CN105701286B - A kind of numerical computation method for predicting automotive interior fuzzy uncertain acoustic pressure - Google Patents
A kind of numerical computation method for predicting automotive interior fuzzy uncertain acoustic pressure Download PDFInfo
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Abstract
The invention discloses a kind of numerical computation methods for predicting automotive interior fuzzy uncertain acoustic pressure, and steps are as follows: the finite element modeling of vehicle structure and internal acoustic field；Consider the coupling of structure and sound field, constructs structural acoustical coupling, and then obtain the finite element discretization equation of this system；Using the uncertain input parameter of fuzzy variable characterization structural acoustical coupling, and then obtain the fuzzy finite element equation of this system；It is theoretical using cut set operation and subinterval, the interval variable under each Truncated set level is further decomposed, fuzzy finite element equation is rewritten as one group of subinterval finite element equation；Sub- interval Finite Element Method equation is solved based on first order perturbation method；The acoustic pressure section under all Truncated set levels is recombinated using fuzzy resolution theorem, finally obtains the subordinating degree function of fuzzy uncertain acoustic pressure.The present invention can effectively improve computational efficiency under the premise of guaranteeing that computational accuracy meets engineering demand, this is that general business software institute is irrealizable.
Description
Technical field
The invention belongs to mechanical engineering fields, and in particular to a kind of numerical value meter for predicting automotive interior fuzzy uncertain acoustic pressure
Calculation method.
Background technique
With the improvement of living standards with the progress of science and technology, noise problem is also increasingly valued by people.Nothing
Still consider from the safety of military field and operational performance by the comfort from daily life, noise reduction engineering is all current most heavy
One of project wanted.In auto industry field, noise problem is especially prominent.Wherein, the indoor noise of car hold is except damage passenger
Health outside, the fatigue of driver is also resulted in, to influence traffic safety indirectly；The structure that excessively high noise generates
Vibration can accelerate the aging of automobile component, shorten the service life of automobile.
In recent years, the acoustic analysis method for deterministic system achieves significant progress.But objective world
In, it is potential each in Practical Project problem due to the limitation of the complexity, manufacturing process of system and the deterioration of Service Environment
Kind various kinds, different degrees of uncertain factor is mainly manifested in geometric dimension, material properties, external load, just/boundary values
In the physical models such as condition.For complication system, even if the uncertain factor of very little, pass through the biography between each subsystem
It broadcasts, accumulate and spreads, it is also possible to which apparent disturbance is generated to final system response.There is clear meaning with randomness itself
Difference, the ambiguity of things refer to that its concept itself is difficult to determine, be it is a kind of due to concept extension is fuzzy and bring is uncertain
Property.Such as in practical projects, the probability distribution rule of certain uncertain parameters is difficult to determination, and can only be according to designer
An empirically determined rough range.Fuzzy theory has achieved some achievements in structure static analysis, but in acoustics
Application in field just starts to walk.The fuzzy uncertainty feature for how quick and precisely predicting automotive interior acoustic pressure, is current
One hot spot of sphere of learning has important engineer application for making up the deficiency of existing vehicle structure noise analysis approach
Value.
Summary of the invention
The technical problems to be solved by the invention: overcoming prior art deficiency present in the prediction of automotive interior acoustic pressure,
The influence for fully considering system ambiguous input parameter, decomposes thought and perturbation theory based on subinterval, and proposing one kind quickly has
The numerical computation method of effect prediction acoustic pressure fuzzy uncertain feature.
Technical solution of the present invention: a kind of numerical computation method for predicting automotive interior fuzzy uncertain acoustic pressure, including with
Lower step:
Step 1: it is discrete to the structure of automobile and internal acoustic field progress respectively using structured grid and fluid grid, it obtains
The finite element model of structure and sound field；
Step 2: for the finite element model in step 1, the discrete equation of structure and sound field is established respectively:
Wherein u andFor the motion vector and vector acceleration of structure, MsAnd KsFor architecture quality matrix and stiffness matrix, Fs
And FbFor structural plane load vectors and body load vectors；P andFor acoustic pressure vector and its second dervative, MaAnd KaFor sound field moment of mass
Battle array and stiffness matrix, FaAnd FqFor sound field face load vectors and other load vectors.
