## Encyclopedia of Artificial Intelligence

For the breakwater to be stable, the armour layer units (stones or concrete pieces) must not be removed by wave action. Stability is basically achieved by weight.
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Artificial Intelligence and Rubble-Mound Breakwater Stability Gregorio Iglesias Rodriguez University of Santiago de Compostela, Spain Alberte Castro Ponte University of Santiago de Compostela, Spain Rodrigo Carballo Sanchez University of Santiago de Compostela, Spain Miguel Ángel Losada Rodriguez University of Granada, Spain

INTRODUCTION Breakwaters are coastal structures constructed to shelter a harbour basin from waves. There are two main types: rubble-mound breakwaters, consisting of various layers of stones or concrete pieces of different sizes (weights), making up a porous mound; and vertical breakwaters, impermeable and monolythic, habitually composed of concrete caissons. This article deals with rubble-mound breakwaters. A typical rubble-mound breakwater consists of an armour layer, a filter layer and a core. For the breakwater to be stable, the armour layer units (stones or concrete pieces) must not be removed by wave action. Stability is basically achieved by weight. Certain types of concrete pieces are capable of achieving a high degree of interlocking, which contributes to stability by impeding the removal of a single unit. The forces that an armour unit must withstand under wave action depend on the hydrodynamics on the breakwater slope, which are extremely complex due to wave breaking and the porous nature of the structure. A detailed description of the flow has not been achieved until now, and it is unclear whether it will be in the future in view of the turbulent phenomena involved. Therefore the instantaneous force exerted on an armour unit is not, at least for the time being, amenable to determination by means of a numerical model of the flow. For this reason, empirical formulations are used in rubble-mound design, calibrated on the basis of laboratory tests of model structures. However, these formulations cannot take into account

all the aspects affecting the stability, mainly because the inherent complexity of the problem does not lend itself to a simple treatment. Consequently the empirical formulations are used as a predesign tool, and physical model tests in a wave flume of the particular design in question under the pertinent sea climate conditions are de rigueur, except for minor structures. The physical model tests naturally integrate all the complexity of the problem. Their drawback lies in that they are expensive and time consuming. In this article, Artificial Neural Networks are trained and tested with the results of stability tests carried out on a model breakwater. They are shown to reproduce very closely the behaviour of the physical model in the wave flume. Thus an ANN model, if trained and tested with sufficient data, may be used in lieu of the physical model tests. A virtual laboratory of this kind will save time and money with respect to the conventional procedure.

BACKGROUND Artificial Neural Networks have been used in civil engineering applications for some time, especially in Hydrology (Ranjithan et al., 1993; Fernando and Jayawardena, 1998; Govindaraju and Rao, 2000; Maier and Dandy, 2000; Dawson and Wilby, 2001; Cigizoglu, 2004); some Ocean Engineering issues have also been tackled (Mase et al., 1995; Tsai et al., 2002; Lee and Jeng, 2002; Medina et al., 2003; Kim and Park, 2005; Yagci et al., 2005). Rubble-mound breakwater stabil-

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AI and Rubble-Mound Breakwater Stability

ity is studied in Mase et al.’s (1995) pioneering work, focusing on a particular stability formula. Medina et al. (2003) train and test an Artificial Neural Network with stability data from six laboratories. The inputs are the relative wave height, the Iribarren number and a variable representing the laboratory. Kim and Park (2005) compare different ANN models on an analysis revolving around one empirical stability formula, as did Mase et al.’s (1995). Yagci et al. (2005) apply different kinds of neural networks and fuzzy logic, characterising the waves by their height, period and steepness.

PHySICAL MODEL AND ANN MODEL The Artificial Neural Networks were trained and tested on the basis of laboratory tests carried out in a wave flume of the CITEEC Laboratory, University of La Coruña. The flume section is 4 m wide and 0.8 m high, with a length of 33 m (Figure 1). Waves are generated by means of a piston-type paddle, controlled by an Active Absorption System (AWACS) which ensures that the waves reflected by the model are absorbed at the paddle. The model represents a typical three-layer rubblemound breakwater in 15 m of water, crowned at +9.00 m, at a 1:30 scale. Its slopes are 1:1.50 and 1:1.25

