Method and device for online identification of wheel lateral stiffness

Abstract

This application proposes a method for the online identification of wheel lateral stiffness. The method comprises the following steps: Step S1: creation of a lateral kinematic model of the vehicle with respect to the parameters to be identified, taking into account the lateral stiffness of the front and rear wheels of the vehicle; Step S2: discretization of the lateral kinematic model of the vehicle to obtain a discrete model with respect to the parameters to be identified; and Step S3: fitting the output of the discrete model using a water circulation algorithm to determine the parameters to be identified online. This application also proposes a device for the online identification of wheel lateral stiffness and a computer program product. This application uses a heuristic algorithm to identify the wheel lateral stiffness online.This takes into account the temporal variability of the wheel lateral stiffness, which significantly improves vehicle stability control.

Description

TECHNICAL AREA The present invention relates to a method for online identification of wheel lateral stiffness, a device for online identification of wheel lateral stiffness, and a computer program product. STATE OF THE ART Wheel lateral stiffness is a crucial parameter influencing vehicle stability control, and its accuracy is critical for handling. Because it is a time-varying parameter affected by multiple factors, online identification of wheel lateral stiffness presents a significant challenge. Conventional offline testing methods cannot capture the dynamic changes in parameters in real time, leading to inaccurate identification results. While some online identification methods exist, they are currently inadequate in terms of accuracy and real-time capability and cannot meet the demands of vehicle dynamics simulation and stability control. Therefore, developing a method capable of accurately determining wheel lateral stiffness online is of paramount importance for improving vehicle safety and handling. CONTENT OF THE INVENTION The aim of this application is to provide a method for online identification of wheel lateral stiffness, a device for online identification of wheel lateral stiffness and a computer program product to solve at least some of the problems of the prior art. According to a first aspect of the present invention, a method for displaying images of a vehicle is provided, the method comprising the following steps: Step S1: Creating a lateral kinematic model of the vehicle with respect to the parameters to be identified, wherein the parameters to be identified include the lateral stiffness of the front wheels and the lateral stiffness of the rear wheels of the vehicle. Step S2 involves discretizing the lateral kinematic model of the vehicle to obtain a discrete model of the parameters to be identified; and Step S3: Fitting the output of the discrete model using the water cycle algorithm to determine the parameters to be identified online. This application incorporates the following technical concept: This solution uses a heuristic algorithm to solve the model output, effectively increasing the algorithm's search capability and improving its adaptability to complex problems. The online identification method accounts for the temporal variability of the wheel's lateral stiffness and ensures that the accuracy of parameter identification is not affected by the magnitude of the initial value. Since it can correct modeling errors online, it simultaneously provides a more accurate mathematical model of the vehicle's dynamic lateral behavior. Overall, this application's method significantly improves vehicle stability control. In an exemplary embodiment, step S1 comprises the following: Setting up the following lateral kinematic model using a two-degrees-of-freedom vehicle dynamics model: M · ay = Fyf + Fyr, In, M For the quality of the vehicle, ay For the lateral acceleration of the vehicle, Fyf This refers to the lateral force acting on the front wheels of the vehicle. Fyr The lateral force is the lateral force at the rear wheel of the vehicle; the lateral kinematic model is parameterized based on the linear lateral force model of the wheel to obtain the following lateral kinematic model for the parameters to be identified: ay = Cαf · bf + Cαr · br, In, ay For the lateral acceleration of the vehicle, bf As the first coefficient, br As the second coefficient, Cαf For the lateral stiffness of the front wheel, Cαr This refers to the lateral stiffness of the rear wheel. In an exemplary embodiment, the parameterization of the lateral kinematic model based on the linear lateral force model of the wheel comprises the following: establishing a linear lateral force model of the wheel based on the lateral stiffness of the wheel and the lateral angle of the vehicle's wheel; establishing a lateral angle model of the wheel based on the steering angle of the front wheel and the velocity angle of the wheel; establishing a velocity angle model of the wheel based on the wheelbase of the vehicle, the yaw rate of the vehicle, the lateral speed of the vehicle, and the longitudinal speed of the vehicle; and integrating the linear lateral force model of the wheel, the lateral angle model of the wheel, and the velocity angle model of the wheel into the lateral kinematic model to express the lateral acceleration of the vehicle as a function of the lateral stiffness of the front wheel and the lateral stiffness of the rear wheel of the vehicle.In an exemplary implementation, step S3 comprises the following: Inputting the error value between the actual and predicted dynamic response data of the vehicle into a water cycle algorithm for iterative adjustment