John R.-C. Hsu

FUZZY LOGIC DERIVATION OF NEURAL NETWORK MODELS WITH TIME DELAYS IN SUBSYSTEMS

This paper extends the Takagi-Sugeno (T-S) fuzzy model representation to analyze the stability of interconnected systems in which there exist time delays in subsystems. A novel stability criterion which can be solved numerically is presented in terms of Lyapunovs theory for fuzzy interconnected models. In this paper, we use linear difference inclusion (LDI) state-space representation to represent the fuzzy model. Then, the linear matrix inequality (LMI) optimization algorithm is employed to find common solution and then guarantee the asymptotic stability.

NONLINEAR WATER WAVES ON UNIFORM CURRENT IN LAGRANGIAN COORDINATES

This paper presents a new third-order trajectory solution in Lagrangian form for the water particles in a wave-current interaction flow based on an Euler–Lagrange transformation. The explicit parametric solution highlights the trajectory of a water particle and the wave kinematics above the mean water level and within a vertical water column, which were calculated previously by an approximation method using Eulerian approach. Mass transport associated with a particle displacement can now be obtained directly in Lagrangian form. The angular frequency and Lagrangian mean level of the particle motion in Lagrangian form differ from those of the Eulerian. The variations in the wave profile and the water particle orbits resulting from the interaction with a steady uniform current of different magnitudes are also investigated. Comparison on the wave profiles given by the Eulerian and Lagrangian solution to a third-order reveals that the latter is more accurate than the former in describing the shape of the wave profile. Moreover, the influence of a following current is found to increase the relative horizontal distance traveled by a water particle, while the converse is true in the case of an opposing current.

Beaches downcoast of harbours in bays

Abstract In spite of beach berms being removed during each storm sequence the waterline may be retained constant either by a constant supply of littoral drift or static equilibrium bays being formed between headlands. The construction of salients behind offshore breakwaters may be at the expense of the adjoining coast, which resembles the ubiquitous bay shapes formed between headlands that can be either in dynamic or static equilibrium. This is the same silting situation in the lee of breakwaters extending from the coast where beach erosion results downcoast. Ports constructed upcoast of a bay in dynamic equilibrium can have their breakwaters so located that the bay can become statically stable. In the case of the bay being already in static equilibrium breakwater extension often causes massive accretion in its lee and concomitant erosion further downcoast, thus demanding prodigious expense for beach protection installations. Appropriate procedures are now suggested to minimise this undesirable effect of beach erosion associated with the construction and extension of breakwaters to ports upcoast of a bay.

COMPUTATIONS OF THE ALMOST HIGHEST SHORT-CRESTED WAVES IN DEEP WATER

Abstract The highest short-crested waves have been studied analytically and numerically by several workers, but without a conclusive view. An efficient numerical scheme is proposed in this paper which retains the water-surface elevations in an implicit form in the governing equations, rather than using a series approximation, thus improving the accuracy of the numerical results. Convergence of the numerical scheme is verified. The almost highest short-crested waves in deep water are then evaluated, which are defined for the condition with the largest wave energies. It is found that the critical angle for wave frequency reversal also demarcates the wave characteristics near breaking, for either kinematic or dynamic prominence. The known results available for the limiting two-dimensional cases of standing and progressive waves are compared favourably.

Effect of wave non-linearity on the standing-wave-induced seabed response

A standing wave in front of a seawall may reach a height more than twice of its incident component. When excess pore pressure occurs, it may even induce seabed instability, hence endangering the structure. This issue was studied previously using only linear wave theory. In this paper, standing-wave theory to a second-order approximation is applied, in order to demonstrate the differences between these two solutions. The spatial arid temporal variations in the instantaneous pore pressure are first calculated, in addition to their vertical distributions. The effects of wave height, water depth and the degree of soil saturation on pore pressure distributions are then discussed, followed by the net pore pressure averaged over one wave cycle. The results suggest the existence of a residual pore pressure in the seabed and its net pore pressure can be used to estimate the wave-induced liquefaction potential in a soil column. It also indicates that, in deep water, the second-order solution predicts that a negative pore pressure at an antinode which may be greater than a positive pressure. Overall, the second-order solution is found to agree better with the experimental results of the pore pressures available, compared to the linear solution.

