CN107871036A - Sensitivity analysis method and system for suspension hard point - Google Patents
Sensitivity analysis method and system for suspension hard point Download PDFInfo
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Abstract
The invention provides a sensitivity analysis method and system for a suspension hard point. The method comprises the following steps: establishing a response surface model between a suspension hard point and a response quantity, and determining a design variable according to the suspension hard point; establishing a response surface model between the response quantity and the design variable according to the design variable space and the corresponding response value; sampling the design variables to obtain a first parameter matrix and a second parameter matrix; performing column transformation on the second parameter matrix according to the column of the first parameter matrix to obtain a third parameter matrix, and performing column transformation on the first parameter matrix according to the column of the second parameter matrix to obtain a fourth parameter matrix; and solving the response surface model between the response quantity and the design variable according to the first to fourth parameter matrixes to obtain the sensitivity of the design variable. The method can accurately analyze the sensitivity of the suspension hard point, thereby greatly shortening the research and development period and reducing the research and development cost.
Description
Technical field
The present invention relates to automobile technical field, the more particularly to a kind of Sensitivity Analysis Method and system of suspension hard spot.
Background technology
In correlation technique, the Sensitivity Analysis Method of hard spot generally establishes the fortune of suspension based on many-body dynamics
It is dynamic to learn model, but in actual suspension, the connection generally use bushing connection of suspension and subframe, as shown in Fig. 2 and bushing is
Flexible body, therefore rigid body kinematics has certain error in actual Suspension Model, causes the sensitivity analysis of hard spot to be forbidden
Really.
The content of the invention
It is contemplated that at least solves one of technical problem in correlation technique to a certain extent.
Therefore, first purpose of the present invention is to propose a kind of Sensitivity Analysis Method of suspension hard spot.This method can
To analyze the sensitivity of suspension hard spot exactly, so as to be substantially reduced the R＆D cycle, development costs are reduced.
Second object of the present invention is to propose a kind of Sensitivity Analysis Method of suspension hard spot.
To achieve these goals, the first aspect of the present invention embodiment discloses a kind of sensitivity of suspension hard spot point
Analysis method, comprises the following steps：The response surface model established between suspension hard spot and response quautity, and according to the suspension hard spot
Determine design variable；Established according to design variable space and corresponding response between the response quautity and the design variable
Response surface model；The design variable is sampled, to obtain the first parameter matrix and the second parameter matrix；According to institute
The row for stating the first parameter matrix enter row-column transform to obtain the 3rd parameter matrix, and according to described to second parameter matrix
The row of second parameter matrix enter row-column transform to obtain the 4th parameter matrix to first parameter matrix；According to described first
The response surface model between the response quautity and the design variable is solved to the 4th parameter matrix, it is described to obtain
The sensitivity of design variable.
The Sensitivity Analysis Method of suspension hard spot according to embodiments of the present invention, suspension hard spot can be analyzed exactly
Sensitivity, so as to be substantially reduced the R＆D cycle, reduce development costs.
In some instances, the response quautity includes castor θ, Kingpin inclination angle beta, toeing-in angle τ, wheel
Camber angle γ.
In some instances, the row according to first parameter matrix enter ranks change to second parameter matrix
Change to obtain the 3rd parameter matrix, and row-column transform is entered to first parameter matrix according to the row of second parameter matrix
To obtain the 4th parameter matrix, including：The i-th row of the first parameter matrix are chosen, and i-th value arranged are assigned to described
I-th row of the second parameter matrix, to obtain the 3rd parameter matrix；The i-th row of the second parameter matrix are chosen, and by described in
The value of i-th row is assigned to the i-th row of first parameter matrix, to obtain the 4th parameter matrix.
In some instances, the sensitivity of the design variable includes one order and global sensitivity.
In some instances, the one order is expressed as：
The global sensitivity is expressed as：
The embodiment of the second aspect of the present invention discloses a kind of sensitivity analysis system of suspension hard spot, including：Establish
Module, determine that design becomes for establishing the response surface model between suspension hard spot and response quautity, and according to the suspension hard spot
Amount, and the response surface established according to design variable space and corresponding response between the response quautity and the design variable
Model；Computing module, for being sampled to the design variable, to obtain the first parameter matrix and the second parameter matrix, and
Row-column transform is entered to second parameter matrix according to the row of first parameter matrix to obtain the 3rd parameter matrix, and root
Row-column transform is entered to first parameter matrix to obtain the 4th parameter matrix, Yi Jigen according to the row of second parameter matrix
The response surface model between the response quautity and the design variable is solved according to first to fourth parameter matrix,
To obtain the sensitivity of the design variable.
