Multi-objective Optimization in Vehicle Concept Modeling Marco Danti, Maurizio Meneguzzo, Raffaele Saponaro, Izabela Kowarska 1 , 1 Centro Ricerche Fiat Strada Torino 50, I-10043, Orbassano (TO) – Italy ABSTRACT The decrease of the time to market is crucial for every carmaker as it is easier to meet the customers’ needs and expectations. A virtual assessment of the new proposed design is tremendously useful if it can be applied in the early stage of development because it is possible to modify some of the dimensions of the structural parts (rail, rocket), that are fixed at the beginning of the design phase, in order to improve the performances of the structure. This task has been widely explored in the EU-funded initial training network VECOM - “VEhicle COncept Modeling” - in which several numerical methodologies have been applied. The proposed methodology consists of a multi-objective optimization which aims to improve the car body in automatic way, taking in account performance attributes (NVH, static stiffness, global modes, crash performance, ergonomics etc.). In this article multi-objective optimization considered on morphing the automobile structure is presented. Morphing methodology is one of the easiest ways to change the automobile structure with minimal elements distortion. Morphing tool from a state of the art Mesh Morphing methodology is used to re-shape the automobile structure due to possibility of generating and editing shape variables for optimization. To make optimization more effective, morphing was divided into a global (which is to morph the entire automobile structure) and a local one (morphing single parts of the automobile structure). The entire procedure is made automatically from calculations to synthesis of the output data. The results of the application of this method have been shown and some interesting considerations have been derived. 1 INTRODUCTION Almost everyone claims that time is nowadays the most valuable thing, especially in industry due to such a rapid development of technology. Automotive companies are trying to outrun each others with designing cheaper, better, quieter and safer cars. A lot of researchers have been working on this issue (see Refs. [1- 3]) trying to find the best compromise between quality of the car and its price. This forces to face with the problem of evaluating wide range of different design models in a very short time to meet the needs of all requirements. The fastest way to improve automobile structure is not to create it from the beginning but optimize existing one, as the weaknesses of those structures are well known. And it can be achieved in a different ways. The most popular one is changing the geometry of the body directly by changing values of specified variables. This solution is easy but obliges to create each time automatically new finite element mesh (FE mesh). It is not satisfying because, for example, if the model has complex geometry with exactly specified loads conditions, changing the mesh each time is almost impossible. In this paper another solution mesh morphing methodology to obtain optimized automobile structure from base one without necessity of creating new mesh is presented. Similar approaches have been introduced for local optimization of the car body (see Refs. [4-5]). 4095
Transcript
Multi-objective Optimization in Vehicle Concept Modeling
Marco Danti, Maurizio Meneguzzo, Raffaele Saponaro, Izabela Kowarska1, 1Centro Ricerche Fiat Strada Torino 50, I-10043, Orbassano (TO) – Italy
ABSTRACT The decrease of the time to market is crucial for every carmaker as it is easier to meet the customers’ needs and expectations. A virtual assessment of the new proposed design is tremendously useful if it can be applied in the early stage of development because it is possible to modify some of the dimensions of the structural parts (rail, rocket), that are fixed at the beginning of the design phase, in order to improve the performances of the structure. This task has been widely explored in the EU-funded initial training network VECOM - “VEhicle COncept Modeling” - in which several numerical methodologies have been applied. The proposed methodology consists of a multi-objective optimization which aims to improve the car body in automatic way, taking in account performance attributes (NVH, static stiffness, global modes, crash performance, ergonomics etc.). In this article multi-objective optimization considered on morphing the automobile structure is presented. Morphing methodology is one of the easiest ways to change the automobile structure with minimal elements distortion. Morphing tool from a state of the art Mesh Morphing methodology is used to re-shape the automobile structure due to possibility of generating and editing shape variables for optimization. To make optimization more effective, morphing was divided into a global (which is to morph the entire automobile structure) and a local one (morphing single parts of the automobile structure). The entire procedure is made automatically from calculations to synthesis of the output data. The results of the application of this method have been shown and some interesting considerations have been derived.
1 INTRODUCTION
Almost everyone claims that time is nowadays the most valuable thing, especially in industry due to such a rapid development of technology. Automotive companies are trying to outrun each others with designing cheaper, better, quieter and safer cars. A lot of researchers have been working on this issue (see Refs. [1-3]) trying to find the best compromise between quality of the car and its price. This forces to face with the problem of evaluating wide range of different design models in a very short time to meet the needs of all requirements. The fastest way to improve automobile structure is not to create it from the beginning but optimize existing one, as the weaknesses of those structures are well known. And it can be achieved in a different ways. The most popular one is changing the geometry of the body directly by changing values of specified variables. This solution is easy but obliges to create each time automatically new finite element mesh (FE mesh). It is not satisfying because, for example, if the model has complex geometry with exactly specified loads conditions, changing the mesh each time is almost impossible.
