A Soft Fault-concept Diagnosis Method of Analog Circuits Based on ...
JOURNAL OF NETWORKS, VOL. 8, NO. 7, JULY 2013
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A Soft Fault-concept Diagnosis Method of Analog Circuits Based on Cloud Model Theory Qi Liu 1,2 1
2
School of Information Engineering, Hebei University of Technology, Tianjin, China School of Computer and Information Engineering, Tianjin University of Urban Construction, Tianjin, China
Email: [email protected] Jun Cui School of Electronics and Information Engineering, Tianjin Polytechnic University, Tianjin, China Email: [email protected]
HongDong Zhao, and Hong Shen School of Information Engineering, Hebei University of Technology, Tianjin, China Email: [email protected], [email protected]
Abstract—As the component parameters of analog circuits are influenced by tolerance, a soft fault-concept diagnosis model in this paper, which is based on the qualitative concepts of cloud model theory, is proposed to achieve the complete description of fault states and the fast diagnosis. The diagnosis model uses the cloud transform method to represent the conceptual soft classification of the multiple test-point voltage intervals. At first the model generates the atomic concepts of test-point voltages which are indicated by the characteristic values of cloud model, and promotes these atomic concepts to the qualitative concepts of test-point voltage which are easy to be understood. Then the model forms the fault category concept table based on a combination of qualitative concepts of multiple test-point voltages which are associated with the range of fault component parameters. Lastly according to the table, the soft fault-concept classification and diagnosis of analog circuits are achieved in this paper based on these formalization concepts. The simulation results show that the soft fault-concept method provides a good solution of analog circuits fault diagnosis avoiding the effect of component tolerance, at the same time the method has achieved a higher diagnosis accuracy rate. Index Terms—Cloud Model, Tolerance, Soft Classification, Soft Fault Diagnosis
I.
INTRODUCTION
With the increasing scale of integrated circuits, since 1960’ the fault diagnosis of circuits has become one of the hot topics of concern to investigators [1, 2, 3, 4]. The fault diagnosis researches of analog circuits are influenced by some factors such as the lack of fault model, the parameter tolerance of analog components, the widespread presence of nonlinear problems and the limitation of the actual test point numbers that could be measured, the researches on fault diagnosis are the bottleneck of mixed-signal integrated circuits. And the
© 2013 ACADEMY PUBLISHER doi:10.4304/jnw.8.7.1497-1503
soft fault diagnosis of analog circuits is more difficult than hard fault [5]. Modern diagnostic methods based on artificial intelligence such as neural networks and SVM [1, 3] have been widely used in analog circuit fault diagnosis because of not depending on the complex models of circuits. The main drawbacks of these methods are the high requirements on the samples and the large probability of misdiagnosis and missed diagnosis for the circuits of less test points measured. And most of the methods are used to diagnose hard fault and soft fault of a few fixed parameter offsets, the fault states corresponding to soft fault cannot be described completely [6, 7, 8]. LUO et al [9] divides these voltage intervals into several subintervals based on the tolerance of component parameters to achieve the complete description of fault states. But this method uses subjectively numerical hard classification, and it likely causes some test-point voltage intervals too large or too small to not be distinguished and cannot be diagnosed effectively. Therefore, a fault-concept diagnosis model based on the concepts of cloud theory [10, 11, 12, 13] is proposed in this paper. On the basis of the "soft classification" of the test-point voltage qualitative concepts, a combination of the qualitative concepts of multiple test-point voltages of analog circuits is associated to the range of component parameters corresponding to fault category concepts to realize the complete description of fault states and rapid diagnosis and to improve the diagnostic accuracy in the premise of not increasing test points that can be measured. II.
THE DIAGNOSIS PRINCIPLE OF SOFT FAULT-CONCEPT
At present the diagnostic information with analog circuits is basically by measuring the test-point voltage values or current values to extract fault features, so the test-point voltage simulation data and sampling data of
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the analog circuit are used to fault feature extraction and concept diagnosis in this paper. The relation of component parameters and test-point voltages is given in reference [14]: Let Ni(i=1,2,…,n) indicate the test point that can be measured in the analog circuit, Xj(j=1,2,…,m) represent the component, the corresponding component parameter value is xj. The point voltage of Ni is ui, then the relation between ui and xj that can be drawn from the circuit analysis is uij = fi(xj).
(1)
If test-point voltages for the analog circuit meet: within a specific parameter range of a fault component, the corresponding test-point voltage values are monotonically increasing or decreasing that uij=fi(xj) exists the inverse function xj=fi-1(uij). As long as known the test-point voltage interval values corresponding to the range of fault component parameters when Xj goes wrong before the test, then in comparison with the sampling values of the test-point voltages in the actual diagnosis we can determine Xj whether this fault occurred. Definition 1: the concept-characteristic values of test-point voltage interval concepts On the basis of Formula 1, suppose the concept-characteristic value of the voltage interval for point Ni is cij(j=1,2,…,m), then combined with the theory analysis of cloud model we can draw the relation between cij and uij is cij = μi(uij).
(2)
Here cij indicates the concept characteristic values of some test-point voltage interval which including the voltage value uij of the test point Ni when the parameter value of the component Xj is xj. This function model reflects the membership relations between the cloud drop uij and the cloud cij(Ex,En,He) that the cloud cij(Ex,En,He) represents the test-point voltage interval corresponding to the parameter range of the fault component and cij(Ex,En,He) consists of uij. Definition 2:the relation between the concepts of test-point voltage intervals and component parameters Integrated above two definitions, we can draw the relation of cij and xij is cij=μi(uij)=μi(fi(xj)).
