船舶论文 外文翻译

外文翻译Ship structural safety and reliabilityJ K Paik 1 and P A Frieze 21 Pusan National University, South Korea2 PAFA Consulting Engineers, UKSummaryRecent research and development in the area ofdesign methodologies related to safety andreliability of ship structures is reviewed, focusing onsome relevant probabilistic approaches used for theload and resistance factor design (LRFD) of shiphulls against collapse. Important insights andfindings previously obtained in the literature aresummarized, and recommendations are made withrespect to both technologically improved designprocedures and those needed for futuredevelopment.Key words:ship structural safety; ship structural reliability; load and resistance factor design; ship hull collapse;probability-based ship structural design; hull girder load; hull girder strength; ultimate limit state; ultimate strength;target reliability.Hull girder collapse accidentOverall collapse of ships’ hull s rarely occurs in stillwater or in waves. Fig. 1 shows a Capesize bulk carrierthat recently collapsed during discharge in port of her126 000 t of iron ore cargo. While the 23-year-old139 800 dwt ship has not broken in two, her mid-section is reportedly lying on the seabed, indicatingthat the hull girder has, in fact, completely collapsed.After having emptied the bow and aft holds amongfive cargo holds, buckling collapse took place in thevessel’s deck while the central hold was still full. It isconsidered that this incident happened primarily asa result of improper unloading of the cargo from theship, but there is certainly speculation about the hull’slimit state design as well as the relevance of inspectionand maintenance.Fig. 1 A ship hull collapse during unloading of cargo at port(Courtesy of Lloyds List)A ship hull in the intact condition will clearlysustain applied loads smaller than the design loads,and in normal sea and loading conditions it will notsuffer structural failure such as buckling and collapse,except for possible localized yielding. However, theloads acting on the ship hull are uncertain, owing torough seas or unusual loading/unloading of cargo. Inthese cases, applied loads may exceed design loadsand the ship hull may collapse globally. Furthermore,since aging ships may suffer structural degradationdue to corrosion, fatigue and local damage witha consequential reduction of their structuralresistance, the hull may collapse under applied loadseven smaller than the design loads.Probability-based structural designprocedureThe main steps for probability-based ship structuraldesign are normally as follows:●establish a target reliability;●identify all unfavorable failure modes of thestructure;●formulate the limit state function for each failuremode identified above;●identify the probabilistic characteristics (mean,variance, distribution) of the random variables inthe limit state function;●calculate the reliability against the limit state withrespect to each failure mode of the structure;●assess if the predicted reliability is greater than thetarget reliability, and redesign the structureotherwise;●evaluate the reliability analysis results with respectto parametric sensitivity considerations.Modelling of hull girder strengthFour types of limit state can be considered: namely,serviceability limit state, ultimate limit state, fatiguelimit state and accidental limit state . Theserviceability limit state involves deterioration of lessvital functions including:●local damage which may reduce the durability of thestructure or affect the efficiency of structural or non-structural elements;●unacceptable deformations which affect the efficientuse of structural or non-structural elements, or thefunctioning of equipment;●excessive vibrations which cause discomfort topeople or affect non-structural elements, or thefunctioning of equipment.The ultimate limit state represents the collapse of thestructure, from factors such as: ●loss of equilibrium of the structure or part of thestructure, considered as a rigid body (e.g.overturning or capsizing);●attainment of the maximum resistance capacity ofsections, members or connections by gross yielding,rupture or fracture;●instability of the structure or part thereof, such as bybuckling of columns, plates, shells and stiffenedpanels.The fatigue limit state results from damageaccumulation under the action of cyclic loads and theaccidental limit state is due to accidents such ascollisions or grounding. Overall failure of ship hull girders, which rarelyoccurs, is normally governed by buckling and plasticcollapse of the deck, bottom or sometimes the sideshell stiffened panels. Failure of deck, bottom or sideshell stiffened panels can then lead to progressivecollapse and ultimate hull girder failure. For manyyears, ship structural researchers have been workingtowards the goal of reliability-based limit state designof ship structures. However, reliability-based designrequirescalculation of the ultimate limit state, not onlyof the hull girder, but also of all the structural panelsand other members. Also, these calculations must beperformed a large number of times.Therefore, it is notpractical to use iterative finite element analyses forthese calculations. For efficient computations, ultimatestrength formulations must be developed as closed-form expressions, both for structural components andfor the complete hull girder.A number of studies on the ultimate collapsestrength of ships’ hulls have been undertakentheoretically, numerically and experimentally .Some of the results have been reviewed by the ISSCTechnical Committee III.1 on ‘Ultimate Strength’. Theultimate strength reliability of ships’ hulls,considering existing local damage related to corrosion,fatigue and collision/grounding, has also beenstudied.Previous studies on the development ofa formulation for ultimate hull strength predictionmay be classified into three groups. The first is a linearapproach, where the behaviour of the hull up to failureof the compression flange is assumed to be linearelastic, i.e. ignoring buckling, and the ultimatemoment capacity of the hull is basically expressed asthe ultimate strength of the compression flangemultiplied by the elastic section modulus, witha simple correction for buckling and yielding .The second is an empirical approach, where anexpression is derived on the basis of experimental ornumerical data from scaled or real hull models.The third is an analytical approach, based ona presumed stress distribution over the hull section(plane sections remain plane) from which themoment of resistance of the hull is theoreticallycalculated, taking into account buckling in thecompression flange and yielding in the tensionflange.The first approach is quite simple, but its accuracy isusually wanting because, after buckling of thecompression flange, the behaviour of the hull is nolonger linear, and the neutral axis changes position.Empirical formulations (the second approach) mayprovide reasonable solutions for conventional hulls,but one has to be careful in using empiricalformulations for new and general-type hulls, sincethey are usually derived on the basis of limited data, orfor a particular hull form, using an empiricalformulation . On the other hand, analyticalformulations (the third approach) can be applied tonew or general hulls because they include sectioneffects more precisely.The ship hull ultimate strength formula iseventually expressed as a function of designparameters related to geometric and materialproperties including plate thickness, yield strengthand Young’s modulus. When time-variant structuraldegradation (e.g. corrosion) is considered, the value ofmember thickness at any particular time is a functionof such damage. In probability-based design methods,all the design parameters are treated as the randomvariables. The hull ultimate strength formula forhogging normally differs from that for sagging. Limit state functionMathematically, the