Improved multi-objective particle swarm optimization algorithm based semi-active suspension control method

Abstract

The application belongs to the technical field of semi-active suspension control method, and relates to a semi-active suspension control method based on an improved multi-objective particle swarm optimization algorithm, which comprises self-adaptive grid division of an external archive of the MOPSO algorithm to determine a global optimum with the most diversity and a global optimum with the most convergence; evolution state of a population is judged according to a distribution entropy change quantity of all optimal solutions in the external archive, and a global optimum gBest for guiding evolution is selected; flight parameters of population evolution are adjusted according to a change quantity of local crowding distance of current population evolution to balance evolution trend of the population; the above two types of core mechanisms are fused, a multi-information fusion multi-objective particle swarm optimization algorithm is proposed, and the algorithm is used for determination of weight coefficients of a semi-active suspension LQR control strategy. The novel multi-objective optimization algorithm effectively realizes balance between convergence precision and population diversity by synergistically integrating external archive information and current population dynamic information.

Description

Technical Field

[0001] This invention belongs to the technical field of semi-active suspension control methods, specifically relating to a semi-active suspension control method based on an improved multi-objective particle swarm optimization algorithm. Background Technology

[0002] The suspension system plays a crucial role in automotive structure, effectively absorbing road impacts and reducing vibrations, directly affecting handling stability and ride comfort. Compared to traditional passive suspension, semi-active suspension offers better performance through adjustable damping; compared to active suspension, semi-active suspension has become a hot topic in suspension research due to its simpler design, higher robustness, and lower energy consumption. Among numerous semi-active suspension control strategies, the Linear Quadratic Regulator (LQR) control strategy stands out for its strong adaptability and excellent overall performance. Researchers have proposed many improved control strategies based on LQR, but the LQR weight coefficients of these improved strategies are often selected empirically rather than systematically, and the negative correlation between the various weight coefficients makes single-objective optimization difficult to handle this complex trade-off; that is, optimizing one objective often comes at the expense of other objectives. Therefore, multi-objective optimization becomes the optimal choice.

[0003] In multi-objective optimization algorithms, Multi-objective Particle Swarm Optimization (MOPSO) is widely used due to its fast convergence speed. However, algorithmic frameworks based on improved PSO algorithms have an inherent flaw: rapid loss of population diversity, leading to an imbalance between overall convergence and diversity. To alleviate these problems, researchers have proposed several enhanced MOPSO variants, such as Adaptive MOPSO, which balances high convergence accuracy and population diversity by using external archive entropy and particle spacing parameters; MOPSO_PA, which employs a dual-archive mechanism, using two independent external archives to guide convergence and diversity respectively; and ACE-MOPSO, which achieves performance balance by integrating evolutionary state data and utilizing the dominance and distribution information of external archives. Although these improved algorithms achieve a balance between convergence and diversity, they mainly focus on external archive optimization, neglecting the real-time state of the population, resulting in limited information utilization and insufficient responsiveness in complex dynamic problems.

[0004] Therefore, there is an urgent need to develop a semi-active suspension control method based on an improved multi-objective particle swarm optimization algorithm to effectively solve the above problems. Summary of the Invention

[0005] The purpose of this invention is to provide a semi-active suspension LQR control method based on an improved multi-objective particle swarm optimization algorithm. This method is based on a global optimal selection mechanism based on the change of external archive distribution entropy and an adaptive adjustment mechanism of flight parameters based on the local congestion distance of the current population. By fusing external archive and current population information, MIFMOPSO effectively balances particle convergence and population diversity, thereby solving the problems of limited information utilization and insufficient response capability in complex dynamic problems in existing methods.

[0006] This invention is achieved through the following technical solution:

[0007] A semi-active suspension control method based on an improved multi-objective particle swarm optimization algorithm includes the following steps:

[0008] A. Adaptively mesh the external archives of the MOPSO algorithm to determine the most diverse global optimum dgBest and the most convergent global optimum cgBest.

[0009] B. Based on the change in distribution entropy of all optimal solutions in the external archive, determine the evolutionary state of the population and select dgBest or cgBest as the global optimal gBest to guide the evolution.

[0010] C. Adjust the flight parameters of the population evolution based on the change in the local crowding distance of the current population evolution in order to balance the evolutionary trend of the population.

[0011] D. By combining the global optimal selection mechanism and the flight parameter adaptive adjustment mechanism, a multi-information fusion multi-objective particle swarm optimization algorithm MIFMOPSO, which can integrate external archive information and current population information, is obtained and used to determine the weight coefficients of the semi-active suspension LQR control strategy.