Transient soil response in a porous seabed with variable permeability

The soil permeability of many natural marine sediments decreases with depth because of consolidation under overburden pressure. This is accompanied by a decrease in porosity and void ratio that also affect the permeability. Conventional theories for wave-induced soil response have assumed a homogeneous porous seabed. This paper presents a new approach for the wave-induced response in a soil matrix, with variable permeability as a function of burial depth. The soil matrix considered is unsaturated and anisotropic, and is subject to a three-dimensional wave system. The pore pressure and effective stresses induced by such a system are obtained from a set of equations incorporating a variable permeability. Verification is available through reduction to the simple case of uniform permeability. The results indicate that the effect of variable soil permeability on pore pressure and vertical effective stress may be significant, especially in a gravelled seabed and for unsaturated sandy soils.

Calculations of wave transformation across the surf zone

The accuracy of predicting wave transformation in the nearshore is very important to wave hydrodynamics, sediment transport and design of coastal structures. An efficient numerical model based on the time-dependent mild-slope equation is presented in this paper for the estimation of wave deformation across the surf zone. This model incorporates an approximate nonlinear shoaling formula and an energy dissipation factor due to wave breaking to improve the accuracy of the calculation of wave height deformation prior to wave breaking and also in the surf zone. The model also computes the location of first wave breaking, wave recovery and second wave breaking, if physical condition permits. Good agreement is found upon comparison with experimental data over several one-dimensional beach profiles, including uniform slope, bar and step profiles.

STABALIZING BEACHES DOWNCOAST OF HARBOR EXTENSIONS

A study of alternatives including a shoreline evolution numerical modelization has been carried out in order to both diagnose the erosion problem at the beaches located between Cambrils Harbour and Pixerota delta (Tarragona, Spain) and select nourishment alternatives.

Fourth-order theory for multiple-wave interaction

By using a Stokes-type expansion method, a fourth-order solution has been derived for nonlinear interaction among multiple directional wave trains. Since an arbitrary number of free-wave modes with arbitrary propagation directions can be imposed as first-order inputs, this solution may demonstrate more realistic wave fields, as compared to those obtained from periodic wave theories. For the cases of one and two free-wave modes, the present theory is found to coincide with conventional theories such as the Stokes and standing wave theories, indicating the validity and general applicability of the solution. As an application, two particular wave fields are calculated, involving 17 free wave modes. The results indicate that the third- and fourth-order components may produce isolated large crests in random wave fields, and that the fourth-order nonlinearity significantly contributes to low-frequency modulation bound by wave trains.

Second-Order Time-Dependent Mild-Slope Equation for Wave Transformation

This study is to propose a wave model with both wave dispersivity and nonlinearity for the wave field without water depth restriction. A narrow-banded sea state centred around a certain dominant wave frequency is considered for applications in coastal engineering. A system of fully nonlinear governing equations is first derived by depth integration of the incompressible Navier-Stokes equation in conservative form. A set of second-order nonlinear time-dependent mild-slope equations is then developed by a perturbation scheme. The present nonlinear equations can be simplified to the linear time-dependent mild-slope equation, nonlinear long wave equation, and traditional Boussinesq wave equation, respectively. A finite volume method with the fourth-order Adams-Moulton predictor-corrector numerical scheme is adopted to directly compute the wave transformation. The validity of the present model is demonstrated by the simulation of the Stokes wave, cnoidal wave, and solitary wave on uniform depth, nonlinear wave shoaling on a sloping beach, and wave propagation over an elliptic shoal. The nearshore wave transformation across the surf zone is simulated for 1D wave on a uniform slope and on a composite bar profile and 2D wave field around a jetty. These computed wave height distributions show very good agreement with the experimental results available.