limit state function for structuralfailure can be given as a function of the randomvariables, as follows:f （X ）=f （1x ，2x ，………n x ）（1）where f (X) is the limit state function representing themargin between structural capacity and demand (i.e.loads or load effects); x i represents the designparameters.The limit state function f (X) characterizes thecondition of the structure and defines two domains ofsafety with regard to the limit surface (envelope), asfollows:f （X ）>0 in the safe domainf （X ）=0 on the limit surface （2）f （X ）<0 in the unsafe domainWith two independent random variables, theultimate limit state function f (X) for ship hull collapseis usually taken as the margin between ship hullultimate strength u M and total bending moment t M , asfollows:f （X ）=u M -t M （3）where u M and t M are functions of the design variables.Methods of reliability analysisThe methods for structural reliability analysis areusually classified into four types,namely level I, levelII, level III and level IV . The level I methodcorresponds to the deterministic or partial safety factormethod, using only one characteristic mean value foreach variable. A relevant allowable usage factor foreach variable that may be determined by calibration ofa higher level reliability method-based results isapplied in the level I reliability analysis toapproximately supplement the related uncertainties.The level II method uses two values, i.e. mean andstandard deviation, to describe the characteristics ofeach random variable. The reliability index method,e.g. the first-order second-moment method, is a typicalexample of the level II method. The level III method uses the joint probability density function to describethe characteristics of the random variables. Inreliability analyses by the level III method, eitheranalytical approximations (e.g. first- or second-orderreliability methods) or numerical simulations (e.g.Monte Carlo simulation or directional sampling) areapplied. The level IV method compares the integrityand prospect of an object structure with that ofa reference structure through the engineeringeconomic analysis, considering costs and benefitsassociated with construction, consequences ofstructural failure and maintenance/repair. The levelIV method is employed to establish the targetreliabilities.The ship structural reliability analysis is usuallyundertaken by the level III method. Since the theory ofreliability analysis is discussed in many references,e.g. Mansour and Ditlevsen & Madsen , onlya very brief description for the level III method is givenhere. Generally the probability of failure P f can becalculated as follows: f P =⎰≤0f ）（X P （X ）dx （4）where p(X) is the joint probability density function ofthe random variables X=1x ，2x ，………n x associated withloading, material properties, geometric characteristics,etc. andf (X) is the limit state function, defined suchthat negative values imply failure. Since f (X) is usuallya complicated nonlinear function, it is not easy toperform the integration of eq. (4) directly. Therefore,the equation is normally solved by use of approximateprocedures .With these approximations, as indicated in Fig. 2,the limit state surface is usually approximated at thedesign (failure) point by either a tangent hyper-planeor a hyper-parabola, which simplifies the mathematicsrelated to the calculation of the failure probability. Thefirst type of approximation results in the use of aso-called first-order reliability method (FORM) and the second type of approximation is central to theso-called second-order reliability method (SORM).Such methods facilitate the rapid calculation of theprobability of failure, by widely available standardsoftware. Apart from the individual probabilitydistributions of the random variables involved, thecorrelation between them can also be readilyaccounted for in such calculations; all randomvariables for various member types are considereduncorrelated. The result of such a standard reliabilitycalculation is a reliability index β which is related tothe probability of failure f P by:f P =）（βφ-（5） where is the standard normal distribution function.Fig. 2Further considerationsWhile a number of useful methodologies for analyzingthe safety and reliability of ship structures have beendeveloped over the past decades, furtherdevelopments are needed.Some furtherconsiderations in probability-based design of shipstructures are as follows:●geometric parameters may be treated asdeterministic, although this may need to beconfirmed in the case of deck and bottom platingthickness;●elastic modulus may be taken as deterministic, butyield stress needs to be treated as a random variablewith a mean value based on a fuller assessment ofstrain-rate effects on yield in large-scalerepresentative ship-type structures than presentedhere. In the first instance, yield stress values couldbe based on tensile coupon test results when wave-induced bending moments dominate, and similarlyderived static values of yield stress for dominantstill water load conditions.●hull girder and stiffened panel ultimate strengthmodels require benchmarking against realisticmechanical collapse test data so that the distributionparameters for their associated modelling errors canbe evaluated;●when time-variant structural degradation, e.g. dueto corrosion and fatigue, is considered, theprobabilistic characteristics of such damageat any particular time should be quantified. Whilesome work continues in this area, there existprobabilistic corrosion rate estimation models fortanker structures and for bulk carrierstructures;●consensus is required about the preferredmethodology for determining an appropriatereturn period of response for ship designand how this might be achieved given thecurrent status of environmental parameters anddata records;●the load factor methodology promoted in theliterature is extremely promising, particularlybecause its form is compatible with limitstate (LRFD) design code formats. Consensusis required concerning its generality andany further development. Classification Societyand naval experiences should be helpful inidentifying load combinations to be addressed.However, in identifying a safety format, accountshould be taken of relevant ISO codes (e.g. ISO 2394)in this area;●target safety and reliability initially requiresa calibration approach to determine appropriatevalues, followed by adjustments based onjudgments concerning successful designs and targetreliabilities in other industries, whilst recognizingthat floating structures probably need one order ofmagnitude (in probability of failure terms)morereliability than comparable bottom-foundedstructures, and an expectation that component andsystem reliabilities should differ by about one orderin probability of failure terms. In the context oflongitudinally stiffened ships, plate buckling shouldbe treated as a serviceability limit state and not as anultimate limit state;●partial factor determination will require some formof simplified modelling of strength, loading or thereliability process in order that such determinationcan proceed efficiently. Curve- or surface- fitting canbe applied in all cases.船舶结构安全性和可靠性J K帕克[1] P A普莱斯[2]1.韩国釜山国家大学2.英国FAFA工程师顾问摘要最近在研究和发展对该地区船舶结构的设计方法，安全性和可靠性的评估，将阻力、负荷作为因子运用概率的方法来对船体的抗损毁能力进行设计。