(3)
When the component Xj is at fault its parameter value xj would be changed, the voltage uij of each point Ni may change along, then the concept-characteristic value cij of the voltage intervals at each point Ni may also change. Seen by the formula 1, when Xj goes wrong the range of fault component parameters corresponds to the voltage interval values of the test point. Similarly, Definition 2 shows that when Xj goes wrong the range of fault component parameters corresponds to the concept-characteristic value of the test-point voltage intervals. Then in comparison with the concept-characteristic value of the test-point voltage interval belonged the sampling values of the test-point voltage we can determine Xj whether this fault occurred.
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In this paper, the soft fault-concept diagnosis model of analog circuits bases on the relation model on research. III.
THE SOFT FAULT-CONCEPT DIAGNOSIS MODEL OF ANALOG CIRCUITS
On the basis of using the characteristic values of cloud model for the conceptual soft classification of test-point voltages, a soft fault-concept diagnosis model based on cloud theory is proposed (S-FCDM (A Soft fault-concept Diagnosis Model Based on Cloud Method)), as shown in figure 1.
Figure 1. The diagnostic model of fault category S-FCDM
The S-FCDM diagnostic model includes two parts, the fault featrue extraction and the fault category diagnosis. The fault feature extraction part The test-point voltage simulation data are converted to the atomic concepts of test-point voltage by using the cloud transform method, and these atomic concepts are promoted up to the qualitative concepts of test-point voltage which more accord with human thinking, then these test-point voltage concept tables are generated for each specific test point, at last the fault category concept table is generated through the qualitative concept combination, in order to implements in combination form of the qualitative concept rather than the specific voltage interval values as the fault characteristics of analog circuits. The fault category diagnosis part For the test-point voltage simulation data, the maximum membership decision algorithm is used to judge the membership concept of test-point voltage based on the corresponding test-point voltage table. At last, a qualitative concept combination judged by a group of test-point voltages is used to achieve the fault category concept diagnosis of the analog circuit, comparing the qualitative concept combinations of the corresponding many groups of test-point voltages in the fault category concept table. A. Fault Feature Extraction
Converting to the test-point voltage atomic concepts Definition 3: the test-point voltage atomic concepts The cloud transform method is used to realize the quantitative numerical transformation to the qualitative concepts for the test-point voltage simulation data and generate the test-point voltage atomic concepts
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represented by the digital characteristic values of cloud model. ACi={ aciy ( Exy , Eny , Hey ) | 1 y Y }.
(4)
Among them, aciy ( Exy , Eny , Hey ) is said by the atomic concept of the cloud model digital characteristic values represented, Y is the atomic concept number. The cloud transform method, please see reference [12]. The diagnosis model S-FCDM need process all the test-point voltage simulation data respectively for cloud transform to convert the test-point voltage simulation data to the test-point voltage atomic concepts. Enhancing to the test-point voltage qualitative concepts The test-point voltage atomic concepts may be too small size of concepts to be of human understanding and acceptance. Therefore, it is necessary to enhance these atomic concepts to qualitative concepts for higher conceptual levels. Definition 4: the test-point voltage qualitative concepts The test-point voltage atomic concept ACi is processed for the concept promotion algorithm to enhance to the test-point voltage qualitative concepts represented by digital characteristic values of cloud model and to accord with human subject perception. QCi={ qciz ( Exz，Enz，Hez ) | 1 z Z }.
(5)
Among them, qciz ( Exz，Enz，Hez ) is said by the qualitative concept for digital characteristic values of cloud model, Z is the qualitative concept number. The number of qualitative concepts involves concept promotion strategy [15, 16], so the strategy of the pre-specified granularity to enhance the concepts is adopted in this paper that users directly specify the final number of qualitative concepts of the test-points voltages. Generally 7±2 concepts corresponding to the concept granularity is more in line with the psychological characteristics of human cognition. In this paper, the default setting value is 5. Similarly the diagnosis model S-FCDM need enhance the test-point voltage qualitative concepts for all the test-point voltage atomic concepts. Generating the test-point voltage concept table For the specific test-point Ni, on the basis of the qualitative concept of the test-point voltages corresponding to cloud model digital characteristic values, This paper uses the maximum membership decision algorithm to determine that each test-point voltage simulation data ultimately belong to which the specific concept is part of the test-point voltage qualitative concepts. And combines the test-point voltage qualitative concepts corresponding to the test-point voltage intervals and the range of component parameters, generates a test-point voltage concept table of the specific test-point. In table 1, “the test-point voltage intervals” are judged by maximum membership decision algorithm with reference to the characteristic values of test-point voltage qualitative concepts and combined to get the test-point
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qualitative concepts corresponding to the test-point voltage intervals to realize “soft classification” of the test-point voltage intervals. The range of component parameters is reverse calculation of the test-point voltage range and the test-point voltage simulation data Uij, after combining to get the test-point voltage qualitative concepts corresponding to the range of component parameters. TABLE I.
