CN116552548A - Four-wheel distributed electric drive automobile state estimation method - Google Patents
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Abstract
Description
技术领域technical field
本发明涉及电动汽车技术领域,特别是涉及一种四轮分布式电驱动汽车状态估计方法。The invention relates to the technical field of electric vehicles, in particular to a state estimation method for a four-wheel distributed electric drive vehicle.
背景技术Background technique
电动汽车具有节能环保的优点,是实现汽车能源转型的重要手段。四轮分布式电驱动汽车是电动汽车发展的主要类型。与传统车辆相比,其制动力矩和驱动力矩可独立控制,动力传递效率高,更容易实现车辆主动安全控制,是未来汽车的发展方向。Electric vehicles have the advantages of energy saving and environmental protection, and are an important means to realize the energy transformation of vehicles. Four-wheel distributed electric drive vehicle is the main type of electric vehicle development. Compared with traditional vehicles, its braking torque and driving torque can be independently controlled, its power transmission efficiency is high, and it is easier to realize vehicle active safety control, which is the development direction of future automobiles.
然而,车辆主动安全控制系统的控制和决策的前提是准确地获取车辆状态参数信息。由于技术限制或部分传感器价格昂贵,或信号受外界干扰影响较大,难以直接测量。因此,如何根据部分现有低成本的传感器来准确的估计这些不易测量状态参数,如质心侧偏角,是本领域技术人员需要解决的技术问题。However, the premise of the control and decision-making of the vehicle active safety control system is to accurately obtain the vehicle state parameter information. Due to technical limitations or the high price of some sensors, or the signal is greatly affected by external interference, it is difficult to measure directly. Therefore, how to accurately estimate these difficult-to-measure state parameters, such as the center-of-mass slip angle, based on some existing low-cost sensors is a technical problem to be solved by those skilled in the art.
发明内容Contents of the invention
本发明的目的在于提供一种四轮分布式电驱动汽车状态估计方法,以实现四轮分布式电驱动汽车状态的有效实时估计。The purpose of the present invention is to provide a method for estimating the state of a four-wheel distributed electric drive vehicle, so as to realize effective real-time estimation of the state of the four-wheel distributed electric drive vehicle.
一种四轮分布式电驱动汽车状态估计方法,包括以下步骤:A method for state estimation of a four-wheel distributed electric drive vehicle, comprising the following steps:
步骤1,根据分布式电驱动汽车的运动特性,构建纵向、横向、横摆非线性三自由度车辆动力学模型,并根据非线性三自由度车辆模型构建状态空间方程;Step 1. According to the motion characteristics of the distributed electric drive vehicle, construct a longitudinal, lateral, and yaw nonlinear three-degree-of-freedom vehicle dynamics model, and construct a state-space equation based on the nonlinear three-degree-of-freedom vehicle model;
步骤2,基于步骤1中构建的状态空间方程,将平方根容积卡尔曼滤波器与车辆动力学系统对接,建立非线性系统的平方根容积卡尔曼滤波器的离散状态方程和观测方程,确定平方根容积卡尔曼滤波器的待估计量、输入量和观测量,并采用平方根滤波的方式对平方根容积卡尔曼滤波器进行待估计参数的修正及递推更新;Step 2, based on the state space equation constructed in step 1, connect the square root volumetric Kalman filter with the vehicle dynamics system, establish the discrete state equation and observation equation of the square root volumetric Kalman filter of the nonlinear system, and determine the square root volumetric Kalman filter The estimated quantity, input quantity and observed quantity of the Mann filter, and the square root volumetric Kalman filter is used to correct and recursively update the estimated parameters of the square root volumetric Kalman filter;
步骤3,基于步骤2中构建的平方根容积卡尔曼滤波器,采用最大相关熵准则作为优化标准,构建最大相关熵平方根容积卡尔曼滤波器;Step 3, based on the square root volumetric Kalman filter constructed in step 2, using the maximum correlation entropy criterion as an optimization standard to construct a maximum correlation entropy square root volumetric Kalman filter;
步骤4,获取改进的非洲秃鹫算法,并对基于步骤3构建的最大相关熵平方根容积卡尔曼滤波器的非高斯噪声进行寻优处理,通过改进的非洲秃鹫算法优化最大相关熵平方根容积卡尔曼滤波器,最终实现四轮分布式电驱动汽车状态参数的最优估计。Step 4, obtain the improved African vulture algorithm, and optimize the non-Gaussian noise of the maximum correlation entropy square root volumetric Kalman filter based on step 3, and optimize the maximum correlation entropy square root volumetric Kalman filter through the improved African vulture algorithm Finally, the optimal estimation of the state parameters of the four-wheel distributed electric drive vehicle is realized.