of the estimated value of the parameter to be determined. The predicted dynamic response data of the vehicle is the output of the discrete model based on the estimated value of the parameter to be determined. After each iteration, a check is performed to see if a predefined termination condition is met. If not, the iteration continues, and the estimation of the parameter to be determined in the next iteration cycle is controlled by the error value between the actual and predicted dynamic response data of the vehicle in the current iteration cycle.If the termination condition is met, the iteration is terminated and the value of the parameter to be determined, estimated in the current iteration cycle, is output as the optimal solution. In an exemplary embodiment, the fitness function is structured as follows: To measure whether the preset termination condition for the iteration is met: In, e(k) The first time k The deviation between the estimated and the actual values ​​of the lateral acceleration at each sampling time. This is an estimate of the lateral acceleration. ay(k) This represents the actual value of the lateral acceleration. In an exemplary implementation, step S3 performs the following iterative process using a water cycle algorithm: Step S31: Initialization of the population parameters and generation of an initial population of individuals, where each individual in the population represents a potential solution for a set of parameters to be identified; Step S32: Calculation of the fitness value of each individual in the population and classification of all individuals in the population into streams, rivers, and oceans based on the fitness value; Step S33: Iterative optimization of the population by updating the positions of streams, rivers, and oceans; and Step S36: Output of the parameter to be identified, represented by the individual with the highest fitness value in the final population, as the optimal solution once a preset termination condition for the iteration is satisfied. In an exemplary embodiment, the iterative process in step S3 further includes: step S34, triggering an evaporation process to reduce the number of streams and / or rivers when the evaporation conditions are met; conducting a rain process to randomly generate new individuals to join the population; and step S35, adaptively updating the evaporation conditions during the iterative process. In an exemplary embodiment, step S3 further includes: the dynamic adaptation of the internal parameters of the water cycle algorithm to the driving state of the vehicle, the driving environment conditions, the requirements for computation delay and / or the requirements for computation accuracy, wherein the internal parameters include at least one of the following: the initial population size, the maximum number of iterations, the fitness function and / or the evaporation conditions. According to a second aspect of this application, a device for online identification of wheel lateral stiffness is provided. The device comprises a processor and a memory, wherein the memory stores computer program instructions which, when executed by the processor, enable the processor to perform the method according to the first aspect of this application. According to a third aspect of this application, a computer program product is provided with program code units, wherein the program code units are configured such that the computer performs the method described in the first aspect of this application when the computer program product is executed on a computer or stored on a computer-readable storage medium. DESCRIPTION OF THE FIGURES The present invention is described in more detail below with reference to the figures, so that the principles, features, and advantages of the present invention become even clearer. The figures include the following: Fig. 1 shows a flowchart of a method for displaying an image for a vehicle according to an exemplary embodiment of the present invention. Fig. 2 shows a schematic diagram of a vehicle dynamics model with two degrees of freedom according to an exemplary embodiment of this application; Fig. 3 shows a flowchart illustrating the principle of a water circulation algorithm according to an exemplary embodiment of this application; Fig. 4 shows the logic block diagram for online identification of wheel lateral stiffness using a water circulation algorithm; and Fig.Figure 5 shows a block diagram of a device for online identification of wheel lateral stiffness according to an embodiment of this application. DETAILED DESCRIPTION OF THE EXECUTION FORMS To better illustrate the technical problems to be solved, the technical solutions, and the advantageous technical effects of the present invention, the present invention will be described in more detail with reference to the figures and exemplary embodiments. It should be understood that the specific embodiments described here serve only to explain the present invention and not to limit its scope of protection. Fig. 1 shows a flowchart of a method for displaying an image in a vehicle according to an exemplary embodiment of the present invention. The method comprises steps S1, S2, and S3. In step S1, a lateral kinematic model of the vehicle is created with respect to the parameters to be identified, including the lateral stiffness of the front wheel and the lateral stiffness of the rear wheel. The lateral stiffness of a wheel is defined as the ratio between the lateral force acting on the wheel and the corresponding lateral angle, and is an important parameter for measuring a wheel's driving stability. The magnitude of the lateral stiffness directly influences the vehicle's handling and stability. In particular, wheels with higher lateral stiffness can offer