Harmonic excitation effect is applied to system, then the second dervative of displacement structure and internal acoustic pressure can be expressed asWithWherein ω indicates frequency.Other than meter and vehicle structure are to the influence of sound field, acoustic pressure is also fully considered
Reaction to part thin-wall construction constructs structural acoustical coupling, and then obtains the finite element discretization equation of this system；
AT=F
WhereinFor equation coefficient matrix, F=(Fb Fq)TFor right-hand-side vector, T=(u
p)TFor system response vector (including acoustic pressure), C is the coupling matrix introduced.
Step 3: all uncertain parameter α=(α in structural acoustical coupling are indicated with fuzzy vectori)n=(α1,
α2,...,αn), wherein n is the number of fuzzy parameter.This structure-sound may further be obtained according to the discrete equation in step 2
The fuzzy finite element equation of coupled system:
A (α) T (α)=F (α)
Step 4: the fuzzy vector in step 3 can be rewritten using cut set theory are as follows:
Wherein λ is selected Truncated set level in 0 to 1 range, indicates interval variable,α i,λWith for its lower bound and
The upper bound, and indicate interval midpoint and radius, it is standard interval variable
Created symbolIndicate interval variableUncertainty.As uncertainty γk,λWhen > 5%, benefit
It is theoretical with subinterval, by interval variableIt is further broken into NkThe identical subinterval of a size, to guarantee each subinterval
Uncertainty is less than 5%:
WhereinIndicate interval variableJ-th of subinterval.Assuming that each uncertain parameter is mutually indepedent, we are just
Available N=N in total1N2…NnA sub- interval combinations.In order to express easily, symbol is usedUnified representation is all
Subinterval vector, in this way, which the fuzzy finite element equation in step 3 is rewritten as one group of subinterval finite element equation:
WhereinFor subinterval variableUnder the influence of system respond section.
Step 5: the subinterval finite element equation in step 4 is solved based on first order perturbation method, obtains automobile
The section variation range of internal acoustic pressure.Formula is opened up first with first order Taylor, it can be by the coefficient matrix of subinterval finite element equationAnd right-hand-side vectorIt indicates are as follows:
Wherein:
Then system subinterval response can indicate are as follows:
WhereinFor subinterval response midpoint,Indicate it in the disturbance of midpoint.
Using single order Newman law, subinterval inverse of a matrix can be with approximate representation are as follows:
In its generation, is returned in subinterval response expression formula, first order perturbation method is based on, can push away:
It utilizesAbout standard interval variableMonotonicity, we can quickly obtain subinterval response radius △
Tλ:
And then the expression formula of available system subinterval response:
N number of system subinterval response under all subinterval combined situations is combined, interval variable is obtainedIt influences
Under system respond section:
WhereinIndicate N number of subinterval combination.
And then according to expression formula T=(u p)TFrom vectorThe middle section variation range for extracting automotive interior acoustic pressure:
Step 6: all acoustic pressures section obtained in step 5 is recombinated using fuzzy resolution theorem, is finally obtained
Uncertain acoustic pressure subordinating degree function p (α) under the influence of fuzzy parameter vector α:
Wherein m is cut set quantity selected in fuzzy cut-set operation.
The selection of step 4 neutron section quantity is not fixed and invariable；Become according to section under different Truncated set levels
The uncertainty size of amount, the quantity for flexibly choosing subinterval decomposes it, to guarantee the uncertainty in each subinterval
Less than 5%；Subinterval divides closeer, and computational accuracy is higher, but a large amount of combinations in subinterval will lead to the decline of computational efficiency.
Therefore, computational accuracy need to be comprehensively considered and calculate to expend and choose suitable subinterval division numbers.
The advantages of the present invention over the prior art are that:
(1) compared with traditional automobile Analysis of The Acoustic Fields method, the computation model established is fully taken into account in Practical Project
The fuzzy uncertainty of material parameter and load, calculated result analyzes automobile noise and structure design has prior guidance
Meaning.
(2) subinterval decomposition technique is used, the biggish interval variable of uncertainty under certain Truncated set levels is decomposed into more
A sub- interval variable controls the uncertainty in each subinterval within 5%, to ensure that first order Taylor series to subinterval
The approximation accuracy of coefficient matrix and right-hand-side vector in finite element equation.
(3) during the matrix inversion of subinterval, only retain the linear term in Newman law, according to first order perturbation theory
Quickly obtain the expression formula at system response midpoint and radius.
(4) operation of the present invention is simple, easy to implement, effectively increases computational efficiency.
