Optimization Design of Body-in-White Stiffness Test Rig Based on the Global Adaptive Algorithm of the Hybrid Element Model

Abstract

One of the challenging aspects of designing body-in-white stiffness test rigs is measuring test accuracy. This paper proposes a method of integrating the body-in-white stiffness test rig and the body-in-white into an overall model for the optimization design. It establishes an optimization mathematical model based on the overall structure of the stiffness test rig, taking into account the factors affecting the accuracy of the test results of the body-in-white stiffness test rig. The stiffness test rig’s testing accuracy can be significantly increased by designating the degrees of freedom at each connection position as discrete variables. The Hybrid and Adaptive Metamodeling Method (HAM) is used to optimize the mathematical model. This approach uses and integrates three distinct metamodels with various attributes. The body-in-white torsional stiffness test result error is only 1.1%, and the body-in-white bending stiffness test result error is only 3.4%, owing to the optimization result that was used to design and manufacture a set of body-in-white stiffness test rigs and use them for a body-in-white stiffness test verification.

1. Introduction

One challenging aspect of the body-in-white stiffness test rig’s design is its testing accuracy. The body-in-white stiffness CAE analysis is a type of static linear analysis with a comparatively high analytical accuracy. Simultaneously, the accuracy of the stiffness CAE analysis increases with the development of the new model. When developing new vehicle models, the accuracy of the stiffness CAE analysis is relatively high, so the necessity of stiffness tests to verify the results of stiffness CAE analysis is not significant. In automotive enterprises, stiffness tests are more often used to test benchmark vehicles, as most benchmark vehicles cannot undergo CAE analysis, and the results of stiffness tests are directly used as the stiffness values of the benchmark vehicles.

Based on the design concept of people oriented, Kenichi Sato et al. introduced the development of lightweight, highly rigid body structures that achieve good controllability and stability as well as excellent ride comfort and quietness [1]. Xiong et al. proposed a system approach for multi-objective lightweighting and stiffness optimization of vehicle bodies, which provided in-depth insights into the reasonable and optimal multi-objective optimization of vehicle bodies [2]. For the multi-objective optimal design of frontal and offset collision problems for cars, Liao et al. used a multi-objective genetic algorithm [3]. Genetic algorithms were used by M.F. Ashby for material selection using multi-objective optimum design. Pereira et al. provided a detailed account of the main multi-objective optimization algorithms and methods applied in the field of mechanical engineering such as those for design optimization and manufacturing problems [4]. Caramia et al. listed some multi-objective optimization problems and provided some solutions to them [5].

In recent years, Zolpakar et al. reviewed the current and past applications of the MOGA (multi-objective genetic algorithm) [6] in the most commonly used manufacturing/processing techniques in the minority cases and also compared the advantages and limitations of MOGA with those of traditional optimization techniques [7]. The article demonstrated the potential of the MOGA method in engineering applications and attracted the attention of many scholars. Gu et al. developed a global adaptive optimization method based on the hybrid metamodel [8,9], which applies three different types of metamodels in the search process at the same time and solves the problem of the small scope of application of a single metamodel, and the construction of the focus space improves the efficiency and accuracy of this method, which provides an option for solving the optimal design of the computationally concentrated “black-box” problems in practical engineering.

Kim et al. developed a new evaluation standard for local stiffness in BIW (body-in-white) and verified it considering the actual vehicle driving conditions for handling performance [10]. Body stiffness is one of the characteristics of a passenger car that affects the vehicle’s handling, steering, and ride comfort characteristics [11]. Shengqin Li et al. conducted a strength analysis on a certain all-aluminum white body and optimized the body based on the lightweighting goal [12].

A stiffness test rig with high accuracy is required to address longstanding concerns among automotive manufacturers regarding the reliability of stiffness test results, particularly the poor stability observed in these results. Current real-vehicle test data show a discrepancy of approximately 20% when compared with initial CAE analysis results, with significant variability in repeated tests of the same vehicle. To resolve this, an optimization model was developed based on the overall structure of the body-in-white stiffness test rig employing a combination of adaptive mesh modeling for optimization.

2. Factors Affecting the Accuracy of Test-Rig Testing

Matsimbi. et al. reviewed the methods used to determine the overall stiffness of automotive body structures [13]. The structure and principle of the stiffness test rig are shown in Figure 1. The stiffness test bench is generally composed of the front-end loading and restraint mechanism and the rear-end restraint support rods. The front end is further divided into the horizontal support rods and the vertical support rods. The rear-end restraining support bar acts as a support. The front-end loading and restraining mechanism, in addition to playing a restraining role, also plays a role in loading force during the torsional stiffness test: the torsion of the body-in-white is realized by adding rotational moments on both sides of the front-end transverse support bar.

