3 Guidelines for direct stability failure assessment

 3.1 Objective

3.1.1 These Guidelines provide specifications for direct stability assessment procedures for the following stability failure modes:

• .1 dead ship condition;

• .2 excessive acceleration;

• .3 pure loss of stability;

• .4 parametric rolling; and

• .5 surf-riding/broaching.

3.1.2 The criteria, procedures and standards recommended in these guidelines ensure a safety level corresponding to the average stability failure rate not exceeding 2.6·10^-3 per ship per year.

3.1.3 Direct stability assessment procedures are intended to employ latest technology while being sufficiently practical to be uniformly accepted and applied using currently available infrastructure.

3.1.4 The provisions given hereunder apply to all ships and all failure modes. However, the provisions for both the dead ship condition and pure loss of stability failure modes should not apply to ships with an extended low weather deck.

 3.2 Requirements

3.2.1 The failure event is defined as:

• .1 exceedance of roll angle, defined as: 40 degrees, angle of vanishing stability in calm water or angle of submergence of unprotected openings in calm water, whichever is less; or

• .2 exceedance of lateral acceleration of 9.81 m/s², at the highest location along the length of the ship where passengers or crew may be present.

The Administrations may define stricter requirements, if deemed necessary.

3.2.2 Active means of motion reduction, such as active anti-roll fins and anti-roll tanks, can significantly reduce roll motions in seaway. However, the safety of the ship should be ensured in cases of failure of such devices, therefore, the vulnerability assessment according to these Interim Guidelines should be conducted with such devices inactive or retracted, if they are retractable.

3.2.3 The procedure for direct stability assessment consists of two major components:

• .1 a method that adequately replicates ship motions in waves (see 3.3); and

• .2 a prescribed procedure that identifies the process by which input values are obtained for the assessment, how the output values are processed, and how the results are evaluated (see 3.5).

 3.3 Requirements for a method that adequately predicts ship motions

3.3.1 General considerations

3.3.1.1 The motion of ships in waves can be predicted by means of numerical simulations or model tests.

3.3.1.2 The choice between numerical simulations, model tests or their combination should be agreed with the Administration on a case-by-case basis taking into account these Interim Guidelines.

3.3.1.3 The procedures, calibrations and proper application of technology involved in the conduct of model tests should follow "Recommended Procedures, Model Tests on Intact Stability, 7.5-02-07-04.1" issued by the International Towing Tank Conference (ITTC) in 2008. Users may follow recent amended versions of the Recommended Procedures at the time of execution of tests, if deemed necessary.

3.3.1.4 Numerical simulation of ship motions may be defined as the numerical solution of the motion equations of a ship sailing in waves including or excluding the effect of wind (see 3.3.2).

3.3.2 General requirements

3.3.2.1 Modelling of waves

3.3.2.1.1 The mathematical model of waves should be consistent and appropriate for the calculation of the forces.

3.3.2.1.2 Modelling of irregular waves should be statistically and hydrodynamically valid. Caution should be exercised to avoid a self-repetition effect.

3.3.2.2 Modelling of roll damping: avoiding duplication

3.3.2.2.1 Roll damping forces should include wave, lift, vortex (i.e. eddy-making) and skin friction components.

3.3.2.2.2 The data to be used for the calibration of roll damping may be defined from:

• .1 roll decay or forced roll test;

• .2 CFD computations, if sufficient agreement with experimental results in terms of roll damping is demonstrated;

• .3 existing databases of measurements or CFD computations for similar ships, if suitable range is available; or

• .4 empirical formulae, applied within their applicability limits.

3.3.2.2.3 If the wave component of roll damping is already included in the calculation of radiation forces, measures should be taken to avoid including these effects more than once.

3.3.2.2.4 Similarly, if any components of roll damping (e.g. cross-flow drag) are directly computed whereas others are taken from the calibration data, similar measures should be taken to exclude these directly computed elements from the calibration data used.

3.3.2.2.5 Consideration of the essential roll damping elements more than once can be avoided through use of an iterative calibration procedure in which the roll decay or forced roll tests are replicated in numerical simulations. The results should be determined to be reasonably close to the original calibration model test data set.

3.3.2.3 Mathematical modelling of forces and moments

3.3.2.3.1 The Froude-Krylov forces should be calculated using body-exact formulations at least for the dead ship condition, pure loss of stability and parametric rolling failure modes, for instance using panel or strip-theory approaches.

