A multi-objective optimization and road grade identification method for a light car with an inerter negative stiffness suspension

Abstract

The application discloses a light car multi-objective optimization and road grade identification method containing an inertia suspension negative stiffness suspension, and belongs to the technical field of vehicle suspension damping and road sensing. The method is aimed at the structural characteristics and damping requirements of the light car, and inertia suspension negative stiffness mechanisms are arranged between the sprung mass and the unsprung mass. By establishing a vehicle system dynamics model with the suspension and solving the motion equation, the analytical function of the body acceleration, suspension stroke and tire dynamic load is used as the optimization target, and the NSGA-II multi-objective algorithm is used to realize the optimal matching of the suspension parameters. On this basis, combined with the optimized suspension parameters and the vehicle vibration response, the NARX neural network is used to realize the accurate identification of the road grade. The application provides a systematic solution for passive suspension damping design and road sensing, and lays a foundation for subsequent active suspension technology upgrading, and can significantly improve the driving smoothness, safety and steering stability of the vehicle.

Description

Technical Field

[0001] This invention relates to the fields of vehicle system parameter optimization and road surface level identification, and in particular to a multi-objective optimization and road surface level identification method for a light passenger car with an inertial compressive negative stiffness suspension, which combines the strong generalization characteristics of the NARX neural network for road surface level identification. Background Technology

[0002] As the core of vehicle dynamics control, the suspension system's mechanical structure directly determines the physical boundaries of overall vehicle performance. Even in active / semi-active control technologies, the dynamic characteristics of the passive suspension remain the theoretical foundation for system functionality. To further overcome the bottlenecks of traditional passive suspensions, the introduction of inertial capacity and negative stiffness elements has become an important innovative direction in current passive suspension design. However, in practical engineering applications, the topology of inertial capacity-negative stiffness damping suspensions exhibits significant diversity, including complex series and parallel combinations between negative stiffness elements, inertial capacity elements, and other components in the system. This high degree of structural variability poses a severe computational challenge to existing parametric design methods. Currently, the optimization design of such complex suspensions relies excessively on numerical optimization, which is not only computationally inefficient but also fails to intuitively reveal the physical relationships between system parameters. Especially when multi-objective collaborative optimization is required, considering vehicle acceleration, suspension travel, and tire dynamic load, the limitations of numerical methods become increasingly apparent, leading to a cumbersome and slow optimization process for selecting optimal parameters, failing to meet the demands of modern vehicle design for efficient and precise matching. Meanwhile, utilizing vehicle dynamic response signals to identify road surface unevenness and its corresponding road grade is a core approach to achieving intelligent chassis control and environmental perception. In the field of road surface recognition technology, traditional direct measurement and non-contact measurement methods are limited by equipment cost, detection efficiency, and real-time performance, making it difficult to meet the rapid monitoring needs of large-scale road networks. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of existing passive suspension systems, such as limited performance improvement, high cost of road perception, and poor real-time performance, and to provide a multi-objective optimization and road level identification method for light passenger cars with inertial-capacity-negative stiffness suspension. This method first constructs a novel suspension topology with specific coupling of inertial-capacity-negative stiffness elements and establishes a dynamic model; by deriving analytical expressions for key evaluation indicators (vehicle acceleration, suspension travel, and tire dynamic load), complex numerical integration is transformed into algebraic operations, aiming to significantly improve the efficiency of multi-objective optimization; furthermore, using the optimized suspension system as the basis for feature extraction, nonlinear inversion identification of road level is achieved through vehicle dynamic response signals.

[0004] This invention provides a multi-objective optimization and road surface grade identification method for a light-duty passenger car with an inertial-capacitance negative stiffness suspension. The method is characterized by being based on an inertial-capacitance negative stiffness suspension, which includes a first damping structure and a second damping structure connected in parallel between the sprung mass and the unsprung mass. The first damping structure includes a static stiffness element, and the second damping structure includes a first branch and a second branch connected in series. The first branch includes a negative stiffness element and a damping element connected in parallel, and the second branch includes an inertial-capacitance element and a positive stiffness element connected in parallel. The method includes: During the car's operation, the endpoint displacement of the sprung mass, the node displacement between the first and second branches, and the endpoint displacement of the unsprung mass are acquired in real time. Combined with the pre-determined sprung mass, unsprung mass, tire stiffness coefficient, static stiffness coefficient, negative stiffness coefficient, damping coefficient, inertial capacitance coefficient, and positive stiffness coefficient, a dynamic equation is constructed. The transfer function of the car under road surface unevenness excitation is determined based on the aforementioned dynamic equation; The evaluation index is calculated based on the time power spectral density of road surface roughness and the transfer function. The evaluation index is used as the optimization target, and the positive stiffness ratio, negative stiffness ratio and damping ratio are used as variables for parameter optimization. The positive stiffness ratio is the ratio of the positive stiffness coefficient to the static stiffness coefficient, the negative stiffness ratio is the ratio of the negative stiffness coefficient to the static stiffness coefficient, and the damping ratio is determined based on the damping coefficient, the sprung mass and the natural frequency of the sprung mass. The inertial-compass negative stiffness suspension is optimized based on the optimal variables obtained through optimization. The dynamic response data of the optimized inertial-compass negative stiffness suspension is obtained when the car is driving. The dynamic response data is then input into a pre-built recognition model to predict the road surface grade.

[0005] Optionally, the transfer function includes the vehicle body acceleration transfer function, the suspension travel transfer function, and the tire dynamic load transfer function; the evaluation index includes the normalized mean square value of vehicle body acceleration, the normalized mean square value of suspension travel, and the normalized mean square value of tire dynamic load. The normalized mean square value of vehicle acceleration is determined based on the time power spectral density of road surface roughness and the vehicle acceleration transfer function. The normalized mean square value of suspension travel is determined based on the time power spectral density of road surface roughness and the suspension travel transfer function; The normalized tire dynamic loads are all determined based on the time power spectral density of road surface unevenness and the tire dynamic load transfer function.

