1、Determination of Ice Load on Ship Hull by Inverse MethodLIU Ying-hao1,SUOMINEN Mikko2,KUJALA Pentti2,ZHANG Han-xi-zi1,GAO Liang-tian3(1.China Ship Research and Development Academy,Beijing 100101,China;2.Department of AppliedMechanics Marine Technology,Aalto University,Espoo 15300,Finland;3.College o
2、f Shipbuildingand Engineering,Harbin Engineering University,Harbin 150001,China)Abstract:The ice load on a ship hull is directly related to the ship safety during a voyage in ice-covered seas.Two inverse methods,influence coefficient matrix method and Tikhonov regularization,areintroduced to determi
3、ne the ice load on the stern shoulder of a polar supply and research vessel withfull-scaled measurement data.The influence coefficient matrix method is built up experimentally andused to obtain the ice load on frames while Tikhonov regularization is constituted with three discretized approaches and
4、utilized to determine the ice load on the plate field.The results show that bothinverse methods could overcome the ill-conditions of processing data and obtain the ice load on shiphull.Key words:ice load;full-scale measurement;inverse method;load discretizationCLC number:U661.43Document code:Adoi:10
5、.3969/j.issn.1007-7294.2023.06.0100 IntroductionRecently,the increase of marine transportation and activities in Polar Regions has been keptup,since there is a great underground fortune in cold regions and the ice conditions are turning easier.Determination of the ice load acting on a ship structure
6、 is important to ensure the safety and stability of the vessel to operate in ice-covered seas.In mechanics,the inverse problems can be distinguished in two categories1-2:solving systemmodel with given inputs and responses and solving inputs with given system model and responses.The ice load determin
7、ation belongs to the second category of inverse problem.When the measuredresponse and system properties are known,its a process to determine the dynamic load acting onthe structures3.The methods of dynamic load determination have been studied in many areas withthe increasing practical engineering de
8、mand in recent years.Doyle4investigated an inverse deconvolution method with wavelet analysis and Fourier analysis to reconstruct the dynamic load of abeam and plate structure.Romppanen et al5presented an inverse sensing method to achieve theline load of press rolls in paper manufacturing.Ikonen et
9、al6determined the ice-induced momenton the propeller of an ice-going vessel based on different inverse methods,such as truncation of sin第27卷第6期船舶力学Vol.27 No.62023年6月Journal of Ship MechanicsJun.2023Article ID：1007-7294（2023）06-0905-14Received date:2022-12-26Foundation item:Supported by the National
10、Key R&D Program of China(2016YFE0202700)Biography:LIU Ying-hao(1988-),female,Ph.D.,E-mail:;SUOMINE Mikko(1985-),male,Ph.D.;KUJALA Pentti(1954-),male,professor;ZHANG Han-xi-zi(1989-),female,MSc.;GAO Liang-tian(1964-),male,professor.gular value decomposition and Tikhonov regularization,etc.However,the
11、se achievements couldnot be applied to the research of ice-induced load acting on a ship hull directly due to the complication of structures and sea-ice characteristics.This paper is aimed to determine the ice load on the stern shoulder when a ship navigatesthrough ice-covered areas.Two inverse meth
12、ods are investigated to determine ice load on differentstructures.The first is influence coefficient matrix method,which determines the frame load basedon the experimental data.The second is Tikhonov regularization,which is used to obtain the hullload.Three different discretizations have been applie
13、d on a finite element model to analyze the iceload equation based on Tikhonov regularization.The frame load and hull load are constructed withboth methods and compared based on the full-scale measurement data during a voyage in Antarctica.1 Inverse methodEngineering problems usually are divided into
14、 forward and inverse problems based on thecharacteristics of the variables in the problems.The forward problem is to find the output responsesbased on the known system model and inputs while the inverse problem is to obtain the inputs withthe known output responses and system model1.The mathematical
15、 form of the inverse method is=Sf(1)where is output response,S is the system model matrix,and f is the input excitation.In this paper,the output response is the strain vector of full-scale measurement on a polar supply and researchvessel,the input excitation is the ice load vector during ship-ice in
16、teractions,and the system matrixdepicts the interdependency of the two terms.As is well-known,the inverse load identification problems are ill-posed,which means the solutions are unstable and inaccurate.Therefore,a method has to be found to solve Eq.(1)withoutcausing the ill-condition of the equation.Assuming that a set of linearly separate unit load case vectors constitute the unknown ice load vector f,i.e.f=u(2)where u is the vector of load case factors,and the matrix A consists of the column
