CN107741997A - Suitable for crane system variable phase angle response field acquisition methods under the parameter of minizone - Google Patents

Suitable for crane system variable phase angle response field acquisition methods under the parameter of minizone Download PDF

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CN107741997A
CN107741997A CN201710772385.7A CN201710772385A CN107741997A CN 107741997 A CN107741997 A CN 107741997A CN 201710772385 A CN201710772385 A CN 201710772385A CN 107741997 A CN107741997 A CN 107741997A
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mrow
msub
msubsup
msup
luffing
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周斌
訾斌
钱森
王道明
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Hefei University of Technology
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Abstract

The invention discloses one kind to be applied to crane system variable phase angle response field acquisition methods under the parameter of minizone, and step is as follows：Establish variable phase angle response equation of the transportation system under luffing motion；The luffing angular response equivalent equation being converted under luffing motion；Establish interval parameter model；Luffing angular response section equivalent equation, section compound function matrix under transportation system's luffing motion of the foundation with interval parameter model, section compound function vector；Obtain approximate expansion expression formula；Approximate expanded expression is brought into the compound function matrix of section, obtains midrange, the constant interval of luffing angular response interval vector of luffing angular response interval vector；The constant interval of the midrange of luffing angular response interval vector, luffing angular response interval vector is obtained to the upper dividing value and floor value of luffing angular response interval vector.The present invention can solve the variable phase angle response field problem analysis under structural parameters containing minizone in crane system, effectively improve computational accuracy and operation efficiency.

Description

Suitable for crane system variable phase angle response field acquisition methods under the parameter of minizone
Technical field
The invention belongs to reliability engineering field, and be particularly suitable for use in crane system, is specifically that one kind is applied to minizone Crane system variable phase angle response field acquisition methods under parameter.
Background technology
During double flow car crane system simultaneously hoisting heavy, often require that rapidly and accurately solving luffing is moved through Luffing angular response in journey, to ensure safety and reliability of the large-scale lifting appliance in operation process.It is existing to be directed to such The Solve problems of luffing angular response, often regard systematic parameter as deterministic parameter.It is this during practical engineering application Solution throughway often due to ignore design, manufacture and application process in all kinds of uncertain factors and cause weight to overturn, The generation of the accidents such as wire cable rupture.
In recent years, it is relatively small using structural parameters error scope on the premise of uncertain parameter limited sample size Or the less feature of uncertainty, by uncertain structure parameter model into interval parameter, and study corresponding response solution side Method turns into a kind of trend.It is noted that Interval Analytical Method in other field, such as structure, calorifics and acoustics Certain achievement is achieved, but is just started to walk in the engineer applied of double-crane system.At present, built in variable phase angle In mold process, due to compound function be present, often lead to Solve problems complexity, calculate the problem of overlong time.Therefore, how Interval Analytical Method is combined with compound function, and establishes the numerical algorithm of high-accuracy high-efficiency rate, for predicting small uncertain region Between variable phase angle response field problem under parameter, there is important engineering application value.
The content of the invention
It is an object of the invention to provide a kind of method for solving variable phase angle response field problem under small indeterminacy section parameter, enter And obtain be applied to minizone parameter under crane system variable phase angle response field acquisition methods, with solve in the prior art how Rapidly and efficiently predict variable phase angle response field problem of the dual stage autocrane system under containing small indeterminacy section parameter.
In order to achieve the above object, the technical solution adopted in the present invention is：
Suitable for crane system variable phase angle response field acquisition methods under the parameter of minizone, carry out as follows：
Step 1：According to the geometrical model of transportation system, the variable phase angle response equation established under luffing motion；The geometry Model/threedimensional model is the Model Abstraction structure drawn according to three-dimensional software.
Step 2：Variable phase angle response equation under the luffing obtained by step 1 is moved, it is converted under luffing motion Luffing angular response equivalent equation；
Step 3：By the small indeterminacy section parameter of more transportation systems, interval parameter model is established；
Step 4：With reference to step 2 and step 3, establish under more transportation system's luffings motion with interval parameter model Luffing angular response section equivalent equation, section compound function matrix, section compound function vector；
Step 5：The section compound function matrix, the section compound function vector that are obtained by step 4 are deployed respectively, Obtain approximate expansion expression formula；
Step 6：The approximate expansion expression formula obtained by step 5 is brought into the section compound function square obtained by step 4 In battle array, midrange, the constant interval of luffing angular response interval vector of luffing angular response interval vector are obtained；
Step 7：The constant interval of the midrange of luffing angular response interval vector, luffing angular response interval vector is obtained The upper dividing value and floor value of luffing angular response interval vector, and output result.
Furtherly, more transportation systems are made up of the vehicle equipment of more than 2；Vehicle equipment is fixed crane, moved Dynamic formula derrick car or the means of transport with stirrup.
Furtherly, more transportation systems are 2 autocranes, 2 fixed cranes or 1 autocrane and 1 Platform fixed crane.
Furtherly, it is of the present invention to be applied to crane system variable phase angle response field acquisition side under the parameter of minizone Method, concretely comprise the following steps：
Step 1：According to crane system geometrical model, it is established that the variable phase angle responder under the motion of heavy-duty machine system luffing Cheng Wei：
Wherein,
Wherein, D and d is respectively crane spacing A1A2And load C1C2Length, basis coordinates system { B }:O-YZ is seated A1A2The center of tie point, moving coordinate system { P }:Op-YpZpIt is seated C1C2The center of tie point, LiIt is i-th crane arm AiBiLength, γiIt is i-th crane arm AiBiVariable phase angle, y and z are load C respectively1C2Center OpAlong Y-axis and Z The cartesian coordinate value of axle, θ represent moving coordinate system { P } relative to the angle of the rotation of basis coordinates system { B }, SiFor i-th lifting Machine lifting rope BiCiLength.
Step 2：Variable phase angle response equation under being moved according to the crane system luffing obtained by step 1, further The luffing angular response equivalent equation established under the motion of autocrane system luffing：
Si=Tiγi
Wherein, SiAnd TiIt is i-th crane system interval matrix and system interval vector respectively, γiIt is i-th lifting Machine system variable phase angle response vector；I is the integer not less than 2；
Step 4：The luffing angular response established under the dual stage autocrane system luffing motion with interval parameter model Section equivalent equation：
Wherein, Si(Ki) and T (y)i(Ki(y)) be respectively i-th crane section compound function matrix and section it is compound Functional vector,It is i-th crane system luffing angular response interval vector, Ki(y) be interval parameter vector y relation function Vector；
Step 5：To section compound function matrix Si(Ki) and section compound function vector T (y)i(Ki(y)) carry out approximate Expansion, obtains Si(Ki) and T (y)i(Ki(y) approximate expansion expression formula)：
Wherein,WithIt is section compound function matrix S respectivelyi(Ki(y) midrange and section radius)；
Wherein,WithIt is section compound function vector T respectivelyi(Ki(y) midrange and section radius)；
Step 6：The S that step 5 is obtainedi(Ki) and T (y)i(Ki(y) approximate expansion expression formula) substitutes into step 4 Luffing angular response section equivalent equation：
Wherein,WithIt is the midrange and constant interval of luffing angular response interval vector respectively；
Step 7：The midrange and section radius for the luffing angular response interval vector that step 6 is obtained, take the photograph according to section Dynamic method obtains the upper dividing value of luffing angular response interval vector：And floor value：
Furtherly, in step 1, according to dual stage autocrane system geometrical model, the change established under luffing motion Argument response equation is：
Wherein,
Wherein, D and d is respectively crane spacing A1A2And load C1C2Length；Basis coordinates system { B }:O-YZ is seated A1A2The center of tie point；Moving coordinate system { P }:Op-YpZpIt is seated C1C2The center of tie point；LiIt is i-th crane arm AiBiLength；γiIt is i-th crane arm AiBiVariable phase angle；Y and z is load C respectively1C2Center OpAlong Y-axis and Z The cartesian coordinate value of axle；θ represents angle of the moving coordinate system { P } relative to the rotation of basis coordinates system { B }；SiFor i-th lifting Machine lifting rope BiCiLength.
Furtherly, in step 2, according under the dual stage autocrane system luffing motion obtained by step 1 Variable phase angle response equation, the luffing angular response equivalent equation further established under the motion of dual stage autocrane system luffing：
Si=Tiγi, i=1,2
Wherein, SiAnd TiIt is i-th crane system interval matrix and system interval vector respectively, γiIt is i-th lifting Machine system variable phase angle response vector.
