Links between Subjective Assessments and Objective Metrics for Steering

(1)

Postal address Visiting address Telephone Internet

Royal Institute of Technology Teknikringen 8 +46 8 790 6000 www.ave.kth.se

Vehicle Dynamics Stockholm Telefax

SE-100 44 Stockholm +46 8 790 6500

Links between Subjective Assessments

and Objective Metrics for Steering

Xuxin He and Zhicheng Su

Master Thesis in Vehicle Engineering

Vehicle Dynamics

Aeronautical and Vehicle Engineering Royal Institute of Technology

TRITA-AVE 2012:36 ISSN 1651-7660

(2)

TRITA-AVE 2012:36 ISSN 1651-7660

Links between Subjective Assessments and Objective Metrics for Steering Xuxin He and Zhicheng Su

Master's Thesis in the Master's program Vehicle Engineering

©Xuxin He and Zhicheng Su, 2012

(3)

I

Abstract

The characteristics of vehicle steering perception are decisive factors concerning vehicle safety and overall pleasure behind the wheel. It is a challenge for vehicle manufacturers to achieve these features and qualities, because usually vehicle tuning almost only relies on subjective evaluation of test drivers, which is costly and time consuming. In order to optimize suspension design and develop a tool that can be used to evaluate steering with objective metrics instead of subjective assessment, links between them must be confirmed.

In this master thesis, both objective and subjective testing data of over 20 vehicles across four different segments are introduced in linear and nonlinear analysis. Linear regression analysis is applied to investigate simply positive or negative correlation between a pair of subjective-objective parameters. However, even if certain linear correlations are obtained, it is still hard to define the optimal value for objective metrics. Considering that the general shape of a correlation function can reveal which objective range give higher subjective rating, it is possible to define these preferred ranges with Neural Network (NN). The best data available is adopted from three drivers who tested 15 sedans, and some interesting results are found.

The initial results demonstrate that NN is a powerful tool to uncover and graphically illustrate the links between objective metrics and subjective assessments, i.e., the specific range leading to better steering feel. Given a larger sample size, more reliable and optimal links can be defined by following the same method. These confirmed links would enable vehicle dynamics engineers to more effectively develop new vehicles with nearly perfect steering feel.

Keywords: Steering feel, objective measure/metric, subjective assessment, linear regression, nonlinear correlation, Neural Network, preferred range

(4)

(5)

III

Acknowledgment

The thesis work was performed during 2012-01 to 2012-06 at Vehicle Dynamics and Calibration (96520) of Volvo Car Corporation (VCC). We are grateful for financial and technical support from VCC.

It is with great gratitude that we acknowledge the continuous guidance and advices of our supervisor Mikael Nybacka, Assistant Professor at Vehicle Dynamics of KTH Royal Institute of Technology. We also would like to thank Carl Sandberg, the supervisor at VCC, for his support and assistance.

We are indebted to many people, Lars Drugge at KTH and Stefan Karlsson, Egbert Bakker as well as Kenneth Ekström at VCC, for their valuable feedback and suggestions on this thesis.

Finally, our appreciation also goes to all the colleagues and friends at KTH for a wonderful time and interesting discussions about thesis and research.

Xuxin He and Zhicheng Su Stockholm, June 2012

(6)

(7)

V

List of Symbols

Lateral acceleration Bias

Cornering stiffness of front tires

Cornering stiffness of rear tires Frequency

Gravitational acceleration

Lateral slip force on front tires

Lateral slip force on rear tires

Steering ratio between steering wheel and front wheel angle Inertia around the z-axis

Front axle to center of gravity distance Rear axle to center of gravity distance Vehicle mass

Steering wheel torque Curve radius

Time delay

Lateral velocity Longitudinal velocity Weight

Front slip angle Rear slip angle Regression coefficient

(10)

Steering angle

Steering wheel angle Sum

Roll angle

̇ ^{Roll rate} Yaw angle

̇ ^{Yaw rate}

List of Abbreviations

ANFIS Adaptive Neuro Fuzzy Inference System AVES Alliance Vehicle Evaluation Standard

BP Back-propagation

FIS Fuzzy Inference System

KTH Royal Institute of Technology, Stockholm

ME Mean error

MF Membership function

MIRA Motor Industry Research Association

NN Neural Network

OM Objective measure

SA Subjective assessment SS Sum of squares VCC Volvo Car Corporation

(11)

1

1 Introduction

This chapter will give an overview of the background for this thesis. Based on the state-of-the-art of research in subjective-objective links as well as requirements from Volvo Car Corporation (VCC), specific objectives are generated.

1.1 Background

Dynamics quality of a vehicle is a crucial aspect for safety and overall experience of driving pleasure. Nowadays, vehicle dynamics characteristics could vary a lot even with similar components from same suppliers. It is the appropriate calibration that makes a new product, an integration of these components, receive good evaluation about the dynamic properties from customers. Vehicle manufacturers usually use two approaches, subjective evaluation using test drivers and objective metrics, to evaluate the dynamics features of a vehicle.