[0012] Further, step A specifically includes the following steps:

[0013] A1. A multi-objective optimization algorithm based on PSO is introduced into an external archive rep, which records all non-dominated optimal solutions of each generation of the population and forms a Pareto front. The global optimal gBesti,d(t) is transformed into the optimal solution randomly selected from the external archive rep.

[0014] A2. Adaptively divide the grid based on the fitness range of all non-dominated solutions in the rep, then subdivide it uniformly; select the sparsest grid based on the number of solutions in each cell. d And the densest grid c ;

[0015] A3, From Grid d Randomly select a particle as dgBest from Gridc We randomly select a particle as cgBest to represent the most diverse and most convergent non-dominated optimal solutions, respectively.

[0016] Furthermore, in step A1, the evolution rule for particle i in the PSO algorithm is:

[0017] (1)

[0018] (2)

[0019] In the formula, d = 1, 2, 3, ..., D represents the D-th dimension in the search space; v i,d (t) is the velocity vector at time t; x i,d (t) is the position vector at time t; c1 and c2 are inertial weights, c1 and c2 are learning factors, and r1 and r2 are random values ​​uniformly distributed in [0,1]; pBest i,d (t) and gBest i,d (t) are the d-th dimension variables of the individual optimal and global optimal at time t, respectively; the individual optimal is the optimal solution of the evolutionary history of particle i, and the global optimal is the optimal solution of the evolutionary history of all particles. Each time it is iterated, these two optimal solutions will undergo a dominance relationship judgment to achieve the update.

[0020] Furthermore, in step A3, the archive maintenance mechanism randomly removes a particle from Gridd to maintain the diversity of solutions. If the number exceeds m, this operation is repeated m times to maintain the number of solutions in rep.

[0021] Further, in step B, the distribution entropy of the optimal solution in rep is used to evaluate the evolutionary state of the population; dgBest or cgBest is adaptively selected as the current gBest to guide particle evolution.

[0022] Furthermore, step B specifically includes the following steps:

[0023] B1. Determine the evolutionary state of the population to decide whether to use dgBest or cgBest as gBest. Use distribution entropy to evaluate the evolutionary state, which is defined as follows:

[0024] (3)

[0025] In the formula, Gn represents the grid cells occupied by the non-dominated solution in rep, n=1,2,...,N; P(Gn) is the probability distribution function of Gn, defined as follows:

[0026] (4)

[0027] In the formula, Sum is the total number of non-dominated optimal solutions in rep; Sum(Gn) is the total number of non-dominated optimal solutions in Gn;

[0028] B2. The differential entropy method is used to analyze the evolutionary dynamics of a population by evaluating changes in entropy, thereby achieving more adaptive and sensitive state judgments. The calculation process for E(t) is as follows:

[0029] (5)

[0030] B3, Based on E(t) divides the evolutionary state into three categories: early iteration stage, middle iteration stage, and late iteration stage;

[0031] B4, based on Determining the evolutionary state using E(t) requires setting a threshold. Through repeated experiments, the intermediate stage in the iteration process was selected. The maximum value of E(t)| is used as the threshold. ;

[0032] When the population is in a convergent state, dgBest is selected as gBest; in a diverse state, cgBest is selected to accelerate population convergence; if it is in a stagnant state, dgBest and cgBest are selected with probabilities of 0.8 and 0.2 respectively, which maintains diversity and prevents too fast convergence.

[0033] The mathematical expression for the globally optimal selection mechanism is as follows:

[0034] (6).

[0035] Furthermore, in step B3, the early iteration phase, at this point, | E(t) is relatively large, indicating a convergent evolutionary state. Reasons for convergence include: a sudden increase in a large number of non-dominated solutions in the population; new solutions dominating old solutions, leading to the elimination of older solutions; breakthrough progress at the Pareto front or escaping a local optimum; and in the middle of the iteration, at this point, | When E(t) is relatively small, the evolutionary state is diverse. The reason for the diverse evolutionary state is that new solutions with sparser distribution replace old solutions, which enhances the diversity of non-dominated solutions. At the end of the iteration, | When E(t) approaches zero, the evolutionary state tends to stagnate.

