CN113901586A - NSGA-II-based structure optimization method for integrated aluminum alloy precision casting anti-collision beam - Google Patents
NSGA-II-based structure optimization method for integrated aluminum alloy precision casting anti-collision beam Download PDFInfo
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Abstract
The invention discloses an NSGA-II-based structure optimization method for an integrated aluminum alloy precision casting anti-collision beam, which belongs to the technical field of anti-collision beam modeling and structure optimization and comprises the following steps: selecting sample points by an optimal Latin hypercube design method to construct a response surface approximation model; performing deterministic optimization on the mass and specific energy absorption by using an NSGA-II algorithm; a reliability-based 6 sigma quality analysis and optimization is performed on the deterministic optimization solution. The method only optimizes the thickness parameters of all parts of the aluminum alloy precision casting anti-collision beam assembly, improves the crashworthiness and the reliability of the anti-collision beam through the deterministic optimization based on NSGA-II and the reliability optimization based on 6 sigma, and realizes light weight.
Description
Technical Field
The invention relates to the technical field of automobile collision safety, in particular to an NSGA-II-based structure optimization method for an integrated aluminum alloy precision casting anti-collision beam.
Background
The impact beam is a vital component in a passive safety device of an automobile, and protects the safety of a vehicle body, a driver and passengers when the automobile collides, and the light weight and the optimized crashworthiness of the impact beam are more and more concerned. At present, the design of most of traditional anti-collision beams cannot give consideration to light weight and good collision performance, and an algorithm which can ensure excellent collision performance and has an obvious light weight effect is urgently needed. The NSGA-II genetic algorithm can effectively solve the problem of nonlinear optimization, breaks through the bottleneck that traditional multi-objective optimization methods such as a weighted sum method, a linear programming method, a constraint method and the like have poor effects and even fail under the condition of lack of experience, and is an optimization algorithm very suitable for the scheme.
Disclosure of Invention
The invention aims to provide an NSGA-II-based optimization method for an integrated aluminum alloy precision casting anti-collision beam structure, which is optimized through an NSGA-II optimization algorithm to meet RCAR low-speed collision regulations, tow hook regulations, 2021C-NCAP pedestrian protection regulations and the like, and has an obvious light weight effect.
In order to achieve the aim, the invention provides an NSGA-II-based integrated aluminum alloy precision casting anti-collision beam structure optimization method, which comprises the following steps:
step 1: establishing a geometric model of the anti-collision beam in three-dimensional software;
step 2: establishing a front collision finite element model in finite element software, and solving through LS-DYNA software;
and step 3: sample points are adopted to construct an approximate model of peak collision force, maximum longitudinal displacement, specific energy absorption and high-quality and high-precision response surface by an optimal Latin hypercube design method;
and 4, step 4: the maximum longitudinal displacement and the peak collision force are taken as constraint conditions, the thickness of the anti-collision beam is taken as a design variable, and the energy absorption and the quality are compared by adopting an NSGA-II algorithm to carry out deterministic optimization;
and 5: according to the deterministic optimal solution in the step 4, considering the influence of uncertainty factors, and carrying out 6 sigma quality analysis based on reliability on the constraint conditions;
step 6: and 6 sigma quality optimization is carried out on the constraint conditions which do not meet the reliability requirement in the quality analysis result of the step 5.