Though some of objective measures can be applied to describe dynamics behavior of a vehicle, they cannot indicate if these technical settings lead to good interaction between a driver and the vehicle. Thus, the subjective perception of driving or riding a vehicle is an effective measure, in addition to objective metrics, to evaluate the performance of a vehicle.

Subjective evaluation of a vehicle includes various assessments to judge it as a whole.

Instead of monotonous objective data, the concrete driving experience of vehicle users is revealed by drivability, handling, steering, ride comfort and some other specific perceptions.

So far many companies in vehicle industry use subjective evaluation in the tuning process of vehicle development and some of them develop their own evaluation standards. AVES (Alliance Vehicle Evaluation Standard) [1] defined by Renault-Nissan Alliance have been adopted as a major item to evaluate the vehicle quality. Approximately 350 criteria concerning static and dynamic characteristics are listed in this evaluation system. The most common subjective rating scale from SAE Recommended Practice J1441 [2] has been widely applied since 1985, as seen in the figure 1 in [2].

1.2 Problem Formulation

One of the most challenging tasks for vehicle engineers is, under cost and time constraints, to satisfy every requirement of the subjective perception of customers regarding vehicle dynamics characteristics. Subjective evaluation has its own limitations when the vehicle tests need to be carried out in complicated or dangerous driving situations. Moreover, the reliability and repeatability are also somehow weaknesses for pure subjective evaluation.

However, vehicle tuning still mainly relies on purely subjective evaluation of test drivers, owing to a limited knowledge of links between subjective assessments and objective metrics.

This is not cost-effective during development. Therefore, there is a strong need in vehicle industry to improve the efficiency of vehicle calibration.

(12)

2

AVL List GmbH has worked with their developed tool AVL-DRIVE [3] to benchmark vehicle longitudinal drivability. The most significant information captured by this system includes vehicle velocity, longitudinal acceleration, engine speed, pedal position, vibrations and others giving over 500 objective criteria. Through analysis of driving test and calibration both research associations and vehicle industries, such as MIRA (Motor Industry Research Association) [4] and Scania CV AB [5], have already explored subjective-objective correlations in vehicle steering. Links found from such work cannot only save efforts on testing or calibration, but also help to lead to wanted subjective perception of steering feel for general customers. In this thesis the related work is used to validate our findings.

1.3 Objectives

VCC has a strong need to improve development efficiency by testing fewer objective measures that are enough to define excellent vehicle dynamics characteristics in subjective perception.

The aim of this master’s thesis is to explore subjective-objective correlation links based on the data measured and collected at VCC. Both linear and nonlinear correlations between subjective assessments and objective metrics will be investigated by using tools of regression analysis, variance analysis and MATLAB Neural Networks Toolbox.

The main application of these results should be to tell if a vehicle would give good driving experience only according to data of certain objective measures within certain ranges. The outcome is improvement of objective and subjective measuring standards by focusing on the most significant parameters during tests, optimization of their value ranges and producing sufficient data to serve in the practical calibration work.

(13)

3

2 Method

In this chapter the way to deal with data sets will be firstly described. Then, the approaches used to analyze subjective-objective correlations will be introduced.

2.1 Case Study

All data used in this thesis belongs to either subjective or objective part. Each test driver did his or her own assessments on test vehicles. Therefore a number of subjective data sets of a given vehicle can be attained depending on how many test drivers are involved. As for objective metrics only one set of objective data from a specific vehicle is available by using a testing robot [6]. Normally, the average value of the subjective data set and the objective set will be used to carry out data analysis. However, this approach may not cover the true results when considering our small data size. Chen [4] introduced case study method in subjective- objective correlation analysis. It will be an appropriate approach to describe and explain correlation findings for each driver in this case. The way to analyze each case is shown in Figure 1.

Figure 1. Approach of case study with subjective and objective data.

(14)

4

In addition, since every driver has his or her own driving preference, it is not likely to get a general quantitative conclusion even though they are all expert drivers with large testing experience. Instead, the method of case analysis will help to get a qualitative conclusion on subjective-objective correlation by studying the preference tendency of most drivers. As seen in Figure 1, assuming that Driver X is studied now, his subjective assessments and objective measures are picked to conduct linear and nonlinear analysis. Thereafter, the possible findings from this driver should be recorded. Likewise, the same analysis will be conducted for the rest of drivers. If the same linear or nonlinear correlation is presented under most cases (individual drivers), a reliable link can be confirmed.

2.2 Linear Regression Analysis

Linear regression is used to model the relationship between a dependent variable and one or more explanatory variables. In both simple and multiple regression analysis, linear functions and relevant parameters are used to model the data.

2.2.1 Simple Linear

Simple linear regression fits a straight line to estimate a linear model with one single explanatory variable (objective measure in our case) , seen as Equation (1), where is true value (subjective assessment in our case), is the regression value and is a random component, also called error or residual.

(1).

The approach used to find the best fit is to minimize the sum of the squares of the difference between the data and a line, so-called least squares minimization. The correlation coefficient ( [ ]) is widely adopted as a measure of the strength of linear dependence between two variables. Two estimators, the constant and the regression coefficient are determined by following minimization problem. The correlation coefficient can be defined as Equation (2), where , ̅ and are sample size, sample mean and sample standard deviation respectively.