[0036] Further, step C specifically includes the following steps:

[0037] C1. Define the local crowding distance. The Euclidean distance between particle a and particle b is defined as follows:

[0038] (7)

[0039] The local crowding distance of a particle is defined as the average of the Euclidean distances of its K nearest neighbors, which makes its spatial density more robust:

[0040] (8)

[0041] C2. Sum the LD values ​​of all particles at time t and compare them with the sum of the LD values ​​at time t-1 to obtain... LD(t), as shown below:

[0042] (9)

[0043] In the formula, nPop is the total number of particles in the population;

[0044] C3. The Sigmoid nonlinear adjustment function is used to adjust the flight parameters. The adaptive flight parameter adjustment mechanism is as follows:

[0045] (10)

[0046] In the formula, = , from time t It consists of c1 and c2; = ,Depend on The changes in c1 and c2 are composed of the increments;

[0047] During the iteration process The upper and lower bounds are set to [0, 0.9], and the upper and lower bounds of c1 and c2 are both [0.5, 2.5], with an initial value of 1.5; when the population is in a convergent state ( If LD(t) < 0, increase c1 and decrease c2 to enhance global exploitation capabilities; when the population is in a diverse state ( LD(t)>0), decrease Increase c1 and increase c2 to enhance local development capabilities.

[0048] Further, step D specifically includes the following steps:

[0049] D1. Based on the dynamic equations of the semi-active suspension system, the state-space equations of the semi-active suspension system are created. Then, using LQR control theory, the objective function for the performance of the semi-active suspension system is obtained as follows:

[0050] (11)

[0051] In the formula, J represents fitness. Vertical acceleration of the sprung mass (m / s²) 2);z sw =z s -z w , where z is the suspension dynamic travel (m). s and z w These represent the vertical displacement of the sprung mass and the vertical displacement of the unsprung mass, respectively; k w z qw =k w (z q -z w ), where z is the wheel dynamic load (N). q The road surface unevenness is the excitation; q1, q2 and q3 correspond to the control weight coefficients of vertical acceleration, suspension dynamic travel and wheel dynamic load, respectively.

[0052] D2. The objective function of the semi-active suspension system performance is used as the objective function for multi-objective optimization; q3=1 is set for optimization calculation, and q1 and q2 are the decision variables; the initial range of q1 and q2 is set to a wide interval [0.01, 10]. 9 The target variables are vertical acceleration and wheel dynamic load; the maximum absolute value of the suspension dynamic travel must be less than 0.03m; the road excitation uses standard Class B road surface; the vehicle speed is set to 20m / s; the population size is nPop=100, the maximum number of non-dominated solutions in the external archive is nrep=100, and the number of iterations is MaxIt=500; the specific expression is as follows:

[0053] (12)

[0054] D3. According to the design manual of the test vehicle, its sprung mass is 480kg. For the single-wheel semi-active suspension, the optimization conditions are divided into five intervals with a span of 10kg, ranging from 100kg to 140kg.

[0055] On Class B roads, the goal of suspension control is to balance ride comfort and handling stability. The optimization results are normalized, and the solution closest to the straight line y=x is taken as the optimal solution. The normalization formula is as follows:

[0056] (13)

[0057] The weight coefficients of the semi-active suspension LQR control strategy based on the improved multi-objective particle swarm optimization algorithm, namely the MIFMOPSO-LQR control strategy, were obtained for the test vehicle.

[0058] Furthermore, when normalizing the optimization results, the objective variable is constrained to [0,1].

[0059] Compared with the prior art, the beneficial effects of the present invention are:

[0060] 1. The novel multi-objective optimization algorithm proposed in this invention effectively achieves a balance between convergence accuracy and population diversity by collaboratively integrating external archive information and current population dynamics information;

[0061] 2. Based on the novel multi-objective optimization algorithm proposed in this invention, an LQR control strategy based on this algorithm is proposed to overcome the limitations of the traditional empirical method for determining LQR control weight coefficients. Attached Figure Description

[0062] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0063] Figure 1 Adaptive mesh generation for external archive rep;

[0064] Figure 2 Entropy and entropy change evolution curve;

[0065] Figure 3 Multi-objective optimization results of semi-active suspension LQR control;

[0066] Figure 4 Comparison of vertical acceleration, suspension dynamic travel and wheel dynamic load under a 120kg sprung mass;

[0067] Figure 5 The flowchart of the semi-active suspension control method based on the improved multi-objective particle swarm optimization algorithm of this invention is shown in the figure. Detailed Implementation

[0068] The present invention will be further described below with reference to embodiments:

[0069] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the present invention, and not all of the structures.

[0070] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this invention, terms such as "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0071] This invention proposes a Multi-Information Fusion Multi-Objective Particle Swarm Optimization (MIFMOPSO) algorithm. This method combines two core mechanisms: a gBest selection mechanism based on changes in the external archive distribution entropy and an adaptive flight parameter adjustment mechanism based on the local congestion distance of the current population. It synergistically integrates external archive information and current population dynamics information. Based on the multi-objective optimization algorithm, a MIFMOPSO-LQR control framework is developed to determine the control weight coefficients of the experimental vehicle. This algorithm, based on the MOPSO framework, fuses external archive and current population information, improving the convergence accuracy of the optimal solution while maintaining population diversity. This balances the algorithm's ability to explore local scenarios and perform global exploration. The algorithm is then applied to determine the weight coefficients of the LQR control strategy for semi-active suspension.