The dashed circles in Figure 1 denote connection-making elements, such as a ball hinge, a permanent connection, or a single-direction rotating articulated portion. Both the front-end and rear-end restraining mechanisms are attached to the body-in-white by two different connection points, while the front-end loading and restraining mechanism of the rigidity test rig is made up of two connecting elements, as seen in the figure. Based on real-world experience, the majority of the stiffness test rigs today are built with these six connections; the main distinction between different rigs is how these connections are handled. A combination of ball hinges and single-direction rotating hinges is used in some connections, while ball hinges are used in all six connections in others.

Through experimentation with different connection types at the six locations shown in Figure 1, it was found that the choice of connections significantly impacted the test results. For instance, first, the change in structural stiffness: The stiffness at the connection point directly affects the overall stiffness of the test stand. If the stiffness at the connection point is insufficient, the test stand will undergo additional deformation during loading, causing the measured values to deviate from the true values. Second, the alteration of stress distribution: The connection method influences the stress distribution within the test stand. An unreasonable connection design may lead to stress concentration, which intensifies the local deformation and subsequently affects the overall deformation measurement results. Some combinations led to highly volatile results during testing. Additionally, the lengths of the vertical support rods (labeled b and c in Figure 1) at the front and rear ends of the stiffness test rig also influenced the test outcomes. For instance, first, the change in structural stiffness: The variation in the length of the support rods alter the overall stiffness distribution of the test bench. If the support rods are too long, the overall stiffness is reduced, while if they are too short, it may lead to structural instability. Both overly long and overly short support rods can affect the testing accuracy. Second, the introduction of local deformation: The change in the length of the support rods influences the local deformation characteristics of the test bench. If the support rods are too long, local deformation may increase significantly. The local deformation will be superimposed on the overall deformation, resulting in measurement errors. Based on these observations, it was initially concluded that both the connection methods at these six points and the lengths of the vertical support rods at the front and rear ends affected not only the accuracy of the stiffness test results but also the stability of those results. This paper explores optimizing the design of these factors in order to achieve the most effective connection configuration at the six locations.

Choosing a suitable and efficient optimization method has become a significant challenge for engineers. Traditional gradient-based optimization methods can identify only locally optimal solutions; however, their efficiency is often limited, particularly when applied to optimization problems based on finite element or CFD (Computational Fluid Dynamics) simulations. Additionally, the limitations of fitting methods mean that a single metamodel is typically effective for only a specific class of problems. These models may exhibit poor accuracy when applied to different types of problems, or in some cases, they may not be applicable at all. For example, second-order polynomial response surfaces may perform well for fitting low-order problems but show poor accuracy when applied to higher-order problems. These inherent weaknesses of metamodels restrict the practical application of metamodel-based optimization methods in engineering.

The approach presented in this paper involves considering both the stiffness test rig and the body-in-white as part of a unified model to establish an overall optimization mathematical model based on the stiffness test rig. The optimization solution is then obtained using a global adaptive optimization method based on a hybrid element model. By combining the stiffness test rig and the body-in-white into a single model for optimization design, the complexity of the model increases. However, the application of the global adaptive optimization method with the hybrid element model significantly enhances both the optimization efficiency and accuracy.

3. The Design Process

3.1. Models

First, a finite-element model of the vehicle body-in-white was created, followed by the development of a finite-element model for the body-in-white stiffness test rig, including the test bench, using HyperWorks software 2022, as shown in Figure 2. This integrated model combines both the body-in-white and the stiffness test rig. The model consists of 277,142 elements and 2863 weld joints. Shell elements are used for the body-in-white, while solid elements are employed for the stiffness test rig.

3.2. Working Conditions

The stiffness calculation included both torsional and bending stiffness. The calculation and analysis conditions were based on the automotive design manual along with commonly used stiffness analysis methods employed by automotive manufacturers. These conditions were used to determine the relevant stiffness values.

