Method for calculating relative rolling radius of wheel using recursive least squares method

Abstract

The present invention discloses a method for calculating the relative rolling radius of a wheel using the recursive least squares method. A calculation model is constructed based on the linear relationship between the slip ratio and the normalized traction force. The input vector and the output value in the calculation model are known quantities that are updated in real time. By using the RLS algorithm (recursive least squares algorithm), the parameter update model in the calculation model before and after the update is obtained, and then the parameter matrix is obtained. At the same time, according to the relative rolling radius model, the relationship between the slip ratio and the wheel rolling radius is obtained. Subsequently, after substituting the parameter matrix into the constructed relative rolling radius model, the relationship between the rolling radius and the normalized traction force is obtained, and then the relative rolling radii of the four sets of wheels of the vehicle are obtained. In the above manner, the present invention calculates the relative rolling radius of the wheel using the recursive least squares method. Compared with the traditional calculation model using the least squares method, it only performs real-time calculations when the input signal is updated, has a small memory occupancy, and has a higher calculation accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of vehicle tire pressure monitoring, and particularly to a method for calculating the relative rolling radius of a wheel by using the recursive least squares method. Background Art

[0002] With the gradual maturity of iTPMS (Indirect Tire Pressure Monitoring System), compared with dTPMS (Direct Tire Pressure Monitoring System), it does not require additional temperature and pressure sensors, greatly reducing the vehicle development cost. Moreover, iTPMS can operate effectively throughout the life of the vehicle without the need to replace the battery later. iTPMS realizes the tire pressure monitoring function by extracting and calculating the vibration spectrum characteristics in the original wheel speed timestamp signal.

[0003] Among them, the calculation of the relative rolling radius of the wheel plays a relatively important role in the tire pressure monitoring model. At present, most tire pressure monitoring systems calculate the relative rolling radius of the wheel by using the least squares method. This method requires curve fitting for all the collected data within a sampling period, and these collected data will occupy a large amount of memory of the system, which is not conducive to the operation of the monitoring system. The recursive least squares algorithm is an iterative algorithm for unknown vectors, aiming at the minimum variance of the model error. For each sampling period, the unknown vector is calculated by repeated iteration using the existing sampled data. This algorithm can realize the real-time calculation of the collected signal without occupying much memory.

[0004] Therefore, it is necessary to design a method for calculating the relative rolling radius of a wheel by using the recursive least squares algorithm, which has a small memory occupancy and a fast operation of the tire pressure monitoring system. Summary of the Invention

[0005] In order to overcome the above problems, the present invention provides a method for calculating the relative rolling radius of a wheel by using the recursive least squares method. When calculating the relative rolling radius of the wheel by using the recursive least squares method, compared with the traditional calculation model using the least squares method, real-time calculation is only performed when the input signal is updated, with a small memory occupancy and higher calculation accuracy.

[0006] To achieve the above object, the technical solution adopted by the present invention is:

[0007] A method for calculating the relative rolling radius of a wheel by using the recursive least squares method, comprising the following steps:

[0008] S1. According to the dynamic driving model of the vehicle, construct a relational expression between the slip ratio and the normalized traction force:

[0009] F = θ1S + θ2 (1)

[0010] In the formula, F is the normalized traction force, and θ1 and θ2 are polynomial coefficients;

[0011] S2. Build a relationship model between multiple groups of input vectors Xn and output values Yn:

[0012]

[0013] It is derived from the above formula (2):

[0014]

[0015] In the formula, the input vector Xn and the output value Yn are both known quantities, and γ is the relationship parameter to be solved between the input vector Xn and the output value Yn;

[0016] S3. Use the RLS algorithm to build a relationship model of the parameter γ for different groups of input vectors Xn and output values Yn:

[0017] S4. Define the relational expressions for the relative rolling radii between four groups of wheels, and derive the calculation rules for their respective equivalent matrices according to each group of relational expressions;

[0018] S5. Rewrite formula (1) as:

[0019] F = Xγ (4)

[0020] In the formula, X = [S 1] T , γ = [θ1 θ2], and solve the numerical value of the parameter matrix γ according to the two groups of models in steps S2 and S3;

[0021] S6. Substitute the parameter θ2 in the solved parameter matrix γ into step S4 to solve the relative rolling radii of the four groups of wheels.