The sensitivity analysis system of suspension hard spot according to embodiments of the present invention, suspension hard spot can be analyzed exactly
Sensitivity, so as to be substantially reduced the R＆D cycle, reduce development costs.
In some instances, the response quautity includes castor θ, Kingpin inclination angle beta, toeing-in angle τ, wheel
Camber angle γ.
In some instances, the computing module is used for：The i-th row of the first parameter matrix are chosen, and described i-th is arranged
Value be assigned to second parameter matrix i-th row, to obtain the 3rd parameter matrix；Choose the second parameter matrix
I-th row, and i-th value arranged is assigned to the i-th of first parameter matrix and arranged, to obtain the 4th parameter matrix.
In some instances, the sensitivity of the design variable includes one order and global sensitivity.
In some instances, the one order is expressed as：
The global sensitivity is expressed as：
The advantages of aspect that the present invention adds, will be set forth in part in the description, partly will from the following description
Become obvious, or recognized by the practice of the present invention.
Brief description of the drawings
Of the invention above-mentioned and/or additional aspect and advantage will become from the following description of the accompanying drawings of embodiments
Obtain substantially and be readily appreciated that, wherein,
Fig. 1 is the flow chart of the Sensitivity Analysis Method of suspension hard spot according to an embodiment of the invention；
Fig. 2 be suspension hard spot according to an embodiment of the invention Sensitivity Analysis Method in suspension many-body dynamics
Model schematic；
Fig. 3 be suspension hard spot according to an embodiment of the invention Sensitivity Analysis Method in suspension geometry model show
It is intended to；
Fig. 4 is the detail flowchart of the Sensitivity Analysis Method of suspension hard spot according to an embodiment of the invention；
Fig. 5 is the structured flowchart of the sensitivity analysis system of suspension hard spot according to an embodiment of the invention.
Embodiment
Embodiments of the invention are described below in detail, the example of the embodiment is shown in the drawings, wherein from beginning to end
Same or similar label represents same or similar element or the element with same or like function.Below with reference to
The embodiment of accompanying drawing description is exemplary, is only used for explaining the present invention, and is not considered as limiting the invention.On the contrary,
All changes that embodiments of the invention include falling into the range of the spirit and intension of attached claims, change and wait
Jljl.
In the description of the invention, it is to be understood that term " first ", " second " etc. are only used for describing purpose, without
It is understood that to indicate or implying relative importance.In the description of the invention, it is necessary to which explanation, is advised unless otherwise clear and definite
Fixed and restriction, term " connected ", " connection " should be interpreted broadly, for example, it may be being fixedly connected or detachably connecting
Connect, or be integrally connected；Can be mechanical connection or electrical connection；Can be joined directly together, centre can also be passed through
Medium is indirectly connected.For the ordinary skill in the art, above-mentioned term can be understood in the present invention with concrete condition
Concrete meaning.In addition, in the description of the invention, unless otherwise indicated, " multiple " are meant that two or more.
Sensitivity Analysis Method and system below in conjunction with accompanying drawing description according to the suspension hard spot of embodiment of the present invention.
Fig. 1 is the flow chart of the Sensitivity Analysis Method of suspension hard spot according to an embodiment of the invention.
As shown in figure 1, and combine Fig. 4 suspension hard spots according to an embodiment of the invention Sensitivity Analysis Method,
Comprise the following steps：
S101：The response surface model established between suspension hard spot and response quautity, and determine that design becomes according to suspension hard spot
Amount.
By taking McPherson arm sling frame as an example, as shown in Fig. 2 the kinetic model for McPherson arm sling frame.Not inferior arm sling frame
Geometrical model is as shown in Figure 3.
Response quautity includes but is not limited to castor θ, Kingpin inclination angle beta, toeing-in angle τ, camber angle γ.
Specifically, the response surface model established between suspension hard spot and response quautity.Because suspension is symmetrical structure, therefore
Unilateral hard spot only need to be considered.Each hard spot includes the coordinate in 3 directions, then design variable number altogether is
Three times of hard spot number.X=(x1,x2,…,xk) it is design vector, the selection of design variable tries for example with Latin hypercube
Test design method.
S102：The response surface established according to design variable space and corresponding response between response quautity and design variable
Model.
Using the response that castor θ, Kingpin inclination angle beta, toeing-in angle τ, camber angle γ are independent as four
Amount.The response surface model established according to design variable space and corresponding response between response quautity and design variable.Wherein, y
=f (x1,x2,…,xk) the response surface relation for corresponding to.
S103：Design variable is sampled, to obtain the first parameter matrix and the second parameter matrix.