∑ ( ̅

) ( ̅ )

(2).

An example of how to process the data by using the linear regression can be seen in Figure 2.

A data set with five paired subjective ratings and objective data can be fitted with a regression equation . In this case, the value of regression coefficient is -0.84 that is close to -1, so the straight line fits the data set well. In other words, the regression equation can basically represent the raw data.

(15)

5 Figure 2. Example of linear regression based on the data of a test driver.

2.2.2 Multiple Linear

Multi-linear regression basically follows the same procedure to achieve best fit. The only difference is that more than one explanatory variable are introduced as seen in Equation (3).

All the estimators, including regression coefficient are calculated by using least squares minimization and the coefficient of determination ( [ ]), seen as Equation (4), is a measure to study how well the true values are likely to be predicted by the model. In this expression, is the total sum of squares, while is the residual sum of squares and means the predicted model.

(3).

̅ (4).

For multi-linear regression models, F-statistics can be used to check the significance of regression equation and each regression coefficient in the equation. The F-value of regression equation is expressed by Equation (5), which should follow F-distribution (in this thesis, degree of freedom is the number of regressors and is the number of samples). By checking the F-distribution table with certain confidence in Appendix A the significance

2.8 3 3.2 3.4 3.6 3.8 4 4.2

5 5.5 6 6.5 7 7.5 8 8.5

x: Steering Wheel Torque [Nm]

y: Ratings of Parking Efforts

An Example of Linear Regression ( r = - 0.84) y ~= -1.7x + 13

Data Fit

(x3, y

3)

(x4, y

4)

(x1, y

1)

(x5, y

5)

(x2, y

2)

(16)

6

can be verified if the calculated F-value is larger than critical value . The significance of each regression coefficient is checked in a very similar approach. The corresponding F-value of a regression coefficient is calculated by following Equation (6), where and are the new sum of squares for the regression equation without coefficient . Likewise, the significance can be verified only if is larger than .

⁄

⁄ (5).

⁄ (6).

2.3 Nonlinear Regression Analysis

Results from linear correlation basically only tell if there is monotonically positive or negative effect on some subjective assessments from certain objective measures. If an optimal range needs to be defined for an objective measure that will give the best subjective perception, then some other methods have to be used to find nonlinear correlations between them.

2.3.1 Artificial Neural Network

Generally, Fuzzy Logic and Neural Network (NN) are frequently used tools to find out nonlinear correlations between different parameters. The former one can be adopted for non- metric subjective feel, such as ‘good/bad’ or ‘heavy/medium/soft’. The latter one can be used while subjective ratings are in numbered form, which is available in this thesis. Thus, the Neural Network Toolbox in Matlab is utilized.

NN is a kind of mathematical structure that composes of interconnected artificial neurons to imitate the way a biological neural system works (e.g., our brain). It has the ability to learn from data and can be used to explore nonlinear subjective-objective links in this thesis. A typical multi-layer neural network consists of an input layer, hidden layer and output layer of neurons. Its structure is graphically demonstrated as seen in Figure 3.

(17)

7 Figure 3. Structure of three-layer static Neural Network.

The input metrics is transmitted through the connections by first multiplying the scalar weight to form a product . Secondly, it will be added with a scalar bias and processed by a transfer function . Three types of transfer functions are most commonly used. They are called hard-limit, linear and tan-sigmoid, shown in Figure 4. Tan-sigmoid is usually adopted as the transfer function in the hidden layer to find out nonlinear subjective- objective correlations. Linear transfer function will be used in the output layer. The calculated results from the hidden layer will then be added in the output layer, where output is produced and can be compared with target value of subjective ratings. The main principle of neural network is that scalar weight and bias can be adjusted in order to obtain desired results [7].

Figure 4. Three types of most commonly used transfer functions.

(18)

8

There are two types of NN, feed-forward (static) and feed-back (dynamic). Signal flows of both of them start from the input layer and end at the output layer. One of the main differences between them is if the output depends on the previous output or not. Feed- forward NN is mostly applied to model the system where the network is stable and the output is only determined by input signals. This confirms exactly to the case of this thesis.

In a normal NN, there are several layers with neural nodes, including hidden layer and output layer, transfer functions of layers and neurons in each hidden layer. In addition to these main components and constructions, learning algorithm parameters and learning rate have to be selected before training NN. The parameters that need to be decided are the following:

 Type of NN connectivity

As mentioned before, neural connections can be either feed-back or feed-forward. In this thesis, the outputs or subjective ratings of drivers are only decided by the corresponding objective data, and no previous outputs are needed as in the case of feed-back system. Thus, the feed-forward (static) NN is chosen.

 Number of hidden layers

The number of hidden layers varies from zero to two. Without hidden layers, NN does not differ a lot from linear regression, while too many hidden layers contribute to over-fit.

Research of Ash [8] also shows that one hidden layer can be suitable for this kind of problem.

 Learning algorithm

The main learning algorithms available in NN can be divided into three types, supervised, unsupervised and reinforcement learning. In the supervised learning, corresponding targets are provided with each input; while in the unsupervised learning, no such output targets exist.