[0072] Specifically, such as Figure 5 As shown, the semi-active suspension control method of the present invention based on an improved multi-objective particle swarm optimization algorithm includes the following steps:

[0073] Step 1: Adaptively mesh the external archive of the MOPSO algorithm to determine the most diverse global optimum (dgBest) and the most convergent global optimum (cgBest).

[0074] Step 2: Based on the change in distribution entropy of all optimal solutions in the external archive, determine the evolutionary state of the population and select dgBest or cgBest as the global optimal gBest to guide the evolution.

[0075] Step 3: Adjust the flight parameters of the population evolution based on the change in the local crowding distance (LD) of the current population evolution to balance the evolutionary trend of the population.

[0076] Step 4: Integrating the two core mechanisms mentioned above, a multi-information fusion multi-objective particle swarm optimization algorithm is proposed and applied to determine the weight coefficients of the semi-active suspension LQR control strategy.

[0077] Step 1 specifically includes the following steps:

[0078] The evolution rule for particle i in the PSO algorithm is:

[0079] (1)

[0080] (2)

[0081] In the formula, d = 1, 2, 3, ..., D represents the D-th dimension in the search space; v i,d(t) is the velocity vector at time t; x i,d (t) is the position vector at time t; c1 and c2 are inertial weights, c1 and c2 are learning factors, and r1 and r2 are random values ​​uniformly distributed in [0,1]; pBest i,d (t) and gBest i,d (t) are the d-th dimension variables of the individual optimal and global optimal at time t, respectively; the individual optimal is the optimal solution of the evolutionary history of particle i, and the global optimal is the optimal solution of the evolutionary history of all particles. Each time it is iterated, these two optimal solutions will undergo a dominance relationship judgment to achieve the update.

[0082] In PSO, each particle is based on its pBest value. i,d (t) and gBest i,d (t), then multiplied by the inertia weight and the learning factor, to adjust v in subsequent iterations. i,d (t) and x i,d (t).

[0083] The MOPSO algorithm is a multi-objective optimization algorithm based on PSO. It introduces an external archive `rep` to record all non-dominated optimal solutions of each generation of the population and forms a Pareto front, with the global optimum `gBest`. i,d (t) becomes the optimal solution randomly selected from the external archive rep.

[0084] In this invention, the distribution entropy of the optimal solution in `rep` is used to evaluate the evolutionary state of the population. Based on this, the algorithm must adaptively select either `dgBest` or `cgBest` as the current `gBest` to guide particle evolution. The adaptive mesh partitioning of the external archive is as follows: Figure 1 As shown:

[0085] like Figure 1 As shown, the grid is adaptively divided based on the fitness range of all non-dominated solutions in the rep, and then uniformly subdivided: the sparsest grid is selected based on the number of solutions in each cell. d ) and the densest grid (Grid) c From Grid d Randomly select a particle as dgBest from Grid c A particle is randomly selected from the grid as cgBest to represent the most diverse and most convergent non-dominated optimal solution, respectively. Furthermore, to maintain the number of solutions in the rep, the archive maintenance mechanism will... d To maintain the diversity of solutions, a particle is randomly removed from the solution. If the number of particles exceeds m, this operation is repeated m times.

[0086] Step 2 specifically includes the following steps:

[0087] To balance the convergence and diversity of the MIFMOPSO algorithm, first, the evolutionary state of the population (such as convergence, diversity, or stagnation) is determined to decide whether to use dgBest or cgBest as gBest. In the present invention, the distribution entropy is used to evaluate the evolutionary state, and its definition is as follows:

[0088] (3)

[0089] In the formula, Gn is the grid cell occupied by the non-dominated solutions in rep, n = 1, 2,..., N; P(Gn) is the probability distribution function of Gn, and P(Gn) is defined as follows:

[0090] (4)

[0091] In the formula, Sum is the total number of non-dominated optimal solutions in rep; Sum(Gn) is the total number of non-dominated optimal solutions in Gn.