In this paper another solution mesh morphing methodology to obtain optimized automobile structure from base one without necessity of creating new mesh is presented. Similar approaches have been introduced for local optimization of the car body (see Refs. [4-5]).
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2 MORPHING APPROACH FOR PARAMETERIZATION OF THE ENTIRE AUTOMOBILE STRUCTURE
Automatic procedure for optimization in concept modelling requires generating plenty of models with good mesh quality that can be use in different steps (Nastran solutions, post-processing etc.) without any manual interaction. The use of parametric CAD has not been considered as the automatic meshing tool is not enough robust and the complete CAD of the structure is not available. Moreover, the load nodes must be defined with the same numbers that identify the grids.
An easy way to evaluate new model by parameterization without creating new mesh is to use mesh morphing methodology. Mesh can be parameterized in a different ways. Some part of the mesh (for instance which contains loaded nodes) can remain unchanged. Also when there is a need, some part of the model can be remeshed (to avoid elements that can cause problems during any type of calculations). To create models for automatic optimization of the entire automobile structure Morph Volume methodology in HyperMesh has been used.
2.1 Morph volume methodology
Morphing with morph volumes consists on creating 3D boxes (figure 1). Boxes can have different length, width and height. Single box contains part of the mesh of the model. In the corners of each box there are handles which are able to move. If handles are morphed, part of the mesh which is included in the box to which handles belong is also moved (figure 2). Mesh which is connected with the part which is in the moving box but belongs to another box or reminds unchanged but little deformed due to maintenance of the continuity. However the mesh distortion is small and with right limits of parameters, it does not cause problems during different calculations.
Figure 1: Morph volume box
Figure 2: Mesh morphing using Morph Volume
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2.2 Parameterization of mesh morphing in HyperMesh 10
Parameterization of mesh morphing in Hyper Mesh 10 is done by means of an ascii command file which is created by HyperMesh while using it. In this file every operation starting with opening HyperMesh, finishing with closing program is written. In order to have a modifiable script, the definitions of the morph volumes and their modifications have been done manually once. To morph the automobile structure 3D morph volume matrix 15x2x3 has been created (figure 3). Such a structure of a morph volume matrix splits the automobile structure into regions. Two columns in lateral direction split the car structure into left and right, what is useful while morphing pillars. Three rows in vertical direction divide the automobile structure into three regions: roof, middle part and chassis. Also fifteen columns in longitudinal direction are needed while morphing some parts of the car body. Except 4 handles lying in the 4 corners of the big rectangle (contained all morph boxes), each handle belongs at least to two adjacent boxes. Thanks to that, morphing is more efficient because while moving one handle at least two boxes are changing their shape. As a result mesh grid is less distorted.
Figure 3: Morph volume matrix
Appropriate selection of design variables has a decisive impact on goals. For creating several models by morphing the entire automobile structure 7 parameters has been introduced:
- Parameter 1: Greenhouse translation (in lateral direction) - translation of upper part of all the pillars in both sides. If right side of the automobile structure is translated in plus, left side is translated in minus (to save a symmetry). This translation is performed by moving all handles along upper edge of morph volume matrix (figure 4).
Figure 4: Parameter 1- greenhouse translation
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- Parameter 2: C-pillar translation (in longitudinal direction) - translation of C- pillar connected with rear glass and tailgate. Translation is performed by moving 3 last paths of handles in a first row in longitudinal direction (figure 5).
Figure 5: Parameter 2- C-pillar translation
- Parameter 3: B-pillar rotation (pitch) + roof adjustment- rotation is about an axis perpendicular to the longitudinal plane of symmetry with a point of rotation located at the intersection between B-pillar and chassis. Roof adjustment (translation the part of the roof connected with B-pillar) is to avoid deformation of the roof after B-pillar rotation. After rotating pillar in every 1 deg, roof should be translated in every 20 mm (figure 6).
Figure 6: Parameter 3- B-pillar rotation
- Parameter 4: Roof translation (in vertical direction) - this parameter lets to increase/decrease the height of the car. Translation is performed in 5 steps (in each step new morph volume matrix is created but the same paths of handles are shifted by the same value). This solution helps to avoid distortion of the windshield (figure 7).
