FIELD DATA RECOVERY IN TIDAL SYSTEM USING ARTIFICIAL NEURAL NETWORKS

Bernard B. Hsieh and Thad C. Pratt

US Army Engineer R&D Center, Waterways Experiment Station, 3909 Halls Ferry Road,

Vicksburg, Mississippi 39180-6199,  USA

Abstract: Field data collection is expensive and plays a main part in building a numerical modeling system.  However, the missing gaps and abnormal recorded data due to instrumental failure curtail the capability of modeling effort. This deficit can be overcome by the system simulation techniques, such as artificial neural networks (ANNs). Several different data recovery patterns, namely, self-recovery, neighboring station recovery, and multivariate parameter recovery, were defined and solved by the ANN modeling technique. The Biscayne Bay tidal system was used to demonstrate this approach. The results indicated that the recovery reliability depends on the parameter characteristics. The performance of missing window size and its location in the time series were discussed.  The partially recurrent network algorithm was found to be the most accurate data recovery system for this application.      

1    INTRODUCTION

The use of modern computing techniques including soft computing and numerical models and their integration has become commonplace in managing water resources projects.  While the latter methodology has been popular to address the physical phenomena, the former technique is paid less attention by the researchers. The main advantages of using numerical models are based on their capability of prescribing the physical laws in the modeling domain. However, their accurate usage often requires extensive computational resources and validation using extensive field measurements and many system parameters need to be estimated, particularly for large-scale and complex system. Hsieh (1997) has proposed a framework design of flow model validation using the integration method of numerical model, stochastic filter, and system simulation techniques. This paper presents an application to address the missing data recovery problem in that design.

In general, the field data collection program consumes a major portion of modeling budget. However, due to the instrumentation adjustment and failure, the obtained data could be incomplete or producing abnormal recording curves. For instance, complete boundary condition data are often critical to the numerical modeling effort. The data may be unavailable at appropriate points along the computational domain when the modeling design work changes. In addition, the key locations, which usually have high gradient variation in the numerical model, could be partially missing.  Therefore, the judgment of engineering design will lose its reliability if sufficient of measurement is not available for those points. The problem of estimation of temporal and spatial variation as described requires more advanced techniques to solve both time-delay and nonlinearity features. In this paper, ANNs are used to address the missing data recovery problem for the data collection activities for a tidal lagoon, Biscayne Bay in Florida, USA.

2    DATA RECOVERY SYSTEMS

ANNs modeling techniques to solve tidal hydraulic problems are a relatively new area (Dibike and Abbott, 1999; Tsai and Lee 1999). The data recovery system (DRS) for missing data is based on the transfer function (response function) approach. The identification of system response is constructed by the training and cross-validation processes of learning from a common period between input and output series for ANNs. The testing portion (performance), which is not involved in the training, is used to compute the simulated output from additional input series. The simulated output from obtaining optimal weights set can generate a data recovery series. This series is called the missing window.  Three types of DRS are defined as follow:

(1) Self-recovery: this type of recovery is based on a single time-series itself. In this situation no other series can be used as the reference to create the response bridge. The method is to break a long time-series into two portions. The first part of the data is considered as the input, and the second part is regarded as the output function and contains the missing window. More percentage of time-series data set, particularly it contains more significant patterns, is critical to the performance.

(2) Neighboring station recovery: this is the most typical recovery case. Obviously, the local recovery should have better performance than the remote recovery. If the involvement between input and output functions is a different parameter, this recovery is classified as the different parameter recovery. Otherwise, it is called the same parameter recovery.

(3) Multivariate parameter recovery: since the system response from input to output could involve more than one variable and receive different time delay, this more complex system requires physical cause and effect to identify the system structure. For example, the salinity variation for a particular location could be caused by the source tide, local wind, and nearby freshwater inflow for an estuary system.

3    STUDY AREA AND FIELD DATA COLLECTION PROGRAM

Pratt (in preparation) summarizes the field data collection program for the Biscayne Bay, a shallow, subtropical marine lagoon located on the southeast coast of Florida. It covers approximately 100 kilometers from north to south and varies from less than 1.6 kilometers to 13 kilometers in width. It is bordered on the west by the South Florida mainland and on the east by a series of barrier islands and shallow, vegetated mud banks. The developed data sets and numerical models that can aid in the study and management of Biscayne Bay include circulation, salinity, and water quality. Bathymetry and geometry of the navigation channels, interconnecting canals and inlets, astronomical tide-induced currents, wind-induced currents, and freshwater inflow are major factors that determine circulation patterns.