THE TEST-POINT VOLTAGE CONCEPT TABLE OF TEST-POINT N1
The language values of test-point voltage qualitative concepts The characteristic values of test-point voltage qualitative concepts The test-point voltage intervals The range of component parameters
concept1
concept2
…
concept z
qci1
qci2
…
qciz
uri1
uri2
…
uriz
xrij1
xrij2
…
xrijz
The diagnosis model S-FCDM need generate N test-point voltage concept tables for all the test-point voltage qualitative concepts. Generating the fault category concept table Definition5: the fault category concept On the basis of all the test-point voltage concept tables in analog circuits, only a test-point voltage qualitative concept was taken from each test-point voltage concept table, some fault categories in analog circuits are represented by the combination of these test-point voltage qualitative concepts, this paper is called fault category concept. The formal definition of the fault category concept is TC={( qc1z1 , qc 2z2 ,…, qcizi ,…, qc nzn11 , qc nzn ) | qcizi QCi , 1 i n , 1 zi Z }.
(6)
Among them, i represents the ith test-point voltage, zi is anyone in the number Z of qualitative concepts specified by ith test-point voltages. qcizi QCi is that the test-point voltage concept qcizi belongs to the ith testpoint voltage concept collection QCi . After associated with a combination of each test-point voltage qualitative concept, according to the definition and formalization of the fault category concept, the fault categories concept table is generated based on Boolean truth table. In table 2, q is the concept number of the ultimate fault category, n
q c1zi ,
(7)
1
Zi is the number of the qualitative concept of the i-th test-point voltage intervals. In order to facilitate the display, we used “A, B,…,Zi” instead of the test-point voltage qualitative concept language values “concept1, concept2, …, concept Zi” in the test-point voltage concept table.
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TABLE II. Test-point
THE FAULT CATEGORY CONCEPT TABLE
Test-point voltage u1
Language value
…
Z1
qc11 qc 2 1
…
qc1Z1
Voltage interval
ur11 ur 2 1
…
Parameter range Fault concept
xr1j1 xr 2 1j
fc1 fc2 …
1 0 …
fcq
0
characteristic value
A
Test-point voltage u2
…
B
…
Z2
qc12
qc22
…
qc2Z2
…
ur1Z1
ur21
ur22
…
ur2Z2
…
xr1jZ1
xr2j1
xr2j2
…
0 1 …
… … …
0 0 …
1 0 …
0 1 …
0
…
1
0
0
B
A
Comparing the contents of the range of component parameters {xrij1,xrij2,…,xrijz} in the table 1, in the light of the conclusions by the range of component parameters one to one corresponding to the soft classification of test-point voltage intervals and the soft classification of concepts. We can get the meaning of fcq in the fault category concepts{fc1,fc2,…,fcq} of table 3. fcq qc1z1 & qc 2z2 &…& qcizi &...& qc nzn
Test-point voltage un B
…
Zn
qc1n
qcn2
…
qcnZn
…
urn1
urn2
…
urnZn
xr2jZ2
…
xrnj1
xrnj2
…
xrnZj n
… … …
0 0 …
… … …
1 0 …
0 1 …
… … …
0 0 …
Category 1 Category 2 …
…
1
…
0
0
…
1
Category q
IV.
APPLICATION EXAMPLES AND EXPERIMENTAL RESULTS
A
The language values of fault category concepts
A. The Test Circuit and Experimental Data Fault diagnosis simulation circuit is shown in Figure 2, the component parameters R1=R7=2kΩ, R2=R3=R4=R5=R6=1kΩ; Excitation voltages V1=5v; Node 1, 2, 3 can be measurable.
ur1z1 & ur2z2 &…& urizi &...& urnzn (8) xr1jz1 & xr2z2j &…& xrijzi &...& xrnjzn In table 2, the diagnosis model S-FCDM can determine whether the fault category concept is in fault states that the range of parameters of the specific component Xj for fcq corresponding to ( xr1jz1 & xr2z2j &…& xrijzi &...& xrnjzn ) is null. B. The Fault Category Diagnosis The diagnostic model S-FCDM for all test-point sampling, at least need to get a group of test-point voltage sampling data (v1, v2,…,vi,…,vn). The determination of the test-point voltage membership concepts For a test-point voltage sample value vi, the maximum membership decision algorithm [10] is used based on the corresponding test-point voltage concept table to determine which test-point voltage qualitative concept qcizi is affiliated by the value vi in the corresponding test-point voltage concept table and to get the test-point voltage interval urizi that associated with the concept and the range of component parameters xrijzi .
The fault category concept diagnosis Based on a group of test-point voltage sampling data (v1, v2,…,vi,…,vn) corresponding to the group of membership concept ( qc1z1 , qc 2z2 ,…, qcizi ,…,
qc nzn11 , qc nzn ), by comparing all fault category concepts in the fault category concept table we can determine whether ( xr1jz1 & xr2z2j &…& xrijzi &...& xrnjzn ) in the parameter range of the specific component Xj is empty to diagnose the specific fault state. © 2013 ACADEMY PUBLISHER
Figure 2. The test circuit of fault diagnosis
In order to simplify the analysis of experimental results, only R1, R2, R4 and R6 are defined in this paper, these four components may be faulty in the experiment and the parametric analysis functions are used to generate test-point voltage simulation data by ORCAD Pspice. B. Fault Feature Extraction Process
Converting to the atomic concepts and update to the qualitative concepts For the test-point voltage simulation data {U1, U2, U3}, three frequency distribution functions of test-point voltage data are generated and they need be cloud transform to get three atomic concepts {AC1, AC2, AC3} of test-point voltages, at last by promotion of concepts we can obtain three groups of the test-point voltage qualitative concepts {QC1, QC2, QC3} based on five characteristic values represented of cloud model. Here are just listed the expectation curve of test-point voltage atomic concepts and test-point voltage qualitative concepts for the test point 1, as shown in figure 3. Generating test-point voltage concept tables and the fault category concept table For the set {QC1, QC2, QC3} of characteristic values of test-point voltage qualitative concepts corresponding to the test points {N1, N2, N3}, the specific test-point voltage uij is determined which belongs to the qualitative concept
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qcizi
1501
by using the maximum membership decision
algorithm. And the same qualitative concept qcizi corresponding to the test-point voltage uij combines the interval urizi of test-point voltages. According to the test-point voltage simulation data corresponding to the values of component parameters, the range xrijzi of component parameters that associated with the interval urizi of the test-point voltages is deduced to get a test-point voltage concept table in the light of each test point respectively. 90 80 70 60 50 40 30 20 10
0
10
20
30
40
50
60
70
80
90
100
(a) 100 90 80 70 60 50 40 30 20 10 0
0
TABLE III.