Figure 7: Parameter 4- roof translation
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- Parameter 5: Roof rotation (pitch) - similar to B-pillar rotation (figure 8)
Figure 8: Parameter 5- roof rotation
- Parameter 6/7: rear/front part translation (in longitudinal direction) - this performance is used to shortening/elongation the automobile structure. In both cases translation is made in 5 steps (in contrast to roof translation, each time, the same morph volume matrix is used but the numbers of column with handles is decreasing by 1 in every step) (figure 9)
Figure 9: Parameter 6/7- rear/front part translation
As a result of morphing phase several files are obtained. For the following analysis the performances checked are: interior noise, inertance, static and dynamic stiffness, accessibility, visibility, MAC (Modal Assurance Criteria) etc.
2.3 The Analysis of the automobile structure
The main goal of the presented project is to find the best compromise of a car based on pre-existing geometry in order to have a comfortable quite car with high stiffness and suitable accessibility and visibility.
To obtain the best result for the automobile structure several types of analysis has been presented:
- NVH and DYNAMICS analysis (interior noise, inertance, MAC, dynamic stiffness, real part mobility, suspension assessment, compactness index )
- Ergonomics analysis (accessibility, visibility, Body in White/Trimmed Body/Cavity base dimensions)
2.3.1 NVH & DYNAMICS
NVH and Dynamic analysis are carried out separately for Body in White (BiW) and Trimmed Body (TB). All calculation needed for this performance (FE analysis for cavity, BiW, TB, suspension etc,) are made in
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MSC.Nastran 2008r1 using solution SOL 103 for normal modes. Output files are inputs for obtaining P/F (interior noise), A/F (inertance), Dynamic Stiffness, Real Part Mobility and MAC by means of software developed in CRF called Veiprod5. Very important issue is to keep microphones at the same position (because for optimizing the automobile structure it is important to measure improvements in terms of noise always on the same reference coordinate). Keeping these nodes as “frozen” has caused problems with correctness of elements for Nastran calculation. Due to it, special function has been created which locate new nodes which are at the same place as base ones.
Results of Interior Noise, Inertance, Dynamic Stiffness and Real Part Mobility analysis are set of curves. Each curve is a spectrum (value versus frequency) with hundreds of discrete values. If is impossible to use all them as goals to optimize an automobile structure. To resolve this issue the curves synthesis has been introduced. For different performances different type of synthesis can be selected by user (calculating third-octave band, root mean square, average etc.). At the end only few values are obtained for each curve and can be use as a goal for an optimization.
2.3.2 STATIC
Full static analysis is done for Body in White and part of this analysis for rear suspension. Also in this case to achieve a part of input files for static analysis Nastran calculations are performed using solution SOL 101 for Static. Rest of the files is obtained after mesh morphing performance. The static analysis is done by executable file in which torsion stiffness, bending stiffness elastic lines, door deformation, and tailgate deformation also mass, centre of gravity and volume for BiW and Cavity are calculated and torsion stiffness for rear suspension. As a result several text files are stored which are a goal for later optimization.
2.3.3 ERGONOMICS
The automobile structure ergonomic is a very important problem. Plenty of analysts are focused on performance which provides low level of noise and high stiffness etc. Upper listed performances are the main goals for optimization the car body however it can not be achieved at the expense of the ergonomic. All changes must ensure good visibility and accessibility. Due to this reason ergonomics analysis is split into these two tasks. An input to accessibility and visibility is the same: FE model with specific nodes to calculate values important for accessibility and angles for visibility. All significant values are determined by a mathematical relation between some specific nodes which are set in the first base model and written after morphing performance. Outputs of these analyses are set of files with the values of the performances mentioned above.
2.4 The optimization approach
The target of the car design is to obtain the most efficient automobile structure under different constrains.
To achieve this aim all upper mentioned performances are closed in the optimization loop. All of them have been rewritten as a DOS script and run in the DOS batch mode in modeFRONTIER. All optimization is running in the modeFRONTIER (tool from ESTECO for optimization).
First stage of procedure is to create a new model base on pre-existing structure using HyperMesh batch mode on a computer cluster. The parameters are linked to input nodes in modeFRONTIER to let their values be changed automatically every iteration. After morphing performance calculations of the FE model start. All files used by Nastran to obtain output files for post-processing are sent automatically to dedicated servers. When calculations are finished, all correctly achieved out files are sent to the computer cluster where optimization procedure and post-processing starts. Every analysis tool has been converted from Matlab function to executable file. Result files are linked in modeFRONTIER to output nodes.