The purpose of the field data collection program was to provide hydrodynamic results including velocities, flow distributions, circulation patterns, water levels, salinities, and meteorological measurements during long-term monitoring and short-term intensive surveys. The long-term monitoring equipment used to collect the data consisted of five bottom-mounted ADP velocity meters, ADCP, 12 water-level and velocity recorders, and one meteorological station within the study area.

4    KNOWLEDGE BASE AND ANNs MODELING

To perform the data recovery system, a number of stations with 15-min intervals during February 1998 were used to conduct the analysis. To identify the performance of ANNs, a week of data was purposely hidden to compare the simulation results. This recovery information is called the missing window in the system.

For the hydraulic engineering applications, the backpropogation networks, the time-delayed networks, and the recurrent networks are used to perform the comparisons. The best performance was found to be partially recurrent networks. This paper, unless indicated otherwise, will use the recurrent network to demonstrate the results. The software used for this study is NeuroSolutions (version 3.0). The data set is divided into training (2 weeks), cross-validation (1 week), and testing (1 week) portions. The performance analysis is represented by several quantity numbers, including mean square error, normalized mean square error (NMSE), mean/maximum/minimum absolute errors, and correlation coefficient (CC).

The following parameters are used to perform most of the recurrent networks:

     Hidden Layer (HL)=1,  Input Layer AF=TDNN Axon, Depth in samples=10

      HL PE’s= 2, AF=Linear Axon,  Learn Rule=Momentum,   Step Size=1.0,

         Momentum Factor=0.7

      Output Layer AF=LinearAxon, Learn Rule=Momentum,  Step Size=0.1,

         Momentum Factor=0.7

      Maximum Epoches=1000

5    RESULT DEMONSTRATION

(1) Self- recovery of surface elevations: Tidal stations in the bay entrance are sometimes used to serve as the boundary condition for the numerical modeling study. The experience shows this application can avoid the iteration process for numerical modeling when the boundary condition is not available. The worst condition for the data recovery is that no other reference data set, such as neighboring station, can be used to construct the response function. Semi-diurnal, diurnal, and neap-spring components dominate the harmonic constituents in the tidal system. It seems 2 months of surface elevations (two lunar cycles) is sufficient to construct the self-recovery scheme. The record can be divided into two parts: the first month’s data are assumed as the input series and the second month’s data (with missing window) are used as the output series. The testing process of ANNs modeling creates the estimation of the missing window. Very good agreement (Fig. 1) was found from this missing window recovery result (CC=0.9716 and NMSE=0.0996).

Fig. 1    Self-recovery for surface elevation at lagoon entrance (ft) (missing window recovery (dashed line)).

(2) Neighboring station recovery: The first demonstration of this recovery was to use the tidal station (tide8) to recover the partial missing record in a tidal station (tide9) which is 9.6 kilometers away. This is the most typical tidal signal propagation problem due to the friction effect. The excellent performance was obtained by using the recurrent ANNs (CC=0.9906 and NMSE=0.0205). Using the surface elevation to recover the salinity concentration at the same location (station 11) was the second application. The relatively poor results (CC=0.5576 and NMSE=0.6950) were due to the other forcing factors, such as wind stress, freshwater inflow, and particularly the local effect, were not addressed.

(3) Multivariate parameter recovery: The tidal current is a very important parameter in the tidal hydrodynamic system and is costly to collect. The x-component of current in station 3 receives the signals from the ocean tide (station 9 from 6.4 kilometers away) and the x-component wind stress. The data recovery for this case is shown in Fig. 2. Except for the small short periodic variation, the results show very good pattern match.

Fig. 2    Multivariate parameter recovery for tidal current using surface elevation and wind stress as inputs (missing window recovery (dashed line)).