THE COMPONENT PARAMETER RANGE CORRESPONDING TO THE LANGUAGE VALUE “VOLTAGE LOW” OF TEST-POINT VOLTAGE QUALITATIVE CONCEPTS FOR TEST POINT N1 The language values of test-point voltage qualitative concepts “voltage low”
The parameter range of fault components R1 R2 R3 R4
(999,14041]
(0,50000)
(0,50000)
(0,50000)
The meanings of the ranges of component parameters in the fault category concept table and in the test-point voltage concept table are consistent that the specific value of the range ( xrijzi ) of component parameters for each
100
0
interval and 125 permutations and combinations of fault category concept items also did omit.
10
20
30
40
50
60
70
80
90
100
(b) Figure 3. (a). The test-point voltage atomic concepts extracted of test-point 1 (b) the expectation curve of test-point voltage qualitative concepts of test-point 1
The following table 4 lists the test-point voltage concept table of test point 1. It is noted that the specific value of the component parameter ranges corresponding to the specific test-point voltage qualitative concept ( qcizi ) in the test-point voltage concept table is not only one but existing a corresponding range of the component parameter for each component X j. For example, in this experiment the component parameter range corresponding to the test-point voltage qualitative concept value “voltage lower” for the test point N1 includes the component parameter ranges corresponding to four Resistance components (R1,R2,R4,R6). The specific data are shown in Table 3. Using three test-point voltage concept tables in this experiment, we can get one fault category concept table finally that these qualitative concepts are associated to q 3
fault category concept items, q= C51 =125, as shown in 1
table 5. In order to facilitate display in table 5, qualitative concept-characteristic values are truncated in every
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component Xj has a corresponding range of component parameters. So the specific value of the fault category concept item (fcq) in the fault category concept table has a corresponding the “&”operating result of component parameters of every test-point voltage qualitative concept qcizi for each component Xj. For example, in this experiment the component parameter range corresponding to the fault category concept item fc2 includes the “&”operating results of component parameter ranges corresponding to four Resistance components (R1, R2, R4, R6). The specific data are shown in Table 6. The diagnosis model S-FCDM determines the specific fault component state whether the “&”operating result is null. Therefore the fault category concept item fc2 of table 6 means that component R1 is in a fault state. C. Fault Category Diagnosis In this experiment, the data as the test-point voltage sampling data are generated by Pspice simulation method. The voltage simulation data of three test points add up to 500*4*3=6000 voltage values ({U1,U2,U3}) and they can divide into the test-point voltages (v1j, v2j, v3j) corresponding to four components of the respective 500 parameters. In the experimental process of the fault diagnosis, for 2000 groups of sampling data of the test-point voltages(v1j, v2j, v3j,), 1964 groups are diagnosed that the “&”operating results of component parameter ranges basically accord with the ranges of the measured component parameters. The diagnosis rate is 98.2%. D. Analysis of Experimental Results In table 7 the diagnostic model S-FCDM compares with the other two fault diagnosis model for the diagnosis ranges and the advantages and disadvantages. The advantages of the diagnostic model S-FCDM are that 1) the model implements the conceptual soft classification of test-point voltage intervals based on the qualitative concept-characteristic values of cloud model theory. 2) The range of fault component parameters and test-point voltage intervals associate with qualitative concepts one by one to achieve complete descriptions of
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TABLE IV. The language values of test-point voltage qualitative concepts The characteristic values of test-point voltage qualitative concepts The test-point voltage intervals The range of component parameters
THE TEST-POINT VOLTAGE CONCEPT TABLE OF TEST-POINT 1
Voltage higher
hig her
characteristic value
91. 22
Voltage interval
[5,4 .1]
hi gh
Parameter range Fault concept
Voltage low
(52.01,8.87,0.05)
(21.00,6.62,0.06)
(1.00,0.63,0.02)
[5,4.1] (0,117]
[4.1,3.3] (117,288]
[3.2,1.8] (288,999]
[1.7,0.19] (999,14041]
[0.18,0.054] (14041,50000)
norm al
74 .0 8 [4. 1, 3. 3]
Voltage lower
(74.08,6.17,0.08)
. FAULT CATEGORY CONCEPT TABLE OF THE TEST CIRCUIT
Test-point voltage u1
Language value
Voltage normal
(91.22,7.46,0.12)
TABLE V. Test-point
Voltage high
lo w
[3.2,1 .8]
21 .0 0 [1. 7, 0. 19 ]
…
…
52.01
Test-point voltage u2 low er 1.00 [0.1 8,0. 054]
Test-point voltage u3
hi gh
norm al
lo w
low er
high er
hi gh
norma l
lo w
lowe r
61 .5 7
41.00
21. 00
1.44
92.2 2
72 .0 0
51.51
20. 00
1.00
[2. 7, 2. 0]
[1. 9, 1. 4]
[1.3,0 .9]
[0. 89, 0.1 4]
[0.1 3,0. 029]
[3.1, 2.6]
[2. 5, 2. 0]
[1.9,1 .1]
[1. 0,0 .15 ]
[0.14 ,0.03 3]
…
…
…
…
…
…
…
…
…
…
The language values of fault category concepts
…
…
fc1 fc2 …
1 0 …
0 1 …
0 0 …
0 0 …
0 0 …
1 0 …
0 1 …
0 0 …
0 0 …
0 0 …
1 0 …
0 1 …
0 0 …
0 0 …
0 0 …
Category 1 Category 2 …
fcq
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
Category q
TABLE VI.