船舶专业外文翻译一船舶设计优化Ship Design OptimizationThis contribution is devoted to exploiting the analogy between a modern manufacturing plant and a heterogeneous parallel computer to construct a HPCN decision support tool for ship designers. The application is a HPCN one because of the scale of shipbuilding ・ a large container vessel is constructed by assembling about 1.5 million atomic components in a production hierarchy. The role of the decision support tool is to rapidly evaluate the manufacturing consequences of design changes. The implementation as a distributed multi-agent application running on top of PVM is described1 Analogies between Manufacturing and HPCNThere are a number of analogies between the manufacture of complex products such as ships, aircraft and cars and the execution of a parallel program. The manufacture of a ship is carried out according to a production plan which ensures that all the components come together at the right time at the right place.A parallel computer application should ensure that the appropriate data is available on the appropriate processor in a timely fashion.It is not surprising, therefore, that manufacturing is plagued by indeterminacy exactly as are parallel programs executing on multi-processor hardware. This has caused a number of researchers in production engineering to seek inspiration in other areas where managing complexity and unpredictability is important. A number of new paradigms^ such as Holonic Manufacturing and Fractal Factories have emerged [1,2] which contain Ideas rather reminiscent of those to be found inthe field of Multi- Agent Systems [3,4].Manufacturing tasks are analogous to operations carried out on data, within the context of planning, scheduling and control. Also, complex products are assembled at physically distributed workshops or production facilities^ so the components must be transported between them. This is analogous to communication of data between processors in a parallel computer, which thus also makes clear the analogy between workshops and processors.The remainder of this paper reports an attempt to exploit this analogy to build a parallel application for optimizing ship design with regard to manufacturing issues.2 Shipbuilding at Odense Steel ShipyardOdense Steel Shipyard is situated in the town of Munkebo on the island of Funen. It is recognized as being one of the most modern and highly automated in the world. Itspecializes in building VLCC's (supertankers) and very large container ships. The yard was the first in the world to build a double hulled supertanker and is currently building an order of 15 of the largest container ships ever built for the Maersk line. These container ships are about 340 metres long and can carry about 7000 containers at a top speed of 28 knots with a crew of 12.Odense Steel Shipyard is more like a ship factory than a traditional shipyard. The ship design is broken down into manufacturing modules which are assembled and processed in a number of workshops devoted to, for example, cutting, welding and surface treatment. At any one time, up to 3 identical ships are being built and a new ship is launched about every 100 days.The yard survives in the very competitive world of shipbuilding by extensive application of information technology and robots, so there are currently about 40 robots at the yard engaged in various production activities. The yard has a coininitment to research as well, so that there are about 10 industrial Ph・D・students working there, who are enrolled at various engineering schools in Denmark.3 Tomorrow's Manufacturing SystemsThe penetration of Information Technology into our lives will also have its effect in manufacturing Industry. For example, the Internet is expected to becomethe dominant trading medium for goods. This means that the customer can come Into direct digital contact with the manufacturer.The direct digital contact with customers will enable them to participate in the design process so that they get a product over which they have some influence. The element of unpredictability introduced by taking into account customer desires increases the need for flexibility in the manufacturing process, especially in the light of the tendency towards globalization of productioiLIntelligent robot systems, such as AMROSE, rely on the digital CAD model as the primary source of information about the work piece and the work cell [5,6].This information is used to construct task performing, collision avoiding trajectories for the robots, which because of the high precision of the shipbuilding process, can be corrected for small deviations of the actual world from the virtual one using ven r simple sensor systems. The trajectories are generated by numerically solving the constrained equations of motion for a model of the robot moving in an artificial force field designed to attract the tool centre to the goal and repell it from obstacles, such as the work piece and parts of itself. Finally, there are limits to what one can get a robot to do, so the actual manufacturing will be performed as a collaboration between human and mechatronic agents.Most industrial products, such as the windmill housing component shown in Fig. 1, are designed electronically in a variety of CAD systems.Fig> 1. Showing the CAD model for the housing of a windmilL The model, made using Bentley Microstation, includes both the work-piece and task-curve geometries.4 Today v s Manufacturing SystemsThe above scenario should be compared to today's realities enforced by traditional production engineering philosophy based on the ideas of mass production introduced about 100 years ago by Henry Ford. A typical production line has the same structure as a serial computer program, so that the whole process is driven by production requirements. This rigidity is reflected on the types of top-down planning and control systems used in manufacturing industry, which are badly suited to both complexity and unpredictability.In fact, the manufacturing environment has always been characterized by unpredictability. Today's manufacturing systems are based on idealized models where unpredictability is not taken into account but handled using complex and expensive logistics and buffering systems.Manufacturers are also becoming aware that one of the results of the top-down serial approach is an alienation of human workers. For example, some of the car manufacturers have experimented with having teams of human workers responsible for a particular car rather than performing repetitive operations in a production line. This model in fact better reflects the concurrency of the manufacturing process than the assembly line.5 A Decision Support Tool for Ship Design OptimizationLarge ships are, together with aircraft, some of the most complex things ever built A container ship consists of about 1.5 million atomic components which are assembled in a hierarchy of increasingly complex components. Thus any support tool for the manufacturing process can be expected to be a large HPCN application.Ships are designed with both functionality and ease of construction in mind, as well as issues such as economy, safety, insurance issues, maintenance and even decommissioning. Once a functional design is in place, a stepwise decomposition of the overall design into a hierarchy of manufacturing components is performed. The manufacturing process then starts with the individual basic building blocks such as steel plates and pipes. These building blocks are put together into ever more complex structures and finally assembled in the dock to form the flnished ship.Thus a very useful thing to know as soon as possible after design time are the manufacturing consequences of design decisions. This includes issues such as whether the intermediate structures can actually be built bv the availableproduction facilities, the implications on the use of material and whether or not the production can be efficiently scheduled [7].Fig.2. shows schematically how a redesign decision at a point in time during construction implies future costs, only some of which are known at the time. Thus a decision support tool is required to give better estimates of the implied costs as early as possible in the process.Simulation，both of the feasibility of the manufacturing tasks and the efficiency with which these tasks can be performed using the available equipment, is a very compute-intense application of simulation and optimization. In the next section, we describe how a decision support tool can be designed and implemented as a parallel application by