[0022] Furthermore, in step S1, the relational expression between the slip ratio and the normalized traction force holds only when the vehicle does not exceed the maximum adhesion provided by the road surface (at this time, the vehicle is driving normally).

[0023] Furthermore, in step S1, the four groups of wheels of the vehicle are divided into a left-side model, a right-side model, a front-axle model, and a rear-axle model, and the slip ratios of the four groups of models are defined as:

[0024]

[0025]

[0026]

[0027]

[0028] In the formula, ω FL , ω FR , ω RL , ωRR The angular velocities of four groups of wheels representing the left front, right front, left rear, and right rear respectively;

[0029] Subsequently, taking the left slip ratio as an example, its corresponding model is:

[0030]

[0031] In the formula, ω FL , ω RL are respectively the wheel speeds of the current wheels directly read by the wheel speed sensors.

[0032] Furthermore, in step S1, when the normalized traction force F is 0, both groups of wheels in the same slip ratio model are in the free rolling state, and they are only affected by the rolling resistance of their respective wheels. At this time, the slip ratio S in this model represents the rolling radius difference between the two groups of wheels in this model;

[0033] During the normal driving process of the vehicle, the normalized traction force F must not be 0, so the value of the slip ratio S when F is 0 cannot be directly obtained. It is necessary to further solve formula (1) to obtain the value of the slip ratio S when F is 0 (i.e., θ2).

[0034] Furthermore, in step S3, the calculation method of the relationship model of different groups of parameters γ is:

[0035] S31. Define R n = X n T X n ; z n = X n T Y n ; Define the forgetting factor as λ (0 ≤ λ ≤ 1); define the inverse matrix of R n as P n ;

[0036] S32. Calculate the difference between the actual parameter γ and the fitted parameter γ:

[0037]

[0038] S33. Calculate the gain coefficient:

[0039]

[0040] S34. Since use the γ n-1 before update to represent γ n , that is:

[0041] γ n = γ n-1 + kn e n (5).

[0042] Further, in step S4, the relative rolling radii between the four groups of wheels are calibrated as the left relative rolling radius (TGB XL ), the right relative rolling radius (TGB XR ), the front axle relative rolling radius (TGB YF ), and the rear axle relative rolling radius (TGB YR );

[0043] The models of the above four groups of relative rolling radii are:

[0044]

[0045]

[0046]

[0047]

[0048] In the formula, r FL , r FR , r RL , r RR are the rolling radii of the left front wheel, right front wheel, left rear wheel, and right rear wheel respectively, and r0 is the normalized rolling radius (the normalized rolling radius is defined as the average value of the rolling radii of the driven axles).

[0049] Further, in step S4, the equivalent matrix calculation rule of the models of the four groups of relative rolling radii is:

[0050]

[0051] In the formula, H is used to represent

[0052] Further, after deriving and simplifying formula (6), the model is obtained:

[0053]

[0054] Further, in step S5, the respective parameters θ2 in the models of the four groups of relative rolling radii obtained by using the RLS algorithm are defined as θ ZC , θ YC , θ QZ , θ HZ , then substituting into formula (7), it can be known that:

[0055] θ ZC ≈TGB XL

[0056] θYC ≈TGB XR

[0057] θ QZ ≈TGB YF

[0058] θ HZ ≈TGB YR 。

[0059] Further, in step S6, substitute the parameter θ2 in each of the four groups of relative rolling radius models obtained in step S5 into formula (6) to obtain the relational expression of the relative rolling radius of the wheel as:

[0060]

[0061] Compared with the prior art, the beneficial effects of the present invention are:

[0062] The method for calculating the relative rolling radius of a wheel using the recursive least squares method in the present invention constructs a calculation model based on the linear relationship between the slip ratio and the normalized traction force. The input vector and the output value in the calculation model are known quantities that are updated in real time. By using the RLS algorithm (recursive least squares algorithm), the parameter update model in the calculation model before and after the update is obtained, and then the parameter matrix is obtained. At the same time, according to the relative rolling radius model, the relationship between the slip ratio and the wheel rolling radius is obtained. Subsequently, after substituting the parameter matrix into the constructed relative rolling radius model, the relationship between the rolling radius and the normalized traction force is obtained, and then the relative rolling radii of the four groups of wheels of the vehicle are obtained. The present invention uses the recursive least squares method to calculate the relative rolling radius of the wheel. Compared with the traditional calculation model using the least squares method, it only performs real-time calculation when the input signal is updated, has a small memory occupancy, higher calculation accuracy, and better system operation stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 is a schematic flow chart of the method for calculating the relative rolling radius of a wheel using the recursive least squares method in the present invention;

[0064] Figure 2 is a relationship curve diagram of the slip ratio and the normalized traction force of the method for calculating the relative rolling radius of a wheel using the recursive least squares method in the present invention; DETAILED DESCRIPTION OF THE EMBODIMENTS

[0065] In order to make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0066] Here, it should also be noted that in order to avoid obscuring the present invention due to unnecessary details, only the structures or processing steps closely related to the solution of the present invention are shown in the drawings, while other details less relevant to the present invention are omitted.

