Comprehensive evaluation method for performance of unmanned robot applied to automotive test using fuzzy logic and evidence theory and FNN

Computers in Industry 98 (2018) 48–55

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Computers in Industry journal homepage: www.elsevier.com/locate/compind

Comprehensive evaluation method for performance of unmanned robot applied to automotive test using fuzzy logic and evidence theory and FNN Gang Chena,* , Weigong Zhangb a b

School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, China School of Instrument Science and Engineering, Southeast University, Nanjing, China

A R T I C L E I N F O

Article history: Received 20 June 2017 Received in revised form 28 January 2018 Accepted 26 February 2018 Available online xxx Keywords: Unmanned robot Automotive test Performance evaluation Fuzzy logic Evidence theory Fuzzy neural network

A B S T R A C T

In order to obtain reliable and exact evaluation, a new comprehensive evaluation method for performance of an unmanned robot applied to automotive test (URAT) using fuzzy logic, evidence theory and fuzzy neural network (FNN) is presented in this paper. Throttle repeatability, speed tracking accuracy, speed repeatability, driving shock degree are used as the system evaluation index. The subjective evaluation results with various expressions are quantified using fuzzy logic. The group decision making with quantified subjective evaluation results from various drivers is combined through evidence theory. The objective evaluation indexes measured by instrumentation and the corresponding combined subjective evaluation are self-learned and trained with FNN. The comprehensive performance evaluation system of the URAT is established. Finally, real vehicle experiments are conducted. The effectiveness of the presented method for the URAT is experimentally verified. © 2018 Elsevier B.V. All rights reserved.

1. Introduction With the development of the automobile industry, the performance requirements of automotive are increasing. It is necessary for the improvement of vehicle performance to conduct a large number of automotive tests. It takes much time for automotive test [1]. It has the characteristics of time saving, cost saving and safety that conducts automotive test on chassis dynamometer. In the automotive sector, an accurate and repeatable procedure for automotive test is needed. For many automobile tests, such as emission durability test, fuel economy test, the driving behavior of a human driver is one of the sources of statistical and systematic errors. The different driving skills, and physiological and psychological factors of human driver affect the results of automotive test. The test environment is very poor and dangerous, so that it is suitable for a robot to conduct automotive test [2,3]. URAT is a robot which can be equipped in a vehicle cab without any modification [4,5]. It can be used to conduct autonomous driving replace of a human driver. Because the URAT can be directly installed in the different vehicle cab and the vehicle is not needed to be modified, it can be applied to emission

* Corresponding author. E-mail address: [email protected] (G. Chen). https://doi.org/10.1016/j.compind.2018.02.015 0166-3615/© 2018 Elsevier B.V. All rights reserved.

durability test, vehicle performance test, vehicle noise test, high and low temperature environment test, vehicle road test, vehicle bench test, autonomous vehicle, intelligent vehicles, and other fields [6,7]. The performance evaluation method of the URAT is the basis of the robot control and design, which is a key technology of the URAT development. Noguchi S, et al. propose an evaluation method for measuring the driving capability of a robotic driver using regression analysis, however the method does not concern subjective evaluation of various drivers [8]. Jeong S, et al. propose a self-balancing personal mobility vehicle with a hybrid mechanism and discuss its features from the perspectives of power-assist driving performance and a rider’s evaluation, however the method does not concern the vagueness and uncertainty of various drivers [9]. Evaluation method for the performance of the URAT includes subjective evaluation and objective evaluation. Chen Gang, et al. designs an evaluation model for vehicle shift quality based on evidence theory and fuzzy neural network [10]. However, the model does not consider the uncertainty and different expression ways of subjective evaluation from various drivers. Chen Gang, et al. designs an approach to vehicle shift quality subjective evaluation based on fuzzy logic and evidence theory [11].

