Fit a Tire Model to Tire Data and Export Parameter Set

This example uses:

Step 7 of 7 in Get Started with the Extended Tire Features for Vehicle Dynamics Blockset

Use the fit method to fit tire model parameters to tire data. The fit method optimizes parameter values of a tire model to match the tire model response to the target tire data as closely as possible.

Use the export method to write tire model parameters to a tire property file (TIR) or MATLAB file (MAT). The exported file can be imported into these blocks for use in a Simulink® model simulation.

First, import tire data. Next, choose a model as the seed for fitting a new tire model parameter set. You can import an existing tire model or create a new tire model from default parameters for the seed model. Then, fit tire model parameter sets using these fit types. Finally, export the optimized model parameter set.

Fx Pure
Fy Pure
Fx Combined
Fy Combined
Mz Pure
Mz Combined
Mx
My

Pure fit types refer to simple slip in the lateral or longitudinal direction. Combined fit types refer to combined slip in both the lateral and longitudinal direction. The order of fitting is important because some sets of parameters depend on other sets. The previous list reflects the recommended order for fitting. For more information, see fitType.

A tire model has a set of parameters for each response output. The fitType argument value indicates the response to fit. The fit method optimizes the set of parameters for that response to reduce the error between the tire data and the model output.

This example requires the Extended Tire Features for Vehicle Dynamics Blockset™ support package. See Install Support Package.

Note that using a built-in tire model as a seed model is not supported.

Import Tire Data

Build a string array from the TYDEX filenames that contain the tire data.

tirepath = pwd;
tydexdir = dir(fullfile(tirepath,"data_tydex_files","*.tdx"));
tydexstr = join([{tydexdir.folder}',{tydexdir.name}'],filesep);

Import the tire data into an array of tireData objects from the files specified in the string array tydexstr. The length of the tireData objects array is the same length as the input string array. Data from each file is stored in a tireData object. For more information on tire data permitted, see Example Tire Data.

td = tireData(tydexstr);

Use the mean function to preprocess the Fz data channel to remove noise and variation.

td = mean(td, "Fz");

Create a tireModel Object

Create a Magic Formula 6.2 tire model type with default parameters to use as the seed model. Set the dimensional properties of the tire, the nominal test conditions, and the model limits to match the test data supplied to fit the model.

tm = tireModel.new("MF");

% Name the new model
tm.Name = "New Fitted Model";
 
% Dimensional properties
tm.TireSize = "245/45R18";
tm.UNLOADED_RADIUS = 0.33454;
tm.WIDTH = 0.235;
tm.ASPECT_RATIO = 0.45;
tm.RIM_RADIUS = 0.2286;
tm.RIM_WIDTH = 0.2032;
 
% Nominal conditions
tm.INFLPRES = 262000;
tm.NOMPRES = 262000;
tm.FNOMIN = 4300;
 
% Model limits. 
% Note: in this example, 
% the model limits are set by the limits of the test data
tm.PRESMIN = min(vertcat(td.IP));
tm.PRESMAX = max(vertcat(td.IP));
tm.FZMAX = max(vertcat(td.Fz));
tm.KPUMIN = min(vertcat(td.kappa));
tm.KPUMAX = max(vertcat(td.kappa));
tm.ALPMIN = min(vertcat(td.alpha));
tm.ALPMAX = max(vertcat(td.alpha));
tm.CAMMIN = min(vertcat(td.gamma));
tm.CAMMAX = max(vertcat(td.gamma));

Fit Different Parameter Sets

Follow these steps to fit different tire model parameter sets.

Note that this section provides steps for only some of the available parameter sets. You can use these steps to fit all of the available parameter options.

Fit `Pure Fx` Parameters

Extract the longitudinal data from the tire data.

longitudinal_data = td([td.TestMethod] == "Longitudinal");

Using the fit function, set the fitType argument to "Fx Pure", and set the PlotFit argument to true to plot the result.