[0006] Optionally, parameter optimization can be performed using evaluation indicators as optimization targets and positive stiffness ratio, negative stiffness ratio, and damping ratio as variables, including: By using a generalized multi-objective optimization algorithm to perform a frontier search for solutions in the global continuous variable space, a dynamic characteristic solution set space consisting of multiple sets of discrete parameter points with well-defined physical boundaries is obtained. Extract the global physical extremum boundaries of each optimization objective in the solution set space of this dynamic feature to construct a unified decision domain; Within the regularized decision domain, an ideal sequence consisting of the ideal values ​​of each optimization objective is defined, while each discrete parameter point is defined as the actual response sequence. By traversing the entire dynamic characteristic solution set space, the absolute deviation distance between each actual response sequence and the ideal sequence is calculated, and a global deviation matrix is ​​constructed. The similarity of the actual response sequence across each optimization objective dimension is calculated based on the maximum and minimum absolute distances in the global bias matrix. Multi-objective comprehensive stationarity evaluation is performed based on the similarity of the actual response sequences across various optimization objective dimensions to determine the optimal point of global features. The adaptive weight coefficients are determined based on the similarity of the global feature optimum across various optimization objective dimensions. The adaptive weight coefficients are then used to reconstruct multiple evaluation indicators into a single objective evaluation function. For a single-objective evaluation function, a standard genetic algorithm is used to perform a minimization search in the continuous space of all variables to obtain the optimal results for each variable.

[0007] Optionally, extracting the global physical extremum boundaries of each optimization objective in the solution space of this dynamic feature set to construct a unified decision domain includes: For the dynamic index of minimization optimization, a nonlinear inverse deviation mapping operator is used to normalize and reduce the original scale data, as expressed in: ; ; ; In the formula, , , These represent the real-time calculated values ​​of tire dynamic load, vehicle acceleration, and suspension travel corresponding to the i-th leading edge, respectively. and These represent the global maximum and minimum boundaries of the tire dynamic load within the entire dynamic characteristic solution space, respectively. and These represent the global maximum and minimum boundaries of the vehicle acceleration within the entire dynamic feature solution space; and These represent the global maximum and minimum boundaries of the suspension travel within the entire dynamic characteristic solution space, respectively.

[0008] Optionally, the absolute deviation distance between each actual response sequence and the ideal sequence is calculated as follows: ; in, This represents the absolute deviation distance of the i-th actual response sequence on the j-th optimization objective. Let the j-th optimization objective be the ideal value. This represents the actual response value of the i-th actual response sequence to the j-th optimization objective; The similarity of the actual response sequence across each optimization objective dimension is calculated based on the maximum and minimum absolute distances in the global bias matrix, and is represented as follows: ; in, This represents the similarity of the i-th actual response sequence on the j-th optimization objective dimension. and These represent the maximum and minimum absolute distances in the global deviation matrix, respectively. Multi-objective comprehensive stationarity evaluation is performed based on the similarity of the actual response sequences across various optimization objective dimensions to determine the global feature optimum, including: The optimal point of the global features is determined based on the actual response sequence with the highest mean similarity across multiple optimization objective dimensions.

[0009] Optionally, the adaptive weight coefficients are determined based on the similarity of the global feature optimum across each optimization objective dimension, expressed as follows: ; in, , and These represent the weighting coefficients for the tire dynamic load dimension, the vehicle body acceleration dimension, and the suspension travel dimension, respectively. , and These represent the similarity of the global feature optimum in the dimensions of tire dynamic load, vehicle acceleration, and suspension travel, respectively. Optionally, multiple evaluation indicators can be reconstructed into a single-objective comprehensive evaluation function using adaptive weighting coefficients, as follows: ; in, This represents a single-objective comprehensive evaluation function. , and These represent the calculated values ​​for tire dynamic load, vehicle body acceleration, and suspension travel, respectively.

[0010] Optionally, the dynamic response data includes: wheel acceleration. acceleration at nodes Deformation of negative stiffness elements Suspension travel And wheel displacement z3; where z1 represents the end displacement of the sprung mass, z2 represents the node displacement between the first branch and the second branch, and z3 represents the end displacement of the unsprung mass.

[0011] Optionally, the recognition model is constructed based on the NARX neural network.

[0012] Secondly, the present invention provides a multi-objective optimization and road surface level identification system for a light-duty passenger car with an inertial-compassionate negative stiffness suspension, comprising: The acquisition module is used to acquire, in real time, the endpoint displacement of the sprung mass, the node displacement between the first branch and the second branch, and the endpoint displacement of the unsprung mass during the car's operation. It then constructs a dynamic equation by combining these with pre-determined sprung mass, unsprung mass, tire stiffness coefficient, static stiffness coefficient, negative stiffness coefficient, damping coefficient, inertial capacitance coefficient, and positive stiffness coefficient. The car's inertial capacitance negative stiffness suspension includes a first damping structure and a second damping structure connected in parallel between the sprung mass and the unsprung mass. The first damping structure includes a static stiffness element, and the second damping structure includes a first branch and a second branch connected in series. The first branch includes a negative stiffness element and a damping element connected in parallel, and the second branch includes an inertial capacitance element and a positive stiffness element connected in parallel. The determination module is used to determine the transfer function of the car under road surface unevenness excitation based on the dynamic equation; The calculation module is used to calculate the evaluation index based on the time power spectral density of road surface roughness and the transfer function; The optimization module is used to optimize parameters with evaluation indicators as the optimization target and positive stiffness ratio, negative stiffness ratio and damping ratio as variables; the positive stiffness ratio is the ratio of positive stiffness coefficient to static stiffness coefficient, the negative stiffness ratio is the ratio of negative stiffness coefficient to static stiffness coefficient, and the damping ratio is determined based on damping coefficient, sprung mass and sprung mass natural frequency. The road surface grade identification module is used to optimize the inertial-compass negative stiffness suspension based on the optimal variables obtained through optimization, obtain the dynamic response data of the optimized inertial-compass negative stiffness suspension when the car is driving, and input the dynamic response data into the pre-built identification model to predict the road surface grade.