Further, the response surface model in step 3 is as follows:
maximum longitudinal displacement LmaxThe response surface model of (1) is:
Lmax=77.167 4-2.578 0T1-2.947 7T2-3.796 1T3-0.753 2T4+ 0.285 1T1 2+0.340 1T2 2+0.433 5T3 2+0.071 1T4 2-0.023 4T1T2- 0.343 8T1T3-0.122 1T1T4-0.158 0T2T3+0.055 3T2T4+0.076 8T3T4
peak impact force FpeakThe response surface model of (1) is:
Fpeak=50.771 4-1.211 7T1-6.649 1T2-0.470 8T3+1.393 5T4- 0.629 0T1 2+0.068 8T2 2-0.627 2T3 2-0.208 5T4 2+0.847 1T1T2+ 0.793 0T1T3+0.137 6T1T4+0.763 6T2T3-0.189 1T2T4+0.123 0T3T4
the response surface model of the energy absorption SEA is as follows:
SEA=272.836 7-14.064 5T1-15.315 9T2-11.928 8T3-0.763 9T4- 1.345 0T1 2+0.016 9T2 2-0.507 6T3 2-0.383 1T4 2+1.389 0T1T2+ 1.095 2T1T3+0.122 0T1T4+0.929 6T2T3+0.226 6T2T4+0.296 9T3T4
the response surface model for mass M is:
M=0.095 4+0.646 0T1+0.199 6T2+0.269 6T3+0.047 0T4- 3.843 7T1 2-1.355 9T2 2+6.613 0T3 2-3.745 8T4 2+5.714 1T1T2+ 1.606 6T1T3+0.000 1T1T4+9.151 9T2T3-0.000 1T2T4-1.249 7T3T4
wherein: t is1~T4The thickness of the anti-collision beam, the thickness of the longitudinal reinforcing rib, the thickness of the energy absorption box and the thickness of the transverse reinforcing rib are respectively indicated
Further, the multi-objective optimization mathematical model in the step 4 is as follows:
wherein: SEA is specific energy absorption, M is the mass of the anti-collision beam, FpeakIs the peak impact force, LmaxFor maximum longitudinal displacement, T1~T4The thickness of the anti-collision beam, the thickness of the longitudinal reinforcing rib, the thickness of the energy absorption box and the thickness of the transverse reinforcing rib are respectively indicated
Further, the 6 σ quality analysis mathematical model in the step 5 is as follows:
μ[T1]=3.75,σ[T1]=1%*μ[T1]
μ[T2]=3.85,σ[T2]=1%*μ[T2]
μ[T3]=4.55,σ[T3]=1%*μ[T3]
μ[T4]=3.50,σ[T4]=1%*μ[T4]
s.t.Fpeak≤42120N
Lmax≤46.53mm
wherein: SEA is specific energy absorption, M is the mass of the anti-collision beam, FpeakIs the peak impact force, LmaxFor maximum longitudinal displacement, T1~T4The thickness of the anti-collision beam, the thickness of the longitudinal reinforcing rib, the thickness of the energy absorption box and the thickness of the transverse reinforcing rib are respectively indicated, and mu and sigma are respectively a mean value and a variance of normal distribution.
Further, the 6 σ quality optimization mathematical model in the step 6 is as follows:
wherein: SEA is specific energy absorption, M is the mass of the anti-collision beam, FpeakIs the peak impact force, LmaxFor maximum longitudinal displacement, T1~T4The thickness of the anti-collision beam, the thickness of the longitudinal reinforcing rib, the thickness of the energy absorption box and the thickness of the transverse reinforcing rib are respectively indicated, and mu and sigma are respectively a mean value and a variance of normal distribution.
Drawings
FIG. 1 is a schematic thickness diagram of an optimization object;
FIG. 2 is a flow chart of the optimization based on NSGA-II optimization algorithm in the present scheme;
FIG. 3 is a PARETO leading edge solution obtained by optimization of the NSGA-II optimization algorithm of FIG. 2;
Detailed Description
The invention is further described with reference to the accompanying drawings in which:
in order to make the technical solutions of the present invention more clear and definite for those skilled in the art, the present invention is further described in detail below with reference to the examples and the accompanying drawings, but the embodiments of the present invention are not limited thereto.