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Figure 10: Optimization approach for the automobile structure.
2.4.1 DOE
First step of optimization has been to obtain different variants of the automobile structure with results of analysis. For this reason DOE (design of experiment) in modeFRONTIER has been run. To acquire input parameters for morphing tool, Cubic Composite Design- CFC (Cubic Face Centred) sequence has been used. This sequence has been chosen due to possibility of building quadratic model without necessity of using full three levels of factorial experiments. For 7 input variables 143 structure variants have been found. Single iteration has lasted around 7 hours. Depending on the availability of the servers from 2 to 5 iterations could be run at the same time. As a result more than 6500 output variables have been analysed.
2.4.2 RSM
Second step consisted on creating respond surface for DOE results in order to explore relations between design and result variables for future optimization. It has been done with RSM (Response Surface Methodology) in modeFRONTIER using Neural Networks interpolation tool [6]. The choice of this function for interpolation has been decided by experience gained while developing tool for optimizing some parts of front car structure in connection with CFD analysis [5]. A correctness of response surfaces has been checked with residual graphs in modeFRONTIER.
Figure 11: RSM residuals of the goal: the lowest residuals (a) and the highest (b)
For goals maximum residuals (in percentages) ranged between 0,28 % for torsion stiffness (figure 11 a) till 10% for rms evaluation of TB interior noise respecting target (figure 11 b). Such a big error became a purpose to check another RSM- Shepard K-Nearest. For all output variables RSM has lasted around 20 hours. To find the optimal response, it has been decided to focus on the most important response surfaces like static stiffness, interior noise and ergonomic.
2.5 OPTIMIZATION
Last step was an optimization of the automobile structure. The main goals have been to increase the static stiffness of the car body while decreasing the interior noise maintaining constant values of torsion stiffness of rear suspension, important accessibility dimensions and angles of visibility.
For this purpose 3 objectives have been selected: torsion static stiffness, root mean square of BiW and TB interior noise out of target.
To obtain the best result ARMOGA (Adaptive Range Multi-Objective Genetic Algorithm) optimizer has been used. For both response surfaces more than 100 items meeting requirements have been evaluated. For three goals marked in optimization loop analysis of the results has been made to obtain the best result. For this reason in both cases 3 items have been chosen: one with the highest value of torsion stiffness, one with the lowest level of TB interior noise out of target and one with the lowest limit of rms of BiW interior noise (figure 12, figure 13).
To verify trend correctness (relative error) of both response surface methodologies, 5 virtual structures from both have been calculated with Nastran and post-processing and compared with virtual values from ARMOGA optimizator. Results have been shown in table 1.
Object Correctness of NN interpolation
Correctness of S K-N interpolation
Torsion static stiffness 98 % 96%
RMS of TB interior noise out of target 45 % 82%
RMS of WB interior noise out of target 91 % 85%
Table 1: Correctness of used interpolation tools in RSM
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1
RMS TB interior noise versus target [dB]
Kt [
Nm
m/r
ad]
(a)
1
RMS WB interior noise versus target [dB]
Kt
[Nm
m/r
ad]
(b)
selected structures
Figure 12: Feasible virtual structures (after optimization with NN response surface based on 143 DOE) - torsion stiffness in function of RMS of TB interior noise out of target (a) , torsion
stiffness in function of RMS of BiW interior noise out of target (b)
2
1
1
3
Pareto FRONTIER
Pareto FRONTIER
x dB x Nmm/rad
x dB x Nmm/rad x Nmm/rad
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RMS TB interior noise versus target [dB]
Kt
[Nm
m/r
ad]
(a)
RMS WB interior noise versus target [dB]
Kt
[Nm
m/r
ad]
(b)
selected structures
Figure 13: Feasible virtual structures (after optimization with S K-N response surface based on 143 DOE) - torsion stiffness in function of RMS of TB interior noise out of target (a) , torsion stiffness in
function of RMS of BiW interior noise out of target (b)
Five structures marked as the best (3 evaluated with response surface based on: NN tool and 2 based on S K-N tool) have been compared with base structure (figure14, table 2, table 3.) and calculated with procedure mentioned above.
4
4=6
5
x dB
x Nmm/rad x dB
x Nmm/rad
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(a)
(b)
(c)
(d)
(e)
Figure 14: The automobile optimized structures with base structure features (black lines): no 1 (a), no 2 (b), no 3 (c), no 4=6 (d) no 5 (e).