Assuming that design variable number is n, by carrying out l Latin Hypercube Sampling to design variable, two parameters are obtained
Matrix P (the first parameter matrix) and Q (the second parameter matrix), every a line of matrix is all one group of input parameter.Wherein：
S104：Row-column transform is entered to the second parameter matrix to obtain the 3rd parameter matrix according to the row of the first parameter matrix,
And row-column transform is entered to first parameter matrix to obtain the 4th parameter matrix according to the row of the second parameter matrix.
Specifically, including：The i-th row of the first parameter matrix are chosen, and i-th value arranged is assigned to described the
I-th row of two parameter matrixs, to obtain the 3rd parameter matrix；The i-th row of the second parameter matrix are chosen, and by described i-th
The value of row is assigned to the i-th row of first parameter matrix, to obtain the 4th parameter matrix.
Such as：Matrix P the i-th row are chosen, and this columns value is assigned to matrix Q the i-th row, the matrix of gained is denoted as
Matrix Hi(the 3rd parameter matrix)；Matrix Q the i-th row are chosen, and this columns value is assigned to matrix P the i-th row, gained
Matrix is denoted as matrix H-i(the 4th parameter matrix).Wherein：
S105：The response surface model between response quautity and design variable is asked according to first to fourth parameter matrix
Solution, to obtain the sensitivity of design variable.I.e.：Data above is updated in object function in the form of organizing and calculated, can
Obtain the output response of corresponding every group of design parameter, by Monte carlo algorithm can obtain system response one order,
Global sensitivity.
Wherein, on xiOne orderFor：
On xiGlobal sensitivityFor：
Wherein：
Function f be Response Face Function (such as：Castor θ, Kingpin inclination angle beta, toeing-in angle τ, camber angle
γ)。
As a specific example, because the basic function number of response surface model isIt is individual, Fig. 2
Middle McPherson suspension (because suspension is symmetrical structure, thus only need to consider the hard spot of side with) hard spot is a lot of and each
Individual hard spot correspond to the coordinate value in 3 directions, and the McPherson suspension has 7 crucial hard spots, then corresponds to 21 design variables, base
Function number is 253, and due to length problem, 5 parameters that only have chosen herein in 2 hard spots establish response surface model.It is right
In general suspension, it should choose all hard spots and establish corresponding response surface model.
With B in Fig. 33Hard spot x, y are to coordinate and A3Point is institute's example, and this 2 hard spots optimize ginseng comprising 5 design variables altogether
Number (B3Point x, y are to A3Point x, y, z directions).It is designated as X=(x1,x2,x3,x4,x5),
In this example, using Latin hypercube experimental design method, two are built in the space of standardized variable composition
Rank response surface model.
These sample points are brought into model, and carries out the parallel wheel of suspension and jumps emulation, wheel jumps scope and is：- 80mm~
80mm, with castor θ, Kingpin inclination angle beta, toeing-in angle τ, this four parameters of camber angle γ in wheel jump process
In maximum for response output quantity.The response surface model established between response quautity and design variable.What is used in this example is secondary
The citation form of polynomial response surface approximate model is：
Wherein a is response surface coefficient matrix, and i is abscissa, and j is ordinate label.
Here, the response surface approximate function of structure is：
After the foundation for completing response surface model, any one group of suspension hard spot (design parameter) all can directly pass through response surface
Expression formula calculates corresponding response.
It should be noted that because the basic function number of response surface model isIndividual, McPherson is hanged
Frame (because suspension be symmetrical structure, thus only need to consider the hard spot of side with) hard spot is a lot of, and each hard spot correspondence
The coordinate value in 3 directions, the McPherson suspension there are 7 crucial hard spots, then corresponds to 21 design variables, and basic function number is
253, due to length problem, 5 parameters that only have chosen herein in 2 hard spots establish response surface model.For general outstanding
Frame, it should choose all hard spots and establish corresponding response surface model.
Using McPherson suspension shown in Fig. 2 as Sensitivity Analysis, B in figure is chosen1、B2、B3、A2And A3Become as design
Amount.Table 1 is suspension hard spot design parameter, and sets the range of disturbance of each suspension hard spot as -10~10mm.
The initial hard spot coordinate of the suspension of table 1
Latin hypercube sampling is carried out to above-mentioned 15 parameters in design space, extracts the sample that 2 capacity are 3000
This, respectively with matrix Pl×n、Ql×nRepresent, wherein l=3000, n=15.