3.3.2.3.2 Radiation and diffraction forces should be represented in one of three ways: one is to use approximate coefficients and the other two involve either a body linear formulation or a body-exact solution of the appropriate boundary-value problem.

3.3.2.3.3 Resistance forces should include wave, vortex and skin friction components. The preferred source for these data is a model test. The added resistance in waves can be approximated, if this element is not already included in the calculation of diffraction and radiation forces. If the radiation and diffraction forces are calculated as a solution of the hull boundary-value problem, measures must be taken to avoid including these effects more than once.

3.3.2.3.4 Hydrodynamic reaction sway forces, roll moment and yaw moments could be approximated, based on:

• .1 Coefficients derived from model tests in calm water with planar motion mechanism (PMM) or in stationary circular tests, by means of a rotating arm or an x-y carriage.^footnote

• .2 CFD computations, provided that sufficient agreement is demonstrated with a model experiment in terms of values of sway force and yaw moment. If the radiation and diffraction forces are calculated as a solution of the hull boundary-value problem, measures must be taken to avoid including these effects more than once.

• .3 Empirical database or empirical formulae, used within their applicability range.

3.3.2.3.5 Thrust may be obtained by use of a coefficient-based model with approximate coefficients to account for propulsor-hull interactions.

3.3.3 Requirements for particular stability failure modes

3.3.3.1 For the dead ship condition failure mode:

• .1 Ship motion simulations should include at least the following four degrees of freedom: sway, heave, roll and pitch.

• .2 Three-component aerodynamic forces and moments generated on topside surfaces may be evaluated using model test results. CFD results may be admitted upon demonstration of sufficient agreement with a model experiment in terms of values of aerodynamic force and moments. Empirical data or formulae could be applied within their applicability range.

3.3.3.2 For the excessive acceleration failure mode, the ship motion simulations should include at least the following three degrees of freedom: heave, pitch and roll. If sway motion is not modelled, consideration should be given to accurate reproduction of lateral acceleration.

3.3.3.3 For the pure loss of stability failure mode, ship motion simulations should include at least the following four degrees of freedom: surge, sway, roll and yaw. For those degrees of freedom not included in the dynamic modelling, static equilibrium should be assumed.

3.3.3.4 For the parametric rolling failure mode, ship motion simulations should include at least the following three degrees of freedom: heave, roll and pitch.

3.3.3.5 For the surf-riding/broaching failure mode:

• .1 Ship motion simulations should include at least the following four degrees of freedom: surge, sway, roll and yaw. For those degrees of freedom not included in the dynamic modelling, static equilibrium should be assumed.

• .2 Hydrodynamic forces due to vortex shedding from a hull should be properly modelled. This should include hydrodynamic lift forces and moments due to the coexistence of wave particle velocity and ship forward velocity, other than manoeuvring forces and moments in calm water.

3.3.3.6 For the pure loss of stability and surf-riding/broaching failure modes, an appropriate autopilot should be used.

3.3.3.7 For the pure loss of stability and surf-riding/broaching failure modes, the initial condition should be set with a sufficiently small forward speed in order to avoid artificial surf-riding, which cannot occur for a self-propelled ship.

 3.4 Requirements for validation of software for numerical simulation of ship motions

3.4.1 Validation

3.4.1.1 Validation is the process of determining the degree to which a numerical simulation is an accurate representation of the real physical world from the perspective of each intended use of the model or simulation.

3.4.1.2 Different physical phenomena are responsible for different modes of stability failure. Therefore, the validation of software for the numerical simulation of ship motions is failure-mode specific.

3.4.1.3 The validation data should be compatible with the general characteristics of the ship for which the direct stability assessment is intended to be carried out.

3.4.1.4 The process of validation should be performed in two phases: one qualitative and the other quantitative. In the qualitative phase, the objective is to demonstrate that the software is capable of reproducing the relevant physics of the failure mode considered. The objective of the quantitative phase is to determine the degree to which the software is capable of predicting the specific failure mode considered.

3.4.2 Qualitative validation requirements

Table 3.4.2 – Requirements and acceptance criteria for qualitative validation

3.4.3 Quantitative validation requirements

3.4.3.1 There are two objectives of quantitative validation of numerical simulation. The first is to find the degree to which the results of numerical simulation differ from the model test results. The results of a model test carried out in accordance with 3.3.1.3 should be recognized as reference values. The second objective is to judge if the observed difference between simulations and model tests is sufficiently small or conservative for direct stability assessment to be performed for the considered failure modes.

