Metamodels for seakeeping assessment of fishing vessels

Abstract

Keywords: Metamodels; seakeeping; fishing vessels

Introduction

Pressure to design and build safe and efficient fishing vessels compels scientists and designers to review current design practices. Whichever methods, computer codes, and/ or approaches are used through the design process, it is well

known that design requirements for seakeeping and other issues (resistance, static stability and so forth) are generally in conflict. Whilst important reductions of the wave making resistance and powering are still achievable as a result of even small changes in both hull foremost and aftermost local details, seakeeping performance is normally governed

*Corresponding author. *E-mail address: trincas@units.it Published by Yıldız Technical University Press, İstanbul, Turkey Copyright 2021, Yıldız Technical University. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

by the main geometrical characteristics and gross overall hull form. Thus, seakeeping characteristics have to be incorporated into the design process since the very initial stages, as related enhancement is difficult and expensive to obtain in design stages following the concept design. Indeed, despite continuous advances in computing power and speed, the expense of running computer-intensive codes remains non-trivial and makes their application impractical. Several prediction models (regression equations) developed for fishing vessels, are available in the specialized international literature for assessment of heave (h), pitch (p), and vertical stern acceleration (av) in head sea in regular and irregular seas. They have been applied to a set of Mediterranean fishing vessels, but what resulted is their inadequacy as reliable design tools, even for ranking among existing vessels or competitive designs. This fact suggested the opportunity for an approach that should take into account hull form descriptors directly obtainable from the lines plans and ‘physically close-correlated’ to seakeeping responses. The first strip-theory was developed by Korvin-Kroukovsky (1955), whilst the first solution to the inverse problem (design problem) was suggested only twenty-five years later by Bales (1980) who used analytical seakeeping responses to build a regression formula correlating the performance of destroyer-type hull forms in head seas and at various speeds to a set of geometrical variables. Since then, many simplified approaches have been proposed, based on multivariate regression analysis. These approaches to predictive models range from approximate prediction of seakeeping qualities for conventional merchant ships (Loukakis & Chryssostomidis, 1975; Moor & Murdey, 1968) and gulets (Cakici & Aydin, 2014), to generation of design charts (Hearn et al., 1991) and to application of different forms of seakeeping rank (Kishev, 1992; McCreight, 1983; Nabergoj et al., 2003; Trincas et al., 2000; Trincas & Nabergoj, 2000; Trincas et al., 2001; Walden & Grundmann, 1985; Wijngaarden, 1984; Zborowski & Shiaw-Jyh, 1992) to identify the comparative merit of alternative hull forms. The first approach is absolutely unfeasible for modern ships, which have proportions and hull forms quite different from the ones tested and analyzed many decades ago. The other approaches found their limitation in a single objective optimization, whereas the problem can be undertaken only by multicriterial optimization in a probabilistic environment. Finally, the so-called rank factor is derived as a weighted summation of a number of seakeeping responses yielding an empirical relationship between selected hull form parameters and an operational estimator, described by a linear regression formula. The drawback of rank estimator scheme consists in a certain ambiguity deriving from subjective preference in the procedure of their building and the absence of a clear physical content. Therefore, approaches based on seakeeping indices possessing a clear physical

meaning are preferable, provided they are more sensitive to variations of hull form geometry. Among different approaches, at concept design the most promising strategy to model vessel hydrodynamics is to employ approximating functions, which describe single responses. That is particularly true as regards seakeeping assessment. Statistical techniques are widely used in multicriterial design to build surrogate models, the so-called metamodels, since they are much more efficient to run and easier to integrate in a comprehensive design suite. At the same time, they may yield insight into the functional relationship between design variables and performance responses carrying out screening tests preliminary to sensitive analysis. The very scope of this paper is to develop efficient seakeeping prediction models as analytical modules to insert into a multiattribute optimization procedure. For the time being, multivariate linear regression equations are proposed to predict heave, pitch and vertical accelerations of small and medium-sized Mediterranean fishing vessels stored in an extended database with 57 cases considered. Domain of applicability of independent variables is given, while sea state and other specifications are available in publications (Moor & Murdey, (1968; Trincas et al., 2001). It is demonstrated that the very simple and design-oriented metamodels here proposed fit well with the design responses obtained from direct computations. At the same time, metamodels provide information on the range of the responses values, thus allowing the designer and the customer to identify feasible targets at top-level specifications. This bulk of structured information constitutes the basic data to create more robust predictive metamodels.