For additional information available for a fit, see Output Arguments.

[tm, diffTable]  = tm.fit(longitudinal_data,"Fx Pure",PlotFit=true);

Local minimum possible. Constraints satisfied.

fmincon stopped because the size of the current step is less than
the value of the step size tolerance and constraints are 
satisfied to within the value of the constraint tolerance.

View the diffTable variable to inspect which variables were optimized.

diffTable

diffTable=19×8 table
    Parameter    Initial Value    Final Value    Difference     % Difference    Lower Bounds    Upper Bounds                             Parameter Description                         
    _________    _____________    ___________    ___________    ____________    ____________    ____________    _______________________________________________________________________

     "PCX1"            1.579           1.5138      -0.065167           -4.1         -Inf            Inf         "Shape factor Cfx for longitudinal force"                              
     "PDX1"           1.0422           1.1786        0.13637           13.1         -Inf            Inf         "Longitudinal friction Mux at Fznom"                                   
     "PDX2"         -0.08285        -0.040475       0.042375          -51.1         -Inf            Inf         "Variation of friction Mux with load"                                  
     "PDX3"                0         0.070744       0.070744            Inf         -Inf            Inf         "Variation of friction Mux with camber"                                
     "PEX1"          0.11113          0.33671        0.22558            203         -Inf            Inf         "Longitudinal curvature Efx at Fznom"                                  
     "PEX2"           0.3143         -0.49929       -0.81359         -258.9         -Inf            Inf         "Variation of curvature Efx with load"                                 
     "PEX3"                0          0.16845        0.16845            Inf         -Inf            Inf         "Variation of curvature Efx with load squared"                         
     "PEX4"         0.001719        -0.098788       -0.10051        -5846.8         -Inf            Inf         "Factor in curvature Efx while driving"                                
     "PKX1"           21.687           46.607          24.92          114.9         -Inf            Inf         "Longitudinal slip stiffness Kfx/Fz at Fznom"                          
     "PKX2"           13.728         0.001589        -13.726           -100         -Inf            Inf         "Variation of slip stiffness Kfx/Fz with load"                         
     "PKX3"          -0.4098          0.10053        0.51033         -124.5         -Inf            Inf         "Exponent in slip stiffness Kfx/Fz with load"                          
     "PHX1"       0.00021615      -0.00098607     -0.0012022         -556.2         -Inf            Inf         "Horizontal shift Shx at Fznom"                                        
     "PHX2"        0.0011598       0.00048149    -0.00067831          -58.5         -Inf            Inf         "Variation of shift Shx with load"                                     
     "PVX1"       2.0283e-05         0.049022       0.049002     2.4159e+05         -Inf            Inf         "Vertical shift Svx/Fz at Fznom"                                       
     "PVX2"       0.00010568       -0.0070435     -0.0071492        -6764.9         -Inf            Inf         "Variation of shift Svx/Fz with load"                                  
     "PPX1"          -0.3485          -0.3485              0              0         -Inf            Inf         "Linear influence of inflation pressure on longitudinal slip stiffness"
      ⋮

Fit `Pure Fy` Parameters

Extract the lateral data from the tire data.

lateral_data = td([td.TestMethod] == "Lateral");

Using the fit function, set the fitType argument to "Fy Pure", and set the PlotFit argument to true to plot the result.

For additional information available for a fit, see Output Arguments.

[tm, diffTable]  = tm.fit(lateral_data,"Fy Pure",PlotFit=true);

Local minimum possible. Constraints satisfied.

fmincon stopped because the size of the current step is less than
the value of the step size tolerance and constraints are 
satisfied to within the value of the constraint tolerance.