根据本发明提供的四轮分布式电驱动汽车状态估计方法,具有以下有益效果:According to the method for estimating the state of a four-wheel distributed electric drive vehicle provided by the present invention, it has the following beneficial effects:
1、本发明考虑四轮分布式电驱动汽车的运动,建立三自由度车辆动力学模型,以四轮分布式电驱动汽车实时反馈的行驶参数(车轮转角和侧向加速度)为模型输入量,利用系统输入参数、车辆结构参数、实时测量参数,建立改进非洲秃鹫算法优化最大相关熵平方根容积卡尔曼滤波器对四轮分布式电驱动汽车操纵稳定性关键状态参数进行实时估计;1. The present invention considers the motion of the four-wheel distributed electric drive vehicle, establishes a three-degree-of-freedom vehicle dynamics model, and takes the driving parameters (wheel rotation angle and lateral acceleration) fed back in real time by the four-wheel distributed electric drive vehicle as model input, Using the system input parameters, vehicle structure parameters, and real-time measurement parameters, an improved African vulture algorithm is established to optimize the maximum correlation entropy square root volumetric Kalman filter to estimate the key state parameters of the handling stability of the four-wheel distributed electric drive vehicle in real time;
2、不同于一般的车辆状态参数在线估计方法,本发明充分考虑了分布式驱动电动汽车车辆参数即时反馈的特性和对系统非高斯噪声的寻优能力,同时模型考虑车辆的纵向运动、横向运动和横摆运动,可以较为准确的反映分布式驱动电动汽车在各种工况下的行驶特点;2. Different from the general online estimation method of vehicle state parameters, the present invention fully considers the characteristics of real-time feedback of vehicle parameters of distributed drive electric vehicles and the ability to optimize the non-Gaussian noise of the system, and at the same time, the model considers the longitudinal and lateral movements of the vehicle and yaw motion, which can accurately reflect the driving characteristics of distributed drive electric vehicles under various working conditions;
3、不同于一般的无迹卡尔曼滤波算法和扩展卡尔曼滤波算法,本发明采用改进非洲秃鹫优化最大相关熵平方根容积卡尔曼滤波器,对建立的汽车动力学系统模型状态进行估计。考虑普遍路况下行驶的分布式电驱动汽车动力学模型是一个非线性的系统,传统的无迹卡尔曼滤波算法和扩展卡尔曼滤波算法估计精度不高,而容积卡尔曼滤波算法使用三阶球面径向容积准则,并使用一组容积点来逼近具有附加高斯噪声的非线性系统的状态均值和协方差,是理论上当前最接近贝叶斯滤波的近似算法,是解决高阶非线性系统状态估计的强有力工具。但容积卡尔曼滤波器在递推过程中,计算量大、数值不稳定。因此,本发明在容积卡尔曼滤波的基础上,引入平方根滤波的思想且采用最大相关熵准则对过程噪声的协方差矩阵进行约束,采用改进非洲秃鹫算法对最大相关熵平方根容积卡尔曼滤波器的非高斯噪声自适应寻优,可以一定程度上减弱滤波过程不稳定的影响,并使得估计精度有所提高;3. Different from the general unscented Kalman filter algorithm and the extended Kalman filter algorithm, the present invention uses the improved African vulture optimized maximum correlation entropy square root volumetric Kalman filter to estimate the state of the established vehicle dynamics system model. Considering the dynamic model of distributed electric drive vehicles driving under common road conditions is a nonlinear system, the traditional unscented Kalman filter algorithm and extended Kalman filter algorithm have low estimation accuracy, while the volumetric Kalman filter algorithm uses a third-order sphere The radial volume criterion, and using a set of volume points to approximate the state mean and covariance of a nonlinear system with additional Gaussian noise, is currently the closest approximation algorithm to Bayesian filtering in theory, and is a solution to high-order nonlinear system states A powerful tool for estimation. However, in the recursive process of the volumetric Kalman filter, the calculation amount is large and the value is unstable. Therefore, on the basis of the volumetric Kalman filter, the present invention introduces the idea of the square root filter and uses the maximum correlation entropy criterion to constrain the covariance matrix of the process noise, and adopts the improved African vulture algorithm to the maximum correlation entropy square root volumetric Kalman filter. Adaptive optimization of non-Gaussian noise can reduce the influence of unstable filtering process to a certain extent and improve the estimation accuracy;