[0067] In addition, it should be noted that the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, such that a process, method, article or device comprising a series of elements not only includes those elements but also includes other elements not expressly listed, or elements inherent to such process, method, article or device.

[0068] Embodiment

[0069] As Figures 1 to 2 shown, a method 100 for calculating the relative rolling radius of a wheel using the recursive least squares method constructs a calculation model based on the linear relationship between the slip ratio and the normalized traction force. The input vector and the output value in the calculation model are known quantities that are updated in real time. By using the RLS algorithm (recursive least squares algorithm), the parameter update model in the calculation model before and after the update is obtained, and then the parameter matrix is obtained. At the same time, according to the relative rolling radius model, the relationship between the slip ratio and the wheel rolling radius is obtained. Subsequently, after substituting the parameter matrix into the constructed relative rolling radius model, the relationship between the rolling radius and the normalized traction force is obtained, and then the relative rolling radii of the four sets of wheels of the vehicle are calculated.

[0070] Traditional calculation models all use the least squares method to calculate the relative rolling radius of the wheel. This method requires curve fitting of all the collected data within a sampling period, and these collected data will occupy a large amount of memory in the system, which is not conducive to the operation of the monitoring system. The recursive least squares algorithm, as an advanced fast algorithm of the least squares algorithm, is an iterative algorithm for unknown vectors, aiming at the minimum variance of the model error. For each sampling period, the unknown vector is calculated by repeated iteration using the existing sampled data. This algorithm can realize real-time calculation of the collected signal and will not occupy much memory.

[0071] The present invention uses the recursive least squares method to calculate the relative rolling radius of the wheel. Compared with the traditional calculation model using the least squares method, it only performs real-time calculation when the input signal is updated, has a small memory occupancy space, higher calculation accuracy, and better system operation stability.

[0072] Specifically, the method for calculating the relative rolling radius of the wheel using the recursive least squares method includes the following steps:

[0073] S1. According to the vehicle dynamic driving model, construct the relationship between the slip ratio and the normalized traction force:

[0074] F = θ1S + θ2 (1)

[0075] Wherein, F is the normalized traction force, and θ1 and θ2 are polynomial coefficients.

[0076] In this step, the four sets of wheels of the vehicle are divided into a left-side model, a right-side model, a front-axle model, and a rear-axle model. The slip ratios of the four sets of models are defined as:

[0077]

[0078]

[0079]

[0080]

[0081] Wherein, ω FL 、ω FR 、ω RL 、ω RR respectively represent the angular velocities of the four sets of wheels of the left front, right front, left rear, and right rear;

[0082] Subsequently, taking the left-side slip ratio as an example, its corresponding model is:

[0083]

[0084] Wherein, ω FL 、ω RL are respectively the wheel speeds of the current wheels directly read by the wheel speed sensors.

[0085] Specifically, only when the vehicle does not exceed the maximum adhesion provided by the road surface (at this time, the vehicle is driving normally and the slip ratio is a small-range slip ratio), the relationship between the slip ratio and the normalized traction force holds. Under high slip ratio conditions, the assumption that the normalized traction force is proportional to the slip slope no longer holds, and the above relationship cannot be used either. Normalizing the traction force F can map different traction force data to the interval [0, 1] uniformly, thereby removing the unit limitation of the data and converting it into a dimensionless pure numerical value, which is convenient for comparing and weighting indicators with different units or magnitudes.

[0086] At the same time, according to formula (1), when the normalized traction force F is 0, both sets of wheels in the same slip ratio model are in a free rolling state, and they are only subject to the rolling resistance of their respective wheels. At this time, the slip ratio S in this model characterizes the rolling radius difference between the two sets of wheels in this model.