For the CAE analysis of the torsional stiffness of the unbenched body-in-white, a pair of opposite forces, each with a magnitude of 2000 N in the Z-direction, was applied at the center points of the left and right front overhangs of the body-in-white. The front cross-member, near its midpoint (SPC = 3), and the center of the rear suspension (SPC = 123, as defined in Section 3) were constrained. For the torsional stiffness calculation of the stiffness test rig model based on the monolithic structure, forces were applied to both sides of the transverse support beams at the front end of the rig, as shown in Figure 3.

For the CAE analysis of the bending stiffness of the unbenched body-in-white, a vertical force of 1668 N in the Z-direction was applied at each seat. The front wheel cover center point (SPC = 123) and the center of the rear suspension (SPC = 3) were constrained. For the bending stiffness calculation of the stiffness test rig model based on the overall structure, the constraint position was shifted to both sides of the transverse support beams at the front end of the rig, as shown in Figure 3.

3.3. Body-in-White Stiffness Test Bench Variable Settings

The test rig designed in this paper features a left–right symmetric structure. The variables considered include both degree-of-freedom variables and design variables, with the latter specifically related to the lengths of the vertical support rods at the front and rear ends of the rig.

The setup of the degree of freedom variables is shown in Figure 4 for the rotational degrees of freedom around XYZ for the connected units at pedestals 1, 2, and 3: ${spc}_{14}$, ${spc}_{15}$, ${spc}_{16}$, ${spc}_{24}$, ${spc}_{25}$, ${spc}_{26}$, ${spc}_{34}$, ${spc}_{35}$, ${spc}_{36}$.

The lengths of the left vertical support at the front end of the test stand and the left vertical support at the rear end of the test stand in Figure 4 are taken as variables $L_1$, $L_2$.

At the same time, the stiffness test rig in Figure 4 requires its total weight not to exceed 65 kg, $400 \mathrm{m}\mathrm{m}<L_1<700 \mathrm{m}\mathrm{m}$, $100 \mathrm{m}\mathrm{m}<L_2<300 \mathrm{m}\mathrm{m}$. Thus, the mathematical model for optimization of a torsional stiffness test rig based on a monolithic structure turns out to be as follows:

$$\begin{array}{c}\min f(sp{c}_{ij},L_k)=f_{at}(sp{c}_{ij},L_k)-\mathrm{16,159.5}\\ i=1,2,3 j=4,5,6 k=1,2\\ s.t. { \mathrm{w}}_t(sp{c}_{ij},L_k)\le 65\\ i=1,2,3 j=4,5,6 k=1,2\\ 400\le L_1\le 700\\ 100\le L_2\le 300\\ sp{c}_{i4}\in \{0,4\} i=1,2,3\\ sp{c}_{i5}\in \{0,5\} i=1,2,3\\ sp{c}_{i6}\in \{0,6\} i=1,2,3\end{array}$$

where ${ f}_{at}$ is the calculated value of torsional stiffness based on the monolithic structure (body-in-white plus stiffness test bed model) and ${ w}_t$ is the total weight of the torsional stiffness test bed.

$$\begin{array}{c}\min f(sp{c}_{ij},L_k)=f_{ab}(sp{c}_{ij},L_k)-\mathrm{19,600}\\ i=1,2,3 j=4,5,6 k=1,2\\ s.t. { \mathrm{w}}_b(sp{c}_{ij},L_k)\le 65\\ i=1,2,3 j=4,5,6 k=1,2\\ 400\le L_1\le 700\\ 100\le L_2\le 300\\ sp{c}_{i4}\in \{0,4\} i=1,2,3\\ sp{c}_{i5}\in \{0,5\} i=1,2,3\\ sp{c}_{i6}\in \{0,6\} i=1,2,3\end{array}$$

where ${ f}_{ab}$ is the calculated value of bending stiffness based on the monolithic structure (body-in-white plus stiffness test bed model) and $w_b$ is the total weight of the bending stiffness test bed.

4. Mathematical Model for Optimization of the Stiffness Test Rig Based on a Monolithic Structure

This paper proposes improving the testing accuracy of the stiffness test rig by optimizing the connection types and the lengths of the vertical support rods at the front and rear ends of the six connection positions indicated by the dashed circles in Figure 1. Specifically, the optimization focuses on the connection degrees of freedom (three translational degrees of freedom along the XYZ axes and three rotational degrees of freedom around the XYZ axes) and the lengths of the vertical supports at these six locations. Each connection point is defined by six degrees of freedom variables.