4、本发明涉及的基于动力学模型的车辆状态参数估计算法结合四轮分布式电驱动汽车车辆信息参数可实时获取的特点,降低了对车载传感器的要求。同时估计过程基本不受如车辆质量、车辆横摆转动惯量等车辆结构参数变化影响,具有较广的适用性和良好的鲁棒性。4. The vehicle state parameter estimation algorithm based on the dynamic model involved in the present invention combines the characteristics that the vehicle information parameters of the four-wheel distributed electric drive vehicle can be obtained in real time, which reduces the requirements for the on-board sensors. At the same time, the estimation process is basically not affected by changes in vehicle structural parameters such as vehicle mass and vehicle yaw moment of inertia, and has wide applicability and good robustness.
附图说明Description of drawings
图1为本发明的实施例提供的四轮分布式电驱动汽车状态估计方法的流程图;Fig. 1 is the flow chart of the four-wheel distributed electric drive vehicle state estimation method provided by the embodiment of the present invention;
图2为本发明所提出的方法与传统容积卡尔曼算法、真实值的对比图。Fig. 2 is a comparison diagram between the method proposed by the present invention and the traditional volumetric Kalman algorithm and the actual value.
具体实施方式Detailed ways
为使本发明实施例的目的、技术方案和优点更加清楚,下面将结合本发明实施例中的附图,对本发明实施例中的技术方案进行清楚、完整地描述,显然,所描述的实施例是本发明一部分实施例,而不是全部的实施例。基于本发明中的实施例,本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例,都属于本发明保护的范围。In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments It is a part of embodiments of the present invention, but not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.
请参阅图1,本发明的实施例提供一种四轮分布式电驱动汽车状态估计方法,本实施例中,四轮分布式电驱动汽车状态以质心侧偏角为例进行说明,该方法包括步骤1~步骤4:Please refer to Fig. 1, an embodiment of the present invention provides a method for estimating the state of a four-wheel distributed electric drive vehicle. In this embodiment, the state of a four-wheel distributed electric drive vehicle is described by taking the side slip angle of the center of mass as an example. The method includes Step 1~Step 4:
步骤1,根据分布式电驱动汽车的运动特性,构建纵向、横向、横摆非线性三自由度车辆动力学模型,并根据非线性三自由度车辆模型构建状态空间方程。Step 1. According to the motion characteristics of the distributed electric drive vehicle, construct a longitudinal, lateral, and yaw nonlinear three-degree-of-freedom vehicle dynamics model, and construct a state-space equation based on the nonlinear three-degree-of-freedom vehicle model.
步骤1中,根据分布式电驱动汽车的纵向运动、横向运动、横摆运动建立的非线性三自由度车辆动力学方程如下式所示:In step 1, the nonlinear three-degree-of-freedom vehicle dynamics equation established according to the longitudinal motion, lateral motion, and yaw motion of the distributed electric drive vehicle is shown in the following formula:
其中,、/>分别为车辆横摆角速度、质心侧偏角;/>表示前轮转角;v x、a x、a y分别表示车辆纵向速度、纵向加速度、侧向加速度;k 1、k 2分别为车辆前轴、后轴的等效侧偏刚度;a、b分别为前轴到质心的距离、后轴到质心的距离;I z为质心的转动惯量;m为整车质量;/>表示对所示量的微分;in, , /> are vehicle yaw rate and side slip angle of center of mass respectively; /> represents the front wheel rotation angle; v x , a x , a y represent the longitudinal velocity, longitudinal acceleration and lateral acceleration of the vehicle respectively; k 1 , k 2 represent the equivalent cornering stiffness of the front axle and rear axle of the vehicle respectively; is the distance from the front axle to the center of mass, and the distance from the rear axle to the center of mass; I z is the moment of inertia of the center of mass; m is the mass of the vehicle; /> expresses the differentiation of the indicated quantity;
建立的非线性三自由度车辆模型的状态空间方程如下式所示:The state space equation of the established nonlinear three-degree-of-freedom vehicle model is as follows:
。 .