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Name Base no 1 no 2 no 3 Parameter 1 0 77.985 74.422 -0.400 Parameter 2 0 -103.419 45.337 95.342 Parameter 3 0 -1.747 0.0369 20.381 Parameter 4 0 34.315 34.315 51.655 Parameter 5 0 -0.460 -1.579 6.401 Parameter 6 0 8.1235 -4.835 -2.923 Parameter 7 0 -26.509 22.749 49.966
v r v r v r Kt [%] 100
106 111 109 107 121 119 RMS TB out
of target [db]
0.1385 0.0803 0.220 0.1495 0.124 0.145 0.1001
RMS WB out of target
[db] 0.2840 0.305 0.2967 0.186 0.287 0.332 0.269
Table 2: Values of design and goal variables of optimized and base structures obtained with RS created with NN tool
Table 3: Values of design and goal variables of optimized and base structures obtained with RS created with S K-N tool
Table 1. shows that Shepard K-Nearest interpolation tool can better provide virtual objective values than Neural Network tool. The S K-N method for such a large number of design variables is more precise however analysing results tables (table 2, table 3) and graphs (figure 12, figure 13) can be concluded that optimization with NN gives better results (the structure with a really high torsion stiffness and low interior noise can be achieved) however for such a complex model behaviour of NN function can be unpredictable. For instance level of the interior noise for structure 2 and 3 is lower than for no 1 but in accordance with virtual values for structure no 1 should be the lowest.
To better understand how the parameter change affects goals correlation matrixes have been done (figure 15).
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(a) (b) (c)
Figure 15: Correlation matrix- objects versus input variables obtained after: DOE (a), RSM based on 143 DOE items created with: NN tool (b) and S K-N tool (c).
Analysing correlation matrixes for all cases: real values and interpolated with two tools several conclusions can be found. First of all, dependency between parameters and objectives is always different. Only behaviour of parameter no 3 is the same in all cases (its decrease causes increase of torsion stiffness and decrease of interior noise). It is due to different method of interpolation [6].
For real values and both interpolation functions: NN and S K-N the greatest impact (a “positive dependence”) on torsion static stiffness shows parameter 4. However while its value increases for NN also increases value of rms of TB interior noise while for SK-N decreases and for real values increases.
Separate analysis shows that for NN almost all parameters except 7 and 4 are realising goals (increasing torsion stiffness at the same time decreasing interior noise for while and trimmed body) similar for real values correlation. For S K-N however only parameters 3 and 4 can meet these three requirements. It means that it is better to use NN as an interpolation tool because correlation between design variables and objectives is similar to real values dependency. Even if the results are more unpredictable than those obtained with SK-N it is possible to focus on only three parameters (3,4,5) and evaluate the best automobile structure.
Acknowledgements
In this paper automatic, multi-objective optimization based on morphing methodology, used in pre-design stage has been presented. This approach allows obtaining in very short time a great variety of different structures based on pre-existed one to find an optimized structure considering large number of objectives and constraints. The procedure has been applied in two numerical cases using two different interpolation tools. In both cases it has been proved that method can change the shape of the baseline product taking into account performances targets and improving them in a multi-objective multi-disciplinary approach.
REFERENCES
[1] Danti M., Vige D., Nierop G.V., 2010, “Modal Methodology for the Simulation and Optimization of the Free-Layer Damping Treatment os a Car Body”, ASME J. Vibr. and Acoust., 132(2), pp. 3-8.
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[2] Hambric S.A., 1995, “Approximation Techniques for Broad-Band Acoustic Radiated Noise Design Optimization Problems”, ASME J. Vibr. Acoust. 118(3), pp. 529-532.
[3] Nova M., Berria C., Tamburro A., Pisino E., 1997, “Noise and Vibration Reduction for Small/Medium Car-Market Segment: An Innovative Approach foe Engineering Design and Manufacturing”, IMechE, Birmingham.
[4] Kaufmann M., Lauber B., Katzenschwanz Ch., 2007, “Optimization Of A Vehicle Front Part Structure At Audi Using Ansa Morphing And Optimus”, Fe-Design.
[5] Ribaldone E., Cogotti F., Tregnago R., Scantamburlo G. “Optimizing the aerodynamics during the design of passenger cars: coupling CFD with modeFRONTIER”, ModeFRONTIER User Meeting, (2010)