G. Chen, W. Zhang / Computers in Industry 98 (2018) 48–55

However, the approach does not take into account objective evaluation from instrumentation. It is good for fuzzy logic to express subjective evaluation from various drivers [12]. The evidence reasoning using evidence theory has a good consistency with human’s reasoning [13,14]. Besides, fuzzy neural network (FNN) has not only self-leaning ability of objective indexes but language reasoning ability [15,16]. In this paper, a novel evaluation method for performance of the URAT based on fuzzy logic, evidence theory and FNN is presented. Throttle repeatability, speed tracking accuracy, speed repeatability, driving shock degree are used as the system evaluation index. The subjective evaluation results with various expression ways are quantified using fuzzy logic. Besides, the quantified subjective evaluation results from various drivers are combined by evidence theory. Moreover, the objective evaluation indexes measured by instrumentation and the corresponding subjective evaluation are self-learned and trained by FNN. The comprehensive performance evaluation system of the URAT is established. Real vehicle experiments are conducted. Experimental results show the effectiveness of the presented method. 2. Evaluation indexes Throttle repeatability, speed tracking accuracy, speed repeatability, shock degree of driving are used as the evaluation index of the URAT performance.

49

characterize the global error. vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! u K u X 2 u ðV act ðti Þ  V set ðti ÞÞ u t i¼1 V RMS ¼ K

Where, Vact(ti) is actual speed of chassis dynamometer, Vset(ti) is set speed of chassis dynamometer, ti is sampling time, K is the total number of automotive test data samples. When actual measured speed can accurately track the set speed, VRMS = 0. 2.3. Speed repeatability The control performance of throttle is characterized by the motion speed of the throttle pedal. Assume that the engine speed at the time ti is ne(ti), and in the next sampling time the engine speed at the time ti + Dt is ne(ti + Dt). Where, Dt is the sampling period. The engine speed error Dnei at the time ti

Dnei ¼ ne ðti þ DtÞ  ne ðti Þ

ne ¼

K 1X Dnei K i¼1

ð3Þ

The residual variance of the engine speed S2v ¼

2.2. Speed tracking accuracy Due to that root mean square (RMS) of speed error has large errors weights, and the margin of error can not be offset, it is able to

ð2Þ

In the whole test condition, the average deviation of the engine speed

2.1. Throttle repeatability The sampling data of throttle pedal opening degree at the time ti is defined as f(ti). The repeatability of throttle pedal is obtained by regression analysis method.

ð1Þ

K  1X Dnei  ne Þ2 K i¼1

ð4Þ

If the motion of the throttle pedal is steady in the whole test condition, Sv = 0. When Sv is larger, the motion of throttle pedal is less smooth. 2.4. Driving shock degree Driving shock degree j is the change rate of the longitudinal acceleration during the process of driving. In the process of the shift, the driving shock degree dðT e ig Þ d u r d v2 r ¼ ¼ 2 i0 dt2 dt2 ½ig ðIe þ I1 þ I2 i0 dt 2

j¼

2

ð5Þ

Where, v2 is the angular velocity of vehicle transmission output shaft. Ie is the moment inertia of engine and clutch active disc. I1 is the equivalent moment inertia of rigid connection after converting to vehicle transmission input shaft. I2 is the equivalent moment inertia of total vehicle quality and tires after converting to vehicle transmission input shaft. 3. Evaluation method The multi-index comprehensive evaluation method combined with subjective evaluation and objective evaluation using fuzzy logic, evidence theory and FNN is presented.

Table 1 The definition of human driver’ expression.