NEED For A Simplified Approach In Design For Seakeeping

Evolution and practice in design for seakeeping highlights a return to simple and efficient models as suggested by the first scientists who studied the influence of hull form parameters on seakeeping performance. Turning to simplification is intrinsic also to the strip-theory and the concept of regular design wave. Lewis cleverly supported simplification in using a regular sea instead of an irregular one, stating in his comment to the paper by St. Denis and Pierson (1953) that “It is not clear why an irregular sea will give better criteria of ship performance than a regular one. At intervals any irregular sea will become sufficiently regular so that the motion of the vessel, for a short time, will approach that attained in resonance…. Why is not this motion as ‘realistic’ a criterion of ship performance as any other? A ‘realistic’ irregular sea is at intervals regular”. So, provided simplified models and theories reflect physics with acceptable accuracy for engineering purposes, this

statement is far away from that of the researchers who were scandalized by the poor ‘mathematical philosophy’ of the strip-theory, as quoted by Salvesen et al. (1970), who replied to harsh critics that ‘purists felt that the theory was not derived in a rational mathematical manner but rather by use of physical intuition’. Nevertheless, the strip-theory turned out to be superior to expectations of the authors themselves. Once more, one can discover that intuition often helps more than mathematics, especially if one is forgetting the sentence from the eminent mathematician Henry Poincaré who stated that ‘mathematics can never tell you what is; only what would be if’. This sentence was quoted also by St. Denis and Pierson (1953) in their milestone paper. As stated in literature through decades, substantial changes in hull form design are necessary to improve seakeeping performance. Moreover, at earlier design stages, it is suitable to simplify the significant attributes down to ship motion level, as all responses involved in the seakeeping estimation are directly correlated to ship motions (Kishev, 1992). That is why analysis in this paper is limited to heave, pitch and vertical acceleration. Anyway, naval architects do need reliable and actual answers to their own questions about decision making. Sharing of such an approach drove the authors of this paper to co-operate in broadening the research work developed for many years on hand by many researchers. The new prefixed goal has been to model seakeeping responses more accurately following the ‘spatial screening’ approach introduced since the 1980’s by Rocchi (1988, 1992), who derived descriptors of foremost and aftermost hull form for estimation of calm water resistance by means of multivariate linear regression equations. For instance, it was demonstrated that relative longitudinal positions of the centre of buoyancy and centre of flotation, geometry of transom stern, and bow parameters cannot be neglected to build approximate models accurate enough for engineering purposes.

Role Of The Metamodels

The computation burden in ship design is generally determined by simulation procedures and expensive analysis aimed at reaching a level of accuracy comparable to the one achievable by testing physical models. To this end, metamodeling techniques have been developed from many scientific fields including computer science, chemistry, physics and various engineering disciplines. Despite continuous advances in computing power, the complexity of analysis codes, such as computational fluid dynamics (CFD) and finite element methods (FEM), makes their application unfeasible at very initial design stage where it is necessary to substitute computation-intensive functions with simpler analytical models. These simple models are generally called metamodels.

The metamodels can be considered as ‘surrogates’ of the expensive simulations in order to improve efficiency in decision-making and provide tools to assess attributes/objectives of complex technical systems, such as a ship or an aircraft. Nowadays it is accepted worldwide that they are a valuable tool to support modern engineering design especially at concept stage where the most impacting decisions are made. The advantages of the metamodels can be summarized as follows: 1. building metamodels can better filter the numerical noise than numerical methods; 2. the metamodels encompass the entire design space; 3. they help to detect errors in simulations as the entire design domain is analysed. In the past decades, intensive research has been carried out in employing metamodeling techniques in engineering design (Fang & Sudijanto, 2006; Fox, 2011; Kleijnen & Sargent, 2000; Li & al., 2016; Logan et al. 2013). Among the others, these techniques concern sampling, design space exploration and reduction, model fitting techniques, optimization methods as well as applying metamodeling as a decision support in design decision-making. Issues where metamodels can play a role can be listed as follows: •

they can improve the designers’ understanding of the problem at hand;

they can approximate expensive and intensive computation processes across the entire design space, so reducing the computation costs and lead time;

they may reduce the number and search range of the design variables, so removing ineffective constraints.

