Abstract:
The frequency of accidental discharge of oil into aquatic environment has presented a significant threat to marine biota with related adverse effects on the supply of products and services of importance to human cultures. This threat of economic and environmental devastation led to the development of a number of monitoring and clean-up alternatives such as remote sensing and chemical dispersants, respective. This study proposed a new possible research direction in marine oil spill modeling where the monitoring and clean-up alternatives would be optimized to enhance locations selection for the deployment of containment and combating technique evaluation before actual usage. A novel optimal control theory has been developed through operational research formalism as a critical first step in mitigating the problem of oil spill look-alike phenomenon associated with remote sensing, and the conflicting priorities in the application of chemical dispersants, which may be toxic to marine biota, during marine oil spill clean-up. Markovian decision processes with sequential optimization techniques were utilized in formulating the control-theoretic methodological models that would aid environmental managers in minimizing the uncertainty in the remote sensing data to reduce the high number of false alarms (oil slick look-a-likes) phenomena, minimizing the apparent toxicological effect of clean-up technique like chemical dispersants, determining the control measure that would cause a process to satisfy the physical constraints of chemical dispersants applications, and at the same time optimizing some performance criteria for all future earnings from marine biota. A dynamic model for a new strategy based on a diffusion process, which makes the distinction between two types of optimization objectives: increasing awareness and changing predisposition to adopt coherent pluralistic technique has been developed and the optimality condition forminimization of false alarm in marine oil spill detection was obtainedas: ̇ ( ( )) ( ( )) , where n1 (t )
denote the regions within which the spill originated in the system, n2 (t ) denote other regions
beyond with probable spill threat due to the spill diffusion process and is captured via
remote sensing application, n3 is the potential regions within n2 after verification for
disparity classification, is the decay variable and is time. Furthermore, a penalty cost for
taking, at each time period, any decision following each possible signal was obtained as a
decision rule:
{ ( ) ( )* ( )+ ( ) ( )* ( )+
( ) ( )* ( )+ ( ) ( )* ( )+
6
where is a decision module, z is a decision region,(
misclassification and denotes the observability information
clean-up response model was also obtained as:
max òtt1 f (t , x (t ), u (t ))dt
u0
x¢ (t ) = g (t , x (t ), u (t ))
Subject to x (t 0 ) = 0 and x (t1 ) free
) denotes the cost of dynamic. The optimal
Where u (t ) denote the control and x (t ) the state variables, both of which are functions of time and space, and and are arbitrary functions. The necessary optimality conditions, the existence and uniqueness properties of the optimal control solutions were also established using calculus of variations technique applied to cases with unconstrained states and controls, and Markovian decision process applied to cases with constrained states and control.
These results emphasized the importance of optimal control theory in modelling marine oil spill and reducing the severity of environmental impacts resulting from oil spills in order to preserve the ecological objectives of marine biota. Hence, insight on optimal control formulation for a specific objective function was illustrated theoretically.