The Latin hypercube sampling (P/Q) of the suspension hard spot of table 2
3000 Latin hypercubes samplings are carried out in design space to suspension hard spot can obtain sampling matrix P, Q, right
Matrix P, Q carry out matrixing and can obtain corresponding matrix Hi、H-i, every group of sampled point can be calculated according to suspension Response Face Function
Response, the sensitivity of 15 parameters of suspension hard spot can be obtained further according to sensitivity computing method, is shown in Table 3 to the institute of table 6
Show：
The kingpin inclination Sensitirity va1ue of table 3
The castor Sensitirity va1ue of table 4
The camber angle Sensitirity va1ue of table 5
The toeing-in angular sensitivity value of table 6
As shown in Table 3, suspension hard spot parameter B in jump process is taken turns3yKingpin inclination global sensitivity value it is maximum, remaining
The Sensitirity va1ue of hard spot parameter can be neglected.Knowable to table 4, hard spot parameter B3xSensitirity va1ue it is maximum, be secondly B3z, remaining
It is negligible.Table 5 is understood, the global sensitivity value size of camber angle is ordered as：B3z>A2z>B2z>B3y>A2y>B3x>
B2y；Table 6 is understood, the global sensitivity value size at toeing-in angle is ordered as：A2z>B2z>B3z>A2y>B3y>A2x>B3x.According to
Sensitivity analysis is drawn：Hard spot B on the outside of lower cross arm3, steering linkage medial and lateral hard spot A2、B2Coordinate：B3x,B3y,B3z,A2y,
A2z, B2x,B2zIt is larger to the influence degree of aim parameter.
Wherein, one order illustrates single input parameter XiTo the percentage contribution of Y variance.
Global sensitivity is contained on XiMain effect value, while contain XiEffect is interacted between its dependent variable
Should.
The Sensitivity Analysis Method of suspension hard spot according to embodiments of the present invention, suspension hard spot can be analyzed exactly
Sensitivity, so as to be substantially reduced the R＆D cycle, reduce development costs.
As shown in figure 5, embodiment of the invention discloses that a kind of sensitivity analysis system 500 of suspension hard spot, including：
Establish module 510 and computing module 520.
Wherein, the response surface model that module 510 is used to establish between suspension hard spot and response quautity is established, and according to described
Suspension hard spot determines design variable, and establishes the response quautity according to design variable space and corresponding response and set with described
Count the response surface model between variable.Computing module 520 is used to be sampled the design variable, to obtain the first parameter
Matrix and the second parameter matrix, and according to the row of first parameter matrix second parameter matrix is entered row-column transform with
The 3rd parameter matrix is obtained, and enters row-column transform to first parameter matrix according to the row of second parameter matrix to obtain
To the 4th parameter matrix, and according to first to fourth parameter matrix between the response quautity and the design variable
Response surface model solved, to obtain the sensitivity of the design variable.
In one embodiment of the invention, before the response quautity includes castor θ, Kingpin inclination angle beta, wheel
Beam angle τ, camber angle γ.
In one embodiment of the invention, the computing module 520 is used for：The i-th row of the first parameter matrix are chosen,
And i-th value arranged is assigned to the i-th row of second parameter matrix, to obtain the 3rd parameter matrix；Choose the
I-th row of two parameter matrixs, and i-th value arranged is assigned to the i-th of first parameter matrix and arranged, it is described to obtain
4th parameter matrix.
In one embodiment of the invention, the sensitivity of the design variable includes one order and the overall situation is sensitive
Degree.
Further, the one order is expressed as：
The global sensitivity is expressed as：
The sensitivity analysis system of suspension hard spot according to embodiments of the present invention, suspension hard spot can be analyzed exactly
Sensitivity, so as to be substantially reduced the R＆D cycle, reduce development costs.
It should be noted that the specific implementation of the sensitivity analysis system of the suspension hard spot of the embodiment of the present invention with
The specific implementation of the Sensitivity Analysis Method of the suspension hard spot of the embodiment of the present invention is similar, specifically refers to method part
Description, in order to reduce redundancy, do not repeat herein.
It should be appreciated that each several part of the present invention can be realized with hardware, software, firmware or combinations thereof.Above-mentioned
In embodiment, multiple steps or method can be performed soft in memory and by suitable instruction execution system with storage
Part or firmware are realized.If, and in another embodiment, can be with well known in the art for example, realized with hardware
Any one of following technology or their combination are realized：With the gate for realizing logic function to data-signal
The discrete logic of circuit, the application specific integrated circuit with suitable combinational logic gate circuit, programmable gate array (PGA),
Field programmable gate array (FPGA) etc..