on the seaward and leeward sides, respectively. The armour layer consists in turn of two layers of stones with a weight W=69 g ±10%; those in the upper layer are painted in blue, red and black following horizontal bands, while those in the lower layer are painted in white, in order to easily identify after a test the damaged areas, i.e., the areas where the upper layer has been removed. The filter layer is made up of a gravel with a median size D50 = 15.11 mm and a thickness of 4 cm. Finally, the core consists of a finer gravel, with D50 = 6.95 mm, D15 = 5.45 mm, and D85 = 8.73 mm, and a porosity n = 42%. The density of the stones and gravel is γr = 2700 kg/m3. Waves were measured at six different stations along the longitudinal, or x-axis, of the flume. With the origin of x located at the rest position of the wave paddle, the first wave gauge, S1, was located at x=7.98 m. A group of three sensors, S2, S3 and S4, was used to separate the incident and the reflected waves. The central wave gauge, S3, was placed at x=12.28 m, while the position of the others, S2 and S4, was varied according to the wave generation period of each test (Table 1). Another wave gauge, S5, was located 25 cm in front of the model breakwater toe, at x=13.47 m, and 16 cm to the right (as seen from the wave paddle) of the flume centreline, so as not to interfere with the video recording of the

Figure 1. Experimental set-up

Table 1. Relative water depth (kh), wave period (T), and separation between sensors S2, S3 and S4 in the stability tests Test key

kh

T (s)

S2-S3 (cm)

S3-S4 (cm)

T10, T20

0.98

1.65

35

55

T11, T21

1.36

1.3

20

30

T12, T22

1.68

1.13

20

30

T13, T23

1.97

1.03

20

30

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AI and Rubble-Mound Breakwater Stability

tests. Finally, a wave gauge (S6) was placed to the lee of the model breakwater, at x=18.09 m. Both regular and irregular waves were used in the stability tests. This article is concerned with the eight regular wave tests, carried out with four different wave periods. The water depth in the flume was kept constant throughout the tests (h=0.5 m). Each test consisted of a number of wave runs with a constant value of the wave period T, related to the wavenumber k by T =2

1

[gk tanh(kh)] 2, −

where g is the gravitational acceleration. The wave periods and relative water depths (kh) of the tests are shown in Table 1. Each wave run consisted of 200 waves. In the first run of each test, the generated waves had a model height H=6 cm (corresponding to a wave height in the prototype Hp=1.80 m); in the subsequent runs, the wave height was increased in steps of 1 cm (7 cm, 8 cm, 9 cm, etc.), so that the model breakwater was subject to ever more energetic waves. Four damage levels (Losada et al., 1986) were used to characterize the stability situation of the model breakwater after each wave run: (0) No damage. No armour units have been moved from their positions. (1) Initiation of damage. Five or more armour units have been displaced. (2) Iribarren damage. The displaced units of the armour’s first (outer) layer have left uncovered an area of the second layer large enough for a stone to be removed by waves. (3) Initiation of destruction. The first unit of the armour’s second layer has been removed by wave action. As the wave height was increased through a test, the damage level also augmented from the initial ‘no damage’ to ‘initiation of damage’, ‘Iribarren damage’, and eventually ‘initiation of destruction’, at which point the test was terminated and the model rebuilt for the following test. The number of wave runs in a test varied from 10 to 14. The foregoing damage levels provide a good semiquantitative assessment of the breakwater stability condition. However, the following nondimensional 

damage parameter is more adequate for the Artificial Neural Network model: S=

nD50 (1 − p )b

where D50 is the median size of the armour stones, p is the porosity of the armour layer, b is the width of the model breakwater, and n is the number of units displaced after each wave run. In this case, D50 = 2.95 cm, p = 0.40, and b = 50 cm. The incident wave height was nondimensionalized by means of the zero-damage wave height of the SPM (1984) formulation,

   W KD    H0 =    

3

r w

 − 1 cot  r

1

3      

where KD=4 is the stability coefficient, γw=1000 kg/m3 is the water density (freshwater used in the laboratory tests), and a is the breakwater slope. With these values, H0 = 9.1 cm. The nondimensional incident wave height is given by H* =

H H0

where H stands for the incident wave height. Most of the previous applications of Artificial Neural Networks in Civil Engineering use multilayer feedforward networks trained with the backpropagation algorithm (Freeman and Skapura, 1991; Johansson et al., 1992), which will also be employed in this study; their main advantage lies in their generalisation capabilities. Thus this kind of network may be used, for instance, to predict the armour damage that a model breakwater will sustain under certain conditions, even if these conditions were not exactly part of the data set with which the network was trained. However, the parameters describing the conditions (e. gr., wave height and period) must be within the parameter ranges of the stability tests with which the ANN was trained.