[0013] Compared with the prior art, the present invention has the following beneficial effects:

[0014] This invention discloses a multi-objective optimization and road surface grade identification method for a light-duty passenger car with an inertial-capacitance negative stiffness suspension. The inertial-capacitance negative stiffness suspension includes a first damping structure and a second damping structure connected in parallel between the sprung mass and the unsprung mass. The first damping structure includes a static stiffness element, and the second damping structure includes a first branch and a second branch connected in series. The first branch includes a negative stiffness element and a damping element connected in parallel, and the second branch includes an inertial-capacitance element and a positive stiffness element connected in parallel. Compared to traditional passive suspensions, the inertial-capacitance negative stiffness suspension structure proposed in this invention can effectively broaden the vibration isolation frequency band and significantly reduce the peak resonance of the vehicle body without sacrificing handling stability, thus breaking through the inherent physical limits of traditional suspension performance design.

[0015] Since differences in suspension topology directly lead to changes in system dynamics, their multi-objective cooperative optimal solution space is completely different. This invention targets a suspension with inertial capacity and negative stiffness. During vehicle operation, it acquires in real-time the endpoint displacements of the sprung mass, the node displacements between the first and second branches, and the endpoint displacements of the unsprung mass. A dynamic equation is constructed by combining these with pre-determined parameters: sprung mass, unsprung mass, tire stiffness coefficient, static stiffness coefficient, negative stiffness coefficient, damping coefficient, inertial capacity coefficient, and positive stiffness coefficient. The transfer function of the vehicle under road surface roughness excitation is determined based on this dynamic equation. Evaluation indices are calculated based on the time power spectral density of the road surface roughness and the transfer function. Parameter optimization is performed using the evaluation indices as the optimization objective, with positive stiffness ratio, negative stiffness ratio, and damping ratio as variables. The positive stiffness ratio is the ratio of the positive stiffness coefficient to the static stiffness coefficient, the negative stiffness ratio is the ratio of the negative stiffness coefficient to the static stiffness coefficient, and the damping ratio is determined based on the damping coefficient, sprung mass, and the natural frequency of the sprung mass. This invention derives analytical expressions for key performance evaluation indices of vehicle response, transforming complex dynamic integrals into algebraic operations, and uses these as the objective function of the optimization algorithm. This method avoids the high computational cost of large-scale numerical simulation, greatly improves the convergence speed and matching accuracy of multi-objective collaborative optimization, and provides a theoretical tool for the rapid optimization of suspension parameters.

[0016] This invention optimizes a negative stiffness suspension based on optimal variables obtained through optimization, acquires dynamic response data of the optimized suspension during vehicle operation, and inputs this dynamic response data into a pre-built identification model to predict road surface grade. This invention deeply couples the optimized vehicle dynamic response with road surface excitation, constructing a high-precision nonlinear mapping model. This method eliminates the need for expensive additional road surface measurement sensors, achieving real-time inversion and accurate identification of road surface grade using only vibration data from the suspension and vehicle body. Attached Figure Description

[0017] Figure 1A dynamic model of a suspension system with inertial capacitance and negative stiffness damping;

[0018] Figure 2 A simulation model of a quarter-vehicle with an inertial-capacitance-negative stiffness suspension and a NARX neural network structure;

[0019] Figure 3 A comparison of road surface estimates and actual road surfaces at speeds of 40 km / h and 100 km / h for ABCD grade roads.

[0020] Figure 4 Comparison of spatial power spectral density of predicted signals for Class C road surfaces at a vehicle speed of 30 km / h with standard classification;

[0021] Figure 5 This is a comparison chart of the vehicle body acceleration tests of the classic suspension, the double-sprung suspension, and the model of this invention. Detailed Implementation

[0022] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments and specific features therein are detailed descriptions of the technical solution of the present invention, rather than limitations thereof. Where there is no conflict, the embodiments and technical features therein can be combined with each other.

[0023] This invention proposes a multi-objective optimization and road surface grade identification method for light-duty passenger cars with inertial-capacity-negative stiffness suspension, which includes:

[0024] Step 1: System modeling and transfer function derivation.

[0025] This invention constructs a novel inertial-capacity-negative stiffness series-parallel suspension topology, which fully utilizes the "mass amplification" effect of inertial capacity and the "quasi-zero stiffness" characteristic of negative stiffness. Compared with traditional passive suspensions, this configuration can effectively broaden the vibration isolation frequency band and significantly reduce the peak resonance of the vehicle body without sacrificing handling stability, thus breaking through the inherent physical limits of traditional suspension performance design.

[0026] Existing research has not yet addressed the unique novel topology vehicle suspension vibration reduction model that connects negative stiffness and damping in parallel, and then connects them in series with inertial capacitance and positive stiffness in parallel. Since differences in topology directly alter the system's dynamic characteristics, their multi-objective cooperative optimal solution spaces are entirely different. Furthermore, existing research lacks cooperative optimization based on analytical expressions of multiple performance indicators for light passenger vehicles, and no relevant schemes have been found for identifying road roughness levels using the optimized suspension characteristic response. Therefore, this invention proposes a multi-objective vibration reduction parameter optimization and road level identification method for light passenger vehicles with inertial capacitance-negative stiffness suspension, which is necessary for vibration reduction design and road perception of light passenger vehicles under complex road conditions.