Table 3.4.3 – Indicative requirements and acceptance criteria for quantitative validation

 3.5 Procedures for direct stability assessment

3.5.1 General description

3.5.1.1 The procedures for direct stability assessment contain a description of the necessary calculations of ship motions including the choice of input data, pre- and post-processing.

3.5.1.2 The direct stability assessment procedure is aimed at the estimation of a likelihood of a stability failure in an irregular wave environment and because the stability failures may be rare, the direct stability assessment procedure may require a solution of the problem of rarity. This arises when the mean time to stability failure is very long in comparison with the natural roll period that serves as a main timescale for the roll motion process. The solution of the problem of rarity essentially requires a statistical extrapolation; for this reason, the validation must be performed for all elements of the direct stability assessment procedure.

3.5.1.3 These Guidelines provide two general approaches to circumvent the problem of rarity, namely assessment in design situations and assessment using deterministic criteria. Mathematical techniques are provided that reduce the required number of simulations or simulation time and can be used to accelerate assessment for both, the full assessment and the assessment performed in design situations.

3.5.2 Verification of failure modes

3.5.2.1 Once a failure is identified in a numerical simulation, it is necessary to examine whether it can be regarded as a failure mode for which the numerical method is validated and direct assessment is intended. The suggested judging criteria for this purpose are provided below.

3.5.2.2 If the local period of the obtained roll motion in following waves or in stern quartering waves is nearly equal to the local wave encounter period and the maximum roll angle occurs nearly at the relative wave position in which the metacentric height becomes the smallest, it can be regarded as pure loss of stability failure.

3.5.2.3 If the local period of the obtained roll motion is nearly equal to twice the local wave encounter period and is nearly equal to the ship natural roll period, it can be regarded as the parametric rolling stability failure considered in the vulnerability criteria, which is sometimes called as "principal parametric rolling". Other types of parametric rolling may occur with much smaller probability, which are not addressed by the second generation intact stability criteria.

3.5.2.4 The condition when the ship cannot keep a straight course despite the application of maximum steering efforts is known as broaching. The second generation intact stability criteria address broaching associated with surf-riding. Other types of broaching may occur at slower speed but are not considered here because the centrifugal force, due to such slow-speed broaching which could induce heel, is much smaller. The broaching associated with surf-riding can be identified if both the yaw angle and yaw angular velocity increase over time under the application of the maximum opposite rudder deflection.

3.5.2.5 If the local period of the obtained roll motion in beam waves is nearly equal to the local wave encounter period, it can be regarded as harmonic rolling, which is relevant to the dead ship condition failure mode, as well as the excessive acceleration failure mode.

3.5.3 Environmental and sailing conditions

3.5.3.1 General approaches for selection of environmental and sailing conditions

3.5.3.1.1 The sea states chosen for the direct stability assessment must be representative for the intended service of the ship.

3.5.3.1.2 Sea states are defined by the type of wave spectrum and statistical data of its integral characteristics, such as the significant wave height and the mean zero-crossing wave period. For ships of unrestricted service, the environment should be described by the wave scatter table shown in table 2.7.2.1.2. For ships of restricted service, the wave scatter table accepted by the Administration should be used.

3.5.3.1.3 It is recommended to use the Bretschneider wave energy spectrum (see 2.7.2.1.1) and cosine-squared wave energy spreading with respect to the mean wave direction. If short-crested waves are considered impracticable in model tests or numerical simulations, long-crested waves can be used.

3.5.3.1.4 For a given set of environmental conditions, the assessment can be performed using any of the following equivalent alternatives:

• .1 full probabilistic assessment according to 3.5.3.2;

• .2 assessment in design situations using probabilistic criteria according to 3.5.3.3; or

• .3 assessment in design situations using deterministic criteria according to 3.5.3.4.

3.5.3.2 Full probabilistic assessment

3.5.3.2.1 In this approach, the criterion used is the estimate of the mean long-term rate of stability failures, which is calculated as a weighted average over all relevant sea states, wave directions with respect to the ship heading and ship forward speeds, for each addressed loading condition.

3.5.3.2.2 To satisfy the requirements of this assessment, this criterion should not exceed the standard of 2.6⋅10^-8 (1/s).