[0087] During the normal driving of the vehicle, the normalized traction force F must not be zero, so it is impossible to directly obtain the value of the slip ratio S when F is zero. It is necessary to further solve formula (1) to obtain the value of the slip ratio S when F is zero (i.e., θ2). Based on this, a relationship model is constructed according to the subsequent steps S2 and S3 and then solved.

[0088] S2. Construct a relationship model between multiple groups of input vectors Xn and output values Yn:

[0089]

[0090] It is deduced from the above formula (2) that:

[0091]

[0092] In the formula, the input vector Xn and the output value Yn are both known quantities, and γ is the relationship parameter to be solved between the input vector Xn and the output value Yn.

[0093] In this step, since the indirect tire pressure monitoring system collects various data in real time, most of the data is in a state of real-time update. For the calculation model using the least squares method, when the matrix dimension increases continuously, the matrix inversion operation has too large a computational amount and is not suitable for online identification.

[0094] When new collected data arrives, if Xn and Yn are brought in again, the calculation is very complex and the computational amount of the inverse matrix is extremely large. By using the RLS algorithm, the law of the parameter γ before and after data update can be recursively deduced.

[0095] S3. Use the RLS algorithm to construct a relationship model of the parameter γ for different groups of input vectors Xn and output values Yn.

[0096] In this step, the calculation method of the relationship model of different groups of parameters γ is as follows:

[0097] S31. Define R n = X n T X n ; z n = X n T Y n ; Define the forgetting factor as λ (0 ≤ λ ≤ 1); define the inverse matrix of R n as P n ;

[0098] S32. Calculate the difference between the actual parameter γ and the fitted parameter γ:

[0099]

[0100] S33. Calculate the gain coefficient:

[0101]

[0102] S34. Since Use the γ before update n-1 to represent γ n , that is:

[0103] γ n = γ n-1 + k n e n (5).

[0104] S4. Define the relational expressions for the relative rolling radii between the four groups of wheels, and derive the respective equivalent matrix calculation rules according to each group of relational expressions.

[0105] In this step, the relative rolling radii between the four groups of wheels are calibrated as the left relative rolling radius (TGB XL ), the right relative rolling radius (TGB XR ), the front axle relative rolling radius (TGB YF ), and the rear axle relative rolling radius (TGB YR ).

[0106] The models of the above four groups of relative rolling radii are as follows:

[0107]

[0108]

[0109]

[0110]

[0111] In the formula, r FL , r FR , r RL , r RR are the rolling radii of the left front wheel, right front wheel, left rear wheel, and right rear wheel respectively, and r0 is the normalized rolling radius (the normalized rolling radius is defined as the average value of the rolling radii of the driven axles).

[0112] Subsequently, the equivalent matrix calculation rules for the models of the four groups of relative rolling radii are calculated as follows:

[0113]

[0114] In the formula, use H to represent

[0115] Furthermore, after deriving and simplifying formula (6), the model is obtained as follows:

[0116]

[0117] S5. Rewrite formula (1) as:

[0118] F = Xγ (4)

[0119] where X = [S 1] T , γ = [θ1 θ2], and solve for the numerical value of the parameter matrix γ according to the two sets of models in steps S2 and S3.

[0120] In this step, define the respective parameters θ2 in the four sets of models of the relative rolling radius solved by using the RLS algorithm as θ ZC , θ YC , θ QZ , θ HZ , then substituting into formula (7), it can be known that:

[0121] θ ZC ≈ TGB XL

[0122] θ YC ≈ TGB XR

[0123] θ QZ ≈ TGB YF

[0124] θ HZ ≈ TGB YR .

[0125] S6. Substitute the parameter θ2 in the solved parameter matrix γ into step S4 to solve the relative rolling radius of the four sets of wheels.

[0126] In this step, substitute the respective parameter θ2 in the four sets of models of the relative rolling radius solved in step S5 into formula (6), and the relational expression of the relative rolling radius of the wheels is obtained as:

[0127]

[0128] The above is only used to illustrate the technical solution of the present invention and is not intended to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; any equivalent structural or equivalent process transformation made by using the content of the specification and drawings of the present invention, directly or indirectly applied to other related technical fields, shall be similarly included in the patent protection scope of the present invention.