In step 3, in crane loading operation, due into production manufacture and external environment condition influence, structural parameters With uncertainty.Therefore, n small indeterminacy section parameters are introduced and carry out the small uncertain structure parameter of quantificational expression, establish section Parameter model is as follows：
Wherein,yWithIt is interval parameter vector y lower section and upper section respectively,yrWithIt is r-th of section ginseng respectively NumberLower section and upper section.
Furtherly, in step 4, based under the dual stage autocrane system luffing motion established in step 2 Luffing angular response equivalent equation, the interval parameter model introduced with reference to step 3, establish the dual stage vapour with interval parameter model Luffing angular response section equivalent equation under the motion of car crane system luffing：
Wherein, Si(Ki) and T (y)i(Ki(y)) be respectively i-th crane section compound function matrix and section it is compound Functional vector,It is i-th crane system luffing angular response interval vector, Ki(y) be interval parameter vector y relation function Vector；Expression is as follows：
Ti(Ki(y))=K3i(y)-K2i(y)
Ki(y)={ K1i(y),K2i(y),K3i(y)}T。
Furtherly, in step 5, section is answered according to compound function Differential Properties and first order Taylor series expansion Close Jacobian matrix Si(Ki) and section compound function vector T (y)i(Ki(y) approximate expansion) is carried out, obtains Si(Ki) and T (y)i(Ki (y) approximate expansion expression formula)；
First, based on compound function Differential Properties, higher order term, section compound function matrix S are ignoredi(Ki(y)) join in section The first order Taylor series expansion of number vector y midpoint can be expressed as：
Wherein,WithIt is section compound function matrix S respectivelyi(Ki(y) midrange and section radius), are represented respectively Into：
Wherein,It is interval parameter yr midrange and section radius respectively with Δ yr, standard interval variable δr=[- 1 ,+ 1]。
Secondly, based on compound function Differential Properties, higher order term, section compound function vector T are ignoredi(Ki(y)) join in section The first order Taylor series expansion of number vector y midpoint can be expressed as：
Wherein,WithIt is section compound function vector T respectivelyi(Ki(y) midrange and section radius), are represented respectively Into：
Furtherly, in step 6, S that step 5 is obtainedi(Ki) and T (y)i(Ki(y) approximate expansion expression formula) The luffing angular response section equivalent equation of step 4 is substituted into, and is obtained according to perturbation theory in luffing angular response interval vector Point value and section radius；Specially：
The S that step 5 is obtainedi(Ki) and T (y)i(Ki(y) variable phase angle that approximate expansion expression formula) substitutes into step 4 rings Section equivalent equation is answered to obtain：
Deployed according to Newman law, retain first three items after expansion,Approximate expression be：
, will be above-mentioned based on perturbation theoryApproximate expression substitute into luffing angular response section equivalent equation, protect First order perturbation item is stayed, ignores higher order term and obtains：
Above formula can equivalence write as：
Wherein,WithIt is the midrange and constant interval of luffing angular response interval vector respectively, is expressed as：
Therefore,Relative to standard interval variable δrMonotonicity, the section radius of luffing angular response interval vector can table It is shown as：
In order to preferably illustrate the present invention, now by taking double-crane system as an example, the implementation that an angle illustrates the present invention is changed Step is as follows：
Step 1：According to dual stage autocrane system geometrical model, the variable phase angle response equation established under luffing motion For：
Wherein,
Wherein, D and d is respectively crane spacing A1A2And load C1C2Length.Basis coordinates system { B }:O-YZ is seated A1A2The center of tie point.Moving coordinate system { P }:Op-YpZpIt is seated C1C2The center of tie point.LiIt is i-th crane arm AiBiLength.γiIt is i-th crane arm AiBiVariable phase angle.Y and z is load C respectively1C2Center OpAlong Y-axis and Z The cartesian coordinate value of axle.θ represents angle of the moving coordinate system { P } relative to the rotation of basis coordinates system { B }.SiFor i-th lifting Machine lifting rope BiCiLength.
Step 2：According to the variable phase angle responder under the dual stage autocrane system luffing motion obtained by step 1 Journey, the luffing angular response equivalent equation further established under the motion of dual stage autocrane system luffing：
Si=Tiγi, i=1,2
Wherein, SiAnd TiIt is i-th crane system interval matrix and system interval vector respectively, γiIt is i-th lifting Machine system variable phase angle response vector.
Step 3：In crane loading operation, due to having into production manufacture and the influence of external environment condition, structural parameters It is uncertain.Therefore, n small indeterminacy section parameters are introduced and carry out the small uncertain structure parameter of quantificational expression, establish interval parameter Model is as follows：
Wherein,yWithIt is interval parameter vector y lower section and upper section respectively,yrWithIt is r-th of section ginseng respectively NumberLower section and upper section.
Step 4：It is equivalent based on the luffing angular response under the dual stage autocrane system luffing motion established in step 2 Equation, the interval parameter model introduced with reference to step 3, establish the dual stage autocrane system with interval parameter model and become Luffing angular response section equivalent equation under width motion：
Wherein, Si(Ki) and T (y)i(Ki(y)) be respectively i-th crane section compound function matrix and section it is compound Functional vector,It is i-th crane system luffing angular response interval vector, Ki(y) be interval parameter vector y relation function Vector.Expression is as follows：
Ti(Ki(y))=K3i(y)-K2i(y).
Ki(y)={ K1i(y),K2i(y),K3i(y)}T
Step 5：According to compound function Differential Properties and first order Taylor series expansion to section compound function matrix Si(Ki ) and section compound function vector T (y)i(Ki(y) approximate expansion) is carried out, obtains Si(Ki) and T (y)i(Ki(y) approximate expansion) Expression formula.
First, based on compound function Differential Properties, higher order term, section compound function matrix S are ignoredi(Ki(y)) join in section The first order Taylor series expansion of number vector y midpoint can be expressed as：
Wherein,WithIt is section compound function matrix S respectivelyi(Ki(y) midrange and section radius), are represented respectively Into：
Wherein,With Δ yrIt is interval parameter y respectivelyrMidrange and section radius, standard interval variable δr=[- 1 ,+ 1]。
Secondly, based on compound function Differential Properties, higher order term, section compound function vector T are ignoredi(Ki(y)) join in section The first order Taylor series expansion of number vector y midpoint can be expressed as：
Wherein,WithIt is section compound function vector T respectivelyi(Ki(y) midrange and section radius), are represented respectively Into：
Step 6：The S that step 5 is obtainedi(Ki) and T (y)i(Ki(y) approximate expansion expression formula) substitutes into step 4 Luffing angular response section equivalent equation, and midrange and the section half of luffing angular response interval vector are obtained according to perturbation theory Footpath.
The S that step 5 is obtainedi(Ki) and T (y)i(Ki(y) variable phase angle that approximate expansion expression formula) substitutes into step 4 rings Section equivalent equation is answered to obtain：
Deployed according to Newman law, retain first three items after expansion,Approximate expression be：
, will be above-mentioned based on perturbation theoryApproximate expression substitute into luffing angular response section equivalent equation, protect First order perturbation item is stayed, ignores higher order term and obtains：
Above formula can equivalence write as：
Wherein,WithIt is the midrange and constant interval of luffing angular response interval vector respectively, is expressed as：
Therefore,Relative to standard interval variable δrMonotonicity, the section radius of luffing angular response interval vector can table It is shown as：
Step 7：The midrange and section radius for the luffing angular response interval vector that step 6 is obtained, take the photograph according to section Dynamic method obtains the upper dividing value and floor value of luffing angular response interval vector.
The upper dividing value and floor value of luffing angular response interval vector are obtained according to Interval Perturbation method, are expressed as：
The method of variable phase angle response field problem under small indeterminacy section parameter provided by the invention, it is especially suitable for more than 2 The occasion of crane, in analogue simulation and practice, present invention excellent performance under 2 autocrane systems, in, operation Personnel can be on the basis of the variable phase angle response equation under the motion of dual stage autocrane system luffing, first will be small not true Determine structural parameters and be modeled as interval parameter model, based on compound function Differential Properties and Interval Perturbation method, to obtain variable phase angle sound Answer midrange, section radius, upper dividing value and the floor value of interval vector.Based on this, the present invention gives dual stage automobile crane The side that the Forecasting Methodology of variable phase angle response field is implemented in a computer under small indeterminacy section parameter under the motion of machine system luffing Case.In addition, by the present invention, good thinking is provided in the solution of variable phase angle response problem for more crane systems and is opened Hair.The present invention designs the pre- of variable phase angle response field in the case where taking into full account uncertain less interval parameter structure Survey method, to improve autocrane system section response field predictive ability, there is the characteristics of rapidity and high precision, to carry The reliability of high autocrane system job.Specific advantageous effects of the invention are as follows：
1) compared with traditional more crane Similarity degree methods, dual stage autocrane system provided by the invention Under luffing motion under small indeterminacy section parameter variable phase angle response field problem algorithm, this method taken into full account interval parameter Uncertain less feature, result of calculation to variable phase angle response domain analysis there is important directive significance.Require emphasis It is that this method has two big advantages, first, computational efficiency is higher；Second, precision is preferable.
