equally relevant in the development and application of ANN models in geotechnical engineering, and interested readers are referred to these papers for a detailed treatment on each of these topics. Figure 2, presented earlier, provides a clear summary of the ANN development process recommended by Maier and Dandy (2000). Shahin et al. (2004b) provided guidance in relation to the second step of choice of data sets, using a geotechnical engineering example, and recommended the use of three, statistically consistent but independent data sets, one for each of training, testing and validation. Key issues which have received recent attention and also require further research in the future include developing approaches that: (i) ensure the development of robust models; (ii) increase model transparency and enable knowledge to be extracted from trained ANNs; (iii) improve extrapolation ability; and (iv) deal with uncertainty. Each of these is treated below.
3.1 Model robustness Kingston et al. (2005b) stated for “ANNs are to become more widely accepted and reach their full potential…, they should not only provide a good fit to the calibration and validation data, but the predictions should also be plausible in terms of the relationship modelled and robust under a wide range of conditions.” In addition, the authors stated that while ANNs validated against error alone may produce accurate predictions for situations similar to those contained in the training data, they may not be robust under different conditions unless the relationship by which the data were generated has been adequately estimated. Hence, it is also important to assess the relationship that has been modelled in the validation of an ANN, rather base it on an error measure alone. Shahin et al. (2005c) presented a geotechnical engineering case study of settlement data of shallow foundations on granular soils using two different ANN models. Both models were developed using the same software (NeuralWare, 1997), model parameters and architecture (5 inputs, one hidden layer with two nodes, and a single output), except that they were optimised with different sets of random starting weights. It can be seen from Table 1 that both models perform very well when assessed against traditional measures such as the coefficient of correlation, r; root mean square error, RMSE; and mean absolute error, MAE. In the absence of any further information, one would normally adopt one or other of the two models and use it for predictive purposes within the range of the input data used to train the models. Table 1. Performance of the ANN models developed. Model No.
Data set
1
Training
0.92
Testing
0.94
8.4
5.8
Validation
0.88
12.9
9.8
2
r
RMSE [mm] 10.8
MAE [mm] 7.4
Training
0.94
9.1
6.3
Testing
0.94
9.1
6.8
Validation
0.89
11.8
9.6
Figure 3 shows the results of sensitivity analyses performed to assess the generalisation ability of both models. The results were obtained by adopting the approach used by Goh (1995a), where all input variables, except one, were fixed to the mean values used for training and a set of synthetic data (whose values lie between the minimum and maximum values used for model training), were generated for the single input that was allowed to vary. The synthetic data were generated by increasing their values in increments equal to 5% of the total range between the minimum and maximum values. These input values were then entered into both ANN models and the corresponding outputs obtained. The robustness of the models was then determined by examining how well the predicted outputs, in this case footing settlement, agree with the known underlying physical processes over
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the range of inputs examined. It can be seen that the results obtained for Model-1 agree with those that one would expect based on the known physical behaviour of settlement of shallow foundations on granular soils. For example, in Figures 3(a), (b) and (d), there is an increase in the predicted settlement, in a relatively consistent and smooth fashion, as the footing width, footing net applied pressure and footing geometry, respectively, increase. On the other hand, in Figures 3(c) and (e), the predicted settlement decreases, also in a consistent and smooth fashion, as the average SPT 35
40 35
Predicted settlement (mm)
Predicted settlement (mm)
45 Model-1 Model-2
30 25 20 15 10 5
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Model-2
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500
600
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(b)
(a) 12
70
Model-1
60
Model-2
Predicted settlement (mm)
80 Predicted settlement (mm)
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Footing net applied pressure (kPa)
50 40 30 20 10 0
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Model-2
9 8 7 6 5
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10 15 20 25 30 35 40 45 50 55 60
1
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Average SPT blow count
3
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Footing geometry
(c)
(d)
Predicted settlement (mm)
10 Model-1
9
Model-2 8 7 6 5 0
0.5
1
1.5
2
2.5
3
Footing embedment ratio
(e) Figure 3. Results of the sensitivity analysis to test the robustness of the ANN models. (After Shahin et al., 2005c). blow count and footing embedment ratio, respectively, increase. In contrast, it can be seen from Figure 3 that the results obtained for Model-2 have an unexpected shape that is difficult to justify from a physical understanding of footing settlement. For example, there are abrupt changes in the predicted settlement in some instances and no change in predicted settlement for a range of inputs in others.
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Shahin et al. (2005c) argued that since cross-validation (Stone, 1994) was adopted during the model development phase and an independent validation set was used to test the predictive ability of both models, the only plausible explanation for the different behaviour exhibited by both models was the connection weights included in each model. Garson (1991) suggested the connection weights be examined as part of the interpretation of ANN model behaviour and, as a result, these are shown in Figure 4. It can be seen that the values of the weights obtained for Model-1 are more consistent than those of Model-2. Some of the weight values for Model-2 are significantly larger than the others, which can often indicate a problem with the model (Bailey and Thompson 1990), and result in erratic behaviour. The large values of the weights of Model-2 generally cause the node activations to be large, and as a result, the nodal outputs can become trapped in the flat spots at the extreme values of the transfer functions used in the hidden and output layers of Model-2.