As shown in fig. 2, the embodiment provides an optimization method of an integrated aluminum alloy precision casting anti-collision beam structure based on NSGA-ii, which includes the following steps:
step 1: establishing a geometric model of the anti-collision beam in three-dimensional software;
step 2: establishing a front collision finite element model in finite element software, and solving through LS-DYNA software;
and step 3: sample points are adopted to construct an approximate model of peak collision force, maximum longitudinal displacement, specific energy absorption and high-quality and high-precision response surface by an optimal Latin hypercube design method;
and 4, step 4: the maximum longitudinal displacement and the peak collision force are taken as constraint conditions, the thickness of the anti-collision beam is taken as a design variable, and the energy absorption and the quality are compared by adopting an NSGA-II algorithm to carry out deterministic optimization;
and 5: carrying out 6 sigma quality analysis based on reliability on the constraint condition of the deterministic optimal solution solved according to the step 4 by considering the influence of uncertainty factors;
step 6: and 6 sigma quality optimization is carried out on the maximum longitudinal displacement of the constraint condition which does not meet the reliability requirement in the quality analysis result of the step 5.
Furthermore, a response surface approximate model is constructed in the step 3, the secondary response surface approximate model of the peak collision force, the maximum longitudinal displacement, the specific energy absorption and the mass of the cast aluminum anti-collision beam is constructed by adopting 30 sampling points, and the test design points are continuously increased in the deterministic optimization process to update the approximate model until the precision of the approximate model meets the reliability requirement. The invention mainly adopts the determination coefficient, the root mean square error and the relative average absolute error to check the precision of the approximate model. The results of the response surface model accuracy evaluation are shown in table 1. It can be known that all three evaluation indexes meet the requirements, which indicates that the constructed response surface approximation model is reliable.
TABLE 1 response surface model accuracy evaluation
Response to | Determining coefficients | Root mean square error | Relative mean absolute error |
Acceptable level of | ≥90% | ≤20% | ≤20% |
Maximum longitudinal displacement | 97.87% | 3.26% | 2.55% |
Peak impact force | 92.46% | 6.84% | 5.80% |
Specific energy absorption | 99.74% | 1.21% | 0.94% |
Quality of | 1 | 0.02% | 0.01% |
The response surface model in step 3 is as follows:
maximum longitudinal displacement LmaxThe response surface model of (1) is:
Lmax=77.167 4-2.578 0T1-2.947 7T2-3.796 1T3-0.753 2T4+ 0.285 1T1 2+0.340 1T2 2+0.433 5T3 2+0.071 1T4 2-0.023 4T1T2- 0.343 8T1T3-0.122 1T1T4-0.158 0T2T3+0.055 3T2T4+0.076 8T3T4
peak impact force FpeakThe response surface model of (1) is:
Fpeak=50.771 4-1.211 7T1-6.649 1T2-0.470 8T3+1.393 5T4- 0.629 0T1 2+0.068 8T2 2-0.627 2T3 2-0.208 5T4 2+0.847 1T1T2+ 0.793 0T1T3+0.137 6T1T4+0.763 6T2T3-0.189 1T2T4+0.123 0T3T4
the response surface model of the energy absorption SEA is as follows:
SEA=272.836 7-14.064 5T1-15.315 9T2-11.928 8T3-0.763 9T4- 1.345 0T1 2+0.016 9T2 2-0.507 6T3 2-0.383 1T4 2+1.389 0T1T2+ 1.095 2T1T3+0.122 0T1T4+0.929 6T2T3+0.226 6T2T4+0.296 9T3T4
the response surface model for mass M is:
M=0.095 4+0.646 0T1+0.199 6T2+0.269 6T3+0.047 0T4- 3.843 7T1 2-1.355 9T2 2+6.613 0T3 2-3.745 8T4 2+5.714 1T1T2+ 1.606 6T1T3+0.000 1T1T4+9.151 9T2T3-0.000 1T2T4-1.249 7T3T4
wherein: t is1~T4The thickness of the anti-collision beam, the thickness of the longitudinal reinforcing rib, the thickness of the energy absorption box and the thickness of the transverse reinforcing rib are respectively indicated.