2) the uncertain small occasion of interval parameter is directed to, variable phase angle rings under small indeterminacy section parameter provided by the invention The algorithm of domain problem is answered, using first order Taylor series expansion and single order Newman law expansion under uncertain structure parameter Luffing angular response is analyzed, and effectively increases computational efficiency, greatly simplifies calculating process.Further, according to Interval Perturbation Method quickly obtains the knot of the reflection variable phase angle response field such as upper dividing value and floor value of luffing angular response interval vector section feature Fruit.
3) problem to be solved by this invention is directed to, existing solution is to use Monte-Carlo methods, exists and counts Less efficient problem.And the uncertain parameter sample that the present invention is directed in crane system be optimized it is (and especially suitable Under conditions of double-crane) --- realize that uncertain parameter sample is few, computational efficiency is high, precision is high so that engineering skill Art personnel are according to the complexity Rational choice traditional scheme or the present invention program of engineering problem, to dual stage autocrane system Variable phase angle response field problem carries out rationally efficient prediction under small indeterminacy section parameter under luffing of uniting moves.Technical staff can Known all kinds of certainty load parameters and uncertain less area are directed in conventional method (referring to Fig. 3,4) to use Between structural parameters occasion, solving result；The luffing angular response that the method for the present invention is proposed (referring to Fig. 3,4) can more be implemented The Forecasting Methodology in domain takes into full account the MULTILAYER COMPOSITE functional relation of the variable phase angle response equation under luffing motion, and combines section Analytic approach and perturbation theory derive the midrange of luffing angular response interval vector, section radius, upper dividing value and floor value, both The complexity of engineering problem has been taken into full account, in turn ensure that the relative accuracy of result of calculation, it is notable that using this Invention will can significantly be shortened the calculating time.
Brief description of the drawings
Fig. 1 is the flow chart of the present invention.
Fig. 2 is dual stage autocrane system threedimensional model schematic diagram；First autocrane system is shown in figure Arm A in 1, second autocrane system intermediate station 2 of intermediate station, First autocrane system1B1, second automobile Arm A in crane system2B2, lifting rope B in First autocrane system1C1, hang in second autocrane system Restrict B2C2, load C1C2, load center of gravity Op, pin joint A1、A2、B1、 B2、C1、C2And its position relationship.
Fig. 3 is minizone rate of change (section radius and the ratio of interval midpoint value of interval parameter structure provided by the invention Value) scope is when be [0,0.20%], using luffing under the medium and small indeterminacy section parameter of dual stage autocrane system luffing motion Conventional method is respectively adopted in the Forecasting Methodology in angular response domain in a computer and the inventive method calculates the First vapour of acquisition Dividing value curve map curve map on the section of car crane system variable phase angle response field.
Fig. 4 is minizone rate of change (section radius and the ratio of interval midpoint value of interval parameter structure provided by the invention Value) scope is when be [0,0.20%], using luffing under the medium and small indeterminacy section parameter of dual stage autocrane system luffing motion Conventional method is respectively adopted in the Forecasting Methodology in angular response domain in a computer and the inventive method calculates the First vapour of acquisition The section floor value curve map curve map of car crane system variable phase angle response field.
Embodiment
Describe the design feature and advantage of the present invention in detail in conjunction with accompanying drawing.
Referring to Fig. 1, suitable for crane system variable phase angle response field acquisition methods under the parameter of minizone, enter as follows OK：
Step 1：Establish variable phase angle response equation of the transportation system under luffing motion；
Step 2：Variable phase angle response equation under the luffing obtained by step 1 is moved, it is converted under luffing motion Luffing angular response equivalent equation；
Step 3：By the small indeterminacy section parameter of transportation system, interval parameter model is established；
Step 4：With reference to step 2 and step 3, establish under transportation system's luffing motion with interval parameter model Luffing angular response section equivalent equation, section compound function matrix, section compound function vector；
Step 5：The section compound function matrix, the section compound function vector that are obtained by step 4 are deployed respectively, Obtain approximate expansion expression formula；
Step 6：The approximate expansion expression formula obtained by step 5 is brought into the section compound function square obtained by step 4 In battle array, midrange, the constant interval of luffing angular response interval vector of luffing angular response interval vector are obtained；
Step 7：The constant interval of the midrange of luffing angular response interval vector, luffing angular response interval vector is obtained The upper dividing value and floor value of luffing angular response interval vector.
Furtherly, transportation system is made up of the vehicle equipment of more than 2；Vehicle equipment is fixed crane, movement Formula derrick car or the means of transport with stirrup.
Furtherly, transportation system is 2 autocranes or 2 fixed cranes.
Referring to Fig. 1 and 2, suitable for crane system variable phase angle response field acquisition methods, specific steps under the parameter of minizone For：
Step 1：According to double-crane system geometrical model, it is established that the luffing angular response under the motion of heavy-duty machine system luffing Equation is：
Wherein,
Wherein, D and d is respectively crane spacing A1A2And load C1C2Length, basis coordinates system { B }:O-YZ is seated A1A2The center of tie point, moving coordinate system { P }:Op-YpZpIt is seated C1C2The center of tie point, LiIt is i-th crane arm AiBiLength, γiIt is i-th crane arm AiBiVariable phase angle, y and z are load C respectively1C2Center OpAlong Y-axis and Z The cartesian coordinate value of axle, θ represent moving coordinate system { P } relative to the angle of the rotation of basis coordinates system { B }, SiFor i-th lifting Machine lifting rope BiCiLength.
Step 2：Variable phase angle response equation under being moved according to the crane system luffing obtained by step 1, further The luffing angular response equivalent equation established under the motion of crane system luffing：
Si=Tiγi
Wherein, SiAnd TiIt is i-th crane system interval matrix and system interval vector respectively, γiIt is i-th lifting Machine system variable phase angle response vector；I is the integer not less than 2；
Step 4：Luffing angular response section established under the double-crane system luffing motion with interval parameter model etc. Efficacious prescriptions journey：
Wherein, Si(Ki) and T (y)i(Ki(y)) be respectively i-th crane section compound function matrix and section it is compound Functional vector,It is i-th crane system luffing angular response interval vector, Ki(y) be interval parameter vector y relation function Vector；
Step 5：To section compound function matrix Si(Ki) and section compound function vector T (y)i(Ki(y)) carry out approximate Expansion, obtains Si(Ki) and T (y)i(Ki(y) approximate expansion expression formula)：
Wherein,WithIt is section compound function matrix S respectivelyi(Ki(y) midrange and section radius)；
Wherein,WithIt is section compound function vector T respectivelyi(Ki(y) midrange and section radius)；
Step 6：The S that step 5 is obtainedi(Ki) and T (y)i(Ki(y) approximate expansion expression formula) substitutes into step 4 Luffing angular response section equivalent equation：
Wherein,WithIt is the midrange and constant interval of luffing angular response interval vector respectively；
Step 7：The midrange and section radius for the luffing angular response interval vector that step 6 is obtained, take the photograph according to section Dynamic method obtains the upper dividing value of luffing angular response interval vector：And floor value：
Referring to Fig. 1 and 2, furtherly, in step 1, for double-crane system geometrical model, luffing motion is established Under variable phase angle response equation be：
Wherein,
Wherein, D and d is respectively crane spacing A1A2And load C1C2Length；Basis coordinates system { B }:O-YZ is seated A1A2The center of tie point；Moving coordinate system { P }:Op-YpZpIt is seated C1C2The center of tie point；LiIt is i-th crane arm AiBiLength；γiIt is i-th crane arm AiBiVariable phase angle；Y and z is load C respectively1C2Center OpAlong Y-axis and Z The cartesian coordinate value of axle；θ represents angle of the moving coordinate system { P } relative to the rotation of basis coordinates system { B }；SiFor i-th lifting Machine lifting rope BiCiLength.
Referring to Fig. 1 and 2, furtherly, in step 2, transported according to the double-crane system luffing obtained by step 1 Variable phase angle response equation under dynamic, the luffing angular response equivalent equation further established under the motion of double-crane system luffing：
Si=Tiγi, i=1,2
Wherein, SiAnd TiIt is i-th crane system interval matrix and system interval vector respectively, γiIt is i-th lifting Machine system variable phase angle response vector.