[0027] This step utilizes d'Alembert's principle to establish the differential equations of motion for a quarter-vehicle suspension with inertial capacity and negative stiffness, and derives the transfer functions for vehicle acceleration, suspension travel, and tire dynamic load. Figure 1 A quarter-vehicle model equipped with a capacitive-negative stiffness suspension is presented. The capacitive-negative stiffness suspension includes a first damping structure and a second damping structure connected in parallel between the sprung mass and the unsprung mass. The first damping structure includes a static stiffness element, and the second damping structure includes a first branch and a second branch connected in series. The first branch includes a negative stiffness element and a damping element connected in parallel, and the second branch includes a capacitive element and a positive stiffness element connected in parallel. In this model: m s Indicates sprung mass (vehicle weight), m u k represents the unsprung mass (wheel mass). t k is the tire stiffness coefficient. s k p and k n Z1, Z2, and Z3 represent the static stiffness coefficient, positive stiffness coefficient, and negative stiffness coefficient of the remaining spring elements in the suspension structure, respectively; C and B represent the damping coefficient and inertia coefficient of the suspension structure, respectively; Z1, Z2, and Z3 are the sprung masses m, m, and z3, respectively. s The endpoint displacements, nodal displacements between components in the vibration damping structure, and endpoint displacements of the unsprung mass.

[0028] When a vehicle is stimulated by road surface irregularities When in operation, based on d'Alembert's principle, the dynamic equations for the vehicle suspension system equipped with inertial compressibility and negative stiffness can be established as follows:

[0029] (1)

[0030] To broaden the applicability of the optimization design, a dimensionless analysis method was used to normalize the above dynamic equations:

[0031] (2)

[0032] in, Represents the mass ratio, Represents the inertia-mass ratio. Indicates the external excitation frequency. Indicates the natural frequency of the sprung mass. Indicates the natural frequency of the unsprung mass. Indicates the input frequency ratio. Represents the nominal frequency ratio, It is a positive stiffness ratio. and These represent the negative stiffness ratio and damping ratio of the suspension system, respectively.

[0033] Substituting these parameters into equation (1) and applying the Laplace transform, we obtain the frequency domain expression of equation (1):

[0034] (3)

[0035] Where s represents a complex number, , , and These are the spring-loaded mass displacements. Displacement of vibration reduction structure nodes Unsprung mass displacement and road surface unevenness displacement excitation Amplitude obtained through Laplace transform.

[0036] Further solving formula (3) yields the vehicle body acceleration transfer function of the inertial-capacitance-negative stiffness suspension system under road surface roughness excitation. Represented as:

[0037] (4)

[0038] Suspension travel transfer function Represented as:

[0039] (5)

[0040] Tire dynamic load transfer function Represented as:

[0041] (6)

[0042] In the formula, a0-a6 are specifically represented as follows:

[0043] (7)

[0044] Step 2: Performance metrics parsing.

[0045] This step, based on the H2 norm and combining the road surface roughness power spectral density and transfer function, derives the mean square analytical expressions for each evaluation index (vehicle acceleration, suspension travel, tire dynamic load). Road surface roughness is the vertical deviation of the road surface, and its distribution characteristics significantly affect vehicle ride comfort. Power spectral density is an analytical tool used to describe road surface roughness, providing information on the energy distribution of road surface roughness at different spatial frequencies. Based on the road surface spatial power spectral density recommended by international standards, the road surface spatial power spectral density G can be obtained. q The expression for (n) is:

[0046] (8)

[0047] Among them, G q (n0) is the road surface roughness coefficient, in meters (m). -3 n is the spatial frequency (m -1 This indicates the number of wavelengths contained per meter, where n0 is the reference spatial frequency, n0 = 0.1m. -1 w is the frequency exponent, and its value determines the frequency structure of the road surface power spectral density. We take the frequency exponent w = 2. The eight-level classification standard for road surface roughness is shown in the table below:

[0048]

[0049] The time frequency f, spatial frequency n, and vehicle velocity v satisfy the relationship f = nv. To further analyze the road surface vibration and wave characteristics, the spatial power spectral density G... q (n) is converted to time power spectral density G q (f) This density describes the energy distribution at different time frequencies. The time power spectral density of road surface irregularities can be expressed by the following formula:

[0050] (9)

[0051] In the formula, This represents the power contained in the road surface power spectral density within the frequency band Δn.

[0052] Due to frequency f and angular frequency The relationship is Therefore, the time power spectral density of road surface roughness in equation (7) can be expressed as follows:

[0053] (10)

[0054] Under the random road excitation of the power spectral density described by equation (10), the mean square value of the vehicle acceleration is:

[0055] (11)

[0056] To simplify the above formula, the normalized mean square value of vehicle body acceleration is defined as:

[0057] (12)

[0058] Similarly, the normalized mean square values ​​of suspension travel and tire dynamic load can be obtained:

[0059] (13)

[0060] (14)

[0061] For the infinite integral part contained in the mean square values ​​of each objective in equations (12)-(14) above, we incorporate it into an analytical solution under a unified framework and transform it into an algebraic form:

[0062] (15)

[0063] in, , The expressions for D6 and N6 are as follows:

[0064] (16)

[0065] (17)

[0066] (18)

[0067] (19)

[0068] By applying the analytical solution method of integral theory of the above formulas (15)-(19) to formulas (12)-(14), the analytical expressions of the normalized mean square values ​​can be obtained.

[0069] For the infinite integral part contained in the above target mean square value, using the theory of formulas (15)-(19), the analytical expressions for the mean square values ​​of vehicle acceleration, suspension travel, and tire dynamic load can be obtained:

[0070] (20)

[0071] Among them, the analytical expression for the mean square value of vehicle acceleration is... and The expression is as follows:

[0072] (twenty one)

[0073] (twenty two)

[0074] In the analytical expression of the mean square value of suspension travel and The expression is as follows:

[0075] (twenty three)

[0076] (twenty four)

[0077] In the analytical formula for the mean square value of tire dynamic load and The expression is as follows:

[0078] (25)

[0079] (26)

[0080] in, The expression is as follows:

[0081] (27)

[0082] (28)

[0084] (29)

[0086] Step 3: Multi-objective collaborative optimization and decision-making.