A fixed connection, which imposes a full degree-of-freedom constraint, is represented as SPC = 123,456, with the six degrees of freedom variables numbered 1, 2, 3, 4, 5, and 6. A ball hinge is modeled to allow rotation around the XYZ axes, with a degree-of-freedom constraint defined as SPC = 123,000, where the six degrees of freedom variables are 1, 2, 3, 0, 0, and 0. When one of the six degree-of-freedom variables for a cell is set to 0, the constraint in the direction defined by that variable is removed. Conversely, when a degree-of-freedom variable is set to a nonzero value, the corresponding constraint in that direction is applied.

This system considers both the stiffness test rig and the body-in-white together as a unified structure. The object of analysis is the overall system, which includes both the stiffness test rig and the body-in-white. The finite element model used in the optimization solution of the HAM method is based on this monolithic structure model. This approach is referred to as the stiffness test rig optimization based on the monolithic structure.

The problem of optimization of a stiffness test rig based on the monolithic structure can be described as follows:

(1) Define the variable of degrees of freedom in the $j$-direction of the connected unit at $i$ of the system as ${spc}_{ij}$.

Each degree-of-freedom variable is a nonlinear variable, and the value of the variable is selected only between “0” and “$j$”; when the value is “0”, it means that the $j$-direction constraint is canceled, and when the value is “$j$”, it means that the $j$-direction constraint exists. The system also contains $k$ vertical support bars at the front and rear ends that need to be optimized in length, with the variable defined as $L_k$. In this system, six connections are optimized, each with six degrees of freedom and four vertical support bars at the front and rear ends, i.e., $i=1,\dots ,6, j=1,\dots ,6, k=1,\dots ,4$.

(2) Due to the high accuracy of the CAE analysis of stiffness, the difference between the analysis results and the results of the simulated working conditions required by the company is very small. The purpose of this paper is also to design a stiffness test rig that is consistent with the results of the simulated working conditions of the actual stiffness required by the enterprise. Thus, the goal of the optimization of this system is to minimize the difference between the calculated stiffness values based on the monolithic structure (body-in-white with stiffness test bed) and the results of the calculated stiffness values of the body-in-white without the stiffness test bed frame, while satisfying various performance constraints. Thus, the mathematical model for optimization of the stiffness test rig based on the overall structure can be defined as follows:

$$\begin{array}{c}\min f(sp{c}_{ij},L_k)=f_a(sp{c}_{ij},L_k)-f_c\\ i=1,\cdots ,6 j=1,\cdots ,6 k=1,\cdots ,4\\ s.t. g_a(sp{c}_{ij},L_k)\le 0\\ i=1,\cdots ,6 j=1,\cdots ,6 k=1,\cdots ,6\\ L_k^l\le L_k\le L_k^u k=1,\cdots ,4\\ sp{c}_{i1}\in \{0,1\} i=1,\cdots ,6\\ sp{c}_{i2}\in \{0,2\} i=1,\cdots ,6\\ sp{c}_{i3}\in \{0,3\} i=1,\cdots ,6\\ sp{c}_{i4}\in \{0,4\} i=1,\cdots ,6\\ sp{c}_{i5}\in \{0,5\} i=1,\cdots ,6\\ sp{c}_{i6}\in \{0,6\} i=1,\cdots ,6\end{array}$$

where $f_a$ represents the calculated value of stiffness (torsional or bending) based on a monolithic structure (body-in-white plus stiffness test bed model); $f_c$ denotes the calculated value of the body-in-white stiffness without the stiffness test rig, which is constant when a body-in-white is selected; $L_k$ denotes the length of the vertical support bar at the front and rear ends; $L_k^l L_K^u$ denote the upper and lower limits of the length of the $k$th vertical support bar; and ${spc}_{ij}$ denotes the $j$th degree of freedom variable in the system at the $i$th connection position.

Stiffness test rigs are generally designed as left–right symmetric structures, and all six connection locations in Figure 1 constrain their translational degrees of freedom $i=1, 2, 3, j=4, 5, 6, k=1, 2$. Substituting the above conditions into the above equation yields the following:

$$\begin{array}{c}\min f(sp{c}_{ij},L_k)=f_a(sp{c}_{ij},L_k)-f_c\\ i=1,2,3 j=4,5,6 k=1,2\\ s.t. g_a(sp{c}_{ij},L_k)\le 0\\ i=1,2,3 j=4,5,6 k=1,2\\ L_k^l\le L_k\le L_k^u k=1,2\\ sp{c}_{i4}\in \{0,4\} i=1,2,3\\ sp{c}_{i5}\in \{0,5\} i=1,2,3\\ sp{c}_{i6}\in \{0,6\} i=1,2,3\end{array}$$

5. Hybrid and Adaptive Metamodeling Method (HAM)

The hybrid metamodel-based adaptive global optimization method (HAM) is a recently developed search technique that uses approximate models to address the black-box problem in computational settings. Its main steps are outlined as follows:

(a)

Generating initial points and constructing metamodels: In this paper, we use the Latin hyper-square sampling method to select eight initial points and calculate their function values to construct the three selected metamodel construction methods, which are Kriging [14,15], Radial Basis Functions [16], and second-order polynomial response surfaces [17]. See Figure 5.