Metamodelling techniques are usually categorized according to sampling, model types and model fitting. They evolve from classical Design of Experiments (DoE) theory, in which polynomial functions (regression equations) are used as response surfaces (metamodels). Using computer experiments yields vary small random errors, which might be caused by the random number generation. Since there is no conclusion in the scientific literature about which modelling technique is definitely superior to the others, for the scope of this paper polynomial models have been utilized. The methodology followed to develop the metamodels is based on the Response Surface Methodology (RSM) where polynomial regressions as finalized equations have been chosen because of their simplicity and low order of non-linearity of the response functions. We must emphasize that the main scope of inserting metamodels in the mathematical design model at conceptual design stage stays in the following: to help ship designers in

searching for a new zone in the design space in which the vessel can be improved as a system more than in finding a point, i.e. a design, of optimum single response. To search for a zone of improved responses we utilized the method of steepest descent. Since design economy and metamodel simplicity are very important, a first-order model (a hyperplane) was fitted using an orthogonal design. Then, a path of steepest descent was computed where a set of experimental runs were conducted taking care that no variable goes outside the design space by performing tests for lack of fit. In situations where lack of fit appeared, a second-order response surface model was introduced and the step-by-step procedure was repeated until the diagnostic checks to the residuals and other relevant statistical parameters were satisfactory.

among competitive designs. This discouraging result may be the consequence of a bad application of the models by the user, but frequently the main responsibility is attributable to developers of the regression equations. Indeed, at minimum each proposed metamodel should be followed by: (i) its statistical significance tests (R2adj, S.E., F, t-Student, k, max-min deviation of estimates over database samples); (ii) its domain of applicability (ranges of variables values); (iii) detailed specifications of variability of hull form types in the database (round/chine form, predominant U/V forms, bulb vs. no bulb, high/ low flare, open stern or not, etc.; (iv) the lines plan of the ‘central-case’ and ‘extreme-cases’ of the database should be provided; (v) an exhaustive and clear nomenclature for any mathematical tool should be provided.

Short Review Of Seakeeping Predictive Models

Above all, designers should remember that regression equations behave correctly only for vessels that are of the same class of those that constitute the database: cluster analysis can help in establishing how close characteristics of a new design are to hull forms stored in the database. Moreover, regression equations are applicable only for the same sea conditions, and so forth. In other terms, every class and type of vessel requires its own model. Finally, geometrical boundaries of the population from which the model is derived, become a hard constraint in the design process. Hence, designers are strongly invited to pretend aforesaid information from developers of the predictive models.

Nobody can disagree with Bales & Cummins (1970) in the necessity that “Seakeeping can be rationally included in the ship design process. The prerequisite is determination of trends in seakeeping variables with changes in hull geometry at an early stage in the design process”. Hence, the ultimate goal is to make available simple tools to designers, that can help the in evaluating the merit index for a new design with respect to a number of competitive vessels of the same class. General application of available predictive models often brings to evaluations that do not yield reliable ranks Table 1. Main geometrical characteristics of the set of 18 new cases Case

Hereinafter some seakeeping estimation models are reported from international technical literature in a functional form for the seakeeping rank to highlight that different hull form variables have been utilized. -Bales model -McCreight model -Wijngarden model -Walden model -Trincas and Nabergoj model -Nabergoj et al. model -Alkan et al. model Table 2. Ranges of variables and attributes

Table 3. Values of responses from theoretical computations Vessel Case

Table 4. Statistical characteristics of regression equations for heave (N39) Regression model

We applied all these models to the database of Mediterranean fishing vessels described in the next section. The results were poor enough from a statistical viewpoint, thus making those models unfeasible for conceptual design of Mediterranean fishing vessels. They do not present descriptors of aftermost and foremost hull form and/or details of the sectional area curve and design water line as independent variables. However, the MEDIT models developed by Nabergoj et al. (2003) were the most accurate statistically, also being the more corresponding to physics of seakeeping. They yielded reliable rankings of merit for heave, pitch and vertical accelerations. A relevant enhancement of modelling the seakeeping behaviour of fishing vessels was reached by Şayli et al. (2010) through development of nonlinear metamodels.