[0087] This step uses the analytical expression derived in step 2 as the optimization objective, and optimizes the parameters using the positive stiffness ratio, negative stiffness ratio, and damping ratio as variables.

[0088] This invention derives analytical expressions for key vehicle response performance indicators, transforming complex dynamic integrals into algebraic operations, which are then used as the objective function of the NSGA-II algorithm. This method avoids the high computational costs associated with large-scale numerical simulations, significantly improving the convergence speed and matching accuracy of multi-objective collaborative optimization, and providing a theoretical tool for rapid optimization of suspension parameters.

[0089] To ensure the physical stability of the suspension system with negative stiffness, a Routh-Hurwitz array of the vehicle system is constructed based on the denominator polynomial of the system transfer function, and this array is used as a hard constraint for the algorithm's optimization. That is, the optimization variables must satisfy the following inequality:

[0090] (30)

[0091] Under the aforementioned stability constraints, the NSGA-II multi-objective algorithm is used to perform global cooperative optimization of the objective space.

[0092] Since there are significant differences in the physical dimensions and numerical ranges of each objective, in order to ensure that each dynamic index can approach its ideal boundary with the same geometric space ratio in the subsequent adaptive weighted multi-objective optimization process, this invention first uses the generalized multi-objective optimization algorithm (NSGA-II algorithm) to perform a frontier search of the solution in the global continuous variable space, and obtains a dynamic feature solution set space composed of multiple sets of discrete parameter points with clear physical boundaries.

[0093] A unified decision domain [0, 1] is constructed by extracting the global physical extremum boundaries of each optimization objective in the solution set space of this dynamic feature. For the dynamic index of the minimization optimization, a nonlinear inverse deviation mapping operator is used to normalize and reduce the original scale data.

[0094] For the dynamic index of minimization optimization, a nonlinear inverse deviation mapping operator is used to normalize and reduce the original scale data, as expressed in:

[0095] (31)

[0096] (32)

[0097] (33)

[0098] In the formula, , , These represent the real-time calculated values ​​of tire dynamic load, vehicle acceleration, and suspension travel corresponding to the i-th leading edge, respectively. and These represent the global maximum and minimum boundaries of the tire dynamic load within the entire dynamic characteristic solution space, respectively. and These represent the global maximum and minimum boundaries of the vehicle acceleration within the entire dynamic feature solution space; and These represent the global maximum and minimum boundaries of the suspension travel within the entire dynamic characteristic solution set space, respectively. Each optimization objective is proportionally normalized to the relative decision domain after mapping, and the closer the normalized value is to 1, the closer the objective is to its physical optimal limit boundary.

[0099] Within a regularized decision domain, define an ideal sequence consisting of the ideal values ​​of each optimization objective. Meanwhile, each discrete parameter point is defined as the actual response sequence. By traversing the entire dynamic characteristic solution set space, the absolute deviation distance between each actual response sequence and the ideal sequence is calculated, and a global deviation matrix is ​​constructed:

[0100] (34)

[0101] in, This represents the absolute deviation distance of the i-th actual response sequence on the j-th optimization objective. Let the j-th optimization objective be the ideal value. This represents the actual response value of the i-th actual response sequence on the j-th optimization objective; thus, the maximum absolute distance in the global bias matrix is ​​locked. minimum absolute distance .

[0102] Then, the overall approximation degree of each control to the ideal state in space is evaluated, a regulation mechanism is introduced, and the similarity of the i-th actual response sequence on the j-th optimization objective dimension is quantitatively calculated. :

[0103] (35)

[0104] in, This represents the similarity of the i-th actual response sequence on the j-th optimization objective dimension. and These represent the maximum and minimum absolute distances in the global deviation matrix, respectively.

[0105] Multi-objective comprehensive stability is evaluated based on the similarity of the actual response sequences across various optimization objective dimensions, and the global feature optimum with the highest comprehensive stability across the three objectives is selected. In this embodiment, the optimal point of global features is determined based on the actual response sequence with the highest average similarity across multiple optimization objective dimensions.

[0106] The magnitude of the correlation coefficients for each component directly and quantitatively reflects the relative distance between the optimal solution and the ideal boundary in the corresponding objective dimension. To ensure that the final single-objective function is perfectly aligned with the position of the global optimum, an adaptive normalization mapping is introduced to extract the weight allocation ratio:

[0107] (36)

[0108] in, , and These represent the weighting coefficients for the tire dynamic load dimension, the vehicle body acceleration dimension, and the suspension travel dimension, respectively. , and These represent the similarity of the global feature optimum in the dimensions of tire dynamic load, vehicle acceleration, and suspension travel, respectively.

[0109] After obtaining the adaptive weight coefficients [a1,a2,a3], in order to overcome the discontinuity and limitations of the discrete Pareto front solution set, these weight coefficients are used to reconstruct the global energy dissipation gradient of the system, establishing a single-objective evaluation function J for reconstruction in the global continuous variable space:

[0110] (37)

[0111] in, This represents a single-objective comprehensive evaluation function. , and These represent the calculated values ​​for tire dynamic load, vehicle body acceleration, and suspension travel, respectively.

[0112] Substituting the objective function J into the single-objective comprehensive objective function, and under the hard physical constraints of satisfying the Routh stability criterion, a standard genetic algorithm (GA) is used to re-minimize the function in the continuous space of all variables. Since this function has a continuous algebraic gradient in the continuous variable space, the optimization procedure can overcome the limitations of discrete points and converge towards the deeper physical global extremum of the system. Thus, based on the equilibrium point selected in the first stage, the potential of the inertial capacitance-negative stiffness suspension structure is further explored, achieving a second refinement of dynamic performance.

[0113] Step 4: Road surface grade identification based on NARX neural network.

[0114] Existing road surface recognition research is mostly based on conventional suspension models, failing to fully incorporate the characteristic dynamic responses of novel suspensions, such as those with inertial capacity and negative stiffness, after parameter optimization. If analytically optimized vehicle model parameters and real-time vibration data can be combined to invert and classify road surface excitations, the cumbersome process of repeatedly training existing recognition models for different operating conditions can be overcome, providing more targeted technical support for intelligent vehicle perception and adaptive control.