Claims

1. A method for calculating the relative rolling radius of a wheel using the recursive least squares method, characterized in that, It includes the following steps: S1. According to the vehicle dynamic driving model, construct the relationship between the slip ratio and the normalized traction force: F = θ1S + θ2 (1) In the formula, F is the normalized traction force, and θ1 and θ2 are polynomial coefficients; In step S1, when the normalized traction force F is 0, both sets of wheels in the same slip ratio model are in the free rolling state, and they are only affected by the rolling resistance of their respective wheels. At this time, the slip ratio S in this model represents the rolling radius difference between the two sets of wheels in this model; During the normal driving of the vehicle, the normalized traction force F must not be 0, so the value of the slip ratio S when F is 0 cannot be directly obtained. It is necessary to further solve formula (1) to obtain the value of the slip ratio S when F is 0, denoted as θ2; S2. Construct a relationship model between multiple groups of input vectors Xn and output values Y n as follows: It is deduced from the above formula (2) that: In the formula, the input vector Xn and the output value Yn are both known quantities, and γ is the relationship parameter to be solved between the input vector Xn and the output value Yn; S3. Use the RLS algorithm to construct the relationship model of the parameter γ for different groups of input vectors Xn and output values Yn; S4. Define the relational expressions for the relative rolling radii between the four sets of wheels, and derive the respective equivalent matrix calculation rules based on each set of relational expressions; in step S4, the relative rolling radii between the four sets of wheels are calibrated as the left relative rolling radius TGB XL , the right relative rolling radius TGB XR , the front axle relative rolling radius TGB YF , and the rear axle relative rolling radius TGB YR ; The above four groups of relative rolling radius models are: where r FL , r FR , r RL , r RR are the rolling radii of the left front wheel, right front wheel, left rear wheel, and right rear wheel respectively, and r0 is the normalized rolling radius, which is defined as the average value of the rolling radii of the driven axles; The equivalent matrix calculation rule for the four groups of relative rolling radius models is: In the formula, H is used to represent After deriving and simplifying formula (6), the model is obtained: where F is the normalized traction force. When F is 0, all the wheels in the vehicle model only roll freely and are only subject to the rolling resistance of the wheels, and S ZC(F＝0) represents the left slip ratio in the free rolling state of the wheel; S5. Rewrite formula (1) as: F = Xγ (4) where X = [S 1] T , γ = [θ1 θ2], and the numerical value of the parameter matrix γ is solved according to the two groups of models in steps S2 and S3; In step S5, the parameters θ2 of each of the four relative rolling radius models obtained by solving using the RLS algorithm are defined as θ ZC , θ YC , θ QZ , θ HZ , and substituting the calculation results into formula (7), it can be known that: θ ZC ≈TGB XL θ YC ≈TGB XR θ QZ ≈TGB YF θ HZ ≈TGB YR ; S6. Substitute the parameter θ2 in the solved parameter matrix γ into step S4 to solve the relative rolling radius of the four groups of wheels; In step S6, substitute the respective parameter θ2 in the four groups of relative rolling radius models solved in step S5 into formula (6) to obtain the relationship formula for the relative rolling radius of the wheels as:

2. The method for calculating the relative rolling radius of a wheel using the recursive least squares method according to claim 1, characterized in that In step S1, only when the vehicle does not exceed the maximum adhesion provided by the road surface, the vehicle is driving normally at this time, and the relationship between the slip ratio and the normalized traction force holds.

3. The method for calculating the relative rolling radius of a wheel using the recursive least squares method according to claim 2, characterized in that, In step S1, the four groups of wheels of the vehicle are divided into a left-side model, a right-side model, a front axle model, and a rear axle model, and the slip ratio of each of the four groups of models is defined as: Where ω FL , ω FR , ω RL , ω RR represent the angular velocities of the four groups of wheels at the left front, right front, left rear, and right rear respectively; Subsequently, taking the left-side slip ratio as an example, its corresponding model is: where ω FL and ω RL are respectively the wheel speeds of the current wheels directly read by the wheel speed sensors.

4. The method for calculating the relative rolling radius of a wheel using the recursive least squares method according to claim 1, characterized in that, In step S3, the calculation method for the relationship model of different groups of parameters γ is: S31. Define R n = X n T X n ; z n = X n T Y n ; Define the forgetting factor as λ (0 ≤ λ ≤ 1); Define the inverse matrix of R n as P n ; S32. Calculate the difference between the actual parameter γ and the fitted parameter γ; S33. Calculate the gain coefficient: S34. Since using the pre-update Y n-1 to represent γ n , that is: γ n = γ n-1 + k n e n (5).

Images