Components R1 R2 R3 R4
…
hi gh er 86 .9 1
THE “&”OPERATING RESULTS OF COMPONENT PARAMETER RANGES CORRESPONDING TO THE TEST-POINT QUALITATIVE CONCEPT “VOLTAGE LOW” component parameter ranges corresponding to specific qualitative concepts of test points N1[voltage low] N2[voltage low] N3[voltage low] (117,288] (198,531] (108,306] NULL NULL NULL NULL NULL NULL NULL NULL NULL TABLE VII. Diagnosis method
Reference[17]
using ui
j 1
j
as
Diagnosis range Hard and soft fault
character for fault location of NN Reference[9]
This paper
using voltage intervals of test points as character for fault location of FNN The test-point voltage values are converted to qualitative concepts indicated by the characteristic values of cloud model for fault location
Hard and soft fault
Hard and soft fault
fault states in analog circuits based on Pspice simulation method. 3) In light of the fault category concept table, the qualitative concepts of the test-point voltages, intervals of voltages, the ranges of component parameters are corresponded with fault category concept items one-to-one to diagnose faults of analog circuits fast and the concept representation conforms to human's subjective thinking. Therefore the diagnosis model S-FCDM in fault location and diagnosis of analog circuit boards has practical applications.
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(108,288)(Resistance small,
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A Soft Fault-concept Diagnosis Method of Analog Circuits Based on Cloud Model Theory Qi Liu 1,2 1
2
School of Information Engineering, Hebei University of Technology, Tianjin, China School of Computer and Information Engineering, Tianjin University of Urban Construction, Tianjin, China
Email: [email protected] Jun Cui School of Electronics and Information Engineering, Tianjin Polytechnic University, Tianjin, China Email: [email protected]
HongDong Zhao, and Hong Shen School of Information Engineering, Hebei University of Technology, Tianjin, China Email: [email protected], [email protected]
Abstract—As the component parameters of analog circuits are influenced by tolerance, a soft fault-concept diagnosis model in this paper, which is based on the qualitative concepts of cloud model theory, is proposed to achieve the complete description of fault states and the fast diagnosis. The diagnosis model uses the cloud transform method to represent the conceptual soft classification of the multiple test-point voltage intervals. At first the model generates the atomic concepts of test-point voltages which are indicated by the characteristic values of cloud model, and promotes these atomic concepts to the qualitative concepts of test-point voltage which are easy to be understood. Then the model forms the fault category concept table based on a combination of qualitative concepts of multiple test-point voltages which are associated with the range of fault component parameters. Lastly according to the table, the soft fault-concept classification and diagnosis of analog circuits are achieved in this paper based on these formalization concepts. The simulation results show that the soft fault-concept method provides a good solution of analog circuits fault diagnosis avoiding the effect of component tolerance, at the same time the method has achieved a higher diagnosis accuracy rate. Index Terms—Cloud Model, Tolerance, Soft Classification, Soft Fault Diagnosis
I.
INTRODUCTION
With the increasing scale of integrated circuits, since 1960’ the fault diagnosis of circuits has become one of the hot topics of concern to investigators [1, 2, 3, 4]. The fault diagnosis researches of analog circuits are influenced by some factors such as the lack of fault model, the parameter tolerance of analog components, the widespread presence of nonlinear problems and the limitation of the actual test point numbers that could be measured, the researches on fault diagnosis are the bottleneck of mixed-signal integrated circuits. And the
© 2013 ACADEMY PUBLISHER doi:10.4304/jnw.8.7.1497-1503
soft fault diagnosis of analog circuits is more difficult than hard fault [5]. Modern diagnostic methods based on artificial intelligence such as neural networks and SVM [1, 3] have been widely used in analog circuit fault diagnosis because of not depending on the complex models of circuits. The main drawbacks of these methods are the high requirements on the samples and the large probability of misdiagnosis and missed diagnosis for the circuits of less test points measured. And most of the methods are used to diagnose hard fault and soft fault of a few fixed parameter offsets, the fault states corresponding to soft fault cannot be described completely [6, 7, 8]. LUO et al [9] divides these voltage intervals into several subintervals based on the tolerance of component parameters to achieve the complete description of fault states. But this method uses subjectively numerical hard classification, and it likely causes some test-point voltage intervals too large or too small to not be distinguished and cannot be diagnosed effectively. Therefore, a fault-concept diagnosis model based on the concepts of cloud theory [10, 11, 12, 13] is proposed in this paper. On the basis of the "soft classification" of the test-point voltage qualitative concepts, a combination of the qualitative concepts of multiple test-point voltages of analog circuits is associated to the range of component parameters corresponding to fault category concepts to realize the complete description of fault states and rapid diagnosis and to improve the diagnostic accuracy in the premise of not increasing test points that can be measured. II.