[0115] This step uses the optimal system parameters determined in step 3 to input into the vehicle suspension model, obtaining dynamic response data such as acceleration and displacement of the vehicle under different road surfaces. A time-series mapping model between the vehicle response signal and road surface elevation is constructed using a NARX neural network, thereby achieving real-time and accurate identification of road surface grades. To obtain the training and testing samples required for road surface identification, a road surface roughness time-domain model based on linear filtering is directly used to generate random excitations. The first-order linear differential equation expression of this model is as follows:

[0116] (38)

[0117] In the formula, n1 is the cutoff spatial frequency under road surface unevenness, and n1 = 0.01m. -1 ; is the road surface displacement excitation; w(t) is Gaussian white noise.

[0118] Based on the above filtered white noise road surface time-domain model, a road surface time-domain model coupled with vehicle dynamics simulation model is built in MATLAB / Simulink. The optimal suspension parameters determined in step 3 are used and converted according to the reciprocal relationship between sampling time and sampling frequency, that is, the sampling time is set to 1 / 10v.

[0119] Extracting wheel acceleration acceleration at nodes Deformation of negative stiffness elements Suspension travel Five key parameters, including wheel displacement z3, were used as dynamic response data, and road excitation information was simultaneously acquired as training labels. Simulation time-series data of Class D road surface was selected as the core training dataset. A nonlinear mapping model between suspension dynamic response and road elevation was constructed using a NARX neural network. For the vibration characteristics of the inertial-capacitance-negative stiffness suspension system of a light passenger car, the network structure was adapted and parameters configured, specifically including: temporal feature extraction, where the order of input delay and feedback delay was reasonably set according to the time delay effect of vehicle vibration to capture the historical correlation of dynamic response; network topology construction, using a multi-layer feedforward network structure with hidden layers, and reasonably determining the number of neurons according to the complexity of the mapping relationship; data management and training, where the simulation dataset was divided into training and test sets proportionally, and an adaptive optimization algorithm (such as Bayesian regularization) was used for iterative optimization, and a suitable activation function was selected to handle the nonlinear mapping relationship; performance evaluation metrics, using root mean square error (RMSE) and correlation coefficient (R) to evaluate the model's inversion accuracy. The trained NARX neural network model was used to predict and verify road surface grades. Five real-time vehicle response parameters of a light passenger car under road surface excitations at levels A, B, C, and D are input into the model to obtain the corresponding time-domain prediction signal of road surface elevation. The time-domain signal is then converted to the frequency domain using a Fast Fourier Transform, and the spatial power spectral density at 0.011 m is calculated. -1 Up to 2.83 m -1 The root mean square value within the spatial frequency range is compared with the geometric mean value in the standard pavement roughness classification table to determine the current pavement grade. Furthermore, the pavement grade is visually verified by plotting the frequency domain characteristic curve of the predicted signal on the standard classification chart.

[0120] Figure 2 This paper presents the complete architecture of a nonlinear mapping model between suspension dynamic response and road surface elevation, constructed using a NARX neural network based on the aforementioned extraction of five key parameters and road excitation time-series data. Combining the vibration characteristics and simulation data features of a light-duty passenger car's inertial-capacitance-negative-stiffness suspension, the network is configured with the following parameters: 1. Timing delay: Input delay 1:2, feedback delay 1:2; 2. Network structure: Single hidden layer, 11 neurons; 3. Data partitioning: Training and test sets are allocated in a 7:3 ratio; 4. Training algorithm: Bayesian regularization algorithm (trainbr) is used, requiring no manual setting of the learning rate; the algorithm automatically optimizes the iteration step size; 5. Activation function: Logsig function is used for the hidden layer, and Purelin function is used for the output layer; 6. Training mode: The network is first trained in open-loop mode, then converted to closed-loop mode for model testing; 7. Evaluation metrics: Root mean square error (RMSE), correlation coefficient (R).

[0121] The trained NARX neural network model was used to predict and validate road surface grades. Five real-time vehicle response parameters of a light passenger car under road surface excitations of grades A, B, C, and D were input into the model, and the corresponding time-domain predicted road surface elevation signals were obtained through inversion. The test results are shown in the table below:

[0122]

[0123] Combination Figure 3 The test results show that, covering typical road surfaces of four grades (A, B, C, and D) and a wide speed range from 30 km / h to 120 km / h, the correlation coefficient (R) between the road surface elevation predicted by the NARX neural network model and the actual road surface elevation remains above 98.17%, reaching a maximum of 99.71%. Meanwhile, the root mean square error (RMSE) remains at an extremely low level overall. This indicates that the model can accurately invert the time-domain excitation signal of the road surface and effectively capture the dynamic characteristics of road surface unevenness.

[0124] The time-domain signal is converted to the frequency domain using the Fast Fourier Transform, such as... Figure 4 The frequency domain characteristic curve of the C-level pavement prediction signal is plotted on the standard classification chart to achieve intuitive verification of the pavement grade.

[0125] This invention utilizes a NARX neural network to deeply couple the optimized vehicle dynamic response with road surface excitation, constructing a high-precision nonlinear mapping model. This method eliminates the need for expensive additional road surface measurement sensors, achieving real-time inversion and accurate identification of road surface grades solely using vibration data from the suspension and vehicle body.

[0126] In summary, this invention addresses the optimization of vehicle system parameters and the coordination of multiple performance aspects in vehicle systems with inertial-capacitance-negative stiffness suspensions. Based on the H2 norm, it derives analytical function expressions for key performance parameters such as vehicle acceleration, suspension travel, and the mean square value of tire dynamic load. Building upon this, the NSGA-II algorithm is employed for multi-objective collaborative optimization to obtain vehicle system parameters that guarantee comprehensive performance. Furthermore, utilizing the optimized dynamic response of the vehicle, a nonlinear mapping relationship between the vehicle response signal and road surface elevation is established using a NARX neural network, enabling accurate inversion of road surface grade. This invention not only significantly improves the ride comfort, safety, and handling of vehicles under complex conditions but also provides more forward-looking technical support for the development of vehicle suspensions through road surface recognition technology.