In step 3, in crane loading operation, due into production manufacture and external environment condition influence, structural parameters With uncertainty.Therefore, n small indeterminacy section parameters are introduced and carry out the small uncertain structure parameter of quantificational expression, establish section Parameter model is as follows：
Wherein,yWithIt is interval parameter vector y lower section and upper section respectively,yrWithIt is r-th of interval parameter respectivelyLower section and upper section.
Referring to Fig. 1 and 2, furtherly, in step 4, based on the double-crane system luffing fortune established in step 2 Luffing angular response equivalent equation under dynamic, the interval parameter model introduced with reference to step 3, establish with interval parameter model Luffing angular response section equivalent equation under the motion of dual stage autocrane system luffing：
Wherein, Si(Ki) and T (y)i(Ki(y)) be respectively i-th crane section compound function matrix and section it is compound Functional vector,It is i-th crane system luffing angular response interval vector, Ki(y) be interval parameter vector y relation function Vector；Expression is as follows：
Ti(Ki(y))=K3i(y)-K2i(y).
Ki(y)={ K1i(y),K2i(y),K3i(y)}T。
Referring to Fig. 1 and 2, furtherly, in step 5, according to compound function Differential Properties and first order Taylor series expansion Formula is to section compound function matrix Si(Ki) and section compound function vector T (y)i(Ki(y) approximate expansion) is carried out, obtains Si(Ki ) and T (y)i(Ki(y) approximate expansion expression formula)；
First, based on compound function Differential Properties, higher order term, section compound function matrix S are ignoredi(Ki(y)) join in section The first order Taylor series expansion of number vector y midpoint can be expressed as：
Wherein,WithIt is section compound function matrix S respectivelyi(Ki(y) midrange and section radius), are represented respectively Into：
Wherein,With Δ yrIt is interval parameter y respectivelyrMidrange and section radius, standard interval variable δr=[- 1 ,+ 1]。
Secondly, based on compound function Differential Properties, higher order term, section compound function vector T are ignoredi(Ki(y)) join in section The first order Taylor series expansion of number vector y midpoint can be expressed as：
Wherein,WithIt is section compound function vector T respectivelyi(Ki(y) midrange and section radius), are represented respectively Into：
Referring to Fig. 1 and 2, furtherly, in step 6, S that step 5 is obtainedi(Ki) and T (y)i(Ki(y)) near The luffing angular response section equivalent equation of step 4 is substituted into like expanded expression, and luffing angular response is obtained according to perturbation theory The midrange and section radius of interval vector；Specially：
The S that step 5 is obtainedi(Ki) and T (y)i(Ki(y) variable phase angle that approximate expansion expression formula) substitutes into step 4 rings Section equivalent equation is answered to obtain：
Deployed according to Newman law, retain first three items after expansion,Approximate expression be：
Will be above-mentionedApproximate expression substitute into luffing angular response section equivalent equation, and retain first order perturbation , ignore higher order term and obtain：
Above formula can equivalence write as：
Wherein,WithIt is the midrange and constant interval of luffing angular response interval vector respectively, is expressed as：
And then obtain the section radius of luffing angular response interval vector：
Embodiment 1
Referring to Fig. 1 and 2, apply in the motion of dual stage autocrane system luffing, under small indeterminacy section parameter The solution of variable phase angle response field problem, is carried out as follows：
Step 1：According to dual stage autocrane system geometrical model, the variable phase angle response equation established under luffing motion For：
Wherein, i=1,2, D and d are respectively crane spacing A1A2And load C1C2Length.Basis coordinates system { B }：O-YZ It is seated A1A2The center of tie point.Moving coordinate system { P }:Op-YpZpIt is seated C1C2The center of tie point.LiIt is i-th lifting Machine arm AiBiLength.γiIt is i-th crane arm AiBiVariable phase angle.Y and z is load C respectively1C2Center OpAlong Y The cartesian coordinate value of axle and Z axis.θ represents angle of the moving coordinate system { P } relative to the rotation of basis coordinates system { B }.SiFor i-th Platform crane lifting rope BiCiLength.
Step 2：According to the variable phase angle responder under the dual stage autocrane system luffing motion obtained by step 1 Journey, the luffing angular response equivalent equation further established under the motion of dual stage autocrane system luffing：
Si=Tiγi, i=1,2
Wherein, SiAnd TiIt is i-th crane system interval matrix and system interval vector respectively, γiIt is i-th lifting Machine system variable phase angle response vector.
Step 3：In crane loading operation, due to having into production manufacture and the influence of external environment condition, structural parameters It is uncertain.Therefore, n small indeterminacy section parameters are introduced and carry out the small uncertain structure parameter of quantificational expression, establish interval parameter Model is as follows：
r≥3；n≥3
Wherein,yWithIt is interval parameter vector y lower section and upper section respectively,yr WithIt is r-th of interval parameter respectivelyLower section and upper section.
Step 4：The luffing angular response established under the dual stage autocrane system luffing motion with interval parameter model Section equivalent equation：
Wherein, Si(Ki) and T (y)i(Ki(y)) be respectively the 1st and 2 crane section compound function matrix and section Compound function vector,It is i-th crane system luffing angular response interval vector, Ki(y) be interval parameter vector y relation Functional vector.Expression is as follows：
Ti(Ki(y))=K3i(y)-K2i(y).
Ki(y)={ K1i(y),K2i(y),K3i(y)}T
Step 5：To section compound function matrix Si(Ki) and section compound function vector T (y)i(Ki(y)) carry out approximate Expansion, obtains Si(Ki) and T (y)i(Ki(y) approximate expansion expression formula).
Section compound function matrix Si(Ki(y)) it is in the first order Taylor series expansion of interval parameter vector y midpoint：
Wherein, section compound function matrix Si(Ki(y) midrange)Section compound function matrix Si(Ki (y) section radius) is With Δ yrIt is respectively Interval parameter yrMidrange and section radius, standard interval variable δr=[- 1 ,+1].
Secondly, section compound function vector Ti(Ki(y)) interval parameter vector y midpoint first order Taylor series exhibition Opening to be expressed as：
Wherein, section compound function vector Ti(Ki(y) midrange)Section compound function vector Ti(Ki (y) section radius)
Step 6：The S that step 5 is obtainedi(Ki) and T (y)i(Ki(y) approximate expansion expression formula) substitutes into step 4 Luffing angular response section equivalent equation obtains：
Deployed according to Newman law, retain first three items after expansion,Approximate expression be：
, will be above-mentioned based on perturbation theoryApproximate expression substitute into luffing angular response section equivalent equation, protect First order perturbation item is stayed, ignores higher order term and obtains：
Above formula can equivalence write as：
Wherein,WithIt is the midrange and constant interval of luffing angular response interval vector respectively, is expressed as：
Therefore,Relative to standard interval variable δrMonotonicity, the section radius of luffing angular response interval vector can table It is shown as：
Step 7：The midrange and section radius for the luffing angular response interval vector that step 6 is obtained, take the photograph according to section Dynamic method obtains the upper dividing value and floor value of luffing angular response interval vector.
The upper dividing value and floor value of luffing angular response interval vector are obtained according to Interval Perturbation method, are expressed as：
Fig. 2 is dual stage autocrane system threedimensional model schematic diagram corresponding with the present embodiment, including First automobile Turntable 2, the arm A of First autocrane system of 1, second autocrane system of turntable of crane system1B1、 The arm A of second autocrane system2B2, First autocrane system lifting rope B1C1, second automobile crane The lifting rope B of machine system2C2, load C1C2, load center of gravity Op, pin joint A1、A2、B1、B2、C1、C2.In luffing motion, turntable 1 (turn Platform 2) remains stationary state, i.e., realize load C not by respective slew gear1C2Around crane rotation center axis thereof Motion；Arm A1B1(arm A2B2) remains stationary state, including the telescopic arm that more piece is mutually socketed, i.e. telescopic arm are simultaneously obstructed The telescopic action for crossing telescoping drive mechanism produces relative motion, i.e., does not change arm A1B1(arm A2B2) length to adjust The operating radius of autocrane；Lifting rope B1C1(lifting rope B2C2) remains stationary state, i.e., not by raising in jib lubbing mechanism Lifting rope B in mechanism1C1(lifting rope B2C2) expanding-contracting action realize load C1C2Elevating movement in perpendicular.Amplitude oil cylinder D1E1(amplitude oil cylinder D2E2) one end and turntable 1 (turntable 2) be hinged, the other end and arm A1B1(arm A2B2) be hinged, pass through tune Save amplitude oil cylinder D in jib lubbing mechanism1E1(amplitude oil cylinder D2E2) length, further realize arm A1B1(arm A2B2) vertical Around amplitude oil cylinder D in plane1E1(amplitude oil cylinder D2E2) with being rotated at turntable 1 (turntable 2) pin joint to change arm A1B1(arm A2B2) elevation angle change, so as to change the change angle of autocrane.For above-mentioned dual stage autocrane System, variable phase angle under small indeterminacy section parameter under being moved below to dual stage autocrane system luffing provided by the invention The Forecasting Methodology of response field is described.