Fig. 1. The FNN structure.

uij

1

2

3

4

5

Excellent Good General Bad Poor

1 0.25 0 0 0

0.75 1 0.5 0 0

0 0.75 1 0.75 0

0 0 0.5 1 0.5

0 0 0 0.25 1

50

G. Chen, W. Zhang / Computers in Industry 98 (2018) 48–55

Table 2 The definition between fuzzy expression and feature set. ui(Ak)

1

2

3

4

5

Quality grade (A1) Goods grade (A2) Defective goods grade (A3)

1 0 0

0.5 0.5 0

0 1 0

0 0.5 0.5

0 0 1

3.1. The fuzzy logic and evidence theory The system subjective evaluation data is from the knowledge of language describing driving experience of human driver. The uncertainty is an important feature of language information from various drivers. Fuzzy logic can realize the quantification of subjective evaluation. A specific professional driver’s knowledge and experience are limited, so it is necessary to combine different driving experiences of various drivers. Evidence theory can effectively achieve the combination of evaluation from different drivers. For a question to be judged, a collection of all the answers to the question is Q. Any two elements in the collection Q must be mutually exclusive, and elements of intersect each other is empty set. The corresponding result of each question can only be an element of Q. Q is called an identification framework of the corresponding problem. Assume Bel1 and Bel2 are belief function for identified framework Q, m1 and m2 are basic probability assignment (BPA), A1,   , Ai and B1, B2,   , Bj are focal element. Let X m1 ðAi Þm2 ðBj Þ < 1; K ¼ 1  c ð6Þ c¼ Ai \Bj ¼F

Then the function m: 2Q ! [0, 1] defined by Eq. (7) is BPA after the combination of two evidences. 8 < mðFÞ ¼ 0 X ð7Þ m1 ðAi Þm2 ðBj Þ; A 6¼ F mðAÞ ¼ K 1 : Ai \Bj ¼A

Where, the conflict weight K ¼

X 1Y 1

, m(A) is the

mj ðAi Þ

\Ai ¼F1jn

belief value after the combination of two evidences. Different independent evidences are combined by the Eq. (7). The capacity of each evidence is EðevÞ ¼

X i¼1 Ai 6¼ F

nðAi Þ

mðAi Þ jAi j

ð8Þ

Where, jAi j and n(Ai) is base value and of number focal element, respectively. E(ev) 2 [0, 1]. As E(ev) = 0, the evidence is useless. As E (ev) = 1, the evidence is the most useful. Then, various drivers’

Fig. 3. The calculation flowchart of comprehensive performance evaluation for URAT.

experiences are combined. 8 > < mð0 FÞ ¼ 0 mj ðAi Þ ¼ Ej ðevÞmðAi Þ > : m0 ðQÞ ¼ E ðevÞm ðQÞ þ ð1  E ðevÞÞ j j j j

ð9Þ

By substituting the Eq. (9) into the Eq. (7), an improved combination rule of evidence theory is obtained. 8 X Y 0 00 00 > mj ðAi Þ þ K mj ðAÞ mðAÞ ¼ > > > > \Ai ¼A1jn > Y 0 X > 00 > > > mj ðAi Þ n > 1X 0 > 00 > m ðAÞ mj ðAÞ ¼ > > > n j¼1 j > > > P : mðQÞ ¼ 1  mðAÞ; A 6¼ F; Q 0

Where, mj ðAÞ is average support value for A after each evidence

is weighted. K” is assignment value for total conflict probability after each evidence is weighted. Weighted assignment is achieved by the weight combination in accordance with average support of each subset.

Fig. 2. Subjective evaluation combination of URAT using evidence theory.

G. Chen, W. Zhang / Computers in Industry 98 (2018) 48–55

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Fig. 4. Comprehensive evaluation system model structure of the URAT. Note: ANFIS represented Adaptive Network-based Fuzzy Inference System.

