###### Abstract  
In the realm of van design, researchers have been diligently working to enhance rollover crashworthiness while concurrently achieving lightweight body structures. Unlike front and side impacts, rollover crashworthiness is impacted by a greater number of structural dimensions and material parameters. As such, this paper implements an unreplicated saturated factorial design to conduct factor screening for vehicle rollover crashworthiness. This approach effectively and accurately resolves the screening challenges that arise from large numbers of factors, and eliminates dependence on traditional design experience. Consequently, it shortens the design cycle and reduces development costs. In addition, this paper establishes four Kriging approximate models that describe the specific energy absorption and total mass of the key body structure, the displacement of the roof, and the maximum angular velocity of the body's center of mass. To address the multi-objective optimization problem of improving rollover crashworthiness while reducing mass, this paper combines the particle swarm optimization algorithm with the artificial immune algorithm. This hybrid algorithm converges rapidly, and the Pareto solution set exhibits superior uniformity and diversity. Finally, the shortest distance method is employed to identify the optimal design scheme that can enhance the rollover crashworthiness of vans and reduce the mass of body parts. vans' rollover crashworthiness; weight reduction; unreplicated saturated factorial design; multi-objective optimization; hybrid optimization algorithm +
Footnote †: journal: Applied  
impact, side impact, and side impact scenarios, successfully reducing the vehicle mass while improving the crashworthiness and NVH attributes of the vehicle. [PERSON] et al. [7] carried out multi-objective optimization on the body thickness as well as the beam section shape and size. They also modified the structure with implicit parameterization technology, which reduced the total body mass by 32.41 kg, while the passive safety performance in frontal and side impact scenarios was almost unchanged. [PERSON] et al. [8] proposed a collision optimization method that simultaneously considered side impact tests and roof extrusion tests. Topological optimization was used to design the B-pillar stiffener, which reduced the body mass while meeting the crashworthiness requirements. [PERSON] et al. [9] and others applied composite materials to the bumper system to achieve lightweighting while ensuring the crashworthiness of the vehicle. [PERSON] et al. [10] developed a control strategy for wire-controlled auxiliary braking based on body-attitude detection and the overall design of the system, achieving automatic speed reduction. The above research mainly focused on frontal, side, and side impacts, and few studies have been conducted on rollover collisions. Compared with front and side crashes, which usually end within 200 milliseconds, a rollover crash may last more than one second, involving multiple crashes and a large number of body parts, which greatly increases the complexity of the research [11]. A rollover accident refers to an accident in which a vehicle turns over more than 90 degrees on its transverse longitudinal axis. Rollover collision can be divided into two categories: tripping rollover and non-tripping rollover [12]. Tripping rollover is more common, and this paper studies single-vehicle rollover accidents. Due to the complexity of vehicle rollover collisions, crashworthiness is influenced by different potential factors, and factor screening of multivariable crashworthiness and the weight optimization process is particularly important. Factor screening in the optimization process can improve the development efficiency and save time and development costs. [PERSON] et al. [13] proposed a factor screening method based on the response surface method, which uses D-optimal design for sampling and variance analysis to determine coefficients and confidence intervals.