The reinforcement learning concerns with how an agent in an environment should react so as to maximize rewards feedback from the environment, and this algorithm differs from the supervised one in a way that no input/output mapping is presented.

In this thesis, since both numerical input and target output are available, the supervised learning is suitable to be adopted, where the error correction will be used to minimize the error between output and target by modifying weight and bias. In the field of studying subjective-objective links, the most often used algorithm is back-propagation compared with other algorithms such as perception, self-organizing, recurrent, etc [9].

Another important aspect is that the data used for training and testing the NN should be different. This can be achieved by setting the dividing parameters, which decides the ratio of vectors for training and testing as well.

 Learning algorithm parameters (learning rate and momentum factor)

(19)

9 In a NN, the appropriate learning rate and momentum factor should be decided before training. Too small learning rate leads to extremely long training time, while too large one makes it hard for the NN to converge. The well-specified momentum constant helps to reduce the learning time, which decides the proportion of previous weight update to make use of. Problems of insignificance or instability could occur if the momentum factor is set too low or too high. Since unfortunately no systematic method can be used to determine them, both are set relatively low so as to guarantee the convergence of the NN.

 Initial weight value

Initial weight values are decided by experience, and this setting will not make great fundamental difference in generalization quality between using optimal initial weights and random initial weights [10]. Thus, the initial weight value is set to random values.

 Transfer function

The transfer function in the hidden layer is set as tan-sigmoid function, which is considered able to represent the relationships best [11]. The transfer function in the output layer is just to produce the final output by adding all from former hidden layer together, and since the rating range is scaled between 0 and 10, the linear function is selected so that the output value can be transferred into normal range (from 0 to 10), i.e., if the assessment is done by judging

‘good or bad’, the step function can be adopted.

 Number of neurons in each hidden layer

With more neurons in each hidden layer, the NN is capable of training the models with higher complexity. The fit of training gets better with more complicated NN system.

However, the trained network with better fit (more neurons) usually over-fits the model, which leads to larger error between predicted and true ratings for the testing data [11]. Three neurons in the hidden layer are considered to be appropriate for the case studied in this thesis.

Trial Neural Network design with another data sample:

After deciding NN learning process, some example data from another similar research at KTH is introduced to design a trial NN as follows:

 Example data with 16 configurations (16 samples)

 Steering feel (SF) is the assessment

 Five objective parameters

 Data with speed at 80km/h

 Data from 15 expert drivers (with similar driving experience to VCC data)

 Feed-forward NN with gradient descent back-propagation (BP) training function

 One hidden layer with tan-sigmoid transfer function (tansig)

 One output layer with linear transfer function (purelin)

 Three neurons in the hidden layer

(20)

10

 Maximum epochs: 500

 Goal error:

 Learning rate: 0.01 (default value)

 Momentum factor: 0.9 (default value)

 Ratio of vectors for training: 75% (12 samples)

 Ratio of vectors for testing: 25% (4 samples which reach the minimum statistic number) The single-input network is used to find the preferred range of an objective parameter where higher subjective rating can be expected. As seen in Figure 5, the output is steering feel and the input signal is one of five objective measures. Implementing this training process for every driver with each objective parameter results in regression coefficients that are collected and shown in Table 1. When r-value is larger than 0.7 it is marked as red to indicate a model with successful training.

Figure 5. Single-input Neural Network structure with one-hidden-layer and three neurons.

Table 1. Overview of training regression (r-value) for expert drivers at 80km/h.

Expert driver No.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Max. lat.

acceleration 0.30 0.40 0.30 0.20 0.40 0.50 0.40 0.50 0.40 0.20 0.20 0.20 0.30 0.30 0.10 Steering

sensitivity 0.40 0.40 0.40 0.40 0.50 0.80 0.40 0.60 0.30 0.30 0.30 0.50 0.20 0.10 0.50 Steering

stiffness 0.60 0.50 0.80 0.60 0.80 0.30 0.40 0.50 0.40 0.50 0.80 0.30 0.30 0.30 0.60 Torque

gain 0.60 0.50 0.70 0.50 0.70 0.40 0.30 0.80 0.30 0.80 0.30 0.10 0.30 0.10 0.60 Yaw

delay 0.60 0.10 0.10 0.50 0.50 0.20 0.10 0.40 0.50 0.30 0.30 0.40 0.10 0.20 0.20

Most training results with good fit (r-value ≥ 0.7) concern steering stiffness and torque gain, which are defined in Figure 6, and they are similarly defined as torque buildup into the corner in VCC DNA files. If close examination is done, the relationship between these

(21)

11 parameters and steering feel rating should be like Figure 7, where certain preferred or dislike range is visualized.

Figure 6. Definitions of steering stiffness and torque gain.

Figure 7. Relationship between steering feel and steering stiffness for Driver 3.