Then, according to rubber tyre gantry crane design parameter and working condition requirement, the determination value of each load parameter and small uncertain region are determined Between structural parameters midrange and section radius；
Obtained in the determination value of above-mentioned each load parameter and the midrange and section radius of small indeterminacy section structural parameters On the premise of, an optional random value from the section Distribution Value of each structural parameters, and it is input to MATLAB programs；
Programmed using MATLAB and bring the determination value of the random value of each structural parameters and load parameter into dual stage automobile successively Luffing angular response equivalent equation under the motion of crane system luffing.
Therefore, the variable phase angle under the dual stage autocrane system luffing motion under small indeterminacy section structural parameters is obtained Response.
Said process is repeated to number i=10000 times, and exports the dual stage automobile under small indeterminacy section structural parameters and rises Variable phase angle response field distribution curve under the motion of heavy-duty machine system luffing, and small indeterminacy section knot is exported according to computer instruction The upper dividing value and floor value of the lower luffing angular response interval vector of dual stage autocrane system luffing motion under structure parameter.
In order to more intuitively compare and illustrate the present invention, contrast inspection has been done using conventional method (Monte-Carlo methods) Survey.
Referring to Fig. 3 and Fig. 4, section rate of change (section radius and the interval midpoint of interval parameter structure provided by the invention The ratio of value) scope is when being [0,0.20%], using conventional method (Monte-Carlo methods) and the inventive method in computer In, in the double flow car crane system shown in prognostic chart 2, on the section of First autocrane system variable phase angle response field Dividing value and floor value curve map.
First autocrane in dual stage autocrane system is calculated using conventional method and the inventive method respectively The concrete numerical value of dividing value and floor value on the section of system variable phase angle response field, as shown in table 1.Using conventional method and Ben Fa Bright method calculates the section upper bound of First autocrane system variable phase angle response field in dual stage autocrane system respectively The curve map of value, as shown in Figure 3；Calculated respectively in dual stage autocrane system using conventional method and the inventive method The curve map of the section floor value of one autocrane system variable phase angle response field, as shown in Figure 4.Abscissa represents section Rate of change, ordinate represent dividing value and floor value on the section of variable phase angle response field, and solid line and dotted line represent conventional method respectively Acquired results are calculated with the inventive method.
Using First autocrane system as research object, it was found from shown in Fig. 3 and Fig. 4, when interval parameter is in cell Between under rate of change when, dual stage autocrane system luffing moves the pre- of variable phase angle response field under medium and small indeterminacy section parameter The survey method result that conventional method and the inventive method calculate in a computer is consistent substantially, but after the use present invention, fortune Evaluation time significantly shortens --- and calculate time-consuming more original method and shorten 2 orders of magnitude, therefore with computational efficiency height (during calculating Between it is few), solving precision is high, the engineering problem few especially suitable for uncertain parameter sample.
Dividing value and floor value on the section of the First autocrane system variable phase angle response field of table 1
In summary, the present invention can solve dual stage or even the autocrane system of more, fixed crane, movement Formula derrick car or the means of transport with stirrup, in the case where luffing moves medium and small indeterminacy section parameter, variable phase angle response field is pre- Survey problem.Above-mentioned implementation calculated example is only the exemplary embodiments of the present invention, and the present invention is not limited solely to above-described embodiment, All changes made within the principle and content of the present invention should be included in the scope of the protection.
Specification digest
The invention discloses one kind to be applied to crane system variable phase angle response field acquisition methods under the parameter of minizone, step It is as follows：Establish variable phase angle response equation of the transportation system under luffing motion；Luffing angular response being converted under luffing motion etc. Efficacious prescriptions journey；Establish interval parameter model；The luffing angular response established under transportation system's luffing motion with interval parameter model Section equivalent equation, section compound function matrix, section compound function vector；Obtain approximate expansion expression formula；By approximate expansion Expression formula is brought into the compound function matrix of section, obtain the midrange of luffing angular response interval vector, luffing angular response section to The constant interval of amount；The constant interval of the midrange of luffing angular response interval vector, luffing angular response interval vector is obtained and become Argument responds the upper dividing value and floor value of interval vector.The present invention can be solved in crane system under structural parameters containing minizone Variable phase angle response field problem analysis, effectively improves computational accuracy and operation efficiency.

Claims (9)

1. suitable for crane system variable phase angle response field acquisition methods under the parameter of minizone, it is characterised in that as follows Carry out：
Step 1：Establish variable phase angle response equation of the transportation system under luffing motion；
Step 2：Variable phase angle response equation under luffing is moved is converted into the luffing angular response equivalent equation under luffing motion；
Step 3：By the small indeterminacy section parameter of transportation system, interval parameter model is established；
Step 4：The luffing angular response section equivalent equation established under the transportation system luffing motion with interval parameter model, Section compound function matrix, section compound function vector；
Step 5：The section compound function matrix, the section compound function vector that are obtained by step 4 are deployed respectively, obtained Approximate expansion expression formula；
Step 6：The approximate expansion expression formula obtained by step 5 is brought into the section compound function matrix obtained by step 4 In, midrange, the constant interval of luffing angular response interval vector of acquisition luffing angular response interval vector；
Step 7：The constant interval of the midrange of luffing angular response interval vector, luffing angular response interval vector is obtained into luffing The upper dividing value and floor value of angular response interval vector.
2. according to claim 1 be applied to crane system variable phase angle response field acquisition methods under the parameter of minizone, its It is characterised by, transportation system is made up of the vehicle equipment of more than 2；Vehicle equipment is fixed crane, Mobile hoisting car Or the means of transport with stirrup.
3. according to claim 1 be applied to crane system variable phase angle response field acquisition methods under the parameter of minizone, its It is characterised by, transportation system is 2 autocranes or 2 fixed cranes.
4. it is applied to crane system variable phase angle response field acquisition methods under the parameter of minizone according to claim 1 or 3, Characterized in that, concretely comprise the following steps：
Step 1：According to double-crane system geometrical model, it is established that the variable phase angle response equation under the motion of heavy-duty machine system luffing For：
<mrow> <msub> <mi>&amp;gamma;</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>2</mn> <msup> <mi>tan</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mfrac> <mrow> <mo>-</mo> <msub> <mi>K</mi> <mrow> <mn>1</mn> <mi>i</mi> </mrow> </msub> <mo>+</mo> <msqrt> <mrow> <msup> <msub> <mi>K</mi> <mrow> <mn>1</mn> <mi>i</mi> </mrow> </msub> <mn>2</mn> </msup> <mo>+</mo> <msup> <msub> <mi>K</mi> <mrow> <mn>2</mn> <mi>i</mi> </mrow> </msub> <mn>2</mn> </msup> <mo>-</mo> <msup> <msub> <mi>K</mi> <mrow> <mn>3</mn> <mi>i</mi> </mrow> </msub> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> <mrow> <msub> <mi>K</mi> <mrow> <mn>3</mn> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>K</mi> <mrow> <mn>2</mn> <mi>i</mi> </mrow> </msub> </mrow> </mfrac> </mrow>
Wherein,
<mrow> <msub> <mi>K</mi> <mrow> <mn>3</mn> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mi>y</mi> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mrow> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mi>i</mi> </msup> <mfrac> <mrow> <mi>d</mi> <mi> </mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;theta;</mi> </mrow> <mn>2</mn> </mfrac> <mo>-</mo> <msup> <mrow> <mo>(</mo> <mrow> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mi>i</mi> </msup> <mfrac> <mi>D</mi> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mi>z</mi> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mrow> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mi>i</mi> </msup> <mfrac> <mrow> <mi>d</mi> <mi> </mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>&amp;theta;</mi> </mrow> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msubsup> <mi>L</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>S</mi> <mi>i</mi> <mn>2</mn> </msubsup> </mrow>
Wherein, D and d is respectively crane spacing A1A2And load C1C2Length, basis coordinates system { B }:O-YZ is seated A1A2Even The center of contact, moving coordinate system { P }:Op-YpZpIt is seated C1C2The center of tie point, LiIt is i-th crane arm AiBiLength Degree, γiIt is i-th crane arm AiBiVariable phase angle, y and z are load C respectively1C2Center OpAlong Y-axis and the flute card of Z axis That coordinate value, θ represent moving coordinate system { P } relative to the angle of the rotation of basis coordinates system { B }, SiFor i-th crane lifting rope BiCi Length.
