doi:10.1016/j.apor.2007.11.002
Copyright © 2007 Elsevier Ltd All rights reserved.
Genetic programming for retrieving missing information in wave records along the west coast of India
Ruchi Kalraa and M.C. Deo
, a, 
aDepartment of Civil Engineering, Indian Institute of Technology, Bombay Powai, Mumbai 400 076, India
Received 8 May 2007;
revised 20 September 2007;
accepted 26 November 2007.
Available online 3 January 2008.
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Abstract
Instruments such as floating wave rider buoys provide wave data over a long period in a continuous manner; however such information invariably contains missing values resulting from the instrument and telemetry system that is damaged, malfunctioning or otherwise non-operational. The problem of restoring missing wave heights is attempted in this paper using one of the latest soft computing tools, namely, Genetic Programming (GP). The gaps in the time series of significant wave heights collected at every 3 h for a period of four years from January 2000 to December 2003 are filled in at six selected buoy locations along the west coast of India. The performance of GP was judged in terms of the error statistics of bias, root mean square error, correlation coefficient and scatter index. The methodology demonstrated reliable results with fairly good overall agreement between the restored wave records and actual measurements.
Keywords: ANN; GP; Missing data; Soft computing; Wave heights
Fig. 1. Study area along the west coast of India.
Fig. 2. Program [−q+(π)1/2/3p] in the form of a tree structure.
Fig. 5. Comparison of GP restored significant wave height (3 h) data with target data at location DS2 using single input of station SW4. (a) Scatter (b) Time history.
Fig. 6. Comparison of GP restored significant wave height (3 h) data with target data at location DS1 using single input of station SW4. (a) Scatter (b) Time history.
Fig. 7. Comparison of GP restored significant wave height (3 h) data with target data at location DS1 taking multiple inputs of stations SW4 and DS2. (a) Scatter (b) Time history.
Fig. 8. Comparison of GP restored significant wave height (3 h) data with target data at location SW3 taking single input of station SW4. (a) Scatter (b) Time history.
Fig. 9. Comparison of GP restored significant wave height (3 h) data with target data at location SW3 taking multiple inputs of stations SW4, DS2 and DS1. (a) Scatter (b) Time history.
Fig. 10. Comparison of GP restored significant wave height (3 h) data with target data at location SW2 taking single input of station DS1. (a) Scatter (b) Time history.
Fig. 11. Comparison of GP restored significant wave height (3 h) data with target data at location SW1 taking single input of station DS1. (a) Scatter (b) Time history.
Fig. 12. Experiment on peak prediction (case:E1); (a) before correction; (b) after correction; (c) time history comparisons (start date: 06:06:00:00; end date: 08:06:00:21).
Fig. 13. Experiment on peak prediction (case:E3); (a) before correction; (b) after correction; (c) time history comparisons (start date: 11:07:00:06; end date: 13:07:00:21).
Fig. 14. Experiment on peak prediction (case: E5); (a) before correction; (b) after correction; (c) time history comparisons (start date: 05:06:00:00; end date: 09:06:00:03).
Table 1.
Percentage of missing values

Table 2.
Experiments of gaps in-filling

Table 3.
Error statistics

Table 4.
Percentage error in peaks