0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2

Steering stiffness [Nm/deg]

SF(steering feel) rating

Neural Network training result for Expert Driver 3 @ 80km/h (16 configruations) Real values Predicted values

(22)

12

According to the figure above, the preferred steering stiffness is from 0.06 to 0.12Nm/deg, which provides Driver 3 with better steering feel. Table 2 shows all preferred ranges of different objective parameters from well-trained models. The main findings concern steering stiffness and torque gain, both of which are preferred to be low to achieve better steering feel.

Thus, it is possible to find preferred range through NN, especially when the linear correlations have already been confirmed.

Table 2. Preferred range for better SF rating (expert driver).

Objective measure Preferred range for higher rating Max. lat. Acceleration NA

Steering sensitivity NA

Steering stiffness 0.06~0.12 Nm/deg

Torque gain 0.05~0.15 Nm/deg

Yaw delay NA

Apart from expert drivers, the data from other 15 novice drivers are also used to train NN model. The valid findings are also focusing on steering stiffness and torque gain. The preferred ranges of both parameters are almost exactly the same as expert drivers.

Another issue to consider is if the sample size could be smaller to save test time and cost. It depends on how the NN processes data. The NN system chooses the training data and testing data randomly even though the ratio of vectors for training and testing is defined. This fact makes the trained vectors and tested vectors never fixed. Moreover, the data used for testing is always much less than that for training. As a result, sometimes if extreme outliers are included in vectors for testing, the regression will get quite unstable. The regression plots of test in Figure 8 show how much the test regression could vary with different selected data in training and testing.

(23)

13 Figure 8. Different regression-plots under the same data samples.

As seen in Figure 8, for the regression of training data and all data (the blue and red lines), the fit is relatively stable (r-value of all samples fluctuates by 0.1 units). On the other hand, the fit of testing data (the green line) varies remarkably (0.94 vs. 0.096). When the r-value is 0.94 in the first case, the randomly selected testing data by the NN can fit with predicted

2 2.5 3

Target

Output ~= 0.53*Target + 1.2

Training: R=0.73831

Data Fit Y = T

2 2.5 3

2 2.2 2.4 2.6 2.8 3

Target

Test: R=0.93766

Data Fit Y = T

2 2.5 3

Target

All: R=0.73893

Data Fit Y = T

2 2.5 3

Target

Training: R=0.72449

Data Fit Y = T

2 2.5 3

2 2.2 2.4 2.6 2.8 3

Target

Test: R=0.096104

Data Fit Y = T

2 2.5 3

Target

All: R=0.64615

Data Fit Y = T

(24)

14

model very fortunately. On the contrary, due to the small testing sample, if extreme data are selected for testing, the r-value will get worse, i.e., in the second case the r-value is just 0.096.

With 16 samples in all, the fit of training model is stable. However, the error between true value (target) and predicted model (output) will vary randomly for the testing part (only 4 samples). The point is that 16 samples are just enough to train the NN model, but sometimes the stability of testing cannot be ensured. If the sample number is reduced slightly, the reliability of preferred range through NN training will not be guaranteed anymore. In other words, at least 16 test objects (cars) or different settings of the cars are needed in order to use NN to find nonlinear correlations. As for how many test drivers are needed in this kind of study, it will be discussed later on. Furthermore, there is a possibility to add to the data set gathered data from a later test, meaning that if 16 settings could be varied during one test day data from another day with different cars and/or settings can be added in order to reach a better validity of the NN model.

2.3.2 Adaptive Neuro Fuzzy Inference System (ANFIS)

The fuzzy logic system is able to model nonlinear functions as well by mapping inputs into a logic space first, and then inferring some rules to obtain wanted output. However, an ordinary fuzzy logic system cannot learn rules without support from Neural Network. That is why Adaptive Neuro Fuzzy Inference System (ANFIS) is needed.

ANFIS uses a hybrid learning algorithm to identify the membership function parameters of single output, with first order Sugeno-type Fuzzy Inference System. The Tagaki-Sugeno fuzzy if-then rules in ANFIS can be configured as follows:

The n^th rule: if is and is and is , then , where , , and are linear parameters of function and , , and are input signals.

A normal structure of ANFIS is shown in Figure 9, totally with six distinct layers [12] [13]:

For instance, with this illustrated ANFIS, the 5^th rule and the fifth function are valid when is and is and is .

(25)

15 Figure 9. ANFIS structure with first-order Sugeno model.

Layer 1 is the input layer, simply giving incoming signals, can be objective measures.

Layer 2 is the fuzzification layer. The output of each node in this layer is decided by the membership function (MF). For example, given a triangular MF (trimf) shown in Figure 10, it can be presented as Equation (7).

{

}

(7).

(26)

16

Figure 10. Membership function: trimf.

Layer 3 is the rule layer. Each node in this layer computes the weight for the n^th rule. All of the rules can be decided by orthogonalizing various inputs and MFs.

Layer 4 is the normalization layer. The normalized firing strength of a given rule is the output of this layer defined as the ratio of the firing strength of the considered node to the sum of all rule firing strengths. The normalized firing strength for the n^th node is represented as Equation (8).

̅

(8).

Layer 5 is the defuzzification layer. The output of Layer 4 and initial inputs are received and the weighted consequent value of a given rule is calculated as Equation (9).