In the description of this specification, reference term " one embodiment ", " some embodiments ", " example ", " specifically show
The description of example " or " some examples " etc. means specific features, structure, material or the spy for combining the embodiment or example description
Point is contained at least one embodiment or example of the present invention.In this manual, to the schematic representation of above-mentioned term not
Necessarily refer to identical embodiment or example.Moreover, specific features, structure, material or the feature of description can be any
One or more embodiments or example in combine in an appropriate manner.
Although an embodiment of the present invention has been shown and described, it will be understood by those skilled in the art that：Not
In the case of departing from the principle and objective of the present invention a variety of change, modification, replacement and modification can be carried out to these embodiments,
The scope of the present invention is limited by claim and its equivalent.
Claims (10)
1. a kind of Sensitivity Analysis Method of suspension hard spot, it is characterised in that comprise the following steps：
The response surface model established between suspension hard spot and response quautity, and design variable is determined according to the suspension hard spot；
The response face mould established according to design variable space and corresponding response between the response quautity and the design variable
Type；
The design variable is sampled, to obtain the first parameter matrix and the second parameter matrix；
Row-column transform is entered to obtain the 3rd parameter matrix to second parameter matrix according to the row of first parameter matrix, and
Row-column transform is entered to first parameter matrix to obtain the 4th parameter matrix according to the row of second parameter matrix；
The response surface model between the response quautity and the design variable is carried out according to first to fourth parameter matrix
Solve, to obtain the sensitivity of the design variable.
2. the Sensitivity Analysis Method of suspension hard spot according to claim 1, it is characterised in that the response quautity includes master
Sell back rake angle θ, Kingpin inclination angle beta, toeing-in angle τ, camber angle γ.
3. the Sensitivity Analysis Method of suspension hard spot according to claim 1, it is characterised in that described according to described first
The row of parameter matrix enter row-column transform to obtain the 3rd parameter matrix, and according to second parameter to second parameter matrix
Matrix column enters row-column transform to obtain the 4th parameter matrix to first parameter matrix, including：
The i-th row of the first parameter matrix are chosen, and i-th value arranged is assigned to the i-th row of second parameter matrix, with
Obtain the 3rd parameter matrix；
The i-th row of the second parameter matrix are chosen, and i-th value arranged is assigned to the i-th row of first parameter matrix, with
Obtain the 4th parameter matrix.
4. the Sensitivity Analysis Method of the suspension hard spot according to claim any one of 1-3, it is characterised in that the design
The sensitivity of variable includes one order and global sensitivity.
5. the Sensitivity Analysis Method of suspension hard spot according to claim 4, it is characterised in that the one order table
It is shown as：
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A kind of 6. sensitivity analysis system of suspension hard spot, it is characterised in that including：
Module is established, is determined for establishing the response surface model between suspension hard spot and response quautity, and according to the suspension hard spot
Design variable, and the sound established according to design variable space and corresponding response between the response quautity and the design variable
Answer surface model；
Computing module, for being sampled to the design variable, to obtain the first parameter matrix and the second parameter matrix, and root
Row-column transform is entered to second parameter matrix to obtain the 3rd parameter matrix, and according to institute according to the row of first parameter matrix
The row for stating the second parameter matrix enter row-column transform to obtain the 4th parameter matrix, and according to described to first parameter matrix
First to fourth parameter matrix solves to the response surface model between the response quautity and the design variable, to obtain
State the sensitivity of design variable.
7. the sensitivity analysis system of suspension hard spot according to claim 6, it is characterised in that the response quautity includes master
Sell back rake angle θ, Kingpin inclination angle beta, toeing-in angle τ, camber angle γ.
8. the sensitivity analysis system of suspension hard spot according to claim 6, it is characterised in that the computing module is used
In：
The i-th row of the first parameter matrix are chosen, and i-th value arranged is assigned to the i-th row of second parameter matrix, with
Obtain the 3rd parameter matrix；
The i-th row of the second parameter matrix are chosen, and i-th value arranged is assigned to the i-th row of first parameter matrix, with
Obtain the 4th parameter matrix.
9. the sensitivity analysis system of the suspension hard spot according to claim any one of 6-8, it is characterised in that the design
The sensitivity of variable includes one order and global sensitivity.
10. the sensitivity analysis system of suspension hard spot according to claim 9, it is characterised in that the one order
It is expressed as：
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<mn>0</mn>
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<mo>(</mo>
<mi>y</mi>
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</mrow>
</mrow>
</mfrac>
<mo>,</mo>
</mrow>
The global sensitivity is expressed as：
<mrow>
<msubsup>
<mover>
<mi>S</mi>
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<mi>i</mi>
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<mfrac>
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<mn>2</mn>
</msubsup>
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</mrow>
</mrow>
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</mrow>
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<mo>.</mo>
</mrow>
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