better driving stability. This means that the wheels are better able to withstand lateral forces when cornering. Therefore, lateral stiffness is an important factor that must be considered in vehicle dynamics analysis and wheel design. To create a lateral kinematic model, relevant driving and physical parameters can be obtained from the vehicle's sensors. Driving parameters include, among others, lateral speed, longitudinal speed, yaw rate, and the steering angle of the front wheels. These parameters can be acquired using devices such as lateral speed sensors, longitudinal speed sensors, yaw rate sensors, and steering angle sensors. Physical parameters include, for example, the wheelbase (i.e., the distance between the vehicle's center of gravity and the front or rear axle) and the vehicle mass. These parameters can be taken directly from the vehicle's manual or measured and estimated in real time using vehicle dynamics measurement systems (such as wheel speed sensors, mass distribution sensors, etc.). The exemplary process of creating the lateral kinematic model can be explained in the following description in conjunction with Fig. 2; for reasons of brevity, it is not repeated here. In step S2, the lateral kinematic model of the vehicle is discretized to obtain a discrete model of the parameters to be identified. This process involves converting a continuous time model into a discrete time model. Common discretization methods include the forward Euler method, the backward Euler method, the zero-order preservation method, etc. In one embodiment, for example, the zero-order preserve method can be used to convert a continuous transverse dynamics model into a discrete-time model, which is then used as the discrete model. This approach assumes that the input remains constant within each sampling period and transforms the model into a discrete-time model by approximating all states within the entire time step by the model state at the current instant within each discrete time step. For the moment, the discretized lateral kinematic model of the vehicle (discrete model) can be expressed as follows: In, bf(k) and br(k) Starting from the current moment k, the first and second coefficients combine the vehicle's driving and physical parameters. ay(k) indicates the vehicle's current position. k is the lateral acceleration, and Cαf(k) and Cαr(k) represent the lateral stiffness of the front wheel and the lateral stiffness of the rear wheel at any given time. Discretization allows complex continuous systems to be transformed into models suitable for digital control and real-time computing. This is of great importance for subsequent online parameter identification using water circulation algorithms. Discrete models are not only easy to implement, but also enable real-time prediction and feedback of the vehicle's lateral dynamic behavior, thereby significantly improving the accuracy and efficiency of online wheel lateral stiffness identification. Step S3: Adjust the output of the discrete model using the water cycle algorithm to determine the parameters to be identified online. The Water Cycle Algorithm is a bio-inspired algorithm designed to solve multi-criteria optimization problems. It mimics the dynamic process of the water cycle in nature, specifically how streams and rivers eventually flow into the sea. Water enters the atmosphere through evaporation, forms clouds, and condenses under suitable conditions before falling to the ground—thus completing the water cycle. The Water Cycle Algorithm utilizes this natural phenomenon and applies the water transfer mechanism between the Earth's surface, ocean, and atmosphere to optimize parameters. It searches the solution space and seeks the optimal solution by simulating water flow and transformation processes. This method not only features powerful global search capabilities but can also adaptively adjust its search strategy to tackle complex optimization problems. In contrast to one-off, static identification, the core of online identification lies in its continuity and dynamism. By using the water cycle algorithm, the output of the discrete model can be continuously iteratively adjusted and combined with actual vehicle feedback data to continuously optimize the solution results for the parameters to be identified. This dynamic parameter identification process not only captures the time-varying properties of wheel lateral stiffness but also enables more precise vehicle dynamics during operation, thus allowing for real-time monitoring and adjustment of dynamic driving behavior. The principle, process, and logical implementation of the water cycle algorithm are explained in more detail below with reference to Figures 3 and 4. For the sake of brevity, they are not repeated here. This method enables the precise determination of important parameters such as the vehicle's lateral stiffness and thus provides a scientific basis for optimizing driving behavior. Fig. 2 shows a schematic diagram of a vehicle dynamics model with two degrees of freedom according to an exemplary embodiment of this application. The modeling process of a two-degree-of-freedom vehicle dynamics model involves modeling the vehicle in the lateral direction (...). The motion is described using two degrees of freedom: the z-axis and the yaw axis (rotation about the z-axis). As shown in Fig. 2, a coordinate system is first established with the vehicle's center of gravity as the origin. In this coordinate system, the x-axis points longitudinally to the vehicle and the y-axis transversely to the vehicle. For lateral movements, the lateral force acting on the front wheels of the vehicle is the primary factor, as is the lateral force acting on the rear wheels. According to Newton's second law, the following