modeling the main actors in the process as agents.Fig>2> Economic consequences of design decisions. A design decision implies a future commitment of economic resources which is only partially known at design time.6 Multi-Agent SystemsThe notion of a software agent, a sort of autonomous, dynamic generalization of an object (in the sense of Object Orientation) is probably unfamiliar to the typical HPCN reader in the area of scientific computation. An agent possesses its own beliefs, desires and intentions and is able to reason about and act oil its perceptionof other agents and the environment.A multi-agent system is a collection of agents which try to cooperate to solve some problem, typically in the areas of control and optimization. A good example is the process of learning to drive a car in traffic. Each driver is an autonomous agent which observes and reasons about the intentions of other drivers. Agents are in fact a very useful tool for modeling a wide range of dynamical processes in the real worlds such as the motion of protein molecules [8] or multi-link robots [9]. For other applications, see [4].One of the interesting properties of multi-agent systems is the way global behavior of the system emerges from the individual interactions of the agents [10]. The notion of emergence can be thought of as generalizing the concept of evolution in dynamical systems.Examples of agents present in the system are the assembly network generator agent which encapsulates knowledge about shipbuilding production methods for planning assembly sequences, the robot motion verification agent, which is a simulator capable of generating collision-free trajectories for robots carrying out their tasks, the quantity surveyor agent which possesses knowledge about various costs involved in the manufacturing process and the scheduling agent which designs a schedule for performing the manufacturing tasks using the production resources available.7 Parallel ImplementationThe decision support tool which implements all these agents is a piece of Object- Oriented software targeted at a multi-processor system, in this case, a network of Silicon Graphics workstations in the Design Department at Odense Steel Shipyard. Rather than hand-code all the communication between agents and meta-code for load balancing the parallel application, abstract interaction mechanisms were developed. These mechanisms are based on a task distribution agent being present on each processor. The society of task distribution agents is responsible for all aspects of communication and migration of tasks in the system.The overall agent system runs on top of PVM and achieves good speedup and load balancing. To give some idea of the size of the shipbuilding application^ it takes 7 hours to evaluate a single design on 25 SGI workstations.From：Applied Parallel Computing Large Scale Scientific and Industrial Problems LectureNotes in Computer Science, 1998, Volume1541/199& 476-482, DOI: 10.1007/BFb0095371.中文翻译：船舶设计优化这一贡献致力于开拓类比现代先进制造工厂和一个异构并行计算机，构建了一种HPCN决策支援工具给船舶设计师。

附录二、外文翻译<文献翻译一：原文>ship squat in open water andin confined channelsWhat exactly is ship squat?When a ship proceeds through water, she pushes water ahead of her. In order not to leave a ‘hole’ in the water, this volume of water must return down the sides and under the bottom of the ship. The streamlines of return flow are speeded up under the ship. This causes a drop in pressure, resulting in the ship dropping vertically in the water.As well as dropping vertically, the ship generally trims for’d or aft. Ship squat thus is made up of two components, namely mean bodily sinkage plus a trimming effect. If the ship is on evenC being considered.keel when static, the trimming effect depends on the ship type andbThe overall decrease in the static underkeel clearance (ukc), for’d or aft, is called ship squat. It is not the difference between the draughts when stationary and the draughts when the ship is moving ahead.If the ship moves forward at too great a speed when she is in shallow water, say where this static even-keel ukc is 1.0–1.5 m, then grounding due to excessive squat could occur at the bow or at the stern.For full-form ships such as Supertankers or OBO vessels, grounding will occur generally at the bow. For fine-form vessels such as Passenger Liners or Container ships the grounding will generally occur at the stern. This is assuming that they are on even keel when stationary.C is >0.700, then maximum squat will occur at the bow.IfbC is <0.700, then maximum squat will occur at the stern.IfbC is very near to 0.700, then maximum squat will occur at the stern,amidships and at theIfbbow. The squat will consist only of mean bodilysinkage, with no trimming effects.It must be generally, because in the last two decades, several ship types have tended to be shorter in length between perpendiculars (LBP) and wider in Breadth Moulded (Br. Mld). This has lead to reported groundings due to ship squat at the bilge strakes at or near to amidships when rolling motions have been present.Why has ship squat become so important in the last 40 years?Ship squat has always existed on smaller and slower vessels when under-way. These squats have only been a matter of centimetres and thus have been inconsequential.However, from the mid-1960s to this new millennium, ship size steadily has grown until we have Supertankers of the order of 350 000 tonnes dead-weight (dwt) and above. These Supertankers have almost out-grown the Ports they visit, resulting in small static even-keel ukc of only 1.0–1.5 m.Alongside this development in ship size has been an increase in service speed on several ships, e.g. Container ships, where speeds have gradually increased from 16 up to about 25 kt.Ship design has seen tremendous changes in the 1980s and 1990s. In Oil Tanker design we have the ‘Jahre Viking’ with a dwt of 564 739 tonnes and an LBP of 440 m. This is equivalent tothe length of five football pitches.In 2002, the biggest Container ship to date, namely the ‘Hong Kong Express’ came into service. She has a dwt of 82 800 tonnes, a service speed of 25.3 kt, an LBP of 304 m, Br. Mld of 42.8 m and a draft moulded of 13 m.As the static ukc have decreased and as the service speeds have increased, ship squats have gradually increased. They can now be of the order of 1.50-1.75m, which are of course by no means inconsequential.Department of Transport ‘M’ noticesIn the UK, over the last 20 years the UK Department of Transport have shown their concern by issuing four ‘M’ notices concerning the problems of ship squat and accompanying problems in shallow water. These alert all Mariners to the associated dangers.Signs that a ship has entered shallow water conditions can be one or more of the following:1. Wave-making increases, especially at the forward end of the ship.2. Ship becomes more sluggish to manoeuvre. A pilot’s quote … ‘almost like being in porridge.’3. Draught indicators on the bridge or echo sounders will indicate changes in the end draughts.4. Propeller rpm indicator will show a decrease. If the ship is in ‘open water’ conditions, i.e. without breadth restrictions, this decrease may be up to 15% of the Service rpm in deep water. If the ship is in a confined channel, this decrease in rpm can be up to 20% of the service rpm.5. There will be a drop in speed. If the ship is in open water conditions this decrease may be up to 30%. If the ship is in a confined channel such as a river or a canal then this decrease can be up to 60%.6. The ship may start to vibrate suddenly. This is because of the entrained water effects causing the natural hull frequency to become resonant with another frequency associated with the vessel.7. Any rolling, pitching and heaving motions will all be reduced as ship moves from deep water to shallow water conditions. This is because of the cushioning effects produced by the narrow layer of water under the bottom shell of the