6    RECOVERY RELIABILITY

Due to physical forcings as input

As in the previous analysis, the reliability of data recovery also depends on the selected parameter and how well the forcing functions are included as the model input. A comparison (Table 1) addresses the reliability of tidal current recovery due to physical processes, namely, tidal forcing, surface slope, and related physical parameters. While tidal current due to the surface slope between two neighboring surface elevations shows the best results; two other approaches also obtain very high correlation. The main source of errors comes from small-scale variation. This could be caused by any other local effect or other physical parameters not addressed well enough. The results show that the wind stress contributes only very minor improvement for the analysis. This is probably because the effects of the wind stress are longer duration (sample depth) than the tidal forcing. A further analysis using mixture networks to separate the input influence could be the alternative approach.

    Table 1    Reliability of tidal current recovery due to physical forcing parameters

        (correlation coefficient and NMSE(cm/sec))

Due to missing window size

An important objective for simulating the missing DRS is to determine how the performance might be related to the size of missing window. A comparison was conducted by using a tidal current simulation example with missing window sizes of 100, 200, 300, and 600 values. While the training data used the same length of record, the cross-validation used less information when the missing window enlarged. No significant differences (Table 2) were found from both training and cross-validation (CC and NMSE). The reliability of missing data recovery gets lower as the window size gets smaller. This unexpected result is due mainly to the initial simulation having larger errors than the following time-steps. When the window size gets smaller, these errors contribute higher percentage of total error to the overall performance. This suggests that when the missing window gets very small, the simulation window could enlarge the window in the beginning end (about 20 more time-step from this case).

  Table 2    Recovery reliability of tidal current (tidal forcing and wind stress as inputs)

                 due to missing window size (correlation coefficient and NMSE (cm/sec))

Due to missing window location

The main feature using ANNs is to recognize and learn the historical patterns. Therefore, another critical issue for DRS is the reliability due to the missing window location from the entire data set. This is particularly important when the data length is not very long. This test is applied to the simulation of tidal current due to the surface slope between two neighboring surface elevations. The original data set was divided into four quarters. Two quarters were used to perform the training, one quarter was used to conduct the cross-validation, and the remaining one quarter was used to generate the missing window (testing). Four combinations (Table 3) with the sequences of training, cross-validation, and testing (missing window) were investigated by checking the performance due to the location of the missing window. The highlighted correlations in Table 3 show very satisfactory performance. The analysis indicated that this is due primarily to the pattern similarity between the data from Quarters 2 and 4. The pattern for data from Quarter 1 is quite different patterns from the other quarters. Therefore, the pattern similarities are still the major factor to assure the good performance for missing data recovery. It is not because of the order of data representation during the learning processes.

Table 3    Recovery reliability of tidal current (surface slope) due to the location of

                    missing window (correlation coefficient and NMSE(cm))

7    CONCLUSIONS

Artificial Neural Networks (ANNs) were used to simulate missing data recovery. The partially recurrent networks receive the best performance for a tidal lagoon system in Biscayne Bay data collection program. The surface elevation is the easiest physical parameter for self-recovery, neighboring station recovery, and multivariate recovery while the conservative parameters, such as salinity, are more difficult to recover due to the complex input system and their response speed. The mixture ANN approach may be the alternative to improve the solution. The performance due to missing window size is not only directly related the length of total data but also associated with the initial portion of the simulation. The data representation of assigning the order of learning processes due to the missing window location is not significant. The degree of pattern similarity between the training data and the testing data determines the performance.

Acknowledgements

The U.S. Army Engineer, Research and Development Center, Waterways Experiment funded this work. Permission was granted by the Chief of Engineers to publish this information.

References

[1]    Dibike, Y., and Abbott, M., 1999, “Application of artificial neural networks to the simulation of a two dimensional flow,” Journal of Hydraulic Research, Vol. 37, No. 4,435-446.

[2]    Hsieh, B. B., 1997, “An optimal design of field data collection for improving numerical model verification,” Proceedings of the 27^th Congress of the International Association of Hydraulic Research, San Francisco, 815-820.

[3]    NeuroSolutions v3.02 Developers Level for Windows, NeuroDimension, Inc., Gainsville, FL.

[4]    Pratt, T. C., “Biscayne bay field data report” (in preparation), U.S. Army Engineer Research and Development Center, Vicksburg, MS.

[5]    Tsai, C., and Lee, T., 1999, “Backpropagation neural network in tidal-level forecasting,” ASCE Journal of Waterway, Port, Coastal, and Ocean Engineering, Vol. 125, No. 4, 195-202.