Further, the multi-objective optimization mathematical model in the step 4 is as follows:
wherein: SEA is specific energy absorption, M is the mass of the anti-collision beam, FpeakIs the peak impact force, LmaxFor maximum longitudinal displacement, T1~T4The thickness of the anti-collision beam, the thickness of the longitudinal reinforcing rib, the thickness of the energy absorption box and the thickness of the transverse reinforcing rib are respectively indicated.
In the step 4, the NSGA-II optimization algorithm related parameters are set as follows: the population scale is 150, the evolution generation number is 100, the hybridization probability is 0.9, the hybridization distribution coefficient is 2, and the variation distribution coefficient is 20. The PARETO front edge solution of mass and specific energy absorption is generated through the NSGA-II algorithm, as shown in figure 3, it can be seen from the figure that contradiction exists between the target function mass and the specific energy absorption, multiple factors are comprehensively considered, and finally a satisfactory optimization solution is selected from the PARETO solution to serve as a deterministic optimization solution, namely T1~T43.75mm, 3.85mm, 4.55mm and 3.5mm respectively, the mass is 4.682kg, and the specific energy absorption is 134.69 J.kg-1The mass is reduced by 1.09kg, and the energy absorption is improved by 23.71 J.kg-1However, 6 σ quality analysis shows that the reliability and quality level of the maximum longitudinal displacement of the constraint condition are only 47.73% and 0.63 σ, and 6 σ quality optimization is required for the maximum longitudinal displacement.
Further, the quality optimization mathematical model in the step 6 is as follows:
wherein: SEA is specific energy absorption, M is the mass of the anti-collision beam, FpeakIs the peak impact force, LmaxFor maximum longitudinal displacement, T1~T4The thickness of the anti-collision beam, the thickness of the longitudinal reinforcing rib, the thickness of the energy absorption box and the thickness of the transverse reinforcing rib are respectively indicated, and mu and sigma are respectively a mean value and a variance of normal distribution.
To obtain T1~T43.71mm, 4.77mm, 4.72mm, 4.76mm, M4.943 kg, SAE 128.17J kg-1Compared with the initial design, the specific energy absorption of the anti-collision beam is improved by 15.98 percent, and the mass is reduced by 14.36 percent by adopting the result as the final result; the reliability and quality level of the maximum longitudinal displacement is improved to 99.99% and 6.06 sigma compared to a deterministic design.
The invention carries out integrated design of the anti-collision beam assembly, carries out the deterministic design based on NSGA-II on the initially designed anti-collision beam, and carries out the reliable design based on the deterministic design, thereby finally realizing the invention of the integrated aluminum alloy precision casting anti-collision beam assembly based on the NSGA-II optimization algorithm.
Compare in traditional steel anticollision roof beam, its beneficial effect: the number of relevant parts and material consumption are reduced, and meanwhile, the deterministic design of NSGA-II and the reliability design based on 6 sigma mass analysis are combined, so that the light weight is realized, and the requirements on rigidity, strength, collision safety performance and reliability are met.
Claims (5)
1. An NSGA-II-based integrated aluminum alloy precision casting anti-collision beam structure optimization method is characterized by comprising the following steps:
step 1: establishing a geometric model of the anti-collision beam in three-dimensional software;
step 2: establishing a front collision finite element model in finite element software, and solving through LS-DYNA software;
and step 3: sample points are adopted to construct an approximate model of peak collision force, maximum longitudinal displacement, specific energy absorption and high-quality and high-precision response surface by an optimal Latin hypercube design method;
and 4, step 4: the maximum longitudinal displacement and the peak collision force are taken as constraint conditions, the thickness of the anti-collision beam is taken as a design variable, and the energy absorption and the quality are compared by adopting an NSGA-II algorithm to carry out deterministic optimization;
and 5: carrying out 6 sigma quality analysis based on reliability on the constraint condition of the deterministic optimal solution solved according to the step 4 by considering the influence of uncertainty factors;
step 6: and 6 sigma quality optimization is carried out on the constraint conditions which do not meet the reliability requirement in the quality analysis result of the step 5.