Step 2：According to the variable phase angle response equation under the crane system luffing motion obtained by step 1, further establish Luffing angular response equivalent equation under the motion of crane system luffing：
Si=Tiγi
Wherein, SiAnd TiIt is i-th crane system interval matrix and system interval vector respectively, γiIt is i-th crane system System variable phase angle response vector；I is the integer not less than 2；
Step 4：The efficacious prescriptions such as the luffing angular response section established under the double-crane system luffing motion with interval parameter model Journey：
<mrow> <msub> <mi>S</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>K</mi> <mi>i</mi> </msub> <mo>(</mo> <mi>y</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>T</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>K</mi> <mi>i</mi> </msub> <mo>(</mo> <mi>y</mi> <mo>)</mo> <mo>)</mo> </mrow> <msubsup> <mi>&amp;gamma;</mi> <mi>i</mi> <mi>I</mi> </msubsup> </mrow>
Wherein, Si(Ki) and T (y)i(Ki(y)) be respectively i-th crane section compound function matrix and section compound function Vector,It is i-th crane system luffing angular response interval vector, Ki(y) be interval parameter vector y relation function vector；
Step 5：To section compound function matrix Si(Ki) and section compound function vector T (y)i(Ki(y) approximate expansion) is carried out, Obtain Si(Ki) and T (y)i(Ki(y) approximate expansion expression formula)：
<mrow> <msub> <mi>S</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>K</mi> <mi>i</mi> </msub> <mo>(</mo> <mi>y</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>S</mi> <mi>i</mi> <mi>c</mi> </msubsup> <mo>+</mo> <msub> <mi>&amp;Delta;</mi> <mn>1</mn> </msub> <msubsup> <mi>S</mi> <mi>i</mi> <mi>I</mi> </msubsup> </mrow>
Wherein,WithIt is section compound function matrix S respectivelyi(Ki(y) midrange and section radius)；
<mrow> <msub> <mi>T</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>K</mi> <mi>i</mi> </msub> <mo>(</mo> <mi>y</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>T</mi> <mi>i</mi> <mi>c</mi> </msubsup> <mo>+</mo> <msub> <mi>&amp;Delta;</mi> <mn>1</mn> </msub> <msubsup> <mi>T</mi> <mi>i</mi> <mi>I</mi> </msubsup> </mrow>
Wherein,WithIt is section compound function vector T respectivelyi(Ki(y) midrange and section radius)；
Step 6：The S that step 5 is obtainedi(Ki) and T (y)i(Ki(y) approximate expansion expression formula) substitutes into the variable phase angle of step 4 Respond section equivalent equation：
<mrow> <msubsup> <mi>&amp;gamma;</mi> <mi>i</mi> <mi>I</mi> </msubsup> <mo>=</mo> <msubsup> <mi>&amp;gamma;</mi> <mi>i</mi> <mi>c</mi> </msubsup> <mo>+</mo> <msub> <mi>&amp;Delta;</mi> <mn>1</mn> </msub> <msubsup> <mi>&amp;gamma;</mi> <mi>i</mi> <mi>I</mi> </msubsup> </mrow>
Wherein,WithIt is the midrange and constant interval of luffing angular response interval vector respectively；
Step 7：The midrange and section radius for the luffing angular response interval vector that step 6 is obtained, according to Interval Perturbation method Obtain the upper dividing value of luffing angular response interval vector：And floor value：
5. according to claim 4 be applied to crane system variable phase angle response field acquisition methods under the parameter of minizone, its It is characterised by, in step 1, for double-crane system geometrical model, the variable phase angle response equation established under luffing motion For：
<mrow> <msub> <mi>&amp;gamma;</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>2</mn> <msup> <mi>tan</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mfrac> <mrow> <mo>-</mo> <msub> <mi>K</mi> <mrow> <mn>1</mn> <mi>i</mi> </mrow> </msub> <mo>+</mo> <msqrt> <mrow> <msup> <msub> <mi>K</mi> <mrow> <mn>1</mn> <mi>i</mi> </mrow> </msub> <mn>2</mn> </msup> <mo>+</mo> <msup> <msub> <mi>K</mi> <mrow> <mn>2</mn> <mi>i</mi> </mrow> </msub> <mn>2</mn> </msup> <mo>-</mo> <msup> <msub> <mi>K</mi> <mrow> <mn>3</mn> <mi>i</mi> </mrow> </msub> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> <mrow> <msub> <mi>K</mi> <mrow> <mn>3</mn> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>K</mi> <mrow> <mn>2</mn> <mi>i</mi> </mrow> </msub> </mrow> </mfrac> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow>
Wherein,
<mrow> <msub> <mi>K</mi> <mrow> <mn>1</mn> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <mn>2</mn> <msub> <mi>L</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>z</mi> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mrow> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mi>i</mi> </msup> <mfrac> <mrow> <mi>d</mi> <mi> </mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>&amp;theta;</mi> </mrow> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>K</mi> <mrow> <mn>2</mn> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <mn>2</mn> <msub> <mi>L</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>y</mi> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mrow> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mi>i</mi> </msup> <mfrac> <mrow> <mi>d</mi> <mi> </mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;theta;</mi> </mrow> <mn>2</mn> </mfrac> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mrow> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mi>i</mi> </msup> <mfrac> <mi>D</mi> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>K</mi> <mrow> <mn>3</mn> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mi>y</mi> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mrow> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mi>i</mi> </msup> <mfrac> <mrow> <mi>d</mi> <mi> </mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;theta;</mi> </mrow> <mn>2</mn> </mfrac> <mo>-</mo> <msup> <mrow> <mo>(</mo> <mrow> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mi>i</mi> </msup> <mfrac> <mi>D</mi> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mi>z</mi> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mrow> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mi>i</mi> </msup> <mfrac> <mrow> <mi>d</mi> <mi> </mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>&amp;theta;</mi> </mrow> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msubsup> <mi>L</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>S</mi> <mi>i</mi> <mn>2</mn> </msubsup> </mrow>
Wherein, D and d is respectively crane spacing A1A2And load C1C2Length；Basis coordinates system { B }:O-YZ is seated A1A2Even The center of contact；Moving coordinate system { P }:Op-YpZpIt is seated C1C2The center of tie point；LiIt is i-th crane arm AiBiLength Degree；γiIt is i-th crane arm AiBiVariable phase angle；Y and z is load C respectively1C2Center OpAlong Y-axis and the flute card of Z axis That coordinate value；θ represents angle of the moving coordinate system { P } relative to the rotation of basis coordinates system { B }；SiFor i-th crane lifting rope BiCi Length.
6. according to claim 4 be applied to crane system variable phase angle response field acquisition methods under the parameter of minizone, its It is characterised by,
In step 2, according to the variable phase angle response equation under the double-crane system luffing motion obtained by step 1, enter The luffing angular response equivalent equation that one step is established under the motion of double-crane system luffing：
Si=Tiγi, i=1,2
Wherein, SiAnd TiIt is i-th crane system interval matrix and system interval vector respectively, γiIt is i-th crane system System variable phase angle response vector.
In step 3, in crane loading operation, due to having into production manufacture and the influence of external environment condition, structural parameters It is uncertain.Therefore, n small indeterminacy section parameters are introduced and carry out the small uncertain structure parameter of quantificational expression, establish interval parameter Model is as follows：
<mrow> <mi>y</mi> <mo>=</mo> <mrow> <mo>(</mo> <msubsup> <mi>y</mi> <mi>r</mi> <mi>I</mi> </msubsup> <mo>)</mo> </mrow> <mo>=</mo> <mo>&amp;lsqb;</mo> <munder> <mi>y</mi> <mo>&amp;OverBar;</mo> </munder> <mo>,</mo> <mover> <mi>y</mi> <mo>&amp;OverBar;</mo> </mover> <mo>&amp;rsqb;</mo> <mo>,</mo> <msubsup> <mi>y</mi> <mi>r</mi> <mi>I</mi> </msubsup> <mo>=</mo> <mo>&amp;lsqb;</mo> <munder> <msub> <mi>y</mi> <mi>r</mi> </msub> <mo>&amp;OverBar;</mo> </munder> <mo>,</mo> <mover> <msub> <mi>y</mi> <mi>r</mi> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>&amp;rsqb;</mo> <mo>,</mo> <mi>r</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>n</mi> <mo>.</mo> </mrow>
Wherein,yWithIt is interval parameter vector y lower section and upper section respectively,yr WithIt is r-th of interval parameter respectively's Lower section and upper section.