Database Definition

Seakeeping modelling requires previous building of a database comprising geometric variables and parameters (hull form database) of vessels as well as their responses in specific seaways and operating conditions. In this paper, the starting point was the so-called historical database consisting of thirteen modern Mediterranean fishing vessels, analyzed with the main scope of investigating the effect of different hull forms on seakeeping behaviour in rough sea (Nabergoj et al., 2003). The hull forms were faired with accuracy to predict vertical motions correctly. Evaluation of seakeeping responses for each fishing vessel was performed in three loading conditions giving rise to 39 cases (N39). The main geometrical characteristics derived from the faired lines plans of six small and medium-sized Mediterranean fishing vessels have been derived at three loading conditions to build a new relational geometric database, which has been extended with respect to the historical one (N39). The main geometric particulars of the new 18 cases only

are given in Table 1, being those of the old thirteen vessels reported in Nabergoj et al. (2003). The set of new eighteen cases were then incorporated in the historical database giving rise to the extended database (N57). The extended database has a total population of nineteen vessels and comprehends a large variety of single-screw hull forms: from ‘U’ to ‘V’ sections forward, from rounded sections to underwater chines; from no bulb to large bulbous bows fitted. In Table 1, the locations of the longitudinal centres are given in meters and are relative to amidships (positive forward, negative aft). Static stability of each vessel was checked in detail using hydrostatic curves from hull forms. In defining hull form coefficients and parameters, length was assumed as the overall submerged length (LOS). The ranges of the independent variables and dependent attributes for the samples with N=39 and N=57, respectively, are illustrated in Table 2. Bolded max-min values are those that changed because of the extension of the database.

Seakeeping Performance Attributes

The seakeeping performance of the family of fishing vessels was evaluated in head sea by means of a suite of seakeeping codes based on a strip-theory which solves the potential by means of a modified closed-fit method. For each case the assumption was made that vessels are always in even keel condition with radius of gyration for pitch equal to 0.25 LPP. Each fishing vessel has been evaluated at three loading conditions, denoted by the last digit in each label readable in the first column of Table 1. In particular, digits 1, 2, and 3 refer to leaving to the fishing ground (100% consumables), leaving from the fishing ground (full holds and 40% consumables), and arriving to port (full holds and 10% consumables), respectively.

Table 5. Statistical characteristics of regression equations for pitch (N39) Regression model

Seakeeping performance of existing fishing vessels was estimated assuming a Froude number Fn = 0.10 and significant wave height HS=2.5 m. The selected wave condition corresponds to approximately an 18% probability of exceedance in the East Mediterranean areas. To compare results from statistical metamodels with the theoretical predictions, only average rms single amplitude responses are formulated by separate regression analyses of linear seakeeping computation results. The theoretical performance values for the fishing vessels in all 57 cases are illustrated in Table 3. For the heave motion at centre of gravity, it can be seen that V_013 case presents the highest value, while V_182 case has the best performance. The pitch motion is maximum for V_191 case and minimum for V_122 case. For vertical acceleration at stern working area, it is seen that V_141 case has the highest and V_101 case has the lowest value. Figure 1 shows the body plans of some ‘best extreme type’ (Mazara, V_103),’centred type’ (Flori, V_031; Gemma, V_041) and ‘worst extreme type’ (Foggia, V_191; Dinko, V_013).

Seakeeping Modelling

The strategy was to develop a metamodel for each response, thus renouncing to define a mathematical model for the global rank. Ranks of Mediterranean fishing vessels were estimated for each seakeeping characteristic applying the specific metamodel for each response, namely, heave, pitch, and vertical acceleration at stern working area. ‘Step’, ‘forward’ and ‘backward’ regression techniques were applied recursively to obtain the metamodels. Metamodels from the Historical Database (N39) To improve accuracy of predictive models through introduction of descriptors for foremost and aftermost bodies,

the N39 sample of heave, pitch and vertical acceleration reported in the upper part of Table 3 has been reconsidered first. Different regression equations have been developed for the original family of thirty-nine cases. For each response, the preferred models have been distinguished between a model which considers main geometrical characteristics only and a model which includes some geometrical details of hull form. The former is more suitable in the phase of concept design generation of feasible alternative solutions, while the latter is more dedicated to the phase of optimisation, that is, the robustness analysis of non-dominated designs. The symbolic signs (+) and (-) in the functional relationships described hereinafter mean that the variable has a positive partial correlation or a negative partial correlation with the seakeeping response. Heave For heave at centre of gravity, two models are proposed as a function of either four or ten independent variables. The functional relationships are respectively: (1)