3.2. The FNN structure The Takagi-Sugeno FNN model [17,18] consists of front member network and rear member network. Its convergence rate is fast, and less sample is needed. The FNN structure is shown in Fig. 1. The front member network is composed of four layers. The first layer is input layer. The number of the node is four. Throttle repeatability x1, speed tracking accuracy x2, speed repeatability x3, driving shock degree x4 are the input parameters of the network. The second layer is fuzzy layer. The membership of the each node is calculated by bell function.

mji ¼ 1þ



1

xci ai

2 bi

ð11Þ

The fourth layer is normalized layer. The normalized incentive intensity of the rule is calculated in the normalized layer.

j¼1

yj ¼ rj0 þ rj1 x1 þ rj2 x2 þ rj3 x3 þ þrj4 x4

ð13Þ

ð14Þ

Where, rjd is the weight coefficient, d = 0, 1, 2, 3, 4. The combining layer of the rear member network is used to normalize the rear member weight value. yj ¼ aj  yj

Where, x is the input of the node i(i = 1, 2, 3, 4). j = 1, 2, 3,    , (n  1), n is the number of the fuzzy rules. fai ; bi ; ci g is the premise parameter set, and the shape of the membership function changes with the change of the premise parameters. The third layer is rule layer. The incentive intensity of the each rule is calculated in the rule layer. Y aj ¼ mAi ðxÞ ð12Þ

aj aj ¼ X n aj

The number of the rear member network input layer is more than that of the front member network input layer. The difference of the input layer node is x0 = 1. The node is used to compensate the constant term of the fuzzy rule in the rear member network. The function layer of the rear member network is used to calculate the weight value yj of the each rule in the rear member. The weight coefficient among nodes is the rear member parameter. The output of the function layer is a linear combination of the input.

ð15Þ

There is one node in the output layer of the rear member network. The layer is used to sum the input parameters. A comprehensive evaluation result for performance of the URAT is obtained. Y^¼

n X yj

ð16Þ

j¼1

3.3. Subjective evaluation Physiological and psychological factors, knowledge and experiences of various drivers have an influence on the subjective evaluation results. The fuzzy terms of human expression, such as

Fig. 5. The robot prototype and vehicle test.

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G. Chen, W. Zhang / Computers in Industry 98 (2018) 48–55

Fig. 6. Input data of performance evaluation system for URAT.

G. Chen, W. Zhang / Computers in Industry 98 (2018) 48–55

approximate and possible, are adopted in the process of the subjective evaluation. The fuzzy set of human driver expression is U = {excellent, good, general, bad, poor}. The definition of human driver’ expression is shown in Table 1. Feature set Q = {quality grade A1, goods grade A2, defective goods grade A3} is as an expression of the evaluation results. In order to make the fuzzy expression represented by Q, it is necessary to define each grade of Q by five types (see Table 2). Without the exclusion of the definition of fuzzy expression, the matching degree between the human driver j on the index ti and the grade of Q is 

ðti Þ ðAk Þ j

m

¼

mðtj i Þ ðAk Þ 3 X



;

k ¼ 1; 2; 3;

j ¼ 1; 2;    ; n

ð17Þ

mðtj i Þ ðAk Þ

53

membership function. The hybrid learning algorithm combining with back propagation algorithm and least squares method is used to train the model system. Sugeno model is used as the system fuzzy reasoning model. 4. Experimental verification To verify the effectiveness of the proposed evaluation method for the URAT, vehicle test manipulated by the URAT is performed in Nation Quality Supervision and Inspection Center for Passenger Car of China [19]. The test process is seen in Reference [1]. The robot prototype installed in a cab of test vehicle and the vehicle test is seen in Fig. 5. 4.1. Numerical examples verification

