## 1 Introduction  
Vibration generated by propulsion machinery, ships' services, and auxiliary machinery, for example diesel generators, is one of the five principal groups of radiated noise sources in ships [1]. Much of this noise stems from vibration, which propagates through the structure as structure-borne noise. This means that passive vibration isolators are used extensively to suspend many vibration sources to attenuate vibration transmission. Passive isolators are extremely effective, but there is a trade-off between making them sufficiently soft to adequately attenuate low frequency vibrations and making them sufficiently stiff to ensure correct positioning of the suspended machines [2]. In addition, the damping requirement is different for low and high frequencies. Generally, high damping is required for low frequency isolation and low damping is required for high frequency isolation. To improve the vibration isolation performance, especially at low frequencies, active vibration isolation has been proposed [2; 3; 4; 5; 6; 7; 8; 9]. Secondary vibration sources (actuators), generate control forces to counteract the primary vibration transmission. They are often installed in series or parallel with passive resilient isolators. The actuators, together with the sensors and controller, are collectively called an active vibration isolation system. An active vibration isolation system has been implemented on a diesel engine in a training ship named \"Fukae Maru III\", where four hydraulic actuators were installed in parallel with passive isolators to reduce vibration transmission [3]. [PERSON] et al., [5,6] developed similar active engine mounts by employing hydraulic actuators, but using an adaptive multi-notch filtered control algorithm, instead of the learning method used in [3]. Similar to a pneumatic type actuator described in [4], a hydraulic actuator can generate large forces but has a limited frequency range. Moreover, these types of actuator also need air or oil supply, resulting in a weight, and space penalty. Electromagnetic type actuators are widely used in active vibration control since they are compact and have a wide bandwidth. An example of such a device to control the transmission of vibration from a diesel engine was described in [7]. They used a coil and a magnet which were fixed on the diesel engine and the receiving structure, respectively. An inertial shaker (or proof-mass actuator) is another kind of electrodynamic actuator which only has to be connected at one point on the structure as it generates a force by vibrating the proof-mass [2,8,10,11]. It is most effective at its natural frequency, but it can be used over a range of frequencies with less efficiency. It can also suffer from nonlinear behavior if the displacements of the proof-mass are large. An alternative to the electrodynamic transduction mechanism is the use of piezoelectric elements. They can be arranged as a stack actuator and used in active engine mounts [12, 13, 14]. Piezoelectric actuators can have a very high bandwidth, generate a high force, but the displacement is generally very small. They often require an amplitude enlargement mechanism which will result in a reduction in the force generated [15]. However, the application of piezoelectric actuators opens the possibilities for compact designs and a high level of integration. As such, they have been used in the automobile rather than the marine sector [16,17]. Different type of actuators and their uses in an active vibration isolation system have been compared and discussed in [7]. They suggested that a hydraulic actuator has a detrimental influence on the total stiffness. The high frequency vibration, which is not the target of control, passes through the oil since the actuator has a small, low frequency bandwidth. In [PERSON]'s work [5,6], he demonstrated that it was possible to achieve good performance at low frequencies but found that amplification occurred at higher frequencies because of nonlinearities in the hydraulic system.