[0092] According to formulas (3) and (4), E(t) of the non-dominated solutions reflects the density and distribution uniformity of the solutions. Although E(t) can reflect the population diversity, it is difficult to set a robust threshold, so it is difficult to directly use its value for the evaluation of the evolutionary state. In addition, the increasing trend of E(t) also makes the threshold-based judgment more complex. To solve this problem, the present invention adopts the differential entropy method to analyze the evolutionary dynamics of the population by evaluating the change amount of entropy, so as to achieve a more adaptive and sensitive state judgment. The calculation process of E(t) is as follows:

[0093] (5)

[0094] E(t) of MIFMOPSO and The evolution trend of E(t), as Figure 2 shown. In the figure, Iterations is the number of iterations, abbreviated as It. According to E(t), the evolutionary state is divided into three categories.

[0095] The first category is the early iteration stage (about It < 80). At this time, | E(t)| is relatively large, and the evolutionary state is convergence. The reasons for convergence include: a large number of non-dominated solutions are suddenly added to the population; the new solutions dominate the old solutions, resulting in the elimination of the old solutions; a breakthrough is made on the Pareto front or a local optimum is jumped out.

[0096] The second category is the middle iteration stage (about 80 < It < 260). At this time, | When E(t) is relatively small, the evolutionary state is diverse. The reason for the diverse evolutionary state is that new solutions with a sparser distribution replace old solutions, which enhances the diversity of non-dominated solutions.

[0097] The third stage is the end of the iteration (approximately It>260), at which point, | When E(t) approaches zero, the evolutionary state tends to stagnate.

[0098] based on Determining the evolutionary state using E(t) requires setting a threshold. Through repeated experiments, the intermediate stage in the iteration process was selected. The maximum value of E(t)| is used as the threshold. .

[0099] When the population is in a convergent state, dgBest is chosen as gBest to avoid getting trapped in local optima and to enhance diversity; in a diverse state, cgBest is chosen to accelerate population convergence; if it is in a stagnant state, dgBest and cgBest are chosen with probabilities of 0.8 and 0.2 respectively, to maintain diversity and prevent too fast convergence.

[0100] The mathematical expression for the globally optimal selection mechanism is as follows:

[0101] (6)

[0102] Step 3 specifically includes the following steps:

[0103] Besides the global optimal selection mechanism, adaptive adjustment of flight parameters is also crucial for balancing convergence and diversity. Research shows that a larger learning factor c1 and a smaller c2 result in better global exploration performance; conversely, a smaller c1 and a larger c2 result in better local exploitation performance. To balance global and local exploitation, this invention proposes an adaptive flight parameter adjustment mechanism based on the local crowding distance of the current population. Before introducing this mechanism, the local crowding distance must first be defined. The Euclidean distance between particle a and particle b is defined as:

[0104] (7)

[0105] To avoid the influence of extreme particles, the local crowding distance of a particle is defined as the average of the Euclidean distances of its K nearest neighbors, which makes its spatial density more robust.

[0106] (8)

[0107] Subsequently, the LD values ​​of all particles at time t are summed and compared with the sum of the LD values ​​at time t-1 to obtain... LD(t), as shown below:

[0108] (9)

[0109] In the formula, nPop is the total number of particles in the population.

[0110] Due to the significant nonlinear characteristics of particle swarm evolution, this invention employs a Sigmoid nonlinear adjustment function to regulate flight parameters. The adaptive flight parameter adjustment mechanism is as follows:

[0111] (10)

[0112] In the formula = , from time t It consists of c1 and c2; = ,Depend on The changes in c1 and c2 are composed of increments.

[0113] As shown in formula (10), during the iteration process, The upper and lower bounds are set to [0, 0.9], and the upper and lower bounds of c1 and c2 are both [0.5, 2.5], with an initial value of 1.5. When the population is in a convergent state ( If LD(t) < 0, increase c1 and decrease c2 to enhance global exploitation capabilities; when the population is in a diverse state ( LD(t)>0), decrease Increase c1 and increase c2 to enhance local development capabilities.

[0114] Step 4 specifically includes the following steps:

[0115] Combining the aforementioned global optimal selection mechanism and flight parameter adaptive adjustment mechanism yields the MIFMOPSO multi-information fusion multi-objective particle swarm optimization algorithm, which integrates external archive information and current population information. This algorithm effectively balances particle convergence and population diversity. Applying MIFMOPSO to determine the LQR weight coefficients leads to the MIFMOPSO-LQR control strategy for a semi-active suspension system.

[0116] Based on the dynamic equations of the semi-active suspension system, the state-space equations of the semi-active suspension system are created. Then, using LQR control theory, the objective function for the performance of the semi-active suspension system is obtained as follows:

[0117] (11)

[0118] In the formula, J represents fitness. Vertical acceleration of the sprung mass (m / s²) 2 );z sw =zs -z w , where z is the suspension dynamic travel (m). s and z w These represent the vertical displacement of the sprung mass and the vertical displacement of the unsprung mass, respectively; k w z qw =k w (z q -z w ), where z is the wheel dynamic load (N). q The road surface unevenness is the excitation factor. q1, q2, and q3 correspond to the control weighting coefficients for vertical acceleration, suspension dynamic travel, and wheel dynamic load, respectively.

