Marine Technology - April 2008 - Page#76

<BODY> <span id="lblContents">a research project described by van Daalen et al. (2005). One of the findings from this research project was the significant sensitivity of the resulting probability on the choice of speed and course, that is, the operator's behavior. As one of the outcomes of the SAFEDOR project, Themelis and Spyrou (2007) have proposed a practical methodology that bridges the deterministic and probabilistic viewpoints by exploiting the groupiness of high waves. The method appears to be workable for "resonant" (beam-sea and parametric rolling) as well as for "single wave" (broaching and pureloss of stability) types of instability. 3.4.2. The problem of rarity. The probability of stability failure for an individual vessel may be low. This means that the average time before the failure may be large compared with the natural roll period that serves as the time scale for the roll motion process. This constitutes "The Problem of Rarity," as an attempt to evaluate probability of stability failure may lead to work with two disparate time intervals: natural period of roll and average time before stability failure. This problem becomes especially challenging when numerical simulation is used as the main tool, as it will lead to the necessity of reconstruction of long records of wave elevation. Normally, wave elevations are reconstructed with the inverse Fourier transform: N W Fig. 22 Autocorrelation function of wave elevation--uneven frequency spacing t= i=1 rWi cos it + i (35) where W is the instantaneous wave elevation at time instant t, and the set of initial phases i consists of random numbers distributed uniformly on 0 to 2 ; this is the only stochastic information in the model. The amplitude of component rWi is calculated from the spectral density rWi = 2 i+0.5 i-0.5 i+1 i s d; i = i - i-1 (36) creases computation time. One way is to use many relatively short records; the other is to consider alternative ways to represent irregular waves, such as an autoregression model (a brief description of this can be found in Belenky & Sevastianov 2007). Another problem that affects numerical simulation in irregular waves is the absence of practical ergodicity of roll response. Ergodicity is a general property of a stationary stochastic process that allows one to obtain all statistical characteristics of the process from one record if it is sufficiently long. Wave elevations are known to be an ergodic stochastic process. It is also known that a linear system always produces ergodic response to ergodic excitation. However, response of a nonlinear system may not be ergodic. Nonergodicity is stronger if nonlinearity is stronger, and it is especially noticeable for parametric roll (Belenky 2004, Bulian et al. 2006a). Actually, the process is probably ergodic, but convergence of time-based analysis is so slow that it has to be considered nonergodic for all practical purposes. This is reflected in the term "practical nonergodicity." The practical implication of nonergodicity of roll response means that it is necessary to simulate several records for statistical processing. In addition to these difficulties, work with results of simulation may require use of statistics of extreme events (see McTaggart & de Kat 2000, McTaggart 2000). 3.5. Methodology 3.5.1. Numerical tools. Dramatic improvement in computational capabilities and their universal availability make numerical simulation important not only as a development tool, but also for actual application during the design process. A brief review of several such tools is given below. This review is not complete; for a comprehensive review, see Beck and Reed (2001). The purpose of this review is to illustrate what capabilities are needed for the development and application of performance-based probabilistic criteria. FREDYN is a time-domain potential flow code based on strip theory (de Kat & Paulling 1989) that includes other forces based on systematic model test; FREDYN was developed by MARIN under the sponsorship of CRNAV. FREDYN has both seakeeping and maneuvering capabilities and was validated to reproduce capsizing and broaching using a model of a frigate (de Kat et al. 1994, de Kat & Thomas 1998, 2000) and parametric roll for a post-Panamax containership (France et al. 2003). Large Amplitude Motion Program (LAMP) is a timedomain potential flow code based on a panel method (Lin & Yue 1990, 1993) with the capability to include other forces of physical nature. LAMP was developed by Science Application International Corporation (SAIC) under sponsorship by DARPA, US Navy, US Coast Guard, ABS, and SAIC. LAMP has seakeeping and maneuvering capabilities and was validated to reproduce large wave loads and motions (Shin et al. 2003) using a number of single and multihull vessels, and parametric roll for post-Panamax containership (France et al. 2003). OU-BROACH is a numerical model developed by Umeda and Hashimoto (2006) for broaching and parametric rolling MARINE TECHNOLOGY The set of frequencies i has to cover a significant part of the spectral density s. The choice of the frequency is important for the length of the reconstructed record. It is well known that equal spacing of frequencies leads to the so-called "selfrepetition effect." This can clearly be seen on a plot of the autocorrelation function (Fig. 21). To evaluate the statistical uncertainty that self-repetition may introduce in the time series, a cosine Fourier transform was used to compute the autocorrelation function: R = 0 s cos d (37) Uneven frequency spacing is a commonly used technique employed to avoid self-repetition. However, this leads to spreading of the error rather than its complete elimination (see Fig. 22 and Belenky 2004, 2005). However, it is not clear what influence this "spreading" has on the final results of numerical simulation, so evaluating this influence remains a task for future study. If the "spreading error" is found to be significant to the outcome, two different techniques may be considered, as simply increasing the number of frequencies significantly in- Fig. 21 Autocorrelation function of wave elevation--even frequency spacing 114 APRIL 2008</span> <br /> <br /> <a href="http://www.digitalwavepublishing.com/" title="Digital Magazine">Digital Wave Publishing</a> </BODY>