THE DIAGNOSIS PRINCIPLE OF SOFT FAULT-CONCEPT
At present the diagnostic information with analog circuits is basically by measuring the test-point voltage values or current values to extract fault features, so the test-point voltage simulation data and sampling data of
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the analog circuit are used to fault feature extraction and concept diagnosis in this paper. The relation of component parameters and test-point voltages is given in reference [14]: Let Ni(i=1,2,…,n) indicate the test point that can be measured in the analog circuit, Xj(j=1,2,…,m) represent the component, the corresponding component parameter value is xj. The point voltage of Ni is ui, then the relation between ui and xj that can be drawn from the circuit analysis is uij = fi(xj).
(1)
If test-point voltages for the analog circuit meet: within a specific parameter range of a fault component, the corresponding test-point voltage values are monotonically increasing or decreasing that uij=fi(xj) exists the inverse function xj=fi-1(uij). As long as known the test-point voltage interval values corresponding to the range of fault component parameters when Xj goes wrong before the test, then in comparison with the sampling values of the test-point voltages in the actual diagnosis we can determine Xj whether this fault occurred. Definition 1: the concept-characteristic values of test-point voltage interval concepts On the basis of Formula 1, suppose the concept-characteristic value of the voltage interval for point Ni is cij(j=1,2,…,m), then combined with the theory analysis of cloud model we can draw the relation between cij and uij is cij = μi(uij).
(2)
Here cij indicates the concept characteristic values of some test-point voltage interval which including the voltage value uij of the test point Ni when the parameter value of the component Xj is xj. This function model reflects the membership relations between the cloud drop uij and the cloud cij(Ex,En,He) that the cloud cij(Ex,En,He) represents the test-point voltage interval corresponding to the parameter range of the fault component and cij(Ex,En,He) consists of uij. Definition 2:the relation between the concepts of test-point voltage intervals and component parameters Integrated above two definitions, we can draw the relation of cij and xij is cij=μi(uij)=μi(fi(xj)).
(3)
When the component Xj is at fault its parameter value xj would be changed, the voltage uij of each point Ni may change along, then the concept-characteristic value cij of the voltage intervals at each point Ni may also change. Seen by the formula 1, when Xj goes wrong the range of fault component parameters corresponds to the voltage interval values of the test point. Similarly, Definition 2 shows that when Xj goes wrong the range of fault component parameters corresponds to the concept-characteristic value of the test-point voltage intervals. Then in comparison with the concept-characteristic value of the test-point voltage interval belonged the sampling values of the test-point voltage we can determine Xj whether this fault occurred.
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In this paper, the soft fault-concept diagnosis model of analog circuits bases on the relation model on research. III.
THE SOFT FAULT-CONCEPT DIAGNOSIS MODEL OF ANALOG CIRCUITS
On the basis of using the characteristic values of cloud model for the conceptual soft classification of test-point voltages, a soft fault-concept diagnosis model based on cloud theory is proposed (S-FCDM (A Soft fault-concept Diagnosis Model Based on Cloud Method)), as shown in figure 1.
Figure 1. The diagnostic model of fault category S-FCDM
The S-FCDM diagnostic model includes two parts, the fault featrue extraction and the fault category diagnosis. The fault feature extraction part The test-point voltage simulation data are converted to the atomic concepts of test-point voltage by using the cloud transform method, and these atomic concepts are promoted up to the qualitative concepts of test-point voltage which more accord with human thinking, then these test-point voltage concept tables are generated for each specific test point, at last the fault category concept table is generated through the qualitative concept combination, in order to implements in combination form of the qualitative concept rather than the specific voltage interval values as the fault characteristics of analog circuits. The fault category diagnosis part For the test-point voltage simulation data, the maximum membership decision algorithm is used to judge the membership concept of test-point voltage based on the corresponding test-point voltage table. At last, a qualitative concept combination judged by a group of test-point voltages is used to achieve the fault category concept diagnosis of the analog circuit, comparing the qualitative concept combinations of the corresponding many groups of test-point voltages in the fault category concept table. A. Fault Feature Extraction
Converting to the test-point voltage atomic concepts Definition 3: the test-point voltage atomic concepts The cloud transform method is used to realize the quantitative numerical transformation to the qualitative concepts for the test-point voltage simulation data and generate the test-point voltage atomic concepts
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represented by the digital characteristic values of cloud model. ACi={ aciy ( Exy , Eny , Hey ) | 1 y Y }.
(4)
Among them, aciy ( Exy , Eny , Hey ) is said by the atomic concept of the cloud model digital characteristic values represented, Y is the atomic concept number. The cloud transform method, please see reference [12]. The diagnosis model S-FCDM need process all the test-point voltage simulation data respectively for cloud transform to convert the test-point voltage simulation data to the test-point voltage atomic concepts. Enhancing to the test-point voltage qualitative concepts The test-point voltage atomic concepts may be too small size of concepts to be of human understanding and acceptance. Therefore, it is necessary to enhance these atomic concepts to qualitative concepts for higher conceptual levels. Definition 4: the test-point voltage qualitative concepts The test-point voltage atomic concept ACi is processed for the concept promotion algorithm to enhance to the test-point voltage qualitative concepts represented by digital characteristic values of cloud model and to accord with human subject perception. QCi={ qciz ( Exz，Enz，Hez ) | 1 z Z }.