[0119] The objective function of the semi-active suspension system performance is used as the objective function for multi-objective optimization. Considering the relative nature of the optimization of weight coefficients q1, q2, and q3, q3 is set to 1 for optimization calculation, and q1 and q2 are the decision variables. To fully explore the decision space, avoid missing the global optimal solution, and compensate for the constraint on parameter balance caused by the fixed value of q3, the initial range of q1 and q2 is set to a wide interval [0.01, 10]. 9 The target variables are vertical acceleration and wheel dynamic load. Based on the actual test results of the test vehicle, to prevent collision between the suspension and the limiting block, the maximum absolute value of the suspension dynamic travel must be less than 0.03m. The road surface excitation uses a standard Class B road surface. The vehicle speed is set to 20m / s. The population size is nPop=100, the maximum number of non-dominated solutions in the external archive is nrep=100, and the number of iterations is MaxIt=500. The specific expression is as follows:

[0120] (12)

[0121] According to the design manual of the test vehicle, its sprung mass is 480 kg. Therefore, for the single-wheel semi-active suspension, the optimization conditions were divided into five intervals spanning 10 kg, ranging from 100 kg to 140 kg. The optimization results under each condition are as follows: Figure 3 As shown. On Class B roads, the goal of suspension control is to balance ride comfort and handling stability. Therefore, to select the optimal coefficients, the optimization results need to be normalized (the objective variable is constrained to [0,1]), and the solution closest to the straight line y=x is taken as the optimal solution. The normalization formula is as follows:

[0122] (13)

[0123] Therefore, the weight coefficients of the semi-active suspension LQR control strategy based on the improved multi-objective particle swarm optimization algorithm for the test vehicle, namely the MIFMOPSO-LQR control strategy, are obtained. The optimized values ​​of the LQR control weight coefficients are shown in Table 1.

[0124] Table 1

[0125]

[0126] This invention compares the semi-active suspension MIFMOPSO-LQR control with the semi-active suspension LQR control, passive suspension, and semi-active suspension fuzzy PID control.

[0127] Simulation settings: The nPop, nrep, and MaxIt parameters for all algorithms remain consistent with those described above; the road surface excitation is a standard Class B road surface; vehicle speed = 20 m / s, sampling time dt = 0.01 s. The program is written and run based on MATLAB R2023a.

[0128] Performance metrics: Three key metrics are used: vertical acceleration, suspension travel, and wheel dynamic load. Lower vertical acceleration results in less vibration felt by occupants and better ride smoothness. Lower wheel dynamic load leads to higher tire-road contact stability and better handling stability. Lower suspension travel avoids excessive suspension deformation and the risk of bottom-impact collisions, improving suspension safety and stability.

[0129] Time-domain comparison results of MIFMOPSO-LQR, LQR, passive suspension, and fuzzy PID when the sprung mass is 120kg, as follows: Figure 4 As shown in the figure, under a sprung mass of 120 kg, the semi-active suspension MIFMOPSO-LQR control outperforms traditional LQR control, passive suspension, and fuzzy PID control in terms of vertical acceleration, suspension travel, and wheel dynamic load. This advantage also holds true under other sprung mass conditions; therefore, the image results for other sprung masses will not be repeated in this invention.

[0130] Tables 2 to 4 present and compare the root mean square (RMS) values ​​of the three indicators in the time domain. Specifically, vertical acceleration (RMS) is shown in Table 2, suspension travel (RMS) in Table 3, and wheel dynamic load (RMS) in Table 4. The data shows that the MIFMOPSO-LQR controller achieves improvements in all indicators: compared to traditional LQR control, the RMS values ​​of vertical acceleration, suspension travel, and wheel dynamic load are reduced by an average of 6.26%, 8.78%, and 3.99%, respectively; compared to passive suspension, the reductions are more significant, reaching 22.95%, 32.81%, and 24.77%, respectively; and compared to fuzzy PID control, the reductions are 5.80%, 10.50%, and 22.28%, respectively. These results indicate that the semi-active suspension MIFMOPSO-LQR controller can effectively improve vehicle ride comfort and handling stability, demonstrating good performance in practical applications.