vessel.8.Turning circle diameter (TCD) increases. TCD in shallow water could increase 100%.9. Stopping distances and stopping times increase, compared to when a vessel is in deep waters.10. Rudder is less effective when a ship is in shallow waters.What are the factors governing ship squat?The main factor is ship speed V. Detailed analysis has shown that squat varies as speed to the power of 2.08. However, squat can be said to vary approximately with the speed squared. In other words, we can take as an example that if we have the speed we quarter the squat. Put another way, if we double the speed we quadruple the squat!!In this context, speed V is the ship’s speed relative to the water. Effect of current/tide speed with or against the ship must therefore be taken into account.Another important factor is the block coefficient CB. Squat varies directly with CB. Oil Tankers will therefore have comparatively more squat than Passenger Liners.Procedures for reducing ship squat1. Reduce the mean draft of the vessel if possible by the discharge of water ballast. This causes two reductions in one:(a) At the lower draft, the block coefficient CB will be slightly lower in value, although with Passenger Liners it will not make for a signifi-cant reduction. (b) At the lower draft, for a similar water depth, the H/T will be higher in value. It has been shown that higher H/T values lead to smaller squat values.2. Move the vessel into deeper water depths. For a similar mean ship draft, H/T will increase, leading again to a decrease in ship squat.3. When in a river if possible, avoid interaction effects from nearby moving ships or with adjacent riverbanks. A greater width of water will lead to less ship squat unless the vessel is outside her width of influence.4. The quickest and most effective way to reduce squat is to reduce the speed of the ship.False draftsIf a moored ship’s drafts are read at a quayside when there is an ebb tide of say 4 kt then the draft readings will be false. They will be incorrect because the ebb tide will have caused a mean bodily sinkage and trimming effects. In many respects this is similar to the ship moving forward at a speed of 4 kt. It is actually a case of the squatting of a static ship.It will appear that the ship has more tonnes displacement than she actually has. If a Marine Draft Survey is carried out at the next Port of Call (with zero tide speed), there will be a deficiency in the displacement ‘constant.’ O bviously, larger ships such as Supertankers and Passenger Liners will have greater errors in displacement predictions.SummaryIn conclusion, it can be stated that if we can predict the maximum ship squat for a given situation then the following advantages can be gained:1. The ship operator will know which speed to reduce to in order to ensure the safety of his/her vessel. This could save the cost of a very large repair bill. It has been reported in technical press that the repair bill for the QEII was $13 million … plus an estimate for lost Passenger bookings of $50 million!!2. The ship officers could load the ship up an extra few centimetres (except of course where load-line limits would be exceeded). If a 100 000 tonnesdwt Tanker is loaded by an extra 30 cm or an SD14 General Cargo ship is loaded by an extra 20 cm, the effect is an extra 3% onto their dwt. This gives these ships extra earning capacity.3. If the ship grounds due to excessive squatting in shallow water, then apart from the large repairb ill, there is the time the ship is ‘out of service’. Being ‘out of service’ is indeed very costly because loss of earnings can be as high as £100 000 per day.4. When a vessel goes aground there is always a possibility of leakage of oil resulting in compensation claims for oil pollution and fees for clean-up operations following the incident. These costs eventually may have to be paid for by the shipowner.备注：Dr C.B.Barrass．Ship Design and Performance for Masters and Mates[M]．Butterworth-Hei nemann，2004．148~179<文献翻译一：译文>船舶在开敞水域和受限航道的坐底现象什么是船舶的坐底现象?当船舶在水中向前航行时，她会推开在船首的水。

Spatial scheduling for large assemblyblocks in shipbuilding令狐采学Abstract: This paper addresses the spatial scheduling problem (SPP) for large assembly blocks, which arises in a shipyard assembly shop. The spatial scheduling problem is to schedule a set of jobs, of which each requires its physical space in a restricted space. This problem is complicated because both the scheduling of assemblies with different due dates and earliest starting times and the spatial allocation of blocks with different sizes and loads must be considered simultaneously. This problem under consideration aims to the minimization of both the makespan and the load balance and includes various real-world constraints, which includes the possible directional rotation of blocks, the existence of symmetric blocks, and the assignment of some blocks to designated workplaces or work teams. The problem is formulated as a mixed integer programming (MIP) model and solved by a commercially available solver. A two-stage heuristic algorithm has been developed to use dispatching priority rules and a diagonal fill space allocation method, which is a modification of bottom-left-fill space allocation method. Thecomparison and computational results shows the proposed MIP model accommodates various constraints and the proposed heuristic algorithm solves the spatial scheduling problems effectively and efficiently.Keywords:Large assembly block; Spatial scheduling; Load balancing; Makespan; Shipbuilding1. IntroductionShipbuilding is a complex production process characterized by heavy and large parts, various equipment, skilled professionals, prolonged lead time, and heterogeneous resource requirements. The shipbuilding process is divided into sub processes in the shipyard, including ship design, cutting and bending operations, block assembly, outfitting, painting, pre-erection and erection. The assembly blocks are called the minor assembly block, the sub assembly block, and the large assembly block according to their size and progresses in the course of assembly processes. This paper focuses on the spatial scheduling problem of large assembly blocks in assembly shops. Fig. 1 shows a snapshot of large assembly blocks in a shipyard assembly shop.Recently, the researchers and practitioners at academia and shipbuilding industries recently got together at “Smart Production Technology Forum in Shipbuilding and Ocean Plant Industries” to recognize that there are various spatial scheduling problems in everyaspect of shipbuilding due to the limited space, facilities, equipment, labor and time. The SPPs occur in various working areas such as cutting and blast shops, assembly shops, outfitting shops, pre-erection yard, and dry docks. The SPP at different areas has different requirements and constraints to characterize the unique SPPs. In addition, the depletion of energy resources on land put more emphasis on the ocean development. The shipbuilding industries face the transition of focus from the traditional shipbuilding to ocean plant manufacturing. Therefore, the diversity of assembly blocks, materials, facilities and operations in ship yards increases rapidly.There are some solution providers such as Siemens™ and DassultS ystems™ to provide integrated software including product life management, enterprise resource planning system, simulation and etc. They indicated the needs of efficient algorithms to solve medium- to large-sized SPP problems in 20 min, so that the shop can quicklyre-optimize the production plan upon the frequent and unexpected changes in shop floors with the ongoing operations on exiting blocks intact.There are many different applications which require efficient scheduling algorithms with various constraints and characteristics (Kim and Moon, 2003, Kim et al., 2013, Nguyen and Yun,2014 and Yan et al., 2014). However, the spatial scheduling problemwhich considers