(5)
Among them, qciz ( Exz，Enz，Hez ) is said by the qualitative concept for digital characteristic values of cloud model, Z is the qualitative concept number. The number of qualitative concepts involves concept promotion strategy [15, 16], so the strategy of the pre-specified granularity to enhance the concepts is adopted in this paper that users directly specify the final number of qualitative concepts of the test-points voltages. Generally 7±2 concepts corresponding to the concept granularity is more in line with the psychological characteristics of human cognition. In this paper, the default setting value is 5. Similarly the diagnosis model S-FCDM need enhance the test-point voltage qualitative concepts for all the test-point voltage atomic concepts. Generating the test-point voltage concept table For the specific test-point Ni, on the basis of the qualitative concept of the test-point voltages corresponding to cloud model digital characteristic values, This paper uses the maximum membership decision algorithm to determine that each test-point voltage simulation data ultimately belong to which the specific concept is part of the test-point voltage qualitative concepts. And combines the test-point voltage qualitative concepts corresponding to the test-point voltage intervals and the range of component parameters, generates a test-point voltage concept table of the specific test-point. In table 1, “the test-point voltage intervals” are judged by maximum membership decision algorithm with reference to the characteristic values of test-point voltage qualitative concepts and combined to get the test-point
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qualitative concepts corresponding to the test-point voltage intervals to realize “soft classification” of the test-point voltage intervals. The range of component parameters is reverse calculation of the test-point voltage range and the test-point voltage simulation data Uij, after combining to get the test-point voltage qualitative concepts corresponding to the range of component parameters. TABLE I.
THE TEST-POINT VOLTAGE CONCEPT TABLE OF TEST-POINT N1
The language values of test-point voltage qualitative concepts The characteristic values of test-point voltage qualitative concepts The test-point voltage intervals The range of component parameters
concept1
concept2
…
concept z
qci1
qci2
…
qciz
uri1
uri2
…
uriz
xrij1
xrij2
…
xrijz
The diagnosis model S-FCDM need generate N test-point voltage concept tables for all the test-point voltage qualitative concepts. Generating the fault category concept table Definition5: the fault category concept On the basis of all the test-point voltage concept tables in analog circuits, only a test-point voltage qualitative concept was taken from each test-point voltage concept table, some fault categories in analog circuits are represented by the combination of these test-point voltage qualitative concepts, this paper is called fault category concept. The formal definition of the fault category concept is TC={( qc1z1 , qc 2z2 ,…, qcizi ,…, qc nzn11 , qc nzn ) | qcizi QCi , 1 i n , 1 zi Z }.
(6)
Among them, i represents the ith test-point voltage, zi is anyone in the number Z of qualitative concepts specified by ith test-point voltages. qcizi QCi is that the test-point voltage concept qcizi belongs to the ith testpoint voltage concept collection QCi . After associated with a combination of each test-point voltage qualitative concept, according to the definition and formalization of the fault category concept, the fault categories concept table is generated based on Boolean truth table. In table 2, q is the concept number of the ultimate fault category, n
q c1zi ,
(7)
1
Zi is the number of the qualitative concept of the i-th test-point voltage intervals. In order to facilitate the display, we used “A, B,…,Zi” instead of the test-point voltage qualitative concept language values “concept1, concept2, …, concept Zi” in the test-point voltage concept table.
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TABLE II. Test-point
THE FAULT CATEGORY CONCEPT TABLE
Test-point voltage u1
Language value
…
Z1
qc11 qc 2 1
…
qc1Z1
Voltage interval
ur11 ur 2 1
…
Parameter range Fault concept
xr1j1 xr 2 1j
fc1 fc2 …
1 0 …
fcq
0
characteristic value
A
Test-point voltage u2
…
B
…
Z2
qc12
qc22
…
qc2Z2
…
ur1Z1
ur21
ur22
…
ur2Z2
…
xr1jZ1
xr2j1
xr2j2
…
0 1 …
… … …
0 0 …
1 0 …
0 1 …
0
…
1
0
0
B
A
Comparing the contents of the range of component parameters {xrij1,xrij2,…,xrijz} in the table 1, in the light of the conclusions by the range of component parameters one to one corresponding to the soft classification of test-point voltage intervals and the soft classification of concepts. We can get the meaning of fcq in the fault category concepts{fc1,fc2,…,fcq} of table 3. fcq qc1z1 & qc 2z2 &…& qcizi &...& qc nzn
Test-point voltage un B
…
Zn
qc1n
qcn2
…
qcnZn
…
urn1
urn2
…
urnZn
xr2jZ2
…
xrnj1
xrnj2
…
xrnZj n
… … …
0 0 …
… … …
1 0 …
0 1 …
… … …
0 0 …
Category 1 Category 2 …
…
1
…
0
0
…
1
Category q
IV.