[0131] Table 2

[0132]

[0133] Table 3

[0134]

[0135] Table 4

[0136]

[0137] Note that the design of the digital prototype model, the parameter settings for each material, and the selection of the measuring plane described above are merely preferred embodiments and technical principles of the present invention. Those skilled in the art will understand that the present invention is not limited to the specific embodiments described herein, and various obvious changes, readjustments, and substitutions can be made without departing from the scope of protection of the present invention. Therefore, although the present invention has been described in detail through the above embodiments, the present invention is not limited to the above embodiments, and may include many other equivalent embodiments without departing from the concept of the present invention, the scope of which is determined by the scope of the appended claims.

Claims

1. A semi-active suspension control method based on an improved multi-objective particle swarm optimization algorithm, characterized in that, Includes the following steps: A. Adaptively mesh the external archives of the MOPSO algorithm to determine the most diverse global optimum dgBest and the most convergent global optimum cgBest. A1. A multi-objective optimization algorithm based on PSO is introduced into an external archive rep, which records all non-dominated optimal solutions of each generation of the population and forms a Pareto front. The global optimal gBesti,d(t) is transformed into the optimal solution randomly selected from the external archive rep. A2. Adaptively divide the grid based on the fitness range of all non-dominated solutions in the rep, then subdivide it uniformly; select the sparsest grid based on the number of solutions in each cell. d And the densest grid c ; A3, From Grid d Randomly select a particle as dgBest from Grid c A particle is randomly selected as cgBest to represent the most diverse and most convergent non-dominated optimal solutions, respectively. B. Based on the change in distribution entropy of all optimal solutions in the external archive, determine the evolutionary state of the population and select dgBest or cgBest as the global optimal gBest to guide the evolution. C. Adjust the flight parameters of the population evolution based on the change in the local crowding distance of the current population evolution in order to balance the evolutionary trend of the population. C1. Define the local crowding distance. The Euclidean distance between particle a and particle b is defined as follows: The local crowding distance of a particle is defined as the average of the Euclidean distances of its K nearest neighbors, which makes its spatial density more robust: C2. Sum the LD values ​​of all particles at time t and compare them with the sum of the LD values ​​at time t-1 to obtain ΔLD(t), as shown below: In the formula, nPop is the total number of particles in the population; C3. The Sigmoid nonlinear adjustment function is used to adjust the flight parameters. The adaptive flight parameter adjustment mechanism is as follows: In the formula, λ(t)=[ω(t),c1(t),c2(t)] T It consists of ω, c1, and c2 at time t; δ λ =[δ ω ,δc1,-δc2] T It consists of the increments of ω, c1, and c2; During the iteration process, the upper and lower limits of ω are set to [0, 0.9], and the upper and lower limits of c1 and c2 are both [0.5, 2.5], with 1.5 as the initial value. When the population is in a convergent state (ΔLD(t) < 0), ω and c1 are increased and c2 is decreased to enhance the global exploitation capability. When the population is in a diverse state (ΔLD(t) > 0), ω and c1 are decreased and c2 is increased to enhance the local exploitation capability. D. By combining the global optimal selection mechanism and the flight parameter adaptive adjustment mechanism, a multi-information fusion multi-objective particle swarm optimization algorithm MIFMOPSO, which can integrate external archive information and current population information, is obtained and used to determine the weight coefficients of the semi-active suspension LQR control strategy.

2. The semi-active suspension control method based on an improved multi-objective particle swarm optimization algorithm according to claim 1, characterized in that, Step A1, the evolution rule for particle i in the PSO algorithm is: x i,d (t+1)=x i,d (t)+v i,d (t+1) (2) In the formula, d = 1, 2, 3, ..., D represents the D-th dimension in the search space; v i,d (t) is the velocity vector at time t; x i,d (t) represents the position vector at time t; ω is the inertia weight, c1 and c2 are learning factors, and r1 and r2 are random values ​​uniformly distributed in [0,1]; pBest i,d (t) and gBest i,d (t) are the d-th dimension variables of the individual optimal and global optimal at time t, respectively; the individual optimal is the optimal solution of the evolutionary history of particle i, and the global optimal is the optimal solution of the evolutionary history of all particles. Each time it is iterated, these two optimal solutions will undergo a dominance relationship judgment to achieve the update.

3. The semi-active suspension control method based on an improved multi-objective particle swarm optimization algorithm according to claim 1, characterized in that: Step A3: The archive maintenance mechanism randomly removes a particle from Gridd to maintain the diversity of solutions. If the number exceeds m, this operation is repeated m times to maintain the number of solutions in rep.

4. The semi-active suspension control method based on an improved multi-objective particle swarm optimization algorithm according to claim 1, characterized in that: Step B involves using the distribution entropy of the optimal solution in rep to assess the evolutionary state of the population; and adaptively selecting dgBest or cgBest as the current gBest to guide particle evolution.