k¼1

The quantified subjective performance evaluation of the URAT is acquired by professional and general drivers. Each driver makes an independent evaluation. The combination of the subjective   evaluation for q URAT systems t1 ; t2 ;    ; tq from n professional drivers fx1 ; x2 ;    ; xn g and i general drivers fy1 ; y2 ;    ; yi g using evidence theory is shown in Fig. 2. Each evaluation result from professional and general drivers is as an evidence. The combination of two evidences for the performance of the URAT collected by two professional drivers and two general drivers are computed, respectively. Using the same approach, the combination result is as a new evidence of the next combination. Moreover, the subjective evaluation for the performance of the URAT system is obtained. Finally, the subjective evaluation for performance of a group of the URAT systems is obtained. 3.4. Comprehensive evaluation method The calculation flowchart of comprehensive evaluation method of performance for the URAT combining with subjective and objective evaluation using fuzzy logic, evidence theory and FNN is shown in Fig. 3. The subjective evaluation from various drivers after combination using fuzzy logic and evidence theory is as the input of the FNN evaluation system. The FNN comprehensive evaluation system model structure of the URAT is shown in Fig. 4. The evaluation system model is trained by the normalized the evaluation indexes sample data and corresponding subjective evaluation combined by evidence theory. The evaluation indexes including throttle repeatability, speed tracking accuracy, speed repeatability, driving shock degree are the system input parameters. The comprehensive evaluation result for the performance of the URAT is as the system output parameter. Each parameter has three fuzzy sets. The training error is set to zero. The type of the membership functions is generalized bell

Fig. 7. Comparison of system evaluation and subjective evaluation.

There are forty test drivers during the process of the subjective evaluation, whose average age is thirty seven years old, including seven women. Evaluation grade for the performance of the URAT is divided into quality level, goods level and bad level. The mathematical description of the performance subjective evaluation for the URAT is identification framework Q = {quality grade A1, goods grade A2, defective goods grade A3}. The normalized subjective evaluation from a professional driver x1 and a professional driver x2 is x1 : m1 ðA1 Þ ¼ 0:8; m1 ðA2 Þ ¼ 0:1; m1 ðA3 Þ ¼ 0:1 x2 : m2 ðA1 Þ ¼ 0:6; m2 ðA2 Þ ¼ 0:3; m2 ðA3 Þ ¼ 0:1

ð18Þ

In this case, there is no conflict in the two evidences from the professional drivers. Computation results by the traditional evidence combination Eq. (7) are that conflict probability assignment m(F) is 0.48 and conflict weight k is 1.92. Further computational result is m12 ðA1 Þ ¼ 0:92

m12 ðA2 Þ ¼ 0:06

m12 ðA3 Þ ¼ 0:02

ð19Þ

The presented evidence itself from the Eq. (18) shows that the first evidence of the professional driver x1 supports A1, and the second evidence of the professional driver x2 also supports A1. The combination result of the Eq. (19) also supports A1, which is consistent with the facts. In the other case, the normalized subjective evaluation from a general driver y1 and a general driver y2 is y1 : m1 ðA1 Þ ¼ 0:85; m1 ðA1 ; A2 Þ ¼ 0:1; m1 ðA3 Þ ¼ 0:05 y2 : m2 ðA1 Þ ¼ 0:1; m2 ðA2 ; A3 Þ ¼ 0:15; m2 ðA3 Þ ¼ 0:75

ð20Þ

There are conflicts in above two evidences from the general drivers. On this occasion, the improved evidence combination

Fig. 8. Training error and checking error.

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G. Chen, W. Zhang / Computers in Industry 98 (2018) 48–55

Table 3 Comparison results of subjective evaluation and system evaluation. No.