Detailed description of the invention
Fig. 1 is the calculation process of automotive interior fuzzy uncertain acoustic pressure of the invention；
Fig. 2 is vehicle structure of the invention-sound field coupled system FEM model schematic diagram；
Fig. 3 is the subordinating degree function schematic diagram of fuzzy uncertain acoustic pressure at observation point under 300Hz frequency；
Fig. 4 is the subordinating degree function schematic diagram of fuzzy uncertain acoustic pressure at observation point under 700Hz frequency.
Specific embodiment
The present invention will be further described with reference to the accompanying drawings and examples.
The present invention is suitable for the automotive interior acoustic pressure forecasting problem containing fuzzy uncertain parameter.Embodiment of the present invention with
For the noise prediction of certain car model interior compartment, the fuzzy uncertain acoustic pressure numerical computation method is illustrated.Separately
Outside, this automotive interior fuzzy uncertain acoustic pressure numerical computation method can be generalized to other structure-sound couplings for containing fuzzy parameter
In the response computation of collaboration system.
The calculating process of this automotive interior acoustic pressure establishes coupling as shown in Figure 1, fully consider the coupling of structure and sound field
The finite element equation of collaboration system carries out quantitative description to uncertain parameter using fuzzy variable, and is based on cut set operation and son
Interval decomposed method is further processed uncertain parameter, according to first order perturbation method to automotive interior under all Truncated set levels
The section variation range of acoustic pressure carries out rapid solving, is recombinated using fuzzy resolution theorem to it, finally obtains fuzzy not true
Determine the subordinating degree function of acoustic pressure.The following steps progress can be divided into:
Step 1: establishing the finite element model of vehicle structure and sound field, as shown in Figure 2: vehicle structure such as front screen 1,
Rear window 2, roof 3, vehicle body 4, dashboard 5 are simulated with two-dimentional quadrangle shell unit, the three-dimensional hexahedron solid list of seat 6
Member is next discrete, and internal acoustic field 7 is with three-dimensional hexahedron element of fluid come discrete.8 are applied with amplitude as F at roof center0Simple harmonic quantity
Excitation.A node 9 is extracted in driver position, the observation point as internal acoustic pressure.
Step 2: for the finite element model in step 1, the discrete equation of structure and sound field is established respectively:
Wherein u andFor the motion vector and vector acceleration of structure, MsAnd KsFor architecture quality matrix and stiffness matrix, Fs
And FbFor structural plane load vectors and body load vectors；P andFor acoustic pressure vector and its second dervative, MaAnd KaFor sound field moment of mass
Battle array and stiffness matrix, FaAnd FqFor sound field face load vectors and other load vectors.
Other than meter and vehicle structure are to the influence of sound field, reaction of the acoustic pressure to part thin-wall construction is also fully considered,
Structural acoustical coupling is constructed, and then obtains the finite element discretization equation of this system；
AT=F
WhereinFor equation coefficient matrix, F=(Fb Fq)TFor right-hand-side vector, T=(u
p)TFor system response vector (including acoustic pressure), C is the coupling matrix introduced.
Step 3: in this vehicle structure-acoustical coupling system, front and back window uses density for ρ1, elasticity modulus E1Glass material
Material；Roof and body structure use density for ρ2, elasticity modulus E2Metal material；Dashboard and seat use density for ρ3,
Elasticity modulus is E3Foamed material；Atmospheric density is denoted as ρ in cabina, the aerial spread speed of sound is denoted as c；Automobile
Bearing responsibility by amplitude is F0Harmonic excitation.Limitation and measurement error by material processing technique are influenced, and all system parameters are equal
For fuzzy number, and subordinating degree function meets angular distribution rule, i.e. ρ1=(2500,3000,3500) kg/m3, E1=(55,70,
85) GPa, ρ2=(7000,8500,10000) kg/m3, E2=(160,200,240) GPa, ρ3=(0.9,1.1,1.3) kg/m3,
E3=(0.0024,0.003,0.0036) GPa, ρa=(1.00,1.225,1.45) kg/m3, c=(270,340,410) m/s, F0
=(0.8,1.0,1.2) N.For convenience, all fuzzy parameters involved in this computation model are expressed as vector α's
Form α=(ρ1,ρ2,ρ3,E1,E2,E3,ρa,c,F0), this structure-sound may further be obtained according to the discrete equation in step 2
The fuzzy finite element equation of coupled system:
A (α) T (α)=F (α)
Step 4: 11 Truncated set level λ are definedm=(m-1) × 0.1m=1 ..., 11, can be by step using cut set theory
Fuzzy vector α in rapid three rewrites are as follows:
WhereinIndicate interval variable,α i,λWithFor its lower bound and the upper bound,WithIndicate interval midpoint and radius,For standard interval variable
Created symbolIndicate interval variableUncertainty.As uncertainty γk,λWhen > 5%, benefit
It is theoretical with subinterval, by interval variableIt is further broken into NkThe identical subinterval of a size, to guarantee each subinterval
Uncertainty is less than 5%.Here with Truncated set level λ8=0.7 and λ6For=0.5, respectively with two subintervals and four sub-districts
Between all fuzzy uncertain parameters are divided, as shown in table 1.