3.5.3.2.3 The probabilities of the sea states are defined according to the wave scatter table (see 3.5.3.1). For the excessive accelerations, pure loss of stability, parametric rolling and surf-riding/broaching failure modes, the mean wave directions with respect to the ship heading are assumed uniformly distributed and the ship forward speed should be regarded as uniformly distributed from zero to the maximum service speed. For the dead ship condition failure mode, beam waves and wind should be assumed and the ship forward speed should be taken as zero.

3.5.3.3 Assessment in design situations using probabilistic criteria

3.5.3.3.1 Compared to the full probabilistic assessment, this approach significantly reduces the required simulation time and number of simulations since the assessment is conducted in fewer design situations. These design situations are specified for each stability failure mode as combinations of the ship forward speed, mean wave direction with respect to the ship heading, significant wave height and mean zero-crossing wave period for each addressed loading condition.

3.5.3.3.2 In this approach, the criterion is the maximum (over the design situations corresponding to a particular stability failure mode) stability failure rate, defined in each design situation as the upper boundary of its 95%-confidence interval.

3.5.3.3.3 To satisfy the requirements of this assessment, this criterion should not exceed the threshold corresponding to one stability failure every 2 hours in full scale in design sea states with probability density 10^-5 (m⋅s)^-1.

3.5.3.3.4 Table 3.5.3.3.4 shows the design situations for particular stability failure modes, including mean wave direction with respect to the ship heading, ship forward speed and range of wave periods; and the step of the zero-crossing wave period in the specified ranges should not exceed 1.0 s.

Table 3.5.3.3.4 – Design situations for each stability failure mode

3.5.3.3.5 For each mean zero-crossing wave period, the significant wave height is selected according to the probability density of the sea state, as specified in 3.5.3.3.3. For unrestricted service, the significant wave heights are shown in table 3.5.3.3.5 depending on the mean zero-crossing wave period.

Table 3.5.3.3.5 – Significant wave heights for design sea states with probability density 10^-5 (m⋅s)^-1 for unrestricted service

3.5.3.4 Assessment in design situations using deterministic criteria

3.5.3.4.1 A probabilistic assessment may require a long simulation time even when using design situations and this can make it difficult to use model tests rather than numerical simulations. Applying deterministic criteria, such as the mean 3-hour maximum roll amplitude, may reduce the required simulation time and this may make it easier to use model tests with, or instead of, numerical simulations. However, the inaccuracy of this approach needs to be balanced by additional conservativeness.

3.5.3.4.2 In this approach, the criteria are the greatest (with respect to all design situations for a particular stability failure mode) mean 3-hour maximum roll amplitude and lateral acceleration for each addressed loading condition.

3.5.3.4.3 To satisfy the requirements of this assessment, these criteria should not exceed half of the values in the definition of stability failure in 3.2.1.

3.5.3.4.4 The simulations or model tests for each design situation should comprise at least 15 hours in full scale. This duration can be divided into several parts. The results should be post-processed to provide at least five values of the 3-hour maximum amplitude of roll angle or lateral acceleration, which are averaged to define the mean 3-hour maximum amplitudes.

3.5.3.4.5 This approach uses design situations with the same mean wave directions with respect to the ship heading, the same ship forward speeds and the same ranges of the mean zero-crossing wave periods as the assessment in design situations using probabilistic criteria (see 3.5.3.3).

3.5.3.4.6 For each mean zero-crossing wave period, the significant wave height is selected according to the probability density of the sea state equal to 7⋅10^-5 (m⋅s)^-1. Table 3.5.3.4.6 shows these significant wave heights for unrestricted service depending on the mean zero-crossing wave period.

Table 3.5.3.4.6 Significant wave heights, in metres, for design sea states with probability density 7⋅10^-5 (m⋅s)^-1 for assessment using deterministic criteria for unrestricted service

 3.5.4 Direct counting procedure

3.5.4.1 The direct counting procedure uses ship motions resulting from multiple independent realisations of an irregular seaway to estimate the rate of stability failure, r.

3.5.4.2 The procedure used for direct counting should provide the upper boundary of the 95% confidence interval of the estimated rate of stability failure. This upper boundary is the one which is used in direct stability assessment and operational measures.

3.5.4.3 The counting procedure should ensure independence of the counted stability failure events.

3.5.4.4 The failure rate r and associated confidence interval can be estimated:

• .1 by carrying out a simulation for each realisation of an irregular seaway only until the first stability failure; or

• .2 on the basis of a set of independent simulations with fixed specified exposure time t_exp (s), under the assumption that the relation between the probability p of failure within t_exp and the failure rate r is p = 1 – exp (-r·t_exp).