7. according to claim 4 be applied to crane system variable phase angle response field acquisition methods under the parameter of minizone, its It is characterised by, in step 4, based on luffing angular response under the double-crane system luffing motion established in step 2 etc. Efficacious prescriptions journey, the interval parameter model introduced with reference to step 3, establish the dual stage autocrane system with interval parameter model Luffing angular response section equivalent equation under luffing motion：
<mrow> <msub> <mi>S</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>K</mi> <mi>i</mi> </msub> <mo>(</mo> <mi>y</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>T</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>K</mi> <mi>i</mi> </msub> <mo>(</mo> <mi>y</mi> <mo>)</mo> <mo>)</mo> </mrow> <msubsup> <mi>&amp;gamma;</mi> <mi>i</mi> <mi>I</mi> </msubsup> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow>
Wherein, Si(Ki) and T (y)i(Ki(y)) be respectively i-th crane section compound function matrix and section compound function Vector,It is i-th crane system luffing angular response interval vector, Ki(y) be interval parameter vector y relation function vector； Expression is as follows：
<mrow> <msub> <mi>S</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>K</mi> <mi>i</mi> </msub> <mo>(</mo> <mi>y</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>=</mo> <msqrt> <mrow> <msub> <mi>K</mi> <mrow> <mn>1</mn> <mi>i</mi> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mi>y</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>K</mi> <mrow> <mn>2</mn> <mi>i</mi> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mi>y</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <msub> <mi>K</mi> <mrow> <mn>3</mn> <mi>i</mi> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mi>y</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>-</mo> <msub> <mi>K</mi> <mrow> <mn>1</mn> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>y</mi> <mo>)</mo> </mrow> <mo>,</mo> </mrow>
Ti(Ki(y))=K3i(y)-K2i(y).
Ki(y)={ K1i(y),K2i(y),K3i(y)}T。
8. according to claim 4 be applied to crane system variable phase angle response field acquisition methods under the parameter of minizone, its It is characterised by, in step 5, according to compound function Differential Properties and first order Taylor series expansion to section compound function square Battle array Si(Ki) and section compound function vector T (y)i(Ki(y) approximate expansion) is carried out, obtains Si(Ki) and T (y)i(Ki(y)) near Like expanded expression；
First, based on compound function Differential Properties, higher order term, section compound function matrix S are ignoredi(Ki(y)) interval parameter to Measuring the first order Taylor series expansion of y midpoint can be expressed as：
<mrow> <msub> <mi>S</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>K</mi> <mi>i</mi> </msub> <mo>(</mo> <mi>y</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>S</mi> <mi>i</mi> <mi>c</mi> </msubsup> <mo>+</mo> <msub> <mi>&amp;Delta;</mi> <mn>1</mn> </msub> <msubsup> <mi>S</mi> <mi>i</mi> <mi>I</mi> </msubsup> </mrow>
Wherein,WithIt is section compound function matrix S respectivelyi(Ki(y) midrange and section radius), are expressed as：
<mrow> <msubsup> <mi>S</mi> <mi>i</mi> <mi>c</mi> </msubsup> <mo>=</mo> <msub> <mi>S</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>K</mi> <mi>i</mi> </msub> <mo>(</mo> <msup> <mi>y</mi> <mi>c</mi> </msup> <mo>)</mo> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>&amp;Delta;</mi> <mn>1</mn> </msub> <msubsup> <mi>S</mi> <mi>i</mi> <mi>I</mi> </msubsup> <mo>=</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>r</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>S</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>K</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msup> <mi>y</mi> <mi>c</mi> </msup> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>K</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msup> <mi>y</mi> <mi>c</mi> </msup> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>K</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msup> <mi>y</mi> <mi>c</mi> </msup> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>y</mi> <mi>r</mi> </msub> </mrow> </mfrac> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>y</mi> <mi>r</mi> <mi>I</mi> </msubsup> <mo>-</mo> <msubsup> <mi>y</mi> <mi>r</mi> <mi>c</mi> </msubsup> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>r</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>S</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>K</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msup> <mi>y</mi> <mi>c</mi> </msup> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>K</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msup> <mi>y</mi> <mi>c</mi> </msup> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>K</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msup> <mi>y</mi> <mi>c</mi> </msup> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>y</mi> <mi>r</mi> </msub> </mrow> </mfrac> <msub> <mi>&amp;Delta;y</mi> <mi>r</mi> </msub> <msub> <mi>&amp;delta;</mi> <mi>r</mi> </msub> </mrow>
Wherein,With Δ yrIt is interval parameter y respectivelyrMidrange and section radius, standard interval variable δr=[- 1 ,+1].
Secondly, based on compound function Differential Properties, higher order term, section compound function vector T are ignoredi(Ki(y)) interval parameter to Measuring the first order Taylor series expansion of y midpoint can be expressed as：
<mrow> <msub> <mi>T</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>K</mi> <mi>i</mi> </msub> <mo>(</mo> <mi>y</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>T</mi> <mi>i</mi> <mi>c</mi> </msubsup> <mo>+</mo> <msub> <mi>&amp;Delta;</mi> <mn>1</mn> </msub> <msubsup> <mi>T</mi> <mi>i</mi> <mi>I</mi> </msubsup> </mrow>
Wherein,WithIt is section compound function vector T respectivelyi(Ki(y) midrange and section radius), are expressed as：
<mrow> <msubsup> <mi>T</mi> <mi>i</mi> <mi>c</mi> </msubsup> <mo>=</mo> <msub> <mi>T</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>K</mi> <mi>i</mi> </msub> <mo>(</mo> <msup> <mi>y</mi> <mi>c</mi> </msup> <mo>)</mo> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>&amp;Delta;</mi> <mn>1</mn> </msub> <msubsup> <mi>T</mi> <mi>i</mi> <mi>I</mi> </msubsup> <mo>=</mo> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>r</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>T</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>K</mi> <mi>i</mi> </msub> <mo>(</mo> <msup> <mi>y</mi> <mi>c</mi> </msup> <mo>)</mo> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>K</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msup> <mi>y</mi> <mi>c</mi> </msup> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>K</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msup> <mi>y</mi> <mi>c</mi> </msup> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>y</mi> <mi>r</mi> </msub> </mrow> </mfrac> <mrow> <mo>(</mo> <msubsup> <mi>y</mi> <mi>r</mi> <mi>I</mi> </msubsup> <mo>-</mo> <msubsup> <mi>y</mi> <mi>r</mi> <mi>c</mi> </msubsup> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>r</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>T</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>K</mi> <mi>i</mi> </msub> <mo>(</mo> <msup> <mi>y</mi> <mi>c</mi> </msup> <mo>)</mo> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>K</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msup> <mi>y</mi> <mi>c</mi> </msup> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>K</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msup> <mi>y</mi> <mi>c</mi> </msup> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>y</mi> <mi>r</mi> </msub> </mrow> </mfrac> <msub> <mi>&amp;Delta;y</mi> <mi>r</mi> </msub> <msub> <mi>&amp;delta;</mi> <mi>r</mi> </msub> <mo>.</mo> </mrow>
9. according to claim 4 be applied to crane system variable phase angle response field acquisition methods under the parameter of minizone, its It is characterised by, in step 6, S that step 5 is obtainedi(Ki) and T (y)i(Ki(y) approximate expansion expression formula) substitutes into step Four luffing angular response section equivalent equation, and midrange and the section of luffing angular response interval vector are obtained according to perturbation theory Radius；Specially：
The S that step 5 is obtainedi(Ki) and T (y)i(Ki(y) approximate expansion expression formula) substitutes into the luffing angular response area of step 4 Between equivalent equation obtain：