步骤2,基于步骤1中构建的状态空间方程,将平方根容积卡尔曼滤波器与车辆动力学系统对接,建立非线性系统的平方根容积卡尔曼滤波器的离散状态方程和观测方程,确定平方根容积卡尔曼滤波器的待估计量、输入量和观测量,并采用平方根滤波的方式对平方根容积卡尔曼滤波器进行待估计参数的修正及递推更新。Step 2, based on the state space equation constructed in step 1, connect the square root volumetric Kalman filter with the vehicle dynamics system, establish the discrete state equation and observation equation of the square root volumetric Kalman filter of the nonlinear system, and determine the square root volumetric Kalman filter The estimated quantity, input quantity and observed quantity of the Mann filter, and the square root volumetric Kalman filter is used to correct and recursively update the estimated parameters of the square root volumetric Kalman filter.
其中,步骤2具体包括:Among them, step 2 specifically includes:
构建非线性系统的平方根容积卡尔曼滤波器的离散状态方程、观测方程如下式所示:The discrete state equation and observation equation of the square root volumetric Kalman filter to construct the nonlinear system are as follows:
其中,为k时刻的状态变量,/>,T表示转置操作;/>为k时刻的控制变量,/>;/>为k时刻的观测变量,/>;/>为k-1时刻的状态变量;/>为k-1时刻的控制变量;f为离散状态方程的演化方程;h为观测方程的演化方程,/>和分别为具有零均值的不相关过程噪声和量测噪声;in, is the state variable at time k , /> , T represents the transpose operation; /> is the control variable at time k , /> ;/> is the observed variable at time k , /> ;/> is the state variable at time k -1; /> is the control variable at time k -1; f is the evolution equation of the discrete state equation; h is the evolution equation of the observation equation, /> and are uncorrelated process noise and measurement noise with zero mean, respectively;
采用前向欧拉离散方法,得到离散后的状态方程及量测方程,如下式所示:The forward Euler discretization method is used to obtain the discretized state equation and measurement equation, as shown in the following formula:
其中,、/>分别为k时刻车辆横摆角速度、质心侧偏角;/>、/>分别表示k时刻车辆纵向速度、侧向加速度;/>、/>分别为k-1时刻车辆横摆角速度、质心侧偏角;/>、/>、/>分别表示k-1时刻车辆纵向速度、纵向加速度、侧向加速度;表示k-1时刻车辆前轮转角;in, , /> are respectively the vehicle yaw rate and the side slip angle of the center of mass at time k ; /> , /> Respectively represent the longitudinal velocity and lateral acceleration of the vehicle at time k ; /> , /> are the vehicle yaw rate and the side slip angle of the center of mass at time k -1 respectively; /> , /> , /> Respectively represent the longitudinal velocity, longitudinal acceleration and lateral acceleration of the vehicle at time k -1; Indicates the front wheel angle of the vehicle at time k -1;
将离散后的状态方程及量测方程引入平方根容积卡尔曼滤波器中,进行预测和更新。The discretized state equation and measurement equation are introduced into the square root volumetric Kalman filter for prediction and update.