(b)

A Latin hyper-square design was used to select 104 sample points, and 3 metamodels were used to calculate the function values separately.

(c)

Sorting these sample points according to the function values: The 104 sample points were arranged in ascending order according to the function values calculated in the previous step, and 100 points with smaller function values were selected and put into different groups according to the metamodels calculated, respectively, $A-\widehat{f}\left(x\right),B-\widehat{f}\left(x\right) \mathrm{a}\mathrm{n}\mathrm{d} C-\widehat{f}\left(x\right)$, depending on the metamodel calculated.

(d)

Grouping the points selected in the previous section: In this step, the “cheap points” obtained in the previous step were divided into seven parts according to the number of occurrences in the three groups A, B, and C.

$$\begin{array}{c}E=A\cap B\cap C,F=A\cap B,G=B\cap C\\ H=A\cap C,I=A-\left(E\cup F\right),\\ J=B-\left(E\cup G\right),K=C-\left(E\cup H\right)\end{array}$$

(e)

Calculating the weights given to each component: the sum of the weights is 1.

(f)

Selecting new “expensive” points: The number of new points is about seven. See Figure 6 for the process of selecting “expensive points”.

(g)

Repeating the iterations until the algorithm converges: we merged all the “expensive” ones, reconstructed the metamodel, and repeated (b)–(f) until the termination condition was met.

6. Optimization Processes

6.1. Optimization of Body-in-White Stiffness Test Rig

As shown in

Table 1. Number of iterations and sample points.

	Number of Sample Points	Number of Iterations
Torsional stiffness	17	4
Bending stiffness	14	3

, the optimal solution for the torsional stiffness test rig was obtained after 4 iterations and 17 calls to the finite element model using the adaptive global optimization method based on the hybrid element model. Similarly, the optimal solution for the bending stiffness test rig was achieved after 3 iterations and 14 calls to the finite element model.

The optimization results are shown in

Table 2. Optimization results.

	Torsional Stiffness		Bending Stiffness
	Initial Value	Optimized Value	Initial Value	Optimized Value
$sp{c}_{14}$	4	0	4	4
$sp{c}_{15}$	5	5	5	0
$sp{c}_{16}$	6	6	6	6
$sp{c}_{24}$	4	0	4	0
$sp{c}_{25}$	5	0	5	0
$sp{c}_{26}$	6	0	6	0
$sp{c}_{34}$	4	0	4	0
$sp{c}_{35}$	5	0	5	0
$sp{c}_{36}$	6	0	6	0
$L_1$	550	582	550	400
$L_2$	200	100	200	100
${\mathrm{w}}_b$	65.5	63.8
${\mathrm{w}}_t$			65.5	59.2
$f(sp{c}_{ij},L_k)$	372	7.1	477	23.6

. From Table 2, it can be seen that the optimal solution of the torsional stiffness test rig is achieved when ${spc}_{15}$ is taken to be 5, ${spc}_{16}$ is taken to be 6, the other variables of the degrees of freedom are taken to be 0, and $L_1=582 \mathrm{m}\mathrm{m}$ and $L_2=100 \mathrm{m}\mathrm{m}$ at the 1 connection position in Figure 2. In other words, when a rotating hinge (releasing the rotation only around the X-axis) is selected for the connection positions 1 and 4 in Figure 1, and the ball hinges are selected for positions 2, 3, 5, and 6, the calculated torsional stiffness based on the monolithic structure (body-in-white with stiffness test bed model) has the smallest difference in the results from the calculated torsional stiffness of the body-in-white without a bench.