[0127] To further illustrate the effectiveness and engineering applicability of the inertial-capacity-negative stiffness suspension described in this invention in the multi-objective optimization and road surface grade identification method for light passenger cars, this embodiment uses a quarter-vehicle model of a certain type of light passenger car as an example for analysis and verification. In this example, the basic physical parameters of the quarter-vehicle model of the light passenger car are set as follows: sprung mass m s =250kg, unsprung mass m u =35kg, then the mass ratio μ=0.14; the inertia-mass ratio δ is 0.2; the nominal frequency ratio φ is 7.

[0128] Combination Figure 5 To quantitatively verify the superiority of the proposed light-duty passenger car inertial-capacity-negative stiffness suspension topology in improving ride comfort, this embodiment compares and analyzes the method of the present invention with two typical topologies in the prior art: one is a classic suspension known in the art, and the other is the Shuangming model, which originates from the negative stiffness inertial-capacity damper (NS-ISD) suspension topology proposed in the published literature (Wang et al., 2025, Vehicle System Dynamics).

[0129] The suspension structures described in the aforementioned prior art documents differ from the topology used in this invention. Their structures are all in a parallel configuration of inertial capacitance and negative stiffness, and their objective optimization focuses solely on vehicle acceleration. To ensure the reliability and fairness of the comparison, this embodiment, under the same road surface excitation and physical boundary constraints, degenerates the weighted multi-objective function of this invention into a single-objective optimization focusing only on vehicle acceleration, obtaining the time response output under specific operating conditions.

[0130]

[0131] The inertial-capacitance negative stiffness suspension structure proposed in this invention forcibly limits the maximum transient response peak of the vehicle body acceleration to 1.1465 m / s². 2 Compared to classic passive suspension, its damping rate is reduced by 53.90%, and compared to existing patented models, its ride comfort performance is further reduced by 37.22%.

[0132] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0133] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0134] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0135] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0136] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A multi-objective optimization and road surface grade identification method for a light-duty passenger car with an inertial-compensatory negative stiffness suspension, characterized in that, The method is based on a capacitive negative stiffness suspension, which includes a first damping structure and a second damping structure connected in parallel between the sprung mass and the unsprung mass. The first damping structure includes a static stiffness element, and the second damping structure includes a first branch and a second branch connected in series. The first branch includes a negative stiffness element and a damping element connected in parallel, and the second branch includes a capacitive element and a positive stiffness element connected in parallel. During the car's operation, the endpoint displacement of the sprung mass, the node displacement between the first and second branches, and the endpoint displacement of the unsprung mass are acquired in real time. Combined with the pre-determined sprung mass, unsprung mass, tire stiffness coefficient, static stiffness coefficient, negative stiffness coefficient, damping coefficient, inertial capacitance coefficient, and positive stiffness coefficient, a dynamic equation is constructed. The transfer function of the car under road surface unevenness excitation is determined based on the aforementioned dynamic equation; The evaluation index is calculated based on the time power spectral density of road surface roughness and the transfer function. The evaluation index is used as the optimization target, and the positive stiffness ratio, negative stiffness ratio and damping ratio are used as variables for parameter optimization. The positive stiffness ratio is the ratio of the positive stiffness coefficient to the static stiffness coefficient, the negative stiffness ratio is the ratio of the negative stiffness coefficient to the static stiffness coefficient, and the damping ratio is determined based on the damping coefficient, the sprung mass and the natural frequency of the sprung mass. The inertial-compass negative stiffness suspension is optimized based on the optimal variables obtained through optimization. The dynamic response data of the optimized inertial-compass negative stiffness suspension is obtained when the car is driving. The dynamic response data is then input into a pre-built recognition model to predict the road surface grade.

2. The method for multi-objective optimization and road surface grade identification of a light-duty passenger car with an inertial-compensatory negative stiffness suspension according to claim 1, characterized in that, The transfer functions include the vehicle body acceleration transfer function, the suspension travel transfer function, and the tire dynamic load transfer function; the evaluation indicators include the normalized mean square value of vehicle body acceleration, the normalized mean square value of suspension travel, and the normalized mean square value of tire dynamic load. The normalized mean square value of vehicle acceleration is determined based on the time power spectral density of road surface roughness and the vehicle acceleration transfer function. The normalized mean square value of suspension travel is determined based on the time power spectral density of road surface roughness and the suspension travel transfer function; The normalized tire dynamic loads are all determined based on the time power spectral density of road surface unevenness and the tire dynamic load transfer function.

3. The method for multi-objective optimization and road surface grade identification of a light-duty passenger car with an inertial-compensatory negative stiffness suspension according to claim 1, characterized in that, Using evaluation indicators as optimization objectives, parameter optimization is performed with positive stiffness ratio, negative stiffness ratio, and damping ratio as variables, including: By using a generalized multi-objective optimization algorithm to perform a frontier search for solutions in the global continuous variable space, a dynamic characteristic solution set space consisting of multiple sets of discrete parameter points with well-defined physical boundaries is obtained. Extract the global physical extremum boundaries of each optimization objective in the solution set space of this dynamic feature to construct a unified decision domain; Within the regularized decision domain, an ideal sequence consisting of the ideal values ​​of each optimization objective is defined, while each discrete parameter point is defined as the actual response sequence. By traversing the entire dynamic characteristic solution set space, the absolute deviation distance between each actual response sequence and the ideal sequence is calculated, and a global deviation matrix is ​​constructed. The similarity of the actual response sequence across each optimization objective dimension is calculated based on the maximum and minimum absolute distances in the global bias matrix. Multi-objective comprehensive stationarity evaluation is performed based on the similarity of the actual response sequences across various optimization objective dimensions to determine the optimal point of global features. The adaptive weight coefficients are determined based on the similarity of the global feature optimum across various optimization objective dimensions. The adaptive weight coefficients are then used to reconstruct multiple evaluation indicators into a single objective evaluation function. For a single-objective evaluation function, a standard genetic algorithm is used to perform a minimization search in the continuous space of all variables to obtain the optimal results for each variable.