将离散后的状态方程及量测方程引入平方根容积卡尔曼滤波器中,进行预测和更新具体包括:The discretized state equation and measurement equation are introduced into the square root volumetric Kalman filter, and the prediction and update specifically include:
1)预测:1) Forecast:
在k时刻,定义是k-1时刻状态协方差矩阵/>的平方根,是过程噪声的协方差/>的平方根因子,/>是量测噪声的协方差/>的平方根因子;At time k , define is the state covariance matrix at time k -1 /> the square root of is the covariance of the process noise /> square root factor of , /> is the covariance of the measurement noise /> square root factor of
状态容积点的计算:Calculation of state volume points:
其中,为状态容积点,/>是第i个容积点,/>,n为大于等于1的自然数,/>为k-1时刻的状态估计值;in, is the state volume point, /> is the i-th volume point, /> , n is a natural number greater than or equal to 1, /> is the estimated state value at time k -1;
状态容积点的传播:Propagation of state volume points:
其中,为预测过程中容积点对应的预测值;in, is the predicted value corresponding to the volume point in the prediction process;
先验状态和协方差矩阵的平方根由下式估计:The prior state and the square root of the covariance matrix are estimated by:
其中,为根据k-1时刻预计的k时刻的状态变量;in, is the state variable at time k predicted according to time k -1;
其中,为根据k-1时刻预计的k时刻的状态协方差矩阵的平方根,/>表示矩阵的三角分解,/>为状态向量的偏差矩阵;in, is the square root of the state covariance matrix at k time predicted according to k -1 time, /> represents the triangular decomposition of a matrix, /> is the deviation matrix of the state vector;
2)更新:2) Update:
量测容积点的计算:Calculation of measuring volume points:
其中,为更新阶段重构的容积点对应的状态向量,/>为更新阶段根据k-1时刻预计的k时刻的状态向量,/>为更新重构阶段k-1时刻状态协方差矩阵的平方根;in, The state vector corresponding to the volume point reconstructed for the update phase, /> is the state vector at time k estimated according to time k -1 in the update phase, /> is the square root of the state covariance matrix at time k -1 of the update reconstruction stage;
量测容积点的传播:Measure the spread of volume points:
其中,为量测更新过程中容积点对应的预测值;in, is the predicted value corresponding to the volume point during the measurement update process;
先验测量值和协方差矩阵的平方根由下式估计:The a priori measurements and the square root of the covariance matrix are estimated by:
其中,为根据k-1时刻预计的k时刻的量测变量;in, is the measured variable at time k predicted according to time k -1;
其中,为根据k-1时刻预计的k时刻的量测协方差矩阵,/>为量测向量的偏差矩阵;in, is the measurement covariance matrix at k time predicted according to k -1 time, /> is the deviation matrix of the measurement vector;
计算互协方差矩阵:Compute the cross-covariance matrix:
其中,为量测向量的偏差矩阵的转置矩阵,/>为互协方差矩阵,为状态向量的偏差矩阵;in, is the transpose matrix of the bias matrix of the measurement vector, /> is the cross-covariance matrix, is the deviation matrix of the state vector;
计算卡尔曼增益:Calculate the Kalman gain :
其中,为新息方差的平方根因子,/>为新息方差的平方根因子的转置矩阵;in, is the square root factor of the innovation variance, /> is the transposed matrix of the square root factor of the innovation variance;
后验状态和协方差矩阵的平方根由下式估计:The posterior state and the square root of the covariance matrix are estimated by:
其中,为预计的k时刻的状态变量,/>为采集到的k时刻的量测变量;in, is the expected state variable at time k , /> is the measured variable collected at time k ;
其中,为k时刻状态协方差矩阵的平方根。in, is the square root of the state covariance matrix at time k .
步骤3,基于步骤2中构建的平方根容积卡尔曼滤波器,采用最大相关熵准则作为优化标准,构建最大相关熵平方根容积卡尔曼滤波器。Step 3. Based on the square root volumetric Kalman filter constructed in step 2, the maximum correlation entropy criterion is used as the optimization standard to construct a maximum correlation entropy square root volumetric Kalman filter.
采用最大相关熵准则作为优化标准,构建最大相关熵平方根容积卡尔曼滤波器,充分考虑了估计误差的高阶矩,在处理非高斯噪声时表现出很强的鲁棒性。Using the maximum correlation entropy criterion as the optimization standard, the maximum correlation entropy square root volumetric Kalman filter is constructed, which fully considers the high-order moments of the estimation error, and shows strong robustness when dealing with non-Gaussian noise.