The subinterval of parameter divides under the different Truncated set levels of table 1
In order to express easily, symbol is usedAll subinterval vectors of unified representation, in this way, by step 3
In fuzzy finite element equation be rewritten as one group of subinterval finite element equation:
WhereinFor subinterval variableUnder the influence of system respond section.
Step 5: the subinterval finite element equation in step 4 is solved based on first order perturbation method, obtains automobile
The section variation range of internal acoustic pressure.Formula is opened up first with first order Taylor, it can be by the coefficient matrix of subinterval finite element equationAnd right-hand-side vectorIt indicates are as follows:
Wherein:
Then system subinterval response can indicate are as follows:
WhereinFor subinterval response midpoint,Indicate it in the disturbance of midpoint.
Using single order Newman law, subinterval inverse of a matrix can be with approximate representation are as follows:
In its generation, is returned in subinterval response expression formula, first order perturbation method is based on, can push away:
It utilizesAbout standard interval variableMonotonicity, we can quickly obtain subinterval response radius △
Tλ:
And then the expression formula of available system subinterval response:
N number of system subinterval response under all subinterval combined situations is combined, interval variable is obtainedIt influences
Under system respond section:
WhereinIndicate N number of subinterval combination.
And then according to expression formula T=(u p)TFrom vectorThe middle section variation range for extracting automotive interior acoustic pressure:
Selected 300Hz, 400Hz, 500Hz, five frequencies of 600Hz, 700Hz, above-mentioned λ8=0.7 and λ6=0.5 two cut set
The calculated result of the lower automotive interior acoustic pressure of level is as shown in table 2 and table 3.It is 10 with sample number7Monte-carlo Simulation Method meter
It calculates result to compare, the relative error that the present invention predicts acoustic pressure section bound maintains a reduced levels, can expire completely
The required precision of sufficient Practical Project.In addition, computational efficiency of the invention is significantly larger than Monte Carlo side from calculating from the time
Method.
2 Truncated set level λ of table8=0.7 lower automotive interior acoustic pressure bound
3 Truncated set level λ of table6=0.5 lower automotive interior acoustic pressure bound
Step 6: all acoustic pressures section obtained in step 5 is recombinated using fuzzy resolution theorem, is finally obtained
Uncertain acoustic pressure subordinating degree function p (α) under the influence of fuzzy parameter vector α:
By taking two frequencies of 300Hz and 700Hz as an example, at observation point the subordinating degree function of fuzzy uncertain acoustic pressure such as Fig. 3 and
Shown in Fig. 4.As can be seen that the result that is calculated of the present invention and the reference value degree of agreement that Monte Carlo is sampled are fine,
Computational accuracy fully meets engine request.It can solve the prediction of the automobile noise containing fuzzy uncertain parameter with the present invention to ask
Topic, computational accuracy is high, and the calculating time is short, this function is that general business software institute is irrealizable.
Above-described is only presently preferred embodiments of the present invention, and the present invention is not limited solely to above-described embodiment, all
Part change, equivalent replacement, improvement etc. made by within the spirit and principles in the present invention should be included in protection of the invention
Within the scope of.