AI and Rubble-Mound Breakwater Stability

In this case, the results from the stability tests of the model rubble-mound breakwater described above were used to train and test the Artificial Neural Network. The eight stability tests comprised 96 wave runs. The input to the network was the nondimensional wave height (H*) and the relative water depth (kh) of a wave run, and the output, the resulting nondimensional damage parameter (S). Data from 49 wave runs, corresponding to the four stability tests T20, T21, T22, and T23, were used for training the network; while data from 46 wave runs, pertaining to the remaining four tests (T10, T11, T12, and T13) were used for testing it. This distribution of data made sure that each of the four wave generation periods (Table 1) was present in both the training and the testing data sets. First, an Artificial Neural Network with 10 sigmoid neurons in the hidden layer and a linear output layer was trained and tested 10 times. The ANN was trained by means of the Bayesian Regularisation method (MacKay, 1992), known to be effective in avoiding overfitting. The average MSE values were 0.2880 considering all the data, 0.2224 for the training data set, and 0.3593 for the testing data set. The standard deviations of the MSE values were 5.9651x10-10, 9.0962x10-10, and 7.7356x10-10, for the complete data set, the training and the testing data sets, respectively. Increasing the number of neural units in the hidden layer to 15 did not produce any significant improvement in the average MSE values (0.2879, 0.2222 and 0.3593 for all the data, the training data set and the testing data set, respectively), so the former Artificial Neural Network, with 10 neurons in the hidden layer, was retained. The following results correspond to a training and testing run of this ANN with a global MSE of 0.2513. The linear regression analysis indicates that the ANN data fit very well to the experimental data over the whole range of the nondimensional damage parameter S. In effect, the correlation coefficient is 0.983, and the equation of the best linear fit, y = 0.938 x − 0.00229 , is very close to that of the diagonal line y = x (Figure 2). The results obtained with the training data set (stability tests T20, T21, T22 and T23) show an excellent agreement between the ANN model and the physical model (Figure 3). In three of the four tests (T20, T22 and T23) the ANN data mimic the measurements on the model breakwater almost to perfection. In test T21, the physical model experiences a brusque increase in the damage level at H* =1.65, which is slightly softened by the ANN model. The MSE value is 0.1441.

Figure 2. Regression analysis. Complete data set.

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The testing data set comprised also four stability tests (T10, T11, T12 and T13). The inherent difficulty of the problem is apparent in test T11 (Figure 4), in which the nondimensional damage parameter (S) does not increase in the wave run at H* =1.54, but suddenly soars by about 100% in the next wave run, at H* =1.65. Such differences from one wave run to the next are practically impossible to capture by the ANN model, given that the inputs to the ANN model either vary only slightly, by less than 7% in this case (the nondimensional wave height, H*) or do not vary at all (the relative water depth, kh). It should be remembered that, when computing the damage after a given wave run, the ANN does not have any information about the damage level before that wave run, unlike the physical model. Yet the ANN performs well, yielding an MSE value of 0.3678 with the testing data set.

FUTURE TRENDS In this study, results from stability tests carried out with regular waves were used. Irregular wave tests should also be analyzed by means of Artificial Intelligence, and it is the authors’ intention to do so in the future. Breakwater characteristics are another important aspect of the problem. The ANN cannot extrapolate beyond the ranges of wave and breakwater characteristics on which it was trained. The stability tests used for this 

AI and Rubble-Mound Breakwater Stability

Figure 3. ANN () and physical model results (ο) for the stability tests T20, T21, T22 and T23 (training data set)

Figure 4. ANN () and physical model results (ο) for the stability tests T10, T11, T12 and T13 (testing data set)

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AI and Rubble-Mound Breakwater Stability

study considered one model breakwater; further tests involving physical models with other geometries and materials should be undertaken. Once the potential of Artificial Neural Networks to model the behaviour of a rubble-mound breakwater subject to wave action has been proven, a virtual laboratory could be constructed with the results from these tests.

REFERENCES

CONCLUSION

Fernando, D.A.K., Jayawardena, A.W., 1998. Runoff forecasting using RBF networks with OLS algorithm. Journal of Hydrologic Engineering 3(3), 203-209.