其中,步骤3具体包括:Among them, step 3 specifically includes:
结合步骤1中构建的非线性三自由度车辆动力学模型与步骤2中构建的平方根容积卡尔曼滤波器,引入最大相关熵准则,构造非线性递归模型:Combining the nonlinear three-degree-of-freedom vehicle dynamics model constructed in step 1 with the square root volumetric Kalman filter constructed in step 2, the maximum correlation entropy criterion is introduced to construct a nonlinear recursive model:
其中,为过程变量,/>,/>的协方差/>为:in, for the process variable, /> , /> covariance of for:
其中,为状态误差协方差对应的过程变量,/>为量测误差协方差对应的过程变量,/>是k时刻状态协方差矩阵;in, is the process variable corresponding to the state error covariance, /> is the process variable corresponding to the measurement error covariance, /> is the state covariance matrix at time k ;
然后基于最大相关熵准则的最佳估计得到下式:Then the best estimate based on the maximum correlation entropy criterion is obtained as follows:
其中,为通过最大相关熵准则最佳估计的状态量,/>为核函数,q+m为维度;in, is the state quantity best estimated by the maximum correlation entropy criterion, /> is the kernel function, q + m is the dimension;
然后,定义为最大相关熵准则的过程变量,得到下式:Then, define is the process variable of the maximum correlation entropy criterion, and the following formula is obtained:
其中,为/>前q个元素的对角矩阵,/>为/>的第q+1至q+m个元素的对角矩阵;in, for /> Diagonal matrix of the first q elements, /> for /> The diagonal matrix of the q +1 to q + m elements of ;
将的更新协方差矩阵定义为:Will The updated covariance matrix of is defined as:
其中,为最大相关熵改进后的k时刻状态协方差矩阵,/>最大相关熵改进后的量测误差协方差矩阵;/>为/>的逆矩阵;in, is the state covariance matrix at time k after the maximum correlation entropy improvement, /> The measurement error covariance matrix improved by the maximum correlation entropy; /> for /> the inverse matrix;
先验测量噪声方差可表示为:The prior measurement noise variance can be expressed as:
其中,为/>逆矩阵;in, for /> inverse matrix;
然后,更新后的量测协方差矩阵的平方根由下式获得:Then, the square root of the updated measurement covariance matrix Obtained by the following formula:
最后,将带入平方根容积卡尔曼滤波器中替代/>进行迭代循环,从而构建出最大相关熵平方根容积卡尔曼滤波器。Finally, the into the square root volumetric Kalman filter instead of /> An iterative cycle is performed to construct a maximum correlation entropy square root volumetric Kalman filter.
步骤4,获取改进的非洲秃鹫算法,并对基于步骤3构建的最大相关熵平方根容积卡尔曼滤波器的非高斯噪声进行寻优处理,通过改进的非洲秃鹫算法优化最大相关熵平方根容积卡尔曼滤波器,最终实现四轮分布式电驱动汽车状态参数的最优估计。Step 4, obtain the improved African vulture algorithm, and optimize the non-Gaussian noise of the maximum correlation entropy square root volumetric Kalman filter based on step 3, and optimize the maximum correlation entropy square root volumetric Kalman filter through the improved African vulture algorithm Finally, the optimal estimation of the state parameters of the four-wheel distributed electric drive vehicle is realized.
步骤4中,对非洲秃鹫算法进行以下改进:In step 4, the following improvements are made to the African vulture algorithm:
第一阶段:确定组内最优秃鹫The first stage: determine the best vulture in the group
在非洲秃鹰优化算法中引入混沌优化模式,利用混沌理论的原理来探索搜索空间,表达式如下:The chaotic optimization mode is introduced into the African condor optimization algorithm, and the principle of chaos theory is used to explore the search space. The expression is as follows:
其中,为当前时刻全局最佳位置,/>为下一时刻全局最佳位置;引入混沌优化模式,利用混沌理论的原理来探索搜索空间,让种群初始化更加均匀,避免局部最优。in, is the global best position at the current moment, /> For the global best position at the next moment; introduce chaos optimization mode, use the principle of chaos theory to explore the search space, make the population initialization more uniform, and avoid local optimum.