̅ ̅ (9).

Layer 6 is the layer with one summation node, where adding up all outputs of the previous layer produces the single ANFIS output.

∑ ̅

(10).

The ANFIS training adopts a gradient descent algorithm to optimize the antecedent parameters and a least squares algorithm to solve for the consequent (linear) parameters.

Similar to the procedure of NN, parameters such as MF type, goal error and maximum epochs have to be empirically determined before training. Above all, the number of MFs for each input is extremely important, which decided how many logic divisions should be generated.

(27)

17 Concerning subjective-objective correlation where subjective assessments can be seen as output of the ANFIS and if a certain preferred range exists there should exist upper and lower boundary for a given objective measure. That means only those values in the preferred range will give better perception seen as Figure 11. So the objective measuring data should be divided into three logic zones (three MFs), two of them giving lower rating score. However, in the actual case, extreme values outside the boundaries might not be acquired on testing vehicles. As a result, one or even two logic zones should be removed. Therefore, the number of MFs in ANFIS training cannot be chosen in order to study subjective-objective links unless extreme cases are surely detected.

Figure 11. General shape of subjective-objective correlation function.

ANFIS training with subjective rating of a certain level and of its sub-level

In order to test the ANFIS model a collection of subjective data from a sub-level is introduced with rating range from 100 to 500-points that will replace the objective data in Figure 11. All assessments in the sub-level are considered to have effect on the subjective assessment (top-level) as seen in Figure 12. The 100 or 500-point ratings represent extreme cases. Using these data samples it will be possible to demonstrate how ANFIS works and if the parameters from the sub-level are enough to represent some property.

(28)

18

Figure 12. Explanation of sub-level for subjective assessment.

All four various assessments in the sub-level are included in the fuzzy inference system since each sub-level assessment should give its contribution. With three MFs in each of them shown in Figure 13, the FIS part can be represented as seen in Figure 14.

Figure 13. Example of membership function with Gauss MF (three MFs).

Figure 14. Fuzzy Inference System (FIS) part.

(29)

19 However, due to more complicated structure of ANFIS as seen in Figure 9 when using multi- input, there will be hundreds of unknown parameters needed to be inferred, including linear and nonlinear ones. It turns out that no convincing results can be acquired unless a huge database is provided. Thus, the ANFIS tool could be another option in the future when sufficient data set is given.

(30)

20

(31)

21

3 Parameter Selection and Matching

In this chapter all raw data will be looked through and preprocessed. Some parameters in the raw datasheets are going to be excluded since they are either lacking data samples or not relevant to this thesis. Explanatory subjective assessments will be initially mapped to corresponding objective measures before linear and nonlinear analysis.

Raw objective data from VCC includes four different vehicle classes and subjective data are also made up of same classes. Each test group includes several drivers, but the drivers do not remain the same across different tests (e.g., Driver 3 in C-class is not the same one in D- class). The focus of this thesis is steering characteristics. In addition, some of important data is lacking for drivers or vehicles. For example the testing data is missing for majority of vehicles regarding certain objective measures that will not be considered in analysis. So the work of reorganizing and matching the raw data is necessary.

The classification can be seen in Table 3. Further analysis will be based on each vehicle class. One important aspect that has to be kept in mind is that in some classes not all test drivers did their judgment on every subjective assessment and each vehicle model. That is, the sum of drivers is not consistent with total runs of each vehicle.

Table 3. Overview of test vehicles in each class.

Classification Vehicle 1 Vehicle 2 Vehicle 3 Vehicle 4 Vehicle 5 Vehicle 6 Vehicle 7 Sum of vehicles

C-class C1 C2 C3 C4 C5 C6. - 6

D-class D1 D2 D3 D4 D5 - - 5

E-class E1 E2 E3 E4 E5 E6 E7 7

SUV SUV1 SUV2 SUV3 SUV4 SUV5 - - 5

3.1 Selection of Subjective Assessments

The emphasis in this thesis work should be focused on the vehicle steering characteristics.

Twelve subjective assessment indexes shown in Table 4 will be studied. However, the data under Level 2 (steering disturbances/error states) is not taken into account because there is no corresponding objective data available. Thus, these subjective assessments are not considered while calculating the rating for Level 1 (steering).

(32)

22

Table 4. Selected subjective assessments.

Level 1 Level 2 Level 3 Assessment

Steering

First 50m Test First 50m test SA-1

Park/Maneuvering Efforts SA-2

Returnability SA-3

Straight Ahead Controllability

Response SA-4

Roll Control SA-5

Torque Feedback SA-6

Modulation SA-7

Cornering Controllability

Response SA-8

Roll Control SA-9

Torque Feedback SA-10

Returnability SA-11

Modulation SA-12

3.2 Objective Measures Used in Analysis

First of all, if there is lack of data in some objective measures, they have to be eliminated in order to keep the uniformity on objective data. After that the objective measures that have little effect on subjective assessments of drivers are allowed to be removed, such as (lat. acc.

resp. gain @ max load) and (sine time lag @max load). The reason is that the case with maximum load was never achieved at the subjective data collection scenarios. With these aforementioned work done, the standardized objective measures can be utilized in the following analysis. Totally, 27 categorized parameters are shown in Table 5.

