Global Geometric Analysis of Ship Rolling and Capsizing in Random Waves

The nonlinear biased ship rolling motion and capsizing in randoro waves are studied by utilizing a global geometric method. Thompson＇ s α-parameterized family of restoring functions is adopted in the vessel equation of motion for the representation of bias. To take into account the presence of randomness in the excitation and the response, a stochastic Melnikov method is developed and a mean-square criterion is obtained to provide an upper bound on the domain of the potential chaotic rolling motion. This criterion can be used to predict the qualitative nature of the invariant manifolds which represent the boundary botween safe and unsafe initial conditions, and how these depend on system parameters of the specific ship model. Phase space transport theory and lobe dynamics are used to demonstrate how motions starting from initial conditions inside the regions bounded by the intersected manifolds will evolve and how unexpected capsizing can occur.

NOISE-INDUCED CHAOTIC MOTIONS IN HAMILTONIAN SYSTEMS WITH SLOW-VARYING PARAMETERS

This paper studies chaotic motions in quasi-integrable Hamiltonian systems with slow-varying parameters under both harmonic and noise excitations. Based on the dynamic theory and some assumptions of excited noises, an extended form of the stochastic Melnikov method is presented. Using this extended method, the homoclinic bifurcations and chaotic behavior of a nonlinear Hamiltonian system with weak feed-back control under both harmonic and Gaussian white noise excitations are analyzed in detail. It is shown that the addition of stochastic excitations can make the parameter threshold value for the occurrence of chaotic motions vary in a wider region. Therefore, chaotic motions may arise easily in the system. By the Monte-Carlo method, the numerical results for the time-history and the maximum Lyapunov exponents of an example system are finally given to illustrate that the presented method is effective.

Variable scale-convex-peak method for weak signal detection

Avariable scale-convex-peak method is constructed to identify the frequency of weak harmonic signal. The key of this method is to find a set of optimal identification coefficients to make the transition of dynamic behavior topologically persistent. By the stochastic Melnikov method, the lower bound of the chaotic threshold continuous function is obtained in the mean-square sense.The intermediate value theorem is applied to detect the optimal identification coefficients. For the designated identification system, there is a valuable co-frequency-convex-peak in bifurcation diagram, which indicates the state transition of chaosperiod-chaos. With the change of the weak signal amplitude and external noise intensity in a certain range, the convex peak phenomenon is still maintained, which leads to the identification of frequency. Furthermore, the proposition of the existence of reversible scaling transformation is introduced to detect the frequency of the harmonic signal in engineering. The feasibility of constructing the hardware and software platforms of the variable scale-convex-peak method is verified by the experimental results of circuit design and the results of early fault diagnosis of actual bearings, respectively.

Periodic-phase-diagram similarity method for weak signal detection

The periodic-phase-diagram similarity method is proposed to identify the frequency of weak harmonic signals.The key technology is to find a set of optimal coefficients for Duffing system,which leads to the periodic motion under the influence of weak signal and strong noise.Introducing the phase diagram similarity,the influences of strong noise on the similarity of periodic phase diagram are discussed.The principle of highest similarity of periodic phase diagram with the same frequency is detected by discussing the persistence of similarity of periodic motion phase diagram under the strong noise and the periodic-phase-diagram similarity method is constructed.The weak signals of early fault and strong noise are input into Duffing system to obtain the identified system.The stochastic subharmonic Melnikov method is extended to obtain the conditions of the optimal coefficients for the identified system.Based on the results,the constructed frequency conversion harmonic weak signals are considered to form a datum periodic system.With the change of frequency in the datum periodic system,the phase diagram similarity of the two constructed systems can be calculated.Based on the periodic-phase-diagram similarity method,the frequency of weak harmonic signals can be identified by the principle of highest similarity of periodic phase diagram with the same frequency.The results of numerical simulation and the early fault diagnosis results of actual bearings verify the feasibility of the periodic-phase-diagram similarity method.The accuracy of the detection effect is 97%,and the minimum signal-to-noise ratio is−80.71 dB.