4. The method for multi-objective optimization and road surface grade identification of a light-duty passenger car with an inertial-compensatory negative stiffness suspension according to claim 3, characterized in that, Extracting the global physical extremum boundaries of each optimization objective in the solution space of this dynamic feature to construct a unified decision domain includes: For the dynamic index of minimization optimization, a nonlinear inverse deviation mapping operator is used to normalize and reduce the original scale data, as expressed in: ； ； ； In the formula, , , These represent the real-time calculated values ​​of tire dynamic load, vehicle acceleration, and suspension travel corresponding to the i-th leading edge, respectively. and These represent the global maximum and minimum boundaries of the tire dynamic load within the entire dynamic characteristic solution space, respectively. and These represent the global maximum and minimum boundaries of the vehicle acceleration within the entire dynamic feature solution space; and These represent the global maximum and minimum boundaries of the suspension travel within the entire dynamic characteristic solution space, respectively.

5. The method for multi-objective optimization and road surface grade identification of a light-duty passenger car with an inertial-compensatory negative stiffness suspension according to claim 3, characterized in that, The absolute deviation distance between each actual response sequence and the ideal sequence is expressed as: ； in, This represents the absolute deviation distance of the i-th actual response sequence on the j-th optimization objective. Let the j-th optimization objective be the ideal value. This represents the actual response value of the i-th actual response sequence to the j-th optimization objective; The similarity of the actual response sequence across each optimization objective dimension is calculated based on the maximum and minimum absolute distances in the global bias matrix, and is represented as follows: ； in, This represents the similarity of the i-th actual response sequence on the j-th optimization objective dimension. and These represent the maximum and minimum absolute distances in the global deviation matrix, respectively. Multi-objective comprehensive stationarity evaluation is performed based on the similarity of the actual response sequences across various optimization objective dimensions to determine the global feature optimum, including: The optimal point of the global features is determined based on the actual response sequence with the highest mean similarity across multiple optimization objective dimensions.

6. The method for multi-objective optimization and road surface grade identification of a light-duty passenger car with an inertial compressive negative stiffness suspension according to claim 5, characterized in that, The adaptive weight coefficients are determined based on the similarity of the global feature optimum across various optimization objective dimensions, and are expressed as follows: ； in, , and These represent the weighting coefficients for the tire dynamic load dimension, the vehicle body acceleration dimension, and the suspension travel dimension, respectively. , and These represent the similarity of the global feature optimum in the dimensions of tire dynamic load, vehicle acceleration, and suspension travel, respectively.

7. The method for multi-objective optimization and road surface grade identification of a light-duty passenger car with an inertial-compensatory negative stiffness suspension according to claim 6, characterized in that, Multiple evaluation indicators are reconstructed into a single-objective comprehensive evaluation function using adaptive weighting coefficients, as follows: ； in, This represents a single-objective comprehensive evaluation function. , and These represent the calculated values ​​for tire dynamic load, vehicle body acceleration, and suspension travel, respectively.

8. The method for multi-objective optimization and road surface grade identification of a light-duty passenger car with an inertial-compensatory negative stiffness suspension according to claim 1, characterized in that, The dynamic response data includes: wheel acceleration. acceleration at nodes Deformation of negative stiffness elements Suspension travel And wheel displacement z3; where z1 represents the end displacement of the sprung mass, z2 represents the node displacement between the first branch and the second branch, and z3 represents the end displacement of the unsprung mass.

9. The method for multi-objective optimization and road surface grade identification of a light-duty passenger car with an inertial-compensatory negative stiffness suspension according to claim 1, characterized in that, The recognition model is constructed based on the NARX neural network.

10. A multi-objective optimization and road surface grade recognition system for a light-duty passenger car with an inertial-compensatory negative stiffness suspension, characterized in that, include: The acquisition module is used to acquire, in real time, the endpoint displacement of the sprung mass, the node displacement between the first branch and the second branch, and the endpoint displacement of the unsprung mass during the car's operation. It then constructs a dynamic equation by combining these with pre-determined sprung mass, unsprung mass, tire stiffness coefficient, static stiffness coefficient, negative stiffness coefficient, damping coefficient, inertial capacitance coefficient, and positive stiffness coefficient. The car's inertial capacitance negative stiffness suspension includes a first damping structure and a second damping structure connected in parallel between the sprung mass and the unsprung mass. The first damping structure includes a static stiffness element, and the second damping structure includes a first branch and a second branch connected in series. The first branch includes a negative stiffness element and a damping element connected in parallel, and the second branch includes an inertial capacitance element and a positive stiffness element connected in parallel. The determination module is used to determine the transfer function of the car under road surface unevenness excitation based on the dynamic equation; The calculation module is used to calculate the evaluation index based on the time power spectral density of road surface roughness and the transfer function; The optimization module is used to optimize parameters with evaluation indicators as the optimization target and positive stiffness ratio, negative stiffness ratio and damping ratio as variables; the positive stiffness ratio is the ratio of positive stiffness coefficient to static stiffness coefficient, the negative stiffness ratio is the ratio of negative stiffness coefficient to static stiffness coefficient, and the damping ratio is determined based on damping coefficient, sprung mass and sprung mass natural frequency. The road surface grade identification module is used to optimize the inertial-compass negative stiffness suspension based on the optimal variables obtained through optimization, obtain the dynamic response data of the optimized inertial-compass negative stiffness suspension when the car is driving, and input the dynamic response data into the pre-built identification model to predict the road surface grade.

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