3.5.4.5 Alternatively to direct counting, extrapolation procedures can be used as specified in section 3.5.5.

3.5.5 Extrapolation procedures

3.5.5.1 The extrapolation procedures to be used with these Guidelines should only include those procedures that have been successfully validated and applied and which should also include a detailed description of their application.

3.5.5.2 Cautions

3.5.5.2.1 The extrapolation method may be applied as an alternative to the direct counting procedure.

3.5.5.2.2 Caution should be exercised because uncertainty increases, as the extrapolation is associated with additional assumptions used for describing ship motions in waves.

3.5.5.2.3 The statistical uncertainty of the extrapolated values should be provided in a form of boundaries of the confidence interval evaluated with a confidence level of 95%.

3.5.5.2.4 To control the uncertainty caused by nonlinearity, the principle of separation may be used. Extrapolation methods based on the principle of separation consist of at least two numerical procedures addressing different aspects of the problem: "non-rare" and "rare".

3.5.5.2.5 The "non-rare" procedure focuses on the estimation of ship motions or waves of small-to-moderate level for which the stability failure events can be characterized statistically with acceptable uncertainty.

3.5.5.2.6 The "rare" procedure focuses on ship motions of moderate-to-severe level for which numerical simulation are rarely required. Large motions may be separated from the rest of the time domain data to obtain practical estimates of these motions.

3.5.5.2.7 Different extrapolation methods based on the separation principle may use different assumptions on how the separation is introduced.

3.5.5.3 Extrapolation over wave height

3.5.5.3.1 Extrapolation of the mean time to stability failure or mean rate of stability failures over significant wave height is a technique allowing the reduction of the required simulation time by performing numerical simulations or model tests at greater significant wave heights than those required in the assessment and extrapolating the results to lower significant wave heights.

3.5.5.3.2 The extrapolation is based on the approximation lnT = A + B/H_s², where T (s) is the mean time to stability failure; H_s (m) is the significant wave height; and A, B are coefficients which do not depend on the significant wave height but depend on the other parameters specifying the situation (wave period, wave direction and ship forward speed).

3.5.5.3.3 The extrapolation can be performed when at least three values of the stability failure rate are available. These values should be obtained by direct counting for a range of significant wave heights of at least 2 m. Each of the values used in the extrapolation should correspond to the upper boundary of the 95%-confidence interval of stability failure rate and not exceed 5% of the reciprocal natural roll period of the ship. The results should be checked for the presence of outliers and non-conservative extrapolation and corrected, when necessary, by adding or removing points used for extrapolation.

3.5.5.4 Other extrapolation procedures

3.5.5.4.1 Other extrapolation procedures may be used, taking into account 3.5.5.1 and 3.5.5.2. Such procedures may include those listed below and others:

• .1 envelope peak-over-threshold (EPOT);

• .2 split-time/motion perturbation method (MPM); and

• .3 critical wave method.

3.5.6. Validation of extrapolation procedures

3.5.6.1 Extrapolation procedures used for direct stability assessment should be validated.

3.5.6.2 Validation of an extrapolation procedure is a demonstration that the extrapolated value is in reasonable statistical agreement with the result of the direct counting, if such volume of data would be available.

3.5.6.3 The data for validation of the extrapolation procedure may be produced by a mathematical model of reduced complexity (e.g. a set of ordinary differential equations instead of a numerical solution of a boundary value problem) or by running the full mathematical model on significantly more severe environmental and/or more onerous loading conditions. The objective is to decrease the computational cost by which a large data set can be obtained (the validation data set). Physical experiments can be used for the same purpose.

3.5.6.4 The direct counting procedure applied to the validation data set should produce the "true value". The extrapolation procedure applied to a minimally required fraction of the validation data set should re-produce the "true value" within 95% confidence.

3.5.6.5 Validation of the extrapolation procedure should be performed for 50 statistically independent data sets and evaluated for a number of ship speeds, relative wave headings and sea states.

3.5.6.6 A comparison should be made between the extrapolation and the "true value" for each data set. The comparison should be considered successful if the extrapolation confidence interval and the confidence interval of the "true value" overlap.

3.5.6.7 The validation should be considered successful if at least 88% of individual data set comparisons are successful.