Claims (2)
1. a kind of numerical computation method for predicting automotive interior fuzzy uncertain acoustic pressure, it is characterised in that the following steps are included:
Step 1: it is discrete to the structure of automobile and internal acoustic field progress respectively using structured grid and fluid grid, obtain structure
With the finite element model of sound field；
Step 2: for the finite element model in step 1, the discrete equation of structure and sound field is established respectively:
Wherein u andFor the motion vector and vector acceleration of structure, MsAnd KsFor architecture quality matrix and stiffness matrix, FsAnd Fb
For structural plane load vectors and body load vectors；P andFor acoustic pressure vector and its second dervative, MaAnd KaFor sound field mass matrix
And stiffness matrix, FaAnd FqFor sound field face load vectors and other load vectors；
Consider reaction of the acoustic pressure to part thin-wall construction, constructs structural acoustical coupling, obtain the finite element discretization of this system
Equation；
AT=F
WhereinFor equation coefficient matrix, F=(Fb Fq)TFor right-hand-side vector, T=(u p)TFor
System response vector, C are the coupling matrix introduced, and ω indicates the frequency of harmonic excitation, ρaIndicate the atmospheric density in sound field；
Step 3: all uncertain parameter α=(α in structural acoustical coupling are indicated with fuzzy vectori)n=(α1,α2,...,
αn), wherein n is the number of fuzzy parameter, further obtains this structural acoustical coupling according to the discrete equation in step 2
Fuzzy finite element equation:
A (α) T (α)=F (α)；
Step 4: the fuzzy vector in step 3 can be rewritten using cut set theory are as follows:
Wherein λ is selected Truncated set level in 0 to 1 range,Indicate interval variable,α i,λWithFor its lower bound and upper
Boundary,WithIndicate interval midpoint and radius,For standard interval variable
Created symbolIndicate interval variableUncertainty, as uncertainty γk,λWhen > 5%, son is utilized
Interval theory, by interval variableIt is further broken into NkA subinterval, to guarantee that the uncertainty in each subinterval is less than
5%, whereinIndicate interval variableJ-th of subinterval；Each uncertain parameter is mutually indepedent, obtains N=in total
N1N2…NnA sub- interval combinations, symbolizationAll subinterval vectors of unified representation, fuzzy in step 3 have
It limits first equation and is rewritten as one group of subinterval finite element equation:
WhereinFor subinterval variableUnder the influence of system respond section；
Step 5: the subinterval finite element equation in step 4 is solved based on first order perturbation method, obtains automotive interior
The section variation range of acoustic pressure opens up formula first with first order Taylor, by the coefficient matrix of subinterval finite element equationThe right side and
Hold vectorIt indicates are as follows:
Wherein:
The response of system subinterval indicates are as follows:
WhereinFor subinterval response midpoint,Indicate it in the disturbance of midpoint；
Utilize single order Newman law, subinterval inverse of a matrix approximate representation are as follows:
In its generation, is returned in subinterval response expression formula, first order perturbation method is based on, obtains:
It utilizesAbout standard interval variableMonotonicity, obtain subinterval response radius Δ Tλ:
And then obtain the expression formula of system subinterval response:
N number of system subinterval response under all subinterval combined situations is combined, interval variable is obtainedUnder the influence of be
System response section:
WhereinIndicate N number of subinterval combination；
Step 6: all acoustic pressures section obtained in step 5 is recombinated using fuzzy resolution theorem, is finally obtained fuzzy
Uncertain acoustic pressure subordinating degree function p (α) under the influence of parameter vector α:
Wherein m is cut set quantity selected in fuzzy cut-set operation.
2. a kind of numerical computation method for predicting automotive interior fuzzy uncertain acoustic pressure according to claim 1, feature
Be: the decomposition of interval variable is that the principle based on subinterval uncertainty less than 5% carries out in the step 4.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104504215A (en) * | 2015-01-07 | 2015-04-08 | 西南大学 | Automobile interior acoustic field prediction method based on partition-of-unity finite element-meshless cell |
| CN104850721A (en) * | 2015-06-03 | 2015-08-19 | 湖南大学 | External sound field prediction method and device based on mixing probability and interval |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN104504215A (en) * | 2015-01-07 | 2015-04-08 | 西南大学 | Automobile interior acoustic field prediction method based on partition-of-unity finite element-meshless cell |
| CN104850721A (en) * | 2015-06-03 | 2015-08-19 | 湖南大学 | External sound field prediction method and device based on mixing probability and interval |
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| Title |
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| 《An interval perturbation method for exterior acoustic field prediction with uncertain-but-bounded parameters》;Chong Wang等;《Journal of Fluids and Structures》;20140612;第49卷;第441-449页 |
| 《Hybrid uncertainty propagation of coupled structural-acoustic system with large fuzzy and interval parameters》;Chong Wang等;《Applied Acoustics》;20150927;第102卷;第62-70页 |
| 《Interval finite element analysis and reliability-based optimization of coupled structural-acoustic system with uncertain parameters》;Chong Wang等;《Finite Elements in Analysis and Design》;20140814;第91卷;第108-114页 |
| 《含区间参数的结构-声耦合系统摄动分析方法》;牛明涛等;《振动与冲击》;20150531;第34卷(第10期);第194-198页 |
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