lateral kinematic model of the vehicle can be established for sideways motion: In, M Regarding the quality of the vehicle, ay For the lateral acceleration of the vehicle, Fyf This refers to the lateral force acting on the front wheels of the vehicle. Fyr This refers to the lateral force acting on the rear wheels of the vehicle. The lateral kinematic model of the vehicle can then be parameterized (simplified) using the linear lateral force model of the wheels to obtain the lateral acceleration of the vehicle. Regarding the parameters to be identified, Cf and Cr, the function expression is as follows: Assuming that the lateral force of a wheel is linearly related to its slip angle, a linear lateral force model for the wheel can be formulated as follows: The model of the lateral force at the front wheels of the vehicle is as follows: In,FyfEs refers to the lateral force of the vehicle's front wheels.CafEs refers to the lateral stiffness of the front wheel.afEs refers to the slip angle of the front wheel. The model of the vehicle's rear wheel lateral forces is as follows: In, FyrEs refers to the lateral force of the vehicle's rear wheels. CArEs refers to the lateral stiffness of the rear wheel. arEs refers to the slip angle of the rear wheel. Furthermore, it can be assumed that the wheel slip angle is directly related to the steering angle of the front wheel and the wheel speed angle. Therefore, a wheel slip angle model based on the steering angle of the front wheel and the wheel speed angle can be created as follows: The model for the slip angle of the vehicle's front wheels is as follows: In, afEs is the slip angle of the vehicle's front wheels. δEs is the steering angle of the vehicle's front wheels. θvfEs is the speed angle of the front wheel. The vehicle's rear wheel slip angle model is as follows: In, αrEs is the slip angle of the vehicle's rear wheels.θvrEs is the speed angle of the vehicle's rear wheels. Furthermore, a wheel speed angle model can be created based on the vehicle wheelbase, yaw rate, lateral speed and longitudinal speed as follows: The vehicle's front wheel speed angle model is: In, θvfEs is the velocity angle of the vehicle's front wheels.ẏEs is the vehicle's lateral speed. lfEs is the distance from the vehicle's center of gravity to the front axle (front wheelbase). ψEs is the vehicle's yaw rate.v,Es is the vehicle's longitudinal speed. The model for the speed angle of the vehicle's rear wheels is as follows: In, θvfEs is the velocity angle of the vehicle's front wheels.ẏEs is the vehicle's lateral speed.lrEs is the distance from the vehicle's center of gravity to the rear axle (rear wheelbase).ψEs is the vehicle's yaw rate.v,Es is the vehicle's longitudinal speed. By substituting the linear lateral force model, the wheel velocity angle model, and the wheel slip angle model into the lateral kinematic model, the vehicle's lateral acceleration can be expressed as a function of the front wheel slip stiffness and the rear wheel slip stiffness. That is, by combining the equations above, we obtain the following lateral kinematic model for the parameter to be determined: This equation describes the lateral acceleration of the vehicle. The parameters to be determined are the lateral stiffness of the front and rear wheels, and the relationship between them. Next, we can extract the first coefficient. Second coefficient: The lateral kinematic model can be simplified as follows: In, These coefficients bf and br By integrating the measurable driving parameters of the vehicle and known physical parameters, the lateral acceleration can be determined. The relationships between them are simpler and easier to handle. Fig. 3 shows a flowchart illustrating the principle of a water cycle algorithm according to an exemplary embodiment of this application. The following description, in conjunction with Fig. 3, explains how the water cycle algorithm is used to perform an iterative process for online parameter identification. In step S31, the population parameters are initialized and the individuals of the initial population are generated. Each individual in the population represents a possible solution for a set of parameters to be determined, and the total number of individuals in the population represents the number of possible solutions. The population parameters can include, in particular, the following: the initial total number of individuals in the population (Npop), the number of parameters to be identified (Dvar), the maximum number of algorithm iterations (imax), and evaporation conditions (dmax). Additionally, an upper limit for the parameters to be identified can be defined during the initialization process (UB and the underworld LB). Initial population size Npop: For example, depending on computing power, the larger the total number of individuals in the initial population, the more scenarios are covered and the easier it is to obtain the optimal solution, but the higher the dedicated computing power required for each iteration step. Therefore, based on the current processor performance and the simulation data, a population size value should be chosen that ensures the algorithm effectively explores the solution space without consuming excessive computing resources. The upper limit of the parameter to be determined (UB) and the lower limit (LB) can be adjusted according to the physical properties of the tire. Tire manufacturers typically specify corresponding limits based on different speed ratings. These parameters can be adjusted by increasing the values ​​recommended in the manual, which helps to narrow the search. Furthermore, historical parameter identification results can be used as starting values ​​to define upper and lower limits, thereby improving the efficiency and