Background: Ocean surface currents need to be monitored to minimize accidents at ship crossings. One way to predict ocean currents—and estimate the danger level of the sea—is by finding out the currents’ velocity and their future direction.
Objective: This study aims to predict the velocity and direction of ocean surface currents.
Methods: This research uses the Elman recurrent neural network (ERNN). This study used 3,750 long-term data and 72 short-term data.
Results: The evaluation with Mean Absolute Percentage Error (MAPE) achieved the best results in short-term predictions. The best MAPE of the U currents (east to west) was 14.0279% with five inputs; the first and second hidden layers were 50 and 100, and the learning rate was 0.3. While the best MAPE of the V currents (north to south) was 3.1253% with five inputs, the first and second hidden layers were 20 and 50, and the learning rate was 0.1. The ocean surface currents’ prediction indicates that the current state is from east to south with a magnitude of around 169,5773°-175,7127° resulting in a MAPE of 0.0668%.
Conclusion: ERNN is more effective than single exponential smoothing and RBFNN in ocean current prediction studies because it produces a smaller error value. In addition, the ERNN method is good for short-term ocean surface currents but is not optimal for long-term current predictions.
Keywords: MAPE, ERNN, ocean currents, ocean currents’ velocity, ocean currents’ directions
A semimodule M over semiring S is called a content semimodules if for every x ∈ M, then x ∈ c(x}M which c(x) = ∩{I|I ideal of S, x ∈ IM} and c is a function from M to I is called the content function. Semimodule is generalization of module, so the study of properties content modules that apply in content semimodules is needed. The aim of this study is investigated properties of semimodules that apply in content semimodules. Indeed we prove content semimodule M satisfy s(c(x)) = c(sx) for all x ∈ M if and only if (I:
Ss}M = (IM:
M s}. Furthermore, if M is content torsionfree semimodule over semidomain S then s(c(x)) = c(sx) for all s ∈ S and x ∈ M. By adopting a concept of semidomain, it has been proven that if every principal ideal of S is subtractive and M be a normally flat semimodules then M is torsionfree semimodule, implies that M is normally flat content semimodules so that applies s(c(x)) = c(sx). If M is content semimodule and I ideal of semidomain S that satisfy (I:
S s}M = (IM:
M s) then (I:
S J}M = (IM:
M J} for all I, J ideal of S, implies that for normally flat content semimodule M over semidomain S applies (I:
SJ}M = (IM:
MJ}.
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