This article shows that Artificial Neural Networks are capable of modelling the behaviour of a model rubblemound breakwater in the face of energetic waves. This is a very complex problem for a number of reasons. In the first place, the hydrodynamics of waves breaking on a slope are not well known, so much so that a detailed characterization of the motions of the water particles is not possible for the time being, and may remain so in the future due to the chaotic nature of the processes involved. Second, in the case of a rubblemound breakwater the problem is further compounded by the porous nature of the structure, which brings about a complex wave-structure interaction in which the flux of energy carried by the incident wave is distributed into the following processes: (i) wave reflection; (ii) wave breaking on the slope; (iii) wave transmission through the porous medium; and (iv) dissipation. The subtle interplay between all these processes means that it is not possible to study one of them without taking the others into account. Third, the porous medium itself is of a stochastic nature: no two rubble-mound breakwaters can be said to be identical. This complexity has precluded up to now the development of a numerical model which can reliably analyse the forces acting on the armour layer units and hence the stability situation of the breakwater. As a consequence, physical model tests are a necessity whenever a major rubble-mound structure is envisaged. Notwithstanding the difficulty of the problem, the Artificial Neural Network used in this work has been shown to reproduce very closely the physical model results. Thus, an Artificial Neural Network can constitute, once properly trained and validated, a virtual laboratory. Testing a breakwater in this virtual laboratory is much quicker and far less expensive that testing a physical model of the same structure in a laboratory wave flume.

Cigizoglu, H.K., 2004. Estimation and forecasting of daily suspended sediment data by multilayer perceptrons. Advances in Water Resources 27,185-195. Dawson, C.W., Wilby, R.L., 2001. Hydrological modeling using artificial neural networks. Progress in Physical Geography 25 (1), 80-108. 20

Freeman, J. A., Skapura, D. M., 1991. Neural Networks. Algorithms, Applications, and Programming Techniques. Addison-Wesley. Govindaraju, R.S., Rao, A.R., 2000. Artificial neural networks in hydrology. Kluwer Academic Publishers, Dordrecth Boston, MA, p. 329. Haykin, S. (1999). Neural Networks (2nd ed.). Englewood Cliffs, NJ: Prentice Hall. Johansson, E. M., Dowla, F. U., Goodman, D. M., 1992. Backpropagation learning for multi-layer feed-forward neural networks using the conjugate gradient method. Int. J. of Neural Systems, 2(4), 291-301. Kim, D.H., Park, W.S., 2005. Neural network for design and reliability analysis of rubble mound breakwaters. Ocean Engineering 32 (11-12), 1332-1349. 21 Lee, T.L., Jeng, D.S., 2002. Application of artificial neural networks in tideforecasting. Ocean Engineering 29 (9), 1003–1022. Lippmann, R. P., 1987. An Introduction to Computing with Neural Nets, IEEE, ASSP Magazine. Losada, M. A., Desiré, J. M., Alejo, L. M., 1986. Stability of blocks as breakwater armor units. J. Struc. Engrg., ASCE, 112(11), 2392-2401. MacKay, D. J. C., 1992, Bayesian interpolation, Neural Computation, vol. 4, no. 3, pp. 415-447. Maier, H.R., Dandy, G.C., 2000. Neural network for the prediction and forecasting of water resources variables: a review of modeling issues and applications. Environmental Modeling and Software 15, 101–124. Mase, H., Sakamoto, M., Sakai, T., 1995. Neural network for stability analysis of rubble mound break

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waters. Journal of Waterway, Port, Coastal and Ocean Engineering, ASCE 121 (6), 294–299. Medina, J. R., Garrido, J., Gómez-Martín, M.E., Vidal, C., 2003. Armour damage analysis using Neural Networks. Proc. Coastal Structures ’03, Portland, Oregon (USA). Ranjithan, S., Eheart, J. W., Garrett, J.H., 1993. Neural network-based screening for groundwater reclamation under uncertainty. Water Resources Research 29 (3), 563-574. SPM, 1984. Shore Protection Manual. Dept. of the Army, Coast. Engrg. Res. Ctr., Wtrwy. Experiment Station, Vicksburg, Miss. (USA). Tsai, C.P., Lin, C., Shen, J.N., 2002. Neural network for wave forecasting among multi-stations. Ocean Engineering 29 (13), 1683–1695. Yagci, O., Mercan, D.E., Cigizoglu, H.K., Kabdasli, M.S., 2005. Artificial intelligence methods in breakwater damage ratio estimation. Ocean Engineering 32 (17-18), 2088-2106.

KEy TERMS Armour Damage: Extraction of stones or concrete units from the armour layer by wave action. Armour Layer: Outer layer of a rubble-mound breakwater, consisting of heavy stones or concrete blocks. Artificial Neural Networks: Interconnected set of many simple processing units, commonly called neurons, that use a mathematical model representing an input/output relation. Backpropagation Algorithm: Supervised learning technique used by ANNs that iteratively modifies the weights of the connections of the network so the error given by the network after the comparison of the outputs with the desired one decreases. Breakwater: Coastal structure built for sheltering an area from waves, usually for loading or unloading vessels. Reflection: The process by which the energy of the incoming waves is returned seaward. Significant Wave Height: In wave record analysis, the average height of the highest one-third of a selected number of waves.

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