accuracy of the algorithm. Setting a maximum number of iterations primarily serves to prevent the algorithm from getting stuck in an infinite loop if it fails to find an optimal solution. This is an empirical parameter designed to ensure that the algorithm terminates within a reasonable timeframe. In the initial stage, the individuals of the population are not classified; all individuals are considered "raindrops." The precipitation process can be divided into streams, rivers, or oceans. For a given population, the problem of identifying the parameters is given by the initial population. The total population can be represented as Npop × Dvar. The matrix is: In step S32, the fitness value of each individual in the population is calculated. Based on this fitness value, all individuals in the population are classified as streams: stream, river, and ocean. This classification and initialization helps the algorithm to search the solution space more efficiently in subsequent iterations. In the water cycle algorithm, the fitness value Cj is an indicator used to measure the quality or excellence of a set of potential solutions. The fitness value can be calculated using the following formula: This represents the fitness function, for example, the error between the estimated lateral acceleration and the actual vehicle dynamics data. Based on the value of the fitness function (i.e., the fitness value), all individuals in the population can be sorted and classified according to their fitness, resulting in oceans, rivers, and streams. In one embodiment, the individual with the lowest fitness value can be designated as the ocean, with a count of 1; the total number of individuals from rivers and oceans is [missing information]. The remaining individuals were divided into groups, with a count of [missing number]. For example, the initial population. Total population. It can be reformulated as follows: In, Total population. For the total population, Npop. This is the initial total number of individuals in the population. Dvar. It represents the number of parameters to be determined. Furthermore, this step can be used to calculate, based on fitness values, the number of streams flowing into the sea and the number of streams flowing into rivers in the current population. This process is based on the mechanisms of water accumulation in nature to simulate the distribution of potential solutions in the search space. The number of streams flowing into each river or ocean can be determined using the following formula: In, NSn: This represents the number of streams that flow into the nth river or ocean. Nstreams: This represents the total number of streams; "round" means rounding down. Nsr: This is the sum of all individuals in rivers and oceans. In the formula, Costn: Let be the fitness value of the nth river or ocean. It is the sum of the fitness values ​​of all rivers and oceans. With this method, streams are allocated based on the fitness value of each river or ocean, so that rivers or oceans with higher fitness values ​​can attract more streams. In the water cycle algorithm, this allocation mechanism simulates the natural flow of water from high to low points in nature, helping the algorithm to effectively search for the optimal solution. In step S33, the population is iteratively optimized by updating the positions of streams, rivers, and oceans. These updates can follow specific mathematical formulas. More precisely, the updated position of a river flowing into the sea can be represented as follows: The updated position of a stream flowing into a river can be represented as follows: The updated position of a river flowing into the sea can be represented as follows: where i is the iteration number; rand is a uniformly distributed random number between 0 and 1, intended to represent the randomness of the position updates. C is a constant, usually with the value 2, used to control the update step size. These values ​​represent the current locations of the stream, river, or ocean. These are the updated positions of the stream or ocean. After the stream's position is updated according to the formula above, its corresponding fitness score is calculated. If this score is better than that of the connected river, the stream and river positions are swapped; otherwise, no swap occurs. If a stream has a better fitness score than the rivers connected to it after its position is updated, this means that the stream's new location could represent a potentially better solution. Similar swapping mechanisms also exist between streams and oceans, as well as between rivers and oceans. In this way, the algorithm can simulate the flow and circulation of water in nature and continuously update the positions of streams, rivers, and oceans, thereby achieving population optimization. By swapping positions, the algorithm not only preserves excellent solutions but also promotes population diversity and avoids premature convergence to local optima. This mechanism helps the algorithm achieve a balance between global and local searches. In step S34, if the evaporation conditions are met, the evaporation process is triggered to reduce the number of streams and / or rivers, and the rain process is carried out to randomly create new individuals to join the population. In one embodiment, the evaporation condition can be set as follows: when the distance between a certain number of rivers and the ocean is less than a preset initial distance threshold. Alternatively, when a certain percentage of individuals in the population are more than a preset distance threshold of one second from the ocean. At this point, the evaporation process is triggered. This design strategy prevents the algorithm from converging too early near the global optimum and from