5. The semi-active suspension control method based on an improved multi-objective particle swarm optimization algorithm according to claim 4, characterized in that, Step B specifically includes the following steps: B1. Determine the evolutionary state of the population to decide whether to use dgBest or cgBest as gBest. Use distribution entropy to evaluate the evolutionary state, which is defined as follows: In the formula, Gn represents the grid cells occupied by the non-dominated solution in rep, n = 1, 2, ..., N; P(Gn) is the probability distribution function of Gn, defined as follows: In the formula, Sum is the total number of non-dominated optimal solutions in rep; Sum(Gn) is the total number of non-dominated optimal solutions in Gn; B2. The differential entropy method is used to analyze the evolutionary dynamics of a population by evaluating the change in entropy, thereby achieving more adaptive and sensitive state judgment. The calculation process of ΔE(t) is as follows: ΔE(t)=E(t)-E(t-1) (5) B3. Based on ΔE(t), the evolutionary state is divided into three categories: early iteration stage, middle iteration stage, and late iteration stage; B4. To determine the evolutionary state based on ΔE(t), a threshold needs to be set. After repeated experiments, the maximum value of |ΔE(t)| in the intermediate stage of the iteration process was selected as the threshold. When the population is in a convergent state, dgBest is selected as gBest; in a diverse state, cgBest is selected to accelerate population convergence; if it is in a stagnant state, dgBest and cgBest are selected with probabilities of 0.8 and 0.2 respectively, which maintains diversity and prevents too fast convergence. The mathematical expression for the globally optimal selection mechanism is as follows:

6. The semi-active suspension control method based on an improved multi-objective particle swarm optimization algorithm according to claim 5, characterized in that: Step B3, early iteration stage: At this time, |ΔE(t)| is relatively large, and the evolutionary state is convergent. The reasons for convergence include: a sudden increase in a large number of non-dominated solutions in the population; new solutions dominating old solutions, leading to the elimination of old solutions; breakthrough progress at the Pareto front or escaping local optima. In the middle of the iteration, |ΔE(t)| is relatively small, and the evolutionary state is diverse. The reason for the diverse evolutionary state is: new solutions with a sparser distribution replace old solutions, enhancing the diversity of non-dominated solutions. In the end of the iteration, |ΔE(t)| approaches zero, and the evolutionary state tends to stagnate.

7. The semi-active suspension control method based on an improved multi-objective particle swarm optimization algorithm according to claim 1, characterized in that, Step D specifically includes the following steps: D1. Based on the dynamic equations of the semi-active suspension system, the state-space equations of the semi-active suspension system are created. Then, using LQR control theory, the objective function for the performance of the semi-active suspension system is obtained as follows: In the formula, J represents fitness. Vertical acceleration of the sprung mass (m / s²) 2 );z sw =z s -z w , where z is the suspension dynamic travel (m). s and z w These represent the vertical displacement of the sprung mass and the vertical displacement of the unsprung mass, respectively; k w z qw =k w (z q -z w ), where z is the wheel dynamic load (N). q The road surface unevenness is the excitation; q1, q2 and q3 correspond to the control weight coefficients of vertical acceleration, suspension dynamic travel and wheel dynamic load, respectively. D2. The objective function of the semi-active suspension system performance is used as the objective function for multi-objective optimization; q3 = 1 is set for optimization calculation, and q1 and q2 are the decision variables; the initial range of q1 and q2 is set to a wide interval [0.01, 10]. 9 The target variables are vertical acceleration and wheel dynamic load; the maximum absolute value of the suspension dynamic travel must be less than 0.03m; the road excitation uses standard Class B road surface; the vehicle speed is set to 20m / s; the population size nPop = 100, the maximum number of non-dominated solutions in the external archive nrep = 100, and the number of iterations MaxIt = 500; the specific expression is as follows: D3. According to the design manual of the test vehicle, its sprung mass is 480kg. For the single-wheel semi-active suspension, the optimization conditions are divided into five intervals with a span of 10kg, ranging from 100kg to 140kg. On Class B roads, the goal of suspension control is to balance ride comfort and handling stability. The optimization results are normalized, and the solution closest to the straight line y = x is taken as the optimal solution. The normalization formula is as follows: The weight coefficients of the semi-active suspension LQR control strategy based on the improved multi-objective particle swarm optimization algorithm, namely the MIFMOPSO-LQR control strategy, were obtained for the test vehicle.

8. A semi-active suspension control method based on an improved multi-objective particle swarm optimization algorithm according to claim 7, characterized in that, When normalizing the optimization results, the objective variable is constrained to [0,1].

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