View the diffTable variable to inspect which variables were optimized.

diffTable

diffTable=27×8 table
    Parameter    Initial Value    Final Value    Difference    % Difference    Lower Bounds    Upper Bounds                 Parameter Description              
    _________    _____________    ___________    __________    ____________    ____________    ____________    ________________________________________________

     "PCY1"           1.338          1.4671        0.12914          9.7            -Inf            Inf         "Shape factor Cfy for lateral forces"           
     "PDY1"          0.8785           1.086        0.20754         23.6            -Inf            Inf         "Lateral friction Muy"                          
     "PDY2"        -0.06452        -0.12512      -0.060597         93.9            -Inf            Inf         "Variation of friction Muy with load"           
     "PDY3"               0          1.8342         1.8342          Inf            -Inf            Inf         "Variation of friction Muy with squared camber" 
     "PEY1"         -0.8057         -1.2618       -0.45608         56.6            -Inf            Inf         "Lateral curvature Efy at Fznom"                
     "PEY2"         -0.6046         -1.6084        -1.0038          166            -Inf            Inf         "Variation of curvature Efy with load"          
     "PEY3"         0.09854        0.039894      -0.058646        -59.5            -Inf            Inf         "Zero order camber dependency of curvature Efy" 
     "PEY4"          -6.697         -9.1311        -2.4341         36.3            -Inf            Inf         "Variation of curvature Efy with camber"        
     "PEY5"               0          38.093         38.093          Inf            -Inf            Inf         "Variation of curvature Efy with camber squared"
     "PKY1"         -15.324         -34.639        -19.315          126            -Inf            Inf         "Maximum value of stiffness Kfy/Fznom"          
     "PKY2"           1.715           1.946        0.23099         13.5            -Inf            Inf         "Load at which Kfy reaches maximum value"       
     "PKY3"          0.3695          1.2713         0.9018        244.1            -Inf            Inf         "Variation of Kfy/Fznom with camber"            
     "PKY4"          2.0005          1.5173        -0.4832        -24.2            -Inf            Inf         "Curvature of stiffness Kfy"                    
     "PKY5"               0         -27.421        -27.421         -Inf            -Inf            Inf         "Peak stiffness variation with camber squared"  
     "PKY6"         -0.8987         -1.1744       -0.27568         30.7            -Inf            Inf         "Fy camber stiffness factor"                    
     "PKY7"        -0.23303        -0.54352       -0.31049        133.2            -Inf            Inf         "Vertical load dependency of camber stiffness"  
      ⋮

Fit `Combined Fx` Parameters

Extract the combined data from the tire data.

combined_data = td([td.TestMethod] == "Combined");

Using the fit function, set the fitType argument to "Fx Combined", and set the PlotFit argument to true to plot the result.

For additional information available for a fit, see Output Arguments.

[tm, diffTable]  = tm.fit(combined_data,"Fx Combined",PlotFit=true);

Local minimum possible. Constraints satisfied.

fmincon stopped because the size of the current step is less than
the value of the step size tolerance and constraints are 
satisfied to within the value of the constraint tolerance.

View the diffTable variable to inspect which variables were optimized.

diffTable

diffTable=7×8 table
    Parameter    Initial Value    Final Value    Difference    % Difference    Lower Bounds    Upper Bounds                  Parameter Description               
    _________    _____________    ___________    __________    ____________    ____________    ____________    __________________________________________________

     "RBX1"           13.046          26.396         13.35         102.3           -Inf            Inf         "Slope factor for combined slip Fx reduction"     
     "RBX2"            9.718          24.341        14.623         150.5           -Inf            Inf         "Variation of slope Fx reduction with kappa"      
     "RBX3"                0          237.53        237.53           Inf           -Inf            Inf         "Influence of camber on stiffness for Fx combined"
     "RCX1"           0.9995          1.0661      0.066595           6.7           -Inf            Inf         "Shape factor for combined slip Fx reduction"     
     "REX1"          -0.4403         0.14934       0.58964        -133.9           -Inf            Inf         "Curvature factor of combined Fx"                 
     "REX2"          -0.4663       -0.021369       0.44493         -95.4           -Inf            Inf         "Curvature factor of combined Fx with load"       
     "RHX1"       -9.968e-05        0.002952     0.0030516       -3061.4           -Inf            Inf         "Shift factor for combined slip Fx reduction"

Fit `Mx` Parameters

Using the fit function, set the fitType argument to "Mx", use the combined data, and set the PlotFit argument to true to plot the result.