Table 5. Overview of all needed objective measures.

Level 2 Level 3 Level 4 Unit Measure

Straight Ahead Controllability

Response

Window [ ] OM-1

SWA At 0.05 g

Response Gain Straight Path [ ⁄ ⁄ ] OM-2 On Center Yaw gain straight

Lateral Acc. Resp. Gain [ ⁄ ] OM-3 Overall Steering Sensitivity

Lateral Acc. Resp. Gain [ ⁄ ] OM-4 Overall Steering Sensitivity

Gain Linearity [ ] OM-5

Steering Sensitivity Ratio

Response Time Delay [ ] OM-6

Yaw 45° Phase Lag Time Roll

Control

Roll Control Straight Path [ ⁄ ⁄ ] OM-7 Total Rollrate Gradient @ 1 Hz

Torque Feedback

Torque Deadband [ ] OM-8

SWA at 1.3 Nm

Torque Build Up [ ⁄ ] OM-9 Torsional Rate

(33)

23

Friction Feel [ ] OM-10

Torque at 0 g

Cornering Controllability

Response

Yaw Response Gain [ ⁄ ⁄ ] OM-11 Off Center Yaw Gain

Response Gain Understeer [ ⁄ ] OM-12 Linear Range Understeer Gradient

Response Gain Linearity [ ] OM-13

Yaw Gain Linearity

Rel. yaw gain@max lat. Acc. [ ⁄ ⁄ ] OM-14 Yaw gain@max lat acc/max yaw gain

Sine Time Lag [ ] OM-15

Yaw - SWA phase time lag @ 4m/s2

Ay - SWA phase time lag @ 4m/s2

Ay - Yaw phase time lag @ 4m/s2 Roll

Control

Roll Control Cornering [ ⁄ ] OM-18 Total Roll Gain

Torque Feedback

Torque Buildup Into The Corner [ ⁄ ] OM-19 Torsional Rate Cornering

Torque Buildup Cornering [ ⁄ ] OM-20 Off Center Torque Gradient

On Center Hysteresis [ ] OM-21

Torque Deadband in Degrees

Off Center Hysteresis [ ] OM-22

Torque hysteresis @ 0.3 g

Effort Level [ ] OM-23

Torque @ 0.3 g

50m test (first impression) -

Low Speed Response Gain [ ⁄ ⁄ ] OM-24 On Center Yaw Gain

Low Speed Torque Buildup [ ⁄ ] OM-25 Max. Torsional Rate

Parking Efforts Standstill [ ] OM-26 Parking Efforts Near Center

Parking Efforts Rolling [ ] OM-27

Parking Efforts Just Off Center

3.3 Initial Parameter Matching

Having decided the subjective and objective parameters to be studied, corresponding group mapping are set before conducting the analysis. Not all of the objective inputs should be studied regarding a specific subjective assessment, since only those parameters that are measured under the same test environment should be considered. For example the SA-4, response about straight-ahead controllability, the corresponding objective data should come from OM-1~OM-6, which are listed in Table 5.

Besides, subjective ratings on Level 2 are actually calculated by using the data from Level 3 and expressed in the form of the average value of them. In other words, these values in Level 2 do not directly depend on objective measures. Instead, they are merely decided by the subjective judgment at next level (Level 3). That is why the subjective assessments on Level 2 are not included in Table 6.

Table 6. Corresponding setting for each subjective assessment.

SA Subjective Level 3 Objective Level 4 OM

1 First 50m test Low Speed Response Gain [°/s/100°SWA] 24 Low Speed Torque Buildup [Nm/100°SWA] 25

(34)

24

2 Efforts Parking Efforts Standstill [Nm] 26

Parking Efforts Rolling [Nm] 27

3 Returnability Parking Efforts Standstill [Nm] 26

Parking Efforts Rolling [Nm] 27

4 Response

Window [deg] 1

Response Gain Straight Path [°/s/100°SWA] 2 Lateral Acc. Resp. Gain [°/s/100°SWA] 3 Lateral Acc. Resp. Gain [°/s/100°SWA] 4

Gain Linearity [-] 5

Response Time Delay [ms] 6

5 Roll Control Roll Control Straight Path [°/s/g] 7

6 Torque Feedback

Torque Deadband [°] 8

Torque Build Up [Nm/100°SWA] 9

Friction Feel [Nm] 10

7 Modulation

Window [deg] 1

Response Gain Straight Path [°/s/100°SWA] 2 Lateral Acc. Resp. Gain [°/s/100°SWA] 3 Lateral Acc. Resp. Gain [°/s/100°SWA] 4

Gain Linearity [-] 5

Response Time Delay [ms] 6

Torque Deadband [°] 8

Torque Build Up [Nm/100°SWA] 9

Friction Feel [Nm] 10

8 Response

Yaw Response Gain [°/s/100°SWA] 11 Response Gain Understeer [°/g] 12

Response Gain Linearity [%] 13

Rel. yaw gain@max lat. Acc. 14

Sine Time Lag Yaw-SWA [ms] 15

Sine Time Lag Ay-SWA [ms] 16

Sine Time Lag Ay-Yaw [ms] 17

9 Roll Control Roll Control Cornering [deg/g] 18

10 Torque Feedback

Torque Buildup Into The Corner [Nm/100°SWA] 19 Torque Buildup Cornering [Nm/g] 20