20 Weight absolute value
18
Model-1 Model-2
16 14 12 10 8 6 4 2 0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Weight No
Figure 4. Bar charts of the weights obtained for both ANN models. (After Shahin et al., 2005c). However, individual weights cannot be associated with any physical meaning. This is in contrast with the relative input contributions, which can be associated with physical meaning and hence the use of such measures can facilitate the assessment of a trained ANN and enable constraints to be applied to the objective function during calibration to direct the search for the optimum weight vector into physically feasible regions of the search space (Kingston et al., 2005b). In their study, Kingston et al. (2005b) adopted the Connection Weight Approach of Olden et al. (2004) to determine the input contributions in order to assess the relationship modelled by the ANNs. The authors concluded that this approach provided the best overall methodology for quantifying ANN input importance in comparison to other commonly used methods, albeit with a few limitations. They went on to state that an improved measure for quantifying input contributions is needed.
3.2 Model transparency and knowledge extraction Closely related to the previous issue, and one of the major criticisms often levelled at ANNs, is their lack of transparency; that is, they are often referred to as ‘black-box’ models because they do not consider nor explain the underlying physical processes. Jain et al. (2004), with respect to hydrological engineering, addressed this issue by examining whether or not the physical processes in a watershed were inherent in a trained ANN rainfallrunoff model. They assessed the strengths of the relationships between the distributed components of the ANN model, in terms of the responses from the hidden nodes, and the deterministic components of the hydrological process, computed from a conceptual rainfall runoff model, along with the observed input variables, using correlation coefficients and scatter plots. They concluded that the trained ANN in fact captured different components of the physical process and a careful examination of the distributed information contained in the trained ANN can inform one about the nature of the physical processes captured by various components of the ANN model. Again in the context of hydrological engineering, Sudheer (2005) performed perturbation analysis to assess the influence of each individual input variable on the output variable and found it to be an effective means of identifying the underlying physical process inherent in the trained ANN. Sudheer and Jain (2004) and Kingston et al. (2006) also addressed this issue of model transparency and knowledge extraction. In terms of knowledge extraction, Shahin et al. (2002b) and Shahin and Jaksa (2005a) expressed the results of the trained ANNs in the form of relatively straightforward equations. This was possible due to the relatively small number of input and output variables, and hidden nodes. More recently, Rezania and Javadi (2007), using genetic programming techniques, improved upon and greatly simplified the formula developed by Shahin et al. (2002b), further enhancing the transparency of the ANN model.
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Neurofuzzy applications are another means of knowledge extraction that facilitate model transparency. Examples of such applications in geotechnical engineering include Ni et al. (1996), Shahin et al. (2003a, b, c), Gokceoglu et al. (2004) , Provenzano et al. (2004), Shahin et al. (2005b), and Padmini et al. (2007).
3.3 Extrapolation It is generally accepted that ANNs perform best when they do not extrapolate beyond the range of the data used for calibration (Flood and Kartam, 1994; Minns and Hall, 1996; Tokar and Johnson, 1999). Whilst this is not unlike other models, it is nevertheless an important limitation of ANNs, as it restricts their usefulness and applicability. Extreme value prediction is of particular concern in several areas of civil engineering, such as hydrological engineering, when floods are forecast, as well as in geotechnical engineering when, for example, liquefaction potential and the stability of slopes are assessed. Sudheer et al. (2003) highlighted this issue and proposed a methodology, based on the Wilson-Hilferty transformation, for enabling ANN models to predict extreme values with respect to peak river flows. Their methodology yielded superior predictions when compared with those obtained from an ANN model using untransformed data.
3.4 Uncertainty Finally, a further limitation of ANNs is that the uncertainty in the predictions generated is seldom quantified (Maier and Dandy, 2000). Failure to account for such uncertainty makes it impossible to assess the quality of ANN predictions, which severely limits their efficacy. In an effort to address this, a few researchers have applied Bayesian techniques to ANN training (e.g. Buntine and Weigend, 1991; MacKay, 1992; Neal, 1992; and Kingston et al., 2005a in the context of hydrological engineering; and Goh et al., 2005 with respect to geotechnical engineering). Goh et al. (2005) observed that the integration of the Bayesian framework into the backpropagation algorithm enhanced the neural network prediction capabilities and provided assessment of the confidence associated with the network predictions. Shahin et al. (2005a, b) also incorporated uncertainty in the ANN process by developing a series of design charts expressing the reliability of settlement predictions for shallow foundations on cohesionless soils. Research to date has demonstrated the value of Bayesian neural networks, although further work is needed in the area of geotechnical engineering.
4 Conclusions This paper has presented a brief overview of artificial neural networks (ANNs) and their application in the field of geotechnical engineering. In addition, four issues have been highlighted, namely model robustness, transparency and knowledge extraction, extrapolation, and uncertainty, as areas which require further research attention in the future. Together, improvements in these four areas will greatly enhance the usefulness of ANN models with respect to geotechnical engineering applications.
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