The coefficients of the regression equations and main statistical characteristics are given in Table 4. Pitch The preferred models for pitch are function of either five or seven independent variables. The functional relationships are respectively: 

Table 6. Statistical characteristics of regression equations for vertical acceleration (N39) Regression model

where the latter (k=7) includes details of fore and aft hull form. The B coefficients of the corresponding equations together with t-Student for each variable, and statistics of the two regression equations are illustrated in Table 5. Vertical Acceleration The preferred models for vertical acceleration at stern working area are functional of either four or ten independent variables. The functional relationships are respectively: 

where the latter includes many details of entrance and run bodies. The B coefficients of the corresponding equations together with main statistical parameters are given in Table 6.

Discussion

In approximation models for vertical acceleration it can be observed that variables BML, BMT, and BF are important in both the models with k=4 and k=10 variables. Moreover, these independent variables are present also in models for pitch and result coherent in their effect, in the sense that both responses are reduced by increasing BML and decreasing BMT and BF values. These indications confirm the physical intuition that vertical motions and induced effects are strongly affected by the longitudinal separation between centre of gravity and centre of flotation (BF) and by metacentric radii. Tables 7 and 8 permit a detailed comparison between theoretical and statistical values of pitch and vertical acceleration, respectively, while considering the simple and the more

detailed models. Fishing vessels have been ranked in each subgroup starting from the vessel that presents the best performance for the response considered. Bolded cases and related vessels indicate an exactly alike position in the ranking between theoretical and statistical results. In general, the relative capability of a fishing vessel is confirmed whichever is the approach used to estimate its responses. Maximum and minimum absolute errors, as defined in the nomenclature, are displayed too. It is evident that the models with higher number of independent variables are more accurate in prediction. Metamodels from the Extended Database (N57) For the extended database with nineteen fishing vessels, each at three load conditions for a total of 57 cases, the following functional relationships were derived, which provide a good statistical accuracy while showing consistent physical meaning.  (7) 

It is worth noticing from these relationships that the extension of the database yielded an inversion of correlation for some hull form variables such as MTC, Xi20, and B/∇1/3. Statistical characteristics of the metamodels for h, p, and av, as derived from the extended database (N 57), are illustrated in Table 9, while the corresponding B coefficients and tmin values are given in Tables 10 through 12. In these tables, percentage of errors is given too, showing an acceptable accuracy of the proposed models from an engineering viewpoint. Tables 13 through 15 illustrate the position in rank for the fishing vessels. In the right side of the table one can read the rank for the 57 cases according to the response values as derived from theoretical calculations. In the left side the rank is given according to the results yielded by the statis-

Table 7. Comparison between computed and estimated values for pitch with two different models and (historical database, N39) p Case Vessel pk=5 (theory) (model)

tical model. The percentage error between estimated and computed values for each case is given too. One can observe that positions in the rank are generally maintained when comparing the two situations. Really, the rank position is exactly kept on by many cases; in particular, the best fishing vessel results the same whichever the method followed to determine vertical acceleration rms. The cases presenting an estimated value with error 2.5 percent and higher than theoretical value are bolded in Tables 13 through 15.

SOME Design Guidelines

Analyses of proposed models provide the following design guidelines aimed to reduce values of dynamic characteristics. They can be translated into criteria for hull form optimization purpose such as: •

increase BML to reduce both pitch and vertical acceleration;

increase longitudinal separation between centre of buoyancy and centre of flotation, BF, to reduce pitch and vertical acceleration;

Table 8. Comparison between computed and estimated values for vertical acceleration with two different models: and (historical database, N39) av Case Vessel (theory)

increase the beam at fore shoulder, Bi16, to reduce both pitch and vertical acceleration;

flatten aftermost sections by increasing values of Xi0 and Xi3, to reduce vertical acceleration;

modify shape of section 19 by increasing Xi19 value and decreasing Yi19, to reduce vertical acceleration;

modify shape of section at forward perpendicular by increasing Xi20 value; cylindrical bulbs should be preferred to elliptical bulbs;

increase LOS and Xi1 to reduce pitch; the opposite, even minor, effect is yielded for higher vertical acceleration;