Similarly, from Table 2, it can be seen that the difference between the calculated bending stiffness based on the monolithic structure (body-in-white plus stiffness test bed model) and the calculated bending stiffness of the body-in-white without a bench is minimized when rotating hinges (which let go of the rotation only around the Y-axis) are selected for the connection positions at 1 and 4 in Figure 1, and the ball hinges are selected for the positions at 2, 3, 5, and 6, and when $L_1=400 \mathrm{m}\mathrm{m}$ and $L_2=100 \mathrm{m}\mathrm{m}$.

During the optimization process, changes in the length of the vertical support rods at the front and rear ends of the stiffness test rig have little effect on the bending stiffness. However, the length of the vertical support rod at the front end of the stiffness test rig significantly influences the torsional stiffness. As shown in Figure 7, when the torsional stiffness of the body-in-white is analyzed without the stiffness test rig, the rotation centerline of the body-in-white is defined by the centers of the front and rear wheel covers. In this case, when the body-in-white twists, its rotation occurs around line a.

When analyzing the torsional stiffness of the overall structure with the stiffness test rig, the centerline of rotation for the body-in-white shifts to line b. In torsional stiffness analysis, variations in the length of the vertical support rod at the front end of the stiffness test rig result in different rotation centerlines for the body-in-white. Consequently, under the same applied loading force, the body-in-white experiences different rotational behaviors, leading to varying deformation patterns. This, in turn, causes the calculated torsional stiffness to differ. Thus, it is clear that the length of the vertical support rod at the front end of the stiffness test rig has a significant impact on the results of the torsional stiffness analysis.

6.2. Body-in-White Stiffness Test Bench Design Program

Generally, to reduce costs, the bending and torsional stiffness test rigs are designed on the same test platform, and different stiffness tests are achieved through specific conversion mechanisms.

Based on the optimization scheme in Section 6.1, the final structural design of the bending and torsional stiffness test rig is shown in Figure 8. Parts 2 and 4 are designed as ball hinges with uniform specifications, while part 3 is a swivel hinge. Part 1 functions as a conversion block. When part 1 is mounted in the position shown in Figure 8a, the entire test rig serves as a torsional stiffness test stand. When part 1 is rotated 90 degrees and mounted in its alternative position, the rig becomes a bending stiffness test stand.

7. Experimental Validations

The project culminated in the fabrication of a stiffness test rig based on the design specifications followed by the stiffness testing of a vehicle model. A sample of the upper ball hinge at the front and rear ends of the test rig is shown in Figure 9a, while a sample of the lower swivel hinge at the front and rear ends of the test rig is shown in Figure 9b.

This stiffness test rig was utilized in this project to conduct stiffness tests for a particular vehicle model, as shown in Figure 10.

Meanwhile, the results of the body-in-white stiffness analysis, the stiffness analysis based on the overall structure, and the experimental test results were compared, as shown in

Table 3. Comparison of results.

Objects	Torsional Stiffness N·m/deg	Bending Stiffness N/mm
Analysis of the body-in-white	16,159.5	19,600
Based on an overall structural (optimized) analysis	16,166.6	19,623.6
Body-in-white tests	16,338	20,265

. As indicated in the table, the torsional and bending stiffness test results from the experimental tests using this rig show minimal deviation from the actual body-in-white analysis values owing to the prior optimization of the overall structure-based stiffness test rig. The error between the body-in-white torsional stiffness test results and the torsional stiffness analysis results is 1.1%, while the error between the body-in-white bending stiffness test results and the bending stiffness analysis results is 3.4%. These findings demonstrate that the test accuracy of the stiffness test rig, designed according to the optimization, is relatively high.

8. Conclusions

This paper develops a mathematical model, performs numerical analysis, and, through optimization, completes the design optimization of the stiffness test rig for automotive body-in-white testing. The following conclusions can be drawn:

(1) An optimization mathematical model for the stiffness test rig based on the overall structure was established. This model treats the degrees of freedom of each connection component as variables and uses the difference between the stiffness calculation values of the overall structure and the body-in-white as the objective. The final error in the results is within 5%, demonstrating the accuracy of the optimized stiffness test rig.

(2) An adaptive global optimization method (HAM) based on the hybrid element model was employed to optimize the model, yielding improved results. By defining the degrees of freedom at each connection point of the stiffness test rig as discrete variables, the testing accuracy of the stiffness test rig was significantly enhanced.

(3) Based on the optimization results, the structure of the stiffness test rig was designed and fabricated. The test accuracy of the rig was validated through testing on a specific vehicle model.

This approach can be extended to the design optimization of whole-vehicle or subsystem test rigs, offering a new solution for the design optimization of test stands for entire vehicles or component systems.