On Center Hysteresis [°] 21

Off Center Hysteresis [Nm] 22

Effort Level [Nm] 23

11 Returnability

12 Modulation

Yaw Response Gain [°/s/100°SWA] 11 Response Gain Understeer [°/g] 12

Response Gain Linearity [%] 13

Rel. yaw gain@max lat. Acc. 14

Sine Time Lag Yaw-SWA [ms] 15

Sine Time Lag Ay-SWA [ms] 16

Sine Time Lag Ay-Yaw [ms] 17

(35)

25

4 Mathematical Modeling

In this chapter the bicycle model as well as some time trajectories of steering wheel angle, yaw rate, lateral acceleration and steering wheel torque will be introduced. These models and parameters set the basis of vehicle dynamics system. It is necessary to clarify that the model-based analysis is not used to calculate the value of a specific objective parameter.

The goal of the mathematical modeling is to help understand and explain the data and findings of this thesis work.

4.1 Representation of Simple Vehicle Model

To build and analyze an ideal simple vehicle model, the basic assumption made about the vehicle and its driving environment is adopted.

 The height of the center of gravity over ground is zero.

 The only external force affecting the motion of vehicle is the tire force and the side force is linear functions of the slip angles.

 The slip angles are much smaller than 180°.

 There is constant speed at stationary driving.

Figure 15. Bicycle model (single track model).

(36)

26

The most simplified vehicle model, bicycle model or also called single track model, is a three-degree-of-freedom model as seen in Figure 15. It only represents the horizontal motions in the X-Y plane. The matrix form is generally used to express the equations of motion as seen in Equation (11).

(

)

( ̇) (

) (11).

If the driving maneuver is considered to be a simple stationary case, the definition for steering sensitivity ^̇ and understeer can be expressed as in Equation (14) and (15):

̇ ̈ (12).

̇ (13).

̇

(14).

(15).

In stationary driving, the definition of yaw response gain is similar to steering sensitivity, and with Equation (13), the expression for overall steering sensitivity

is given in Equation (16). The way to transfer understeer to response gain understeer is shown as Equation (17).

̇

[ ] (16).

(17).

These two expressions show that theoretically, overall steering sensitivity and response gain understeer should correspondingly follow steering sensitivity and understeer.

4.2 Parameters with Time Trajectories

All the objective metrics can be divided into two types, instant values or time trajectories. In this thesis, time trajectories are used to show and understand the time lag, deadband or

(37)

27 hysteresis. van Daal [14] introduces all time trajectories regarding friction and compliance in steering system. Examples of these characteristics can be seen in Figure 16 to 18.

Figure 16. Time trajectories of steering wheel angle and lateral acceleration.

Figure 17. Time trajectories, lateral acceleration versus steering wheel torque.

(38)

28

Figure 18. Time trajectories, steering wheel angle versus steering wheel torque.

In Figure 16, there is a time lag between the two time trajectories. Because vehicles need to take a short time period to overcome the inertia and compliance of steering system, compliance of suspension and tire relaxation delay. The vehicles cannot respond immediately with a steering wheel input, and this is also referred to as response time lag.

In Figure 17, friction feel indicates the needed torque to initiate turning when driving at straight path, while off-center hysteresis shows the needed effort to correct the steering in cornering.

In Figure 18, on-center hysteresis indicates when drivers will feel resistance torque when changing steering wheel direction and passing the center region. Torque deadband shows the feeling of play in steering.

(39)

29

5 Evaluation of Acquired Data

In this chapter the goal is to examine the objective-objective correlations and the validity of subjective data. The results could be used to eliminate some unnecessary regressors in the correlation analysis.

5.1 Correlation between Objective Measures

The purpose of correlation coefficient analysis is to find correlations between two objective measures (Level 4) that are under the same level (Level 3). These correlations can be either positive or negative. By doing this with all vehicles, some similar or different tendencies regarding correlation between different classes are supposed to be attained. Such information can be used to take decisions on whether to disregard some objective measures in the initial studies.

The example of C-class is shown in Figure 19. The correlation coefficient between any two different objective measures is calculated. After that, all absolute values larger than 0.7 are shaded dark in the grid. The statistics for the rest of the vehicle classes are tabulated in Appendix B.

Figure 19. Correlation coefficient between two objective measures for C-class (| | is shaded).

R-value of Obj vs Obj

Objective measures

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 1

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

Links between Subjective Assessments and Objective Metrics for Steering

Links between Subjective Assessments

and Objective Metrics for Steering

Xuxin He and Zhicheng Su

Abstract

Acknowledgment

Contents

List of Symbols

List of Abbreviations

1 Introduction

2 Method

3 Parameter Selection and Matching

4 Mathematical Modeling

5 Evaluation of Acquired Data