the potential solutions becoming too widely dispersed in the solution space. This ensures that the algorithm can effectively search the global area while also finding solutions in promising regions. In other embodiments, the evaporation conditions can also be adjusted according to the fitness value of the individual. For example, if the fitness value of an individual does not improve significantly over several successive iterations, or if the overall concentration of individuals in the population is too high, this suggests that the algorithm might be trapped in a local optimum, which can trigger the evaporation process. In this way, the algorithm can regularly "refresh" the population and introduce new potential solutions to maintain the diversity and dynamism of the search. Once the evaporation conditions are met, new individuals can be created through rainfall processes according to the following equation: In represents newly formed raindrops (which can be further subdivided into streams or rivers based on their fitness value). LB is the lower bound of the parameter to be determined. UB is the upper bound of the parameter to be determined. rand are random numbers uniformly distributed between 0 and 1. The rain process can randomly generate new streams and rivers at various points in the solution space. These new elements represent new potential solutions, helping to increase solution diversity and open up new search spaces. By incorporating evaporation and precipitation processes, the algorithm is prevented from converging too early at a local optimum. In the water cycle, streams and rivers that flow too slowly to reach the sea evaporate. This evaporation process attracts new precipitation, creating new streams or rivers. This dynamic adaptation mechanism allows the algorithm to adaptively adjust its search strategy, thereby improving its global search capability and adaptability. In step S35, the evaporation conditions are adaptively updated during the iteration process. For example, the distance threshold can be dynamically updated during the iterations according to the following formula: dmax: In, For the first time, i distance threshold for each iteration cycle, For the updated number i + 1 distance threshold for each iteration cycle, imaxThis represents the maximum number of iterations. As the algorithm is further developed, the conditions for triggering evaporation could become stricter. In the early iteration phases, larger dmax values ​​allow for a broader search spectrum and help explore different regions of the solution space. As the iteration progresses, this dmax value causes the algorithm to focus on regions where the optimal solution is more likely to exist and to perform a more detailed search. This strategy not only facilitates the global search but also improves the depth of the local search, thus increasing the probability of finding the global optimum. By dynamically adjusting the distance threshold, the water cycle algorithm can flexibly switch between different search scales to adapt to the requirements of complex optimization problems. In the optional step S35', the internal parameters of the water recycling algorithm can be dynamically adapted to the vehicle's driving state, the driving environment conditions, the computation delay requirements, and / or the computation accuracy requirements. These internal parameters include at least the initial population size, the maximum number of iterations, the fitness function, and / or the evaporation conditions. In a defined driving scenario, the aforementioned internal parameters of the algorithm are relatively stable and do not require frequent adjustments. However, as soon as the driving scenario changes, these parameters must be recalculated to adapt them to the new driving conditions. This is why online identification is so important. In one embodiment, the aforementioned internal parameters must be re-evaluated and adjusted if the vehicle speed changes significantly or if the road surface conditions (such as humidity and evenness) change. For example, if such changes occur, the maximum number of iterations (imax) and the initial total population of individuals (Npop) can be increased accordingly. This ensures that the algorithm can fully search the solution space and find the optimal solution. Should the vehicle's driving state or the driving environment change, or should the computation process lead to large errors and convergence problems, the initial population parameters can be preset based on empirical values ​​or experimental data (e.g., results from similar scenarios).Using these newly defined initial parameters, the parameters to be determined can then be recalculated more effectively and adapted to the changing driving environment. In one embodiment, more iterations are required at high speeds or under complex road conditions to find better parameters for the wheel's lateral stiffness. Conversely, in scenarios where computing resources are limited or there are high real-time requirements, the maximum number of iterations can be reduced to accelerate the algorithm's convergence. In one embodiment, for applications requiring a fast response, it may be necessary to adjust the initial population size of the algorithm or to reduce the number of iterations in order to shorten the computation time. This dynamic adaptation mechanism allows the water circulation algorithm to react more flexibly to different driving scenarios and achieve optimal performance under varying conditions. This adaptive parameter adjustment strategy not only improves the robustness of the algorithm but also increases its practicality in real-world applications. In step S36, if the preset termination condition of the iteration is met, the