<mrow> <msubsup> <mi>&amp;gamma;</mi> <mi>i</mi> <mi>I</mi> </msubsup> <mo>=</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>T</mi> <mi>i</mi> <mi>c</mi> </msubsup> <mo>+</mo> <msub> <mi>&amp;Delta;</mi> <mn>1</mn> </msub> <msubsup> <mi>T</mi> <mi>i</mi> <mi>I</mi> </msubsup> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <msubsup> <mi>S</mi> <mi>i</mi> <mi>c</mi> </msubsup> <mo>+</mo> <msub> <mi>&amp;Delta;</mi> <mn>1</mn> </msub> <msubsup> <mi>S</mi> <mi>i</mi> <mi>I</mi> </msubsup> <mo>)</mo> </mrow> </mrow>
Deployed according to Newman law, retain first three items after expansion,Approximate expression be：
<mrow> <msup> <mrow> <mo>(</mo> <msubsup> <mi>T</mi> <mi>i</mi> <mi>c</mi> </msubsup> <mo>+</mo> <msub> <mi>&amp;Delta;</mi> <mn>1</mn> </msub> <msubsup> <mi>T</mi> <mi>i</mi> <mi>I</mi> </msubsup> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>=</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>T</mi> <mi>i</mi> <mi>c</mi> </msubsup> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>-</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>T</mi> <mi>i</mi> <mi>c</mi> </msubsup> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msub> <mi>&amp;Delta;</mi> <mn>1</mn> </msub> <msubsup> <mi>T</mi> <mi>i</mi> <mi>I</mi> </msubsup> <msup> <mrow> <mo>(</mo> <msubsup> <mi>T</mi> <mi>i</mi> <mi>c</mi> </msubsup> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>T</mi> <mi>i</mi> <mi>c</mi> </msubsup> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msub> <mi>&amp;Delta;</mi> <mn>1</mn> </msub> <msubsup> <mi>T</mi> <mi>i</mi> <mi>I</mi> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msup> <mrow> <mo>(</mo> <msubsup> <mi>T</mi> <mi>i</mi> <mi>c</mi> </msubsup> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mrow>
Will be above-mentionedApproximate expression substitute into luffing angular response section equivalent equation, and retain first order perturbation item, neglect Slightly higher order term obtains：
<mrow> <msubsup> <mi>&amp;gamma;</mi> <mi>i</mi> <mi>I</mi> </msubsup> <mo>&amp;ap;</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>T</mi> <mi>i</mi> <mi>c</mi> </msubsup> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msubsup> <mi>S</mi> <mi>i</mi> <mi>c</mi> </msubsup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>T</mi> <mi>i</mi> <mi>c</mi> </msubsup> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msub> <mi>&amp;Delta;</mi> <mn>1</mn> </msub> <msubsup> <mi>S</mi> <mi>i</mi> <mi>I</mi> </msubsup> <mo>-</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>T</mi> <mi>i</mi> <mi>c</mi> </msubsup> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msub> <mi>&amp;Delta;</mi> <mn>1</mn> </msub> <msubsup> <mi>T</mi> <mi>i</mi> <mi>I</mi> </msubsup> <msup> <mrow> <mo>(</mo> <msubsup> <mi>T</mi> <mi>i</mi> <mi>c</mi> </msubsup> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msubsup> <mi>S</mi> <mi>i</mi> <mi>c</mi> </msubsup> </mrow>
Above formula can equivalence write as：
<mrow> <msubsup> <mi>&amp;gamma;</mi> <mi>i</mi> <mi>I</mi> </msubsup> <mo>=</mo> <msubsup> <mi>&amp;gamma;</mi> <mi>i</mi> <mi>c</mi> </msubsup> <mo>+</mo> <msub> <mi>&amp;Delta;</mi> <mn>1</mn> </msub> <msubsup> <mi>&amp;gamma;</mi> <mi>i</mi> <mi>I</mi> </msubsup> </mrow>
Wherein,WithIt is the midrange and constant interval of luffing angular response interval vector respectively, is expressed as：
<mrow> <msubsup> <mi>&amp;gamma;</mi> <mi>i</mi> <mi>c</mi> </msubsup> <mo>=</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>T</mi> <mi>i</mi> <mi>c</mi> </msubsup> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msubsup> <mi>S</mi> <mi>i</mi> <mi>c</mi> </msubsup> </mrow>
<mrow> <msub> <mi>&amp;Delta;</mi> <mn>1</mn> </msub> <msubsup> <mi>&amp;gamma;</mi> <mi>i</mi> <mi>I</mi> </msubsup> <mo>=</mo> <msub> <mi>&amp;Delta;</mi> <mn>1</mn> </msub> <msub> <mi>&amp;gamma;</mi> <mi>i</mi> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>&amp;delta;</mi> <mi>r</mi> </msub> </mrow>
And then obtain the section radius of luffing angular response interval vector：
<mrow> <msub> <mi>&amp;Delta;</mi> <mn>1</mn> </msub> <msub> <mi>&amp;gamma;</mi> <mi>i</mi> </msub> <mo>=</mo> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>r</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> <mo>|</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>T</mi> <mi>i</mi> <mi>c</mi> </msubsup> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>S</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>K</mi> <mi>i</mi> </msub> <mo>(</mo> <msup> <mi>y</mi> <mi>c</mi> </msup> <mo>)</mo> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>K</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msup> <mi>y</mi> <mi>c</mi> </msup> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>K</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msup> <mi>y</mi> <mi>c</mi> </msup> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>y</mi> <mi>r</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>T</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>K</mi> <mi>i</mi> </msub> <mo>(</mo> <msup> <mi>y</mi> <mi>c</mi> </msup> <mo>)</mo> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>K</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msup> <mi>y</mi> <mi>c</mi> </msup> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>K</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msup> <mi>y</mi> <mi>c</mi> </msup> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>y</mi> <mi>r</mi> </msub> </mrow> </mfrac> <msup> <mrow> <mo>(</mo> <msubsup> <mi>T</mi> <mi>i</mi> <mi>c</mi> </msubsup> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msubsup> <mi>S</mi> <mi>i</mi> <mi>c</mi> </msubsup> <mo>)</mo> </mrow> <msub> <mi>&amp;Delta;y</mi> <mi>r</mi> </msub> <mo>|</mo> <mo>.</mo> </mrow>
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Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109033667A (en) * 2018-08-08 2018-12-18 东南大学 A kind of bounded-but-unknown uncertainty structural energy response predicting method based on affine perturbation
CN109033020A (en) * 2018-09-07 2018-12-18 北谷电子有限公司 A kind of scissor aerial work platform lift height calculation method
CN110032817A (en) * 2019-04-19 2019-07-19 哈尔滨工程大学 A kind of pair is sling heavy work emulation modelling method
CN111460591A (en) * 2020-03-31 2020-07-28 合肥工业大学 Large uncertainty crane system amplitude-variation angle prediction method based on subinterval theory
CN111631914A (en) * 2020-06-10 2020-09-08 合肥工业大学 State interval response domain prediction method for flexible cable driven waist rehabilitation robot
CN112100756A (en) * 2020-08-13 2020-12-18 合肥工业大学 Double-crane system statics uncertainty analysis method based on fuzzy theory

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106709264A (en) * 2017-01-11 2017-05-24 合肥工业大学 Double-crane system variable amplitude angle response modeling algorithm and random response domain prediction method
CN106897520A (en) * 2017-02-27 2017-06-27 北京航空航天大学 A kind of heat transfer system analysis method for reliability containing fuzzy parameter

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106709264A (en) * 2017-01-11 2017-05-24 合肥工业大学 Double-crane system variable amplitude angle response modeling algorithm and random response domain prediction method
CN106897520A (en) * 2017-02-27 2017-06-27 北京航空航天大学 A kind of heat transfer system analysis method for reliability containing fuzzy parameter

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
ZI BIN 等: "A modified hybrid uncertain analysis method for dynamic response field of the LSOAAC with random and interval parameters", 《JOURNAL OF SOUND AND VIBRATION》 *
訾斌 等: "双台汽车起重机柔索并联装备变幅运动下的动力学建模与分析", 《机械工程学报》 *

Cited By (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109033667A (en) * 2018-08-08 2018-12-18 东南大学 A kind of bounded-but-unknown uncertainty structural energy response predicting method based on affine perturbation
CN109033020A (en) * 2018-09-07 2018-12-18 北谷电子有限公司 A kind of scissor aerial work platform lift height calculation method
CN109033020B (en) * 2018-09-07 2022-09-23 北谷电子有限公司 Scissor-fork type aerial work platform lifting height calculation method
CN110032817A (en) * 2019-04-19 2019-07-19 哈尔滨工程大学 A kind of pair is sling heavy work emulation modelling method
CN110032817B (en) * 2019-04-19 2021-04-06 哈尔滨工程大学 Simulation modeling method for double-crane hoisting operation
CN111460591A (en) * 2020-03-31 2020-07-28 合肥工业大学 Large uncertainty crane system amplitude-variation angle prediction method based on subinterval theory
CN111631914A (en) * 2020-06-10 2020-09-08 合肥工业大学 State interval response domain prediction method for flexible cable driven waist rehabilitation robot
CN112100756A (en) * 2020-08-13 2020-12-18 合肥工业大学 Double-crane system statics uncertainty analysis method based on fuzzy theory
CN112100756B (en) * 2020-08-13 2024-04-26 合肥工业大学 Double-crane system statics uncertainty analysis method based on fuzzy theory

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