For additional information available for a fit, see Output Arguments.

[tm, diffTable]  = tm.fit(lateral_data,"Mx",PlotFit=true);

Solver stopped prematurely.

fmincon stopped because it exceeded the function evaluation limit,
options.MaxFunctionEvaluations = 9.000000e+03.

View the diffTable variable to inspect which variables were optimized.

diffTable

diffTable=11×8 table
    Parameter    Initial Value    Final Value    Difference    % Difference    Lower Bounds    Upper Bounds                  Parameter Description              
    _________    _____________    ___________    __________    ____________    ____________    ____________    _________________________________________________

     "QSX1"        -0.007764      -0.00025648    0.0075075         -96.7           -Inf            Inf         "Vertical shift of overturning moment"           
     "QSX2"           1.1915           63.099       61.908        5195.8           -Inf            Inf         "Camber induced overturning couple"              
     "QSX3"         0.013948        -0.003995    -0.017943        -128.6           -Inf            Inf         "Fy induced overturning couple"                  
     "QSX4"            4.912           8.2812       3.3692          68.6           -Inf            Inf         "Mixed load lateral force and camber on Mx"      
     "QSX5"             1.02           2.3311       1.3111         128.5           -Inf            Inf         "Load effect on Mx with lateral force and camber"
     "QSX6"            22.83           431.51       408.68        1790.1           -Inf            Inf         "B-factor of load with Mx"                       
     "QSX7"           0.7104          -10.635      -11.346       -1597.1           -Inf            Inf         "Camber with load on Mx"                         
     "QSX8"        -0.023393        0.0015782     0.024971        -106.7           -Inf            Inf         "Lateral force with load on Mx"                  
     "QSX9"           0.6581           65.578        64.92        9864.8           -Inf            Inf         "B-factor of lateral force with load on Mx"      
     "QSX10"          0.2824           50.486       50.204         17778           -Inf            Inf         "Vertical force with camber on Mx"               
     "QSX11"           5.349        0.0088587      -5.3401         -99.8           -Inf            Inf         "B-factor of vertical force with camber on Mx"

Continue Fitting Parameter Sets

Use the steps established in the preceding sections to continue fitting the model using the remaining fit types.

Plot Fitted Tire Model Response

After fitting all available fit types, use the plot method to plot the results and compare to the original default model.

plot([tireModel.new("MF"),tm],"Data",td);

Export Tire Model Parameters

Use the export method to write the tire model parameters from the tireModel object TM to a TIR file.

export(tm,"example.tir", overwrite=true);

Update Mask Values from Exported Data

Use the exported tire model parameters in the Combined Slip Wheel 2DOF block from the Vehicle Dynamics Blockset library.

Double-click on the Combined Slip Wheel 2DOF block.

Combined Slip Wheel 2DOF block

For Tire type, select External file.

Data source block property with external file selected for tire type parameter.

On the Wheel and Tire Parameters tab, select the exported file and click Update mask values from file.

External tire source block property with an example TIR file selected for the tire file parameter.

Get Started with the Extended Tire Features for Vehicle Dynamics Blockset

Fit a Tire Model to Tire Data and Export Parameter Set

Import Tire Data

Create a tireModel Object

Fit Different Parameter Sets

Fit Pure Fx Parameters

Fit Pure Fy Parameters

Fit Combined Fx Parameters

Fit Mx Parameters

Continue Fitting Parameter Sets

Plot Fitted Tire Model Response

Export Tire Model Parameters

Update Mask Values from Exported Data

Fit `Pure Fx` Parameters

Fit `Pure Fy` Parameters

Fit `Combined Fx` Parameters

Fit `Mx` Parameters