identification parameter represented by the individual with the highest fitness score in the final population is output as the optimal solution. This is explained in more detail below in connection with the embodiments described in Fig. 4. Fig. 4 shows the logic block diagram for the online identification of wheel lateral stiffness using a water circulation algorithm. As described above in conjunction with Fig. 1, the following discrete model can be obtained by discretizing the established model of vehicle lateral dynamics: See Fig. 4. The lateral stiffnesses of the front and rear wheels, estimated at constant intervals using the water circulation algorithm, are represented in k and compared with the known coefficients of the discrete model, bf(k) and br(k). Multiplying and adding these values ​​yields an estimate of the vehicle's lateral acceleration—that is, the result of the discrete model. In the first iteration of the algorithm, the wheel lateral stiffness determined upon leaving the factory can be used as the initial value of the parameter to be determined, and subsequently, the estimated lateral acceleration can be calculated based on this value. Based on measurements of the vehicle's actual dynamic behavior, the true value of the vehicle's lateral acceleration can be determined. This true value, along with the lateral acceleration estimated by a water-circulation algorithm, is used as feedback. By comparing the results, the error value, e(k), can be calculated. This error value is provided to the water-circulation algorithm for the next iteration. The water-circulation algorithm uses this error value to adjust the estimated value of the parameter being determined. The goal is to reduce the difference between the estimated and true values ​​of the lateral acceleration, thereby accelerating the search and convergence process for the global optimum. The iterative process described above is repeated until the error value e(k) is reached. Approaching a preset threshold (e.g., close to zero) indicates that the estimated lateral acceleration is very close to the actual lateral acceleration, thus fulfilling the iteration termination condition. At this point, the individual with the highest fitness value in the final population generated by the water cycle algorithm represents the parameter to be identified, which is considered the optimal solution. In a specific embodiment, the fitness function can be constructed as follows: To measure whether the preset termination condition for the iteration is met: In,e(k) The first time k The error value at each sampling time, i.e., the difference between the estimated and the actual value of the lateral acceleration. This is an estimate of the lateral acceleration. ay(k) This represents the actual value of the lateral acceleration. In other embodiments, the fitness function can also have other forms of expression. Furthermore, the iteration termination conditions can be varied. For example, the termination condition for an iteration can also be based on a change in the fitness function, reaching a predetermined number of iterations, or a combination of these factors. This online identification process allows the water circulation algorithm to update the estimated wheel lateral stiffness value in real time, thus improving the accuracy and adaptability of the vehicle stability control. This method enables the dynamic determination of wheel lateral stiffness during vehicle operation, allowing it to respond to changing driving conditions and vehicle loads, thereby ensuring the vehicle's handling characteristics and safety. Fig. 5 shows a block diagram of a device for online identification of wheel lateral stiffness according to an embodiment of this application. As shown in Fig. 5, the device 10 comprises a processor 11 and a memory 12. The memory 12 stores instructions for the computer program. When the instructions for the computer program are executed by the processor 11, it can, for example, perform a procedure for online identification of the wheel lateral stiffness (which was described in detail above with reference to Fig. 2 and is not repeated here). The instructions of the computer program can be stored on a computer-readable storage medium. Computer-readable storage media can include, for example, high-speed main memory (RAM), but also non-volatile memory such as hard disks, main memory, plug-in hard disks, smart memory cards, secure digital cards, flash memory cards, at least one hard disk storage device, a flash memory device, or other volatile solid-state storage devices.The processor can be a central processing unit or other general-purpose processors, digital signal processors, application-specific integrated circuits, commercially available programmable gate arrays or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. In one embodiment, Device 10 can be deployed in the cloud to provide users with cloud services or computational results via a cloud infrastructure. Users can purchase parameter identification services from cloud providers and upload sample data or vehicle operating data via programming interfaces. The cloud-based Device 10 then uses this data to perform an online identification of the wheel lateral stiffness and makes the results available to the vehicle user in real time. In another embodiment, the device 10 can also be arranged in a vehicle to enable local parameter identification. Although certain embodiments of the present invention are described in detail herein, they are provided for illustrative purposes only and are not to be regarded as limiting the scope of the present invention. Various substitutions, modifications, and variations may be conceived without departing from the spirit and scope of the present invention.