初始化种群后,计算种群适应度值:After initializing the population, calculate the population fitness value:
其中,为其他秃鹰向最佳秃鹰位置移动的概率,/>和/>为搜索操作之前给定的参数,其值介于0和1之间,且/>和/>之和为1;/>、/>分别为两组最佳秃鹫;/>为使用轮盘赌轮获得选择最佳解的概率;/>为当前非洲秃鹫为最佳秃鹫;in, is the probability that other vultures move to the optimal vulture position, /> and /> is the parameter given before the search operation, with a value between 0 and 1, and /> and /> The sum is 1; /> , /> Two groups of best vultures respectively;/> For obtaining the probability of choosing the best solution using the roulette wheel; /> Best vulture for the current African vulture;
第二阶段:计算秃鹫饥饿率Phase Two: Calculating Vulture Hunger Rate
其中,F为秃鹫饥饿率,表示当前迭代次数,/>表示最大迭代次数,zz是介于-1到1并且每次迭代都变化的随机数,c是介于-2到2之间的随机数,/>是介于0到1之间的随机数,当zz降至0以下,表示秃鹫处于饥饿状态,若zz值增至0,则表示秃鹫已经饱腹,当/>大于1时,秃鹫在不同区域寻找食物,非洲秃鹫算法进入探索阶段;当/>小于1时,非洲秃鹫算法进入开发阶段,秃鹫在最佳解的附近寻找食物;Among them, F is the vulture hunger rate, Indicates the current iteration number, /> Indicates the maximum number of iterations, zz is a random number between -1 and 1 and changes every iteration, c is a random number between -2 and 2, /> It is a random number between 0 and 1. When zz falls below 0, it means that the vulture is hungry. If the value of zz increases to 0, it means that the vulture is full. When /> When it is greater than 1, vultures are looking for food in different areas, and the African vulture algorithm enters the exploration stage; when /> When it is less than 1, the African vulture algorithm enters the development stage, and the vulture looks for food near the optimal solution;
第三阶段:探索Phase Three: Exploration
其中,是介于-1到1之间的随机数,/>为预设的探索参数,用于控制探索策略,/>当前迭代中的秃鹫位置向量,/>是下一次迭代中的秃鹫位置向量,/>和均为介于-1到1之间的随机数,ub和lb分别为寻优的上下边界;in, is a random number between -1 and 1, /> is the preset exploration parameter, used to control the exploration strategy, /> The vulture position vector in the current iteration, /> is the vulture position vector in the next iteration, /> and Both are random numbers between -1 and 1, ub and lb are the upper and lower boundaries of optimization;
第四阶段:开发Phase Four: Development
当介于0.5和1之间时,非洲秃鹫算法进入开发阶段的第一子阶段,在第一子阶段,执行两种不同的旋转飞行和围攻策略,策略根据第一子阶段的探索参数/>进行选择:when Between 0.5 and 1, the African vulture algorithm enters the first sub-phase of the development phase. In the first sub-phase, two different strategies of rotating flight and siege are executed. The strategy is based on the exploration parameters of the first sub-phase /> Make a selection:
其中,、/>、/>均为介于-1到1之间的随机数;/>为秃鹫旋转飞行第一种方程,/>为秃鹫旋转飞行的第二种方程;/>为秃鹫与两组最好秃鹫之间的距离;in, , /> , /> Both are random numbers between -1 and 1;/> For the first equation of vulture rotational flight, /> The second equation for the rotary flight of the vulture; /> is the distance between the vulture and the best two groups of vultures;
如果小于0.5,则执行开发阶段的第二子阶段;if If it is less than 0.5, execute the second sub-phase of the development phase;
此外,用Levy飞行策略改进开发阶段的第二子阶段的开发过程,表达式如下:In addition, the development process of the second sub-phase of the development phase is improved by using the Levy flight strategy, the expression is as follows:
其中,Levy为一种飞行策略,xx为随机步长,为指数参数,u表示服从正态分布;Among them, Levy is a flight strategy, xx is a random step size, is an exponential parameter, and u means obeying a normal distribution;
策略根据第二子阶段的探索参数进行选择,改进后公式为:The policy is based on the exploration parameters of the second subphase To select, the improved formula is:
其中,是当前迭代中第一组的最佳秃鹫,/>是当前迭代中第二组的最佳秃鹫,/>为秃鹫竞争食物的第一种运动方程,/>为秃鹫竞争食物的第二种运动方程;/>为介于-1到1之间的随机数,/>为针对飞行距离d的飞行策略;in, is the best vulture of the first set in the current iteration, /> is the best vulture of the second set in the current iteration, /> The first equations of motion for vultures competing for food, /> A second equation of motion for vultures competing for food;/> is a random number between -1 and 1, /> is the flight strategy for the flight distance d ;
适应度函数为:The fitness function is:
其中,h c为状态信息的实际方差;为最大相关熵平方根容积卡尔曼滤波器的新息序列;/>为权重系数;Among them, hc is the actual variance of state information; is the innovation sequence of the maximum correlation entropy square root volumetric Kalman filter; /> is the weight coefficient;
获取上述改进的非洲秃鹫算法后,对基于步骤3构建的最大相关熵平方根容积卡尔曼滤波器的非高斯噪声进行寻优处理,通过改进的非洲秃鹫算法优化最大相关熵平方根容积卡尔曼滤波器,从而对过程噪声和量测噪声进行优化,最终实现四轮分布式电驱动汽车状态参数的最优估计。After the above-mentioned improved African vulture algorithm is obtained, the non-Gaussian noise of the maximum correlation entropy square root volumetric Kalman filter constructed based on step 3 is optimized, and the maximum correlation entropy square root volumetric Kalman filter is optimized through the improved African vulture algorithm. In this way, the process noise and measurement noise are optimized, and finally the optimal estimation of the state parameters of the four-wheel distributed electric drive vehicle is realized.
图2为本发明所提出的方法与传统容积卡尔曼算法、真实值的对比图,通过carsim软件搭建双移线工况场景进行测试,整车质量设置为1412kg,前轴到质心的距离为1.015m,后轴到质心的距离为1.895m,行驶纵向车速为40km/h,路面附着系数为0.85,车轮半径为0.325m,由图2可知本发明所提出的方法对质心侧偏角的估计精度明显提升,精确度提升约10%。Fig. 2 is a comparison chart of the method proposed by the present invention and the traditional volumetric Kalman algorithm and the real value. The double shifting working condition scene is built by carsim software for testing. The mass of the vehicle is set to 1412kg, and the distance from the front axle to the center of mass is 1.015 m, the distance from the rear axle to the center of mass is 1.895m, the longitudinal vehicle speed is 40km/h, the road surface adhesion coefficient is 0.85, and the wheel radius is 0.325m. It can be seen from Figure 2 that the method proposed by the present invention can estimate the side slip angle of the center of mass. Significantly improved, the accuracy increased by about 10%.
在本说明书的描述中,参考术语“一个实施例”、“一些实施例”、 “示例”、“具体示例”、或“一些示例”等的描述意指结合该实施例或示例描述的具体特征、结构、材料或者特点包含于本发明的至少一个实施例或示例中。在本说明书中,对上述术语的示意性表述不一定指的是相同的实施例或示例。而且,描述的具体特征、结构、材料或者特点可以在任何的一个或多个实施例或示例中以合适的方式结合。In the description of this specification, descriptions referring to the terms "one embodiment", "some embodiments", "example", "specific examples", or "some examples" mean that specific features described in connection with the embodiment or example , structure, material or characteristic is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
尽管已经示出和描述了本发明的实施例,本领域的普通技术人员可以理解:在不脱离本发明的原理和宗旨的情况下可以对这些实施例进行多种变化、修改、替换和变型,本发明的范围由权利要求及其等同物限定。Although the embodiments of the present invention have been shown and described, those skilled in the art can understand that various changes, modifications, substitutions and modifications can be made to these embodiments without departing from the principle and spirit of the present invention. The scope of the invention is defined by the claims and their equivalents.
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