Table 9. Statistical characteristics of regression equations from the extended database (N57)

Table 10. Regression equation and t statistic of independent variables in heave metamodel (N57)

% of errors <6.0%=55/57=96%, % of errors <5.0%=52/57=91%, % of errors <3.0%=48/57=84%

Table 11. Regression equation and t statistic of independent variables in pitch metamodel (N57)

% of errors <3.0%=54/57=95%, % of errors <2.5%=50/57=88%, % of errors <2.0%=46/57=81%

Table 12. Regression equation and t statistic of independent variables in vertical acceleration metamodel (N57)

% of errors <5.0%=52/57=91%, % of errors <4.0%=49/57=86%, % of errors <3.0%=44/57=77%

reduce values of BMT, to get low values for both pitch and vertical acceleration.

Conclusions

The most significant contribution of this paper is twofold. It provides additional insight on the influence of hull form parameters on seakeeping performance of fishing vessels and develops related metamodels to facilitate and speed up the selection of the ‘best possible’ solution at concept design stage, so improving hull design. Results of the analysis carried out on the extended database (N57) of fishing vessels are very promising. They lay the foundations for a more extensive work aimed to determine more accurate and reliable estimation models of seakeeping responses. In this respect, it is interesting to quote Bales and Cummins (1970): “…It is believed to permit variations in all parameters which have a significant effect upon seakeeping. The shape of the waterline effectively governs the longitudinal distribution of both

damping and restoring forces. The end values of the sectional area coefficient curve control the longitudinal distribution of displacement and the longitudinal centre of buoyancy can be shifted independently of the longitudinal centre of flotation, a quality which strongly affects the coupling between heave and pitch”. Foundation of the previous statement has been verified for the examined family of the Mediterranean fishing vessels as shown by the presence in the present metamodels of the variable BF (which depends on waterline and sectional area curve shape) and variables Ai0, Ai15, Bi16, Bi17, Xi1, Xi19, Xi3, Xi1, Xi20, Yi9, Yi13, Yi6, Yi19 which depend on local section shapes. On the contrary, these metamodels do not allow agreement with Bales and Cummins (1970), when they state: “As ship motions do not appear to be sensitive to local details of hull shape, it is possible to select a simplified family of mathematical forms, each of which have motions in waves very near that of many ships in the total population. That this-is-so is demonstrated by the success of the ‘strip theory’ technique for computing ship motions, which replaces the ac-

Table 13. Comparison between computed and estimated values for heave (N57)

Table 14. Comparison between computed and estimated values for pitch (N57)

tual section shape at each section by a so-called ‘Lewis section’ having the same breadth, draft, and area”.

b: there is no more need for any replacement of actual section shapes, since nowadays it is not at all expensive and time consuming to draw a lines plan.

Conversely, on the basis of the results achieved for the extended database, at least for the type of vessel considered the authors arrive to the provisional conclusion that

Really, all variables in the metamodels here presented refer to values obtained directly from the lines plan without any alteration.

a: ship motions appear to be sensitive to local details of the hull form,

Future efforts will be devoted to demonstrate that the above conclusive sentence holds for all type of dis-

Table 15. Comparison between computed and estimated values for vertical acceleration (N57) av (statistics)

drodynamics and statistics may allow appropriate consideration of seakeeping since the very initial design stages. That requires creation of seakeeping databases specialized for classes and types of ships, in order to build metamodels suitable in a multiattribute decision-making environment. The reference framework of this paper is the vessel’s concept design stage where a multiattribute decision making (MADM) technique is considered the most useful approach as opposed to the classical spiral design procedure. The main goal of the paper has been to develop robust equations to assess some seakeeping attributes, as derived from a database of fishing vessels, to be introduced into the mathematical model randomly fed by an adaptive Monte Carlo generator. To facilitate the selection procedure, that is, the core of the MADM, it might be convenient to cluster the feasible solutions into separate groups, as realized by Şayli et al. (2017). 1 This paper is the revised version of the following symposium paper: Rocchi, R., Trincas, G., 2005. The influence of hull form on seakeeping performance of fishing vessels. In: Proceedings of the 10th International Symposium on ‘Technics and Technology of Fishing Vessels’, Ancona, Italy.

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