spatial layout and dynamic job scheduling has not been studied extensively. Until now, spatial scheduling has to be carried out by human schedulers only with their experiences and historical data. Even when human experts have much experience in spatial scheduling, it takes a long time and intensive effort to produce a satisfactory schedule, due to the complexity of considering blocks’ geometric shapes, loads, required facilities, etc. In practice, spatial scheduling for more than a six-month period is beyond the human schedulers’ capacity. Moreover, the space in the working areas tends to be the most critical resource in shipbuilding. Therefore, the effective management of spatial resources through automation of the spatial scheduling process is a critical issue in the improvement of productivity in shipbuilding plants.A shipyard assembly shop is consisted of pinned workplaces, equipment, and overhang cranes. Due to the heavy weight of large assembly block, overhang cranes are used to access any areas over other objects without any hindrance in the assembly shop. The height of cranes can limit the height of blocks that can be assembled in the shop. The shop can be considered as a two-dimensional space. The blocks are placed on precisely pinned workplaces.Once the block is allocated to a certain area in a workplace, it is desirable not to move the block again to different locations due to thesize and weight of the large assembly blocks. Therefore, it is important to allocate the workspace to each block carefully, so that the workspace in an assembly shop can be utilized in a most efficient way. In addition, since each block has its due date which ispre-determined at the stage of ship design, the tardiness of a block assembly can lead to severe delay in the following operations. Therefore, in the spatial scheduling problem for large assembly blocks, the scheduling of assembly processes for blocks and the allocation of blocks to specific locations in workplaces must be considered at the same time. As the terminology suggests, spatial scheduling pursues the optimal spatial layout and the dynamic schedule which can also satisfy traditional scheduling constraints simultaneously. In addition, there are many constraints or requirements which are serious concerns on shop floors and these complicate the SPP. The constraints or requirements this study considered are explained here: (1) Blocks can be put in either directions, horizontal or vertical. (2) Since the ship is symmetric around the centerline, there exist symmetric blocks. These symmetric blocks are required to be put next to each other on the same workplace. (3) Some blocks are required to be put on a certain special area of the workplace, because the work teams on that area has special equipment or skills to achieve a certain level of quality or complete the necessary tasks. (4) Frequently, the production plan may not be implemented as planned, so that frequentmodifications in production plans are required to cope with the changes in the shop. At these modifications, it is required to produce a new modified production plan which does not remove or move the pre-existing blocks in the workplace to complete the ongoing operations. (5) If possible at any time, the load balancing over the work teams, i.e., workplaces are desirable in order to keep all task assignments to work teams fair and uniform.Lee, Lee, and Choi (1996) studied a spatial scheduling that considers not only traditional scheduling constraints like resource capacity and due dates, but also dynamic spatial layout of the objects. They used two-dimensional arrangement algorithm developed by Lozano-Perez (1983) to determine the spatial layout of blocks in shipbuilding. Koh, Park, Choi, and Joo (1999) developed a block assembly scheduling system for a shipbuilding company. They proposed a two-phase approach that includes a scheduling phase and a spatial layout phase. Koh, Eom, and Jang (2008) extended their precious works (Koh et al., 1999) by proposing the largest contact area policy to select a better allocation of blocks. Cho, Chung, Park, Park, and Kim (2001) proposed a spatial scheduling system for block painting process in shipbuilding, including block scheduling, four arrangement algorithms and block assignment algorithm. Park et al. (2002) extended Cho et al. (2001) utilizing strategy simulation in two consecutive operations ofblasting and painting. Shin, Kwon, and Ryu (2008) proposed a bottom-left-fill heuristic method for spatial planning of block assemblies and suggested a placement algorithm for blocks by differential evolution arrangement algorithm. Liu, Chua, and Wee (2011) proposed a simulation model which enabled multiple priority rules to be compared. Zheng, Jiang, and Chen (2012) proposed a mathematical programming model for spatial scheduling and used several heuristic spatial scheduling strategies (grid searching and genetic algorithm). Zhang and Chen (2012) proposed another mathematical programming model and proposed the agglomeration algorithm.This study presents a novel mixed integer programming (MIP) formulation to consider block rotations, symmetrical blocks,pre-existing blocks, load balancing and allocation of certain blocks to pre-determined workspace. The proposed MIP models were implemented by commercially available software, LINGO® and problems of various sizes are tested. The computational results show that the MIP model is extremely difficult to solve as the size of problems grows. To efficiently solve the problem, a two-stage heuristic algorithm has been proposed.Section 2 describes spatial scheduling problems and assumptions which are used in this study. Section 3 presents a mixed integerprogramming formulation. In Section 4, a two-stage heuristic algorithm has been proposed, including block dispatching priority rules and a diagonal fill space allocation heuristic method, which is modified from the bottom-left-fill space allocation method. Computational results are provided in Section 5. The conclusions are given in Section 6.2. Problem descriptionsThe ship design decides how to divide the ship into many smaller pieces. The metal sheets are cut, blast, bend and weld to build small blocks. These small blocks are assembled to bigger assembly blocks. During this shipbuilding process, all blocks have their earliest starting times which are determined from the previous operational step and due dates which are required by the next operational step. At each step, the blocks have their own shapes of various sizes and handling requirements. During the assembly, no block can overlap physically with others or overhang the boundary of workplace.The spatial scheduling problem can be defined as a problem to determine the optimal schedule of a given set of blocks and the layout of workplaces by designating the blocks’ workplace simultaneously. As the term implies, spatial scheduling pursues the optimal dynamic spatial layout schedule which can also satisfy traditional scheduling constraints. Dynamic spatial layout schedule can be including thespatial allocation issue, temporal allocation issue and resource allocation issue.An example of spatial scheduling is given in Fig. 2. There are 4 blocks to be allocated and scheduled in a rectangular workplace. Each block is shaded in different patterns. Fig. 2 shows the 6-day spatial schedule of four large blocks on a given workplace. Blocks 1 and 2 arepre-existed or allocated at day 1. The earliest starting times of blocks 3 and 4 are days 2 and 4, respectively. The processing times of blocks 1, 2 and 3 are 4, 2 and 4 days, respectively.The spatial schedule must satisfy the time and space constraints at the same time. There are many objectives in spatial scheduling, including the minimization of makespan, the minimum tardiness, the maximum utilization of spatial and non-spatial resources and etc. The objective in this study is to minimize the makespan and balance the workload over the workspaces.There are many constraints for spatial scheduling problems in shipbuilding, depending on the types of ships built, the operational strategies of the shop, organizational restrictions and etc. Some basic constraints are given as follows; (1) all blocks must be allocated on given workplaces for assembly processes and must not overstep the boundary of the workplace; (2) any block cannot overlap with other blocks; (3) all blocks have their own earliest starting time and duedates; (4) symmetrical blocks needs to be placed side-by-side in the same workspace. Fig. 3 shows how symmetrical blocks need to be assigned; (5) some blocks need to be placed in the designated workspace; (6) there can be existing blocks before the planning horizon; (7) workloads for workplaces needs to be balanced as much as possible.In addition to the constraints described above, the following assumptions are made.