Throttle repeatability

Speed tracking accuracy Speed repeatability

Driving shock degree Subjective evaluation

Comprehensive system evaluation

Error

1 2 3 4 5 6 7 8 9 10 ... 100

0.7129 0.549 0.9413 0.3299 0.7045 0.9434 0.5816 0.8802 0.7496 0.7129 ... 0.3796

0.671 0.8206 0.9705 0.4869 0.8175 0.6416 0.3063 0.6609 0.358 0.671 ... 0.9382

0.7505 0.1262 0.0431 0.3709 0.6933 0.9358 0.4776 0.1291 0.4838 0.7505 ... 0.9456

0.7204 0.7673 0.4015 0.4329 0.9595 0.8788 0.6941 0.2919 0.855 0.7204 ... 0.9745

0.0032 0.0979 0.0095 0.0081 0.0052 0.0026 0.0045 0.0135 0.0257 0.0032 ... 0.0039

0.8578 0.6098 0.5657 0.6119 0.103 0.1583 0.4136 0.5604 0.2687 0.8578 ... 0.7843

Eq. (10) is used to calculate. Computation results by the improved evidence combination Eq. (10) are that conflict probability assignment m(F) is 0.74, and probability assignment is mðA1 Þ ¼ 0:48 mðA2 Þ ¼ 0:01 mðA3 Þ ¼ 0:35 mðA1 ; A2 Þ ¼ 0:04 mðA2 ; A3 Þ ¼ 0:06 mðFÞ ¼ 0:05

ð21Þ

Belief interval of A1, A2, A3 is A1 ½0:48 ; 0:58

A2 ½0:01 ; 0:16

A3 ½0:35 ; 0:46

ð22Þ

The combination result of the Eq. (22) is reasonable, which is consistent with a human reasoning. The presented method is verified by the two numerical examples. 4.2. Experiment results and analysis The performance evaluation indexes and the corresponding subjective evaluation are collected at the same time. They are used to train the evaluation system model as sample data. The throttle repeatability, speed tracking accuracy, speed repeatability and driving shock degree are acquired real-timely. The number of collected data is one hundred. And the normalized data is adapted as FNN model sample. The input data of the performance evaluation system for the URAT is shown in Fig. 6. The comparison between the system evaluation of the FNN evaluation system and the subjective evaluation after evidence combination is shown in Fig. 7. The error training samples and checking samples is shown in Fig. 8. Fig. 7 shows that the system evaluation is consistent with subjective evaluation, and the effectiveness of the presented method is verified. Fig. 8 shows

0.7172 0.8652 0.411 0.4248 0.9543 0.8814 0.6986 0.3054 0.8293 0.7172 ... 0.9706

that the training error and the checking error are decreasing with the increase of number of steps. The maximum root mean square error of the training data and the checking data is 0.131 and 0.1513, respectively. The effectiveness of the presented approach in this paper is verified again. Comparative results of subjective evaluation and system evaluation are shown in Table 3. The error curve of the comprehensive evaluation is shown in Fig. 9. Where, the input parameters, including throttle repeatability, speed tracking accuracy, speed repeatability and driving shock degree, are normalized evaluation indexes. The data of the system evaluation are a normalized comprehensive evaluation rating. Table 3 and Fig. 9 show that the max error of the comprehensive evaluation is 0.15, and it can be accepted. The results show that the presented approach is valid. 5. Conclusions A novel comprehensive evaluation method for the performance of the URAT based on fuzzy logic, evidence theory and FNN is presented in this paper. The method can obtain reliable and exact evaluation. Throttle repeatability, speed tracking accuracy, speed repeatability, driving shock degree are used as the system evaluation index. The subjective evaluation results with various expressions are quantified using fuzzy logic. The group decision making with quantified subjective evaluation results from various drivers is combined through evidence theory. The objective evaluation indexes measured by instrumentation and the corresponding combined subjective evaluation are self-learned and trained with FNN. The comprehensive performance evaluation system of the URAT is established. Experiments are conducted. Experimental results show that the proposed method can solve the shortcomings of subjective evaluation and objective evaluation, respectively. The proposed method can achieve the performance evaluation of the URAT effectively and objectively, whose evaluation results have a good consistency with reality. The proposed method in this paper provides a development and detection tool of the URAT for designers and engineers, so that the quality problems could be resolved in the early period of the development. Acknowledgements

Fig. 9. Error curve of the comprehensive evaluation.

This project is supported by National Natural Science Foundation of China (Grant No. 51675281 and 51205208), Six Talents Peak Project of Jiangsu Province (Grant no. 2015-JXQC-003), The Fundamental Research Funds for the Central Universities (Grant No. 30916011302).

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