2. The NSGA-II based integrated aluminum alloy precision casting anti-collision beam structure optimization method based on the claim 1, wherein the response surface model in the step 3 is as follows:
maximum longitudinal displacement LmaxThe response surface model of (1) is:
Lmax=77.167 4-2.578 0T1-2.947 7T2-3.796 1T3-0.753 2T4+0.285 1T1 2+0.340 1T2 2+0.433 5T3 2+0.071 1T4 2-0.023 4T1T2-0.343 8T1T3-0.122 1T1T4-0.158 0T2T3+0.055 3T2T4+0.076 8T3T4
peak impact force FpeakThe response surface model of (1) is:
Fpeak=50.771 4-1.211 7T1-6.649 1T2-0.470 8T3+1.393 5T4-0.629 0T1 2+0.068 8T2 2-0.627 2T3 2-0.208 5T4 2+0.847 1T1T2+0.793 0T1T3+0.137 6T1T4+0.763 6T2T3-0.189 1T2T4+0.123 0T3T4
the response surface model of the energy absorption SEA is as follows:
SEA=272.836 7-14.064 5T1-15.315 9T2-11.928 8T3-0.763 9T4-1.345 0T1 2+0.016 9T2 2-0.507 6T3 2-0.383 1T4 2+1.389 0T1T2+1.095 2T1T3+0.122 0T1T4+0.929 6T2T3+0.226 6T2T4+0.296 9T3T4
the response surface model for mass M is:
M=0.095 4+0.646 0T1+0.199 6T2+0.269 6T3+0.047 0T4-3.843 7T1 2-1.355 9T2 2+6.613 0T3 2-3.745 8T4 2+5.714 1T1T2+1.606 6T1T3+0.000 1T1T4+9.151 9T2T3-0.000 1T2T4-1.249 7T3T4
wherein: t is1~T4The thickness of the anti-collision beam, the thickness of the longitudinal reinforcing rib, the thickness of the energy absorption box and the thickness of the transverse reinforcing rib are respectively indicated.
3. The NSGA-II-based integrated aluminum alloy precision casting anti-collision beam structure optimization method based on the claim 1 is characterized in that the multi-objective optimization mathematical model in the step 4 is as follows:
wherein: SEA is specific energy absorption, M is the mass of the anti-collision beam, FpeakIs the peak impact force, LmaxFor maximum longitudinal displacement, T1~T4Respectively the thickness of the anti-collision beam and the thickness of the longitudinal reinforcing ribAnd the thickness of the energy absorption box and the thickness of the transverse reinforcing rib.
4. The NSGA-II-based integrated aluminum alloy precision casting anti-collision beam structure optimization method based on the claim 1 is characterized in that a 6 sigma mass analysis mathematical model in the step 5 is as follows:
μ[T1]=3.75,σ[T1]=1%*μ[T1]
μ[T2]=3.85,σ[T2]=1%*μ[T2]
μ[T3]=4.55,σ[T3]=1%*μ[T3]
μ[T4]=3.50,σ[T4]=1%*μ[T4]
s.t.Fpeak≤42120N
Lmax≤46.53mm
wherein: SEA is specific energy absorption, M is the mass of the anti-collision beam, FpeakIs the peak impact force, LmaxFor maximum longitudinal displacement, T1~T4The thickness of the anti-collision beam, the thickness of the longitudinal reinforcing rib, the thickness of the energy absorption box and the thickness of the transverse reinforcing rib are respectively indicated, and mu and sigma are respectively a mean value and a variance of normal distribution.
5. The NSGA-II based integrated aluminum alloy precision casting anti-collision beam structure optimization method is characterized in that the optimization scheme is to combine the NSGA-II deterministic design and the reliability design based on 6 sigma mass analysis and optimization.
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