(1)The shape of blocks and workplaces is rectangular.(2)Once a block is placed in a workplace, it cannot be moved or removed from its location until the process is completed.(3)Blocks can be rotated at angles of 0° and 90° (see Fig. 4).(4)The symmetric blocks have the same sizes, are rotated at the same angle and should be placed side-by-side on the same workplace. (5)The non-spatial resources (such as personnel or equipment) are adequate.3. A mixed integer programming modelA MIP model is formulated and given in this section. The objective function is to minimize makespan and the sum of deviation from average workload per workplace, considering the block rotation, the symmetrical blocks, pre-existing blocks, load balancing and theallocation of certain blocks to pre-determined workspace.A workspace with the length LENW and the width WIDW is considered two-dimensional rectangular space. Since the rectangular shapes for the blocks have been assumed, a block can be placed on workspace by determining (x, y) coordinates, where 0 ⩽ x ⩽ LENW and 0 ⩽ y ⩽ WIDW. Hence, the dynamic layout of blocks on workplaces is similar to two-dimensional bin packing problem. In addition to the block allocation, the optimal schedule needs to be considered at the same time in spatial scheduling problems. Z axis is introduced to describe the time dimension. Then, spatial scheduling problem becomes a three-dimensional bin packing problem with various objectives and constraints.The decision variables of spatial scheduling problem are (x, y, z) coordinates of all blocks within a three-dimensional space whose sizes are LENW, WIDW and T in x, y and z axes, where T represents the planning horizon. This space is illustrated in Fig. 5.In Fig. 6, the spatial scheduling of two blocks into a workplace is illustrated as an example. The parameters p1 and p2 indicate the processing times for Blocks 1 and 2, respectively. As shown in z axis, Block 2 is scheduled after Block 1 is completed.4. A two-stage heuristic algorithmThe computational experiments for the MIP model in Section 3 have been conducted using a commercially available solver, LINGO®. Obtaining global optimum solutions is very time consuming, considering the number of variables and constraints. A ship is consisted of more than 8 hundred large blocks and the size of problem using MIP model is beyond today’s computational ability.A two-stage heuristic algorithm has been proposed using the dispatching priority rules and a diagonal fill method.4.1. Stage 1: Load balancing and sequencingPast research on spatial scheduling problems considers various priority rules. Lee et al. (1996) used a priority rule for the minimum slack time of blocks. Cho et al. (2001) and Park et al. (2002) used the earliest due date. Shin et al. (2008) considered three dispatching priority rules for start date, finish date and geometric characteristics (length, breadth, and area) of blocks. Liu and Teng (1999) compared 9 different dispatching priority rules including first-come first-serve, shortest processing time, least slack, earliest due date, critical ratio, most waiting time multiplied by tonnage, minimal area residue, and random job selection. Zheng et al. (2012) used a dispatching rule of longest processing time and earliest start time.Two priority rules are used in this study to divide all blocks into groups for load balancing and to sequence them considering the duedate and earliest starting time. Two priority rules are streamlined to load-balance and sequence the blocks into an algorithm which is illustrated in Fig. 7. The first step of the algorithm in this stage is to group the blocks based on the urgency priority. The urgency priority is calculated by subtracting the earliest starting time and the processing time from the due date for each block. The smaller the urgency priority, the more urgent the block needs to bed scheduled. Then all blocks are grouped into an appropriate number of groups for a reasonable number of levels in urgency priorities. Let g be this discretionary number of groups. There are g groups of blocks based on the urgency of blocks. The number of blocks in each group does not need to be identical.Blocks in each group are re-ordered grouped into as many subgroups as workplaces, considering the workload of blocks such as the weight or welding length. The blocks in each subgroup have the similar urgency and workloads. Then, these blocks in each subgroup are ordered in an ascending order of the earliest starting time. This ordering will be used to block allocations in sequence. The subgroup corresponds to the workplace.If block i must be processed at workplace w and is currently allocated to other workplace or subgroup than w, block i is swapped with a block at the same position of block i in an ascending order of theearliest starting time at its workplace (or subgroup). Since the symmetric blocks must be located on a same workplace, a similar swapping method can be used. One of symmetric blocks which are allocated into different workplace (or subgroups) needs to be selected first. In this study, we selected one of symmetric blocks whichever has shown up earlier in an ascending order of the earliest starting time at their corresponding workplace (or subgroup). Then, the selected block is swapped with a block at the same position of symmetric blocks in an ascending order of the earliest starting time at its workplace (or subgroups).4.2. Stage 2: Spatial allocationOnce the blocks in a workplace (or subgroup) are sequentially ordered in different urgency priority groups, each block can be assigned to workplaces one by one, and allocated to a specific location on a workplace. There has been previous research on heuristic placement methods. The bottom-left (BL) placement method was proposed by Baker, Coffman, and Rivest (1980) and places rectangles sequentially in a bottom-left most position. Jakobs (1996) used a bottom-left method that is combined with a hybrid genetic algorithm (see Fig. 8). Liu and Teng (1999) developed an extended bottom-left heuristic which gives priority to downward movement, where the rectangles is only slide leftwards if no downward movement is possible. Chazele(1983) proposed the bottom-left-fill (BLF) method, which searches for lowest bottom-left point, holes at the lowest bottom-left point and then place the rectangle sequentially in that bottom-left position. If the rectangle is not overlapped, the rectangle is placed and the point list is updated to indicate new placement positions. If the rectangle is overlapped, the next point in the point list is selected until the rectangle can be placed without any overlap. Hopper and Turton (2000) made a comparison between the BL and BLF methods. They concluded that the BLF method algorithm achieves better assignment patterns than the BL method for Hopper’s example problems. Spatial allocation in shipbuilding is different from two-dimensional packing problem. Blocks have irregular polygonal