Claims

A method for online identification of lateral wheel stiffness, comprising the following steps: Step S1: Creating a model of the vehicle's transverse kinematics with respect to the parameters to be identified, wherein the parameters to be identified include the lateral stiffness of the front wheels and the lateral stiffness of the rear wheels of the vehicle; Step S2: Performing a discretization of the vehicle's transverse kinematics model to obtain a discrete model with respect to the parameters to be identified; and Step S3: Fitting the output of the discrete model using the Water Cycle Algorithm (WCA) to determine parameters to be identified online. The method of claim 1, wherein step S1 comprises: using a two-degrees-of-freedom vehicle dynamics model to create the following model of the vehicle's transverse kinematics: M ⋅ ay = F yf + F yr where M is the mass of the vehicle, a y the lateral acceleration of the vehicle is F yf the front wheel lateral force and F yr the rear wheel lateral force; Parameterization of the transverse kinematics model based on the linear lateral force model of the wheels to obtain the following transverse kinematics model for the parameters to be identified: ay = C α f ⋅ bf + C α r ⋅ br where a y the lateral acceleration of the vehicle is, b f the first factor and b r the second coefficient is and C af for front wheel lateral stiffness and C ar stands for the rear wheel lateral stiffness. The method of claim 2, wherein the parameterization of the lateral kinematics model based on the linear lateral force model of the wheels comprises: creating a linear lateral force model of the wheels based on the lateral wheel stiffness and the slip angle of the wheels; creating a lateral wheel stiffness model based on the steering angle of the front wheels and the wheel speed angle; creating a wheel speed angle model based on the wheelbase, yaw rate, lateral speed, and longitudinal speed of the vehicle; integrating the linear lateral force model, the lateral wheel stiffness model, and the wheel speed angle model into the lateral kinematics model to express the lateral acceleration of the vehicle as a function of the front wheel lateral stiffness and the rear wheel lateral stiffness. Method according to any one of claims 1 to 3, wherein step S3 comprises: inputting the value of the deviation between the data of the actual dynamic response and the data of the predicted dynamic response of the vehicle into the Water Circulation Algorithm (WCA) to iteratively adjust the estimated value of the parameter to be identified, wherein the data of the predicted dynamic response of the vehicle is the output of the discrete model based on the estimated value of the parameter to be identified;After each iteration, check whether the preset condition for terminating the iterations is met; if the preset condition for terminating the iterations is not met, continue the iterations and control the estimation of the parameter to be determined in the next iteration round based on the value of the deviation between the data of the actual dynamic response and the data of the predicted dynamic response of the vehicle in the current iteration cycle; and, as soon as the condition for terminating the iterations is met, terminate the iterations and output the estimated value of the parameter to be determined in the current iteration cycle as the optimal solution. The method of claim 4, wherein a fitness function Cjb is created to assess whether the preset condition for terminating the iterations is satisfied: Cj = e(k)² = [ay^(k) − ay(k)]² where e(k) is the value of the deviation between the estimated value of the lateral acceleration and the actual value of the lateral acceleration at sampling time k, ay ^ ( k ) the estimated value of the lateral acceleration and a y (k) is the actual value of the lateral acceleration. A method according to any one of claims 1 to 5, wherein in step S3 the following iteration process is performed using the Water Cycle Algorithm (WCA): Step S31: Initializing the population parameter and generating the first individuals of the population, each individual in the population representing a possible solution for a set of parameters to be determined; Step S32: Computing the fitness value of each individual in the population and classifying all individuals in the population into streams, rivers, and oceans based on the fitness value; Step S33: Iteratively optimizing the population by updating the locations of streams, rivers, and oceans; and Step S36: When the preset condition for terminating the iterations is met, outputting the parameter to be identified, represented by the individual with the highest fitness value in the final population, as the optimal solution. The method of claim 6, wherein in step S3 the iteration process comprises: Step S34: When the evaporation conditions are met, triggering the evaporation process to reduce the number of streams and / or rivers, and performing a rain process to randomly generate new individuals to join the population; and Step S35: Adaptively updating the evaporation conditions during the iteration process. Method according to any one of claims 1 to 7, wherein step S3 further comprises: Dynamically adjusting the internal parameters of the water cycle algorithm (WCA) based on the driving status of the vehicle, the driving environment conditions, the latency requirements for the calculation and / or the accuracy requirements for the calculation, wherein the internal parameters include at least one of the following: initial population size, maximum number of iterations, fitness function and / or evaporation conditions. Device (10) for online identification of lateral wheel stiffness, wherein the device (10) comprises a processor (11) and a memory (12), wherein computer program instructions are stored on the memory (12) which, when executed by the processor (11), enable the processor (11) to perform the method according to any one of claims 1 to 8. A computer program product comprising program code units, wherein the program code units are configured to assist the computer in performing the method according to any one of claims 1 to 8 when the computer program product is executed on a computer or stored on a computer-readable storage medium.

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