shapes in the spatial allocation and blocks continuously appear and disappear since they have their processing times. This frequent placement and removal of blocks makes BLF method less effective in spatial allocation of large assembly block.In order to solve these drawbacks, we have modified the BLF method appropriate to spatial scheduling for large assembly blocks. In a workplace, since the blocks are placed and removed continuously, it is more efficient to consider both the bottom-left and top-right points of placed blocks instead of bottom-left points only. We denote it as diagonal fill placement (see Fig. 9). Since the number of potentialplacement considerations increases, it takes a bit more time to implement diagonal fill but the computational results shows that it is negligible.The diagonal fill method shows better performances than the BLF method in spatial scheduling problems. When the BLF method is used in spatial allocation, the algorithm makes the allocation of some blocks delayed until the interference by pre-positioned blocks are removed. It generates a less effective and less efficient spatial schedule. The proposed diagonal fill placement method resolve this delays better by allocating the blocks as soon as possible in a greedy way, as shown in Fig. 10. The potential drawbacks from the greedy approaches is resolved by another placement strategy to minimize the possible dead spaces, which will be explained in the following paragraphs.The BLF method only focused on two-dimensional bin packing. Frequent removal and placement of blocks in a workspace may lead to accumulation of dead spaces, which are small and unusable spaces among blocks. A minimal possible-dead space strategy has been used along with the BLF method. Possible-dead spaces are being generated over the spatial scheduling and they have less chance to be allocated for future blocks. The minimal possible-dead space strategy minimizes the potential dead space after allocating the followingblocks (Chung, 2001 and Koh et al., 2008) by considering the 0° and 90° rotation of the block and allocating the following block for minimal possible-dead space. Fig. 11 shows an example of three possible-dead space calculations using the neighbor block search method. When a new scheduling block is considered to be allocated, the rectangular boundary of neighboring blocks and the scheduling blocks is searched. This boundary can be calculated by obtaining the smallest and the largest x and y coordinates of neighboring blocks and the scheduling blocks. Through this procedure, the possible-dead space can be calculated as shown in Fig. 11. Considering the rotation of the scheduling blocks and the placement consideration points from the diagonal fill placement methods, the scheduling blocks will be finally allocated.In this two-stage algorithm, blocks tend to be placed adjacent to one of the alternative edges and their assignments are done preferentially to minimize fractured spaces.5. Computational resultsTo demonstrate the effectiveness and efficiency of the proposed MIP formulation and heuristic algorithm, the actual data about 800+ large assembly blocks from one of major shipbuilding companies has been obtained and used. All test problems are generated from thisreal-world data.All computational experiments have been carried out on a personal computer with a Intel® Core™ i3*********************** RAM. The MIP model in Section 3 has been programmed and solved using LINGO® version 10.0, a commercially available software which can solve linear and nonlinear models. The proposed two-stage heuristic algorithm has been programmed in JAVA programming language.Because our computational efforts to obtain the optimal solutions for even small problems are more than significant, the complexity of SPP can be recognized as one of most difficult and time consuming problems.Depending on the scaling factor α in objective function of the proposed MIP formulation, the performance of the MIP model varies significantly. Setting α less than 0.01 makes the load balancing capability to be ignored from the optimal solution in the MIP model. For computational experiments in this study, the results with the scaling factor set to 0.01 is shown and discussed. The value needs to be fine-turned to obtain the desirable outcomes.Table 1 shows a comparison of computational results and performance between the MIP models and two-stage heuristic algorithm. As shown in Table 1, the proposed two-stage heuristic algorithm finds the near-optimal solutions for medium and largeproblems very quickly while the optimal MIP models was not able to solve the problems of medium or large sizes due to the memory shortage on computers. It is observed that the computational times for the MIP problems are rapidly growing as the problem sizes increases. The test problems in Table 1 have 2 workplaces.Table 1.Computational results and performance between the MIP models and two-stage heuristic algorithm.The MIP model Two-stage heuristic algorithm Number of blocksOptimal solution Time (s) Best known solution Time (s)10 12.360 1014.000 12.360 0.02620 22.380a 38250.000 21.380 0.07830 98.344a 38255.000 30.740 0.21850 ––53.760 0.719100 ––133.780 2.948200 ––328.860 12.523300 ––416.060 40.154400 ––532.360 73.214Best feasible solution after 10 h in Global Solver of LINGO®.Full-size tableTable optionsView in workspaceDownload as CSVThe optimal solutions for test problems with more than 50 blocks in Table 1 have been not obtained even after 24 h. The best known feasible solutions after 10 h for the test problems with 20 blocks and 30 blocks are reported in Table 1. It is observed that the LINGO® does not solve the nonlinear constraints very well as shown in Table 1. For very small problem with 10 blocks, the LINGO® was able to achieve the optimal solutions. For slightly bigger problems, the LINGO® took significantly more time to find feasible solutions. From this observation, the approaches to obtain the lower bound through the relaxation method and upper bounds are significant required in future research.In contrary, the proposed two-stage heuristic algorithm was able to find the good solutions very quickly. For the smallest test problem with 10 blocks, it was able to find the optimal solution as well. The computational times are 1014 and 0.026 s, respectively, for the MIP approach and the proposed algorithm. Interestingly, the proposed heuristic algorithm found significantly better solutions in only 0.078 and 0.218 s, respectively, for the test problems with 20 and 30 blocks. For these two problems, the LINGO® generates the worse solutions than the heuristics after 10 h of computational times. The symbol‘–’ in Table 1 indicates that the Global Solver of LINGO® didnot find the feasible solutions.Another observation on the two-stage heuristic algorithms is the robust computational times. The computation times does not change much as the problem sizes increase. It is because the simple priority rules are used without considering many combinatorial configurations.Fig. 12 shows partial solutions of test problems with 20 and 30 blocks on 2 workplaces. The purpose of Fig. 12 is to show the progress of production planning generated by the two-stage heuristic algorithm. Two workplaces are in different sizes of (40, 30) and (35, 40), respectively.6. ConclusionsAs global warming is expected to open a new way to transport among continent through North Pole Sea and to expedite the oceans more aggressively, the needs for more ships and ocean plants are forthcoming. The shipbuilding industries currently face increased diversity of assembly blocks in limited production shipyard. Spatial scheduling for large assembly blocks holds the key role in successful operations of the shipbuilding companies.The task of spatial scheduling takes place at almost every stage of shipbuilding processes and the large assembly shop is one of the most。