APPLICATION EXAMPLES AND EXPERIMENTAL RESULTS
A
The language values of fault category concepts
A. The Test Circuit and Experimental Data Fault diagnosis simulation circuit is shown in Figure 2, the component parameters R1=R7=2kΩ, R2=R3=R4=R5=R6=1kΩ; Excitation voltages V1=5v; Node 1, 2, 3 can be measurable.
ur1z1 & ur2z2 &…& urizi &...& urnzn (8) xr1jz1 & xr2z2j &…& xrijzi &...& xrnjzn In table 2, the diagnosis model S-FCDM can determine whether the fault category concept is in fault states that the range of parameters of the specific component Xj for fcq corresponding to ( xr1jz1 & xr2z2j &…& xrijzi &...& xrnjzn ) is null. B. The Fault Category Diagnosis The diagnostic model S-FCDM for all test-point sampling, at least need to get a group of test-point voltage sampling data (v1, v2,…,vi,…,vn). The determination of the test-point voltage membership concepts For a test-point voltage sample value vi, the maximum membership decision algorithm [10] is used based on the corresponding test-point voltage concept table to determine which test-point voltage qualitative concept qcizi is affiliated by the value vi in the corresponding test-point voltage concept table and to get the test-point voltage interval urizi that associated with the concept and the range of component parameters xrijzi .
The fault category concept diagnosis Based on a group of test-point voltage sampling data (v1, v2,…,vi,…,vn) corresponding to the group of membership concept ( qc1z1 , qc 2z2 ,…, qcizi ,…,
qc nzn11 , qc nzn ), by comparing all fault category concepts in the fault category concept table we can determine whether ( xr1jz1 & xr2z2j &…& xrijzi &...& xrnjzn ) in the parameter range of the specific component Xj is empty to diagnose the specific fault state. © 2013 ACADEMY PUBLISHER
Figure 2. The test circuit of fault diagnosis
In order to simplify the analysis of experimental results, only R1, R2, R4 and R6 are defined in this paper, these four components may be faulty in the experiment and the parametric analysis functions are used to generate test-point voltage simulation data by ORCAD Pspice. B. Fault Feature Extraction Process
Converting to the atomic concepts and update to the qualitative concepts For the test-point voltage simulation data {U1, U2, U3}, three frequency distribution functions of test-point voltage data are generated and they need be cloud transform to get three atomic concepts {AC1, AC2, AC3} of test-point voltages, at last by promotion of concepts we can obtain three groups of the test-point voltage qualitative concepts {QC1, QC2, QC3} based on five characteristic values represented of cloud model. Here are just listed the expectation curve of test-point voltage atomic concepts and test-point voltage qualitative concepts for the test point 1, as shown in figure 3. Generating test-point voltage concept tables and the fault category concept table For the set {QC1, QC2, QC3} of characteristic values of test-point voltage qualitative concepts corresponding to the test points {N1, N2, N3}, the specific test-point voltage uij is determined which belongs to the qualitative concept
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qcizi
1501
by using the maximum membership decision
algorithm. And the same qualitative concept qcizi corresponding to the test-point voltage uij combines the interval urizi of test-point voltages. According to the test-point voltage simulation data corresponding to the values of component parameters, the range xrijzi of component parameters that associated with the interval urizi of the test-point voltages is deduced to get a test-point voltage concept table in the light of each test point respectively. 90 80 70 60 50 40 30 20 10
0
10
20
30
40
50
60
70
80
90
100
(a) 100 90 80 70 60 50 40 30 20 10 0
0
TABLE III.
THE COMPONENT PARAMETER RANGE CORRESPONDING TO THE LANGUAGE VALUE “VOLTAGE LOW” OF TEST-POINT VOLTAGE QUALITATIVE CONCEPTS FOR TEST POINT N1 The language values of test-point voltage qualitative concepts “voltage low”
The parameter range of fault components R1 R2 R3 R4
(999,14041]
(0,50000)
(0,50000)
(0,50000)
The meanings of the ranges of component parameters in the fault category concept table and in the test-point voltage concept table are consistent that the specific value of the range ( xrijzi ) of component parameters for each
100
0
interval and 125 permutations and combinations of fault category concept items also did omit.
10
20
30
40
50
60
70
80
90
100
(b) Figure 3. (a). The test-point voltage atomic concepts extracted of test-point 1 (b) the expectation curve of test-point voltage qualitative concepts of test-point 1
The following table 4 lists the test-point voltage concept table of test point 1. It is noted that the specific value of the component parameter ranges corresponding to the specific test-point voltage qualitative concept ( qcizi ) in the test-point voltage concept table is not only one but existing a corresponding range of the component parameter for each component X j. For example, in this experiment the component parameter range corresponding to the test-point voltage qualitative concept value “voltage lower” for the test point N1 includes the component parameter ranges corresponding to four Resistance components (R1,R2,R4,R6). The specific data are shown in Table 3. Using three test-point voltage concept tables in this experiment, we can get one fault category concept table finally that these qualitative concepts are associated to q 3
fault category concept items, q= C51 =125, as shown in 1
table 5. In order to facilitate display in table 5, qualitative concept-characteristic values are truncated in every
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component Xj has a corresponding range of component parameters. So the specific value of the fault category concept item (fcq) in the fault category concept table has a corresponding the “&”operating result of component parameters of every test-point voltage qualitative concept qcizi for each component Xj. For example, in this experiment the component parameter range corresponding to the fault category concept item fc2 includes the “&”operating results of component parameter ranges corresponding to four Resistance components (R1, R2, R4, R6). The specific data are shown in Table 6. The diagnosis model S-FCDM determines the specific fault component state whether the “&”operating result is null. Therefore the fault category concept item fc2 of table 6 means that component R1 is in a fault state. C. Fault Category Diagnosis In this experiment, the data as the test-point voltage sampling data are generated by Pspice simulation method. The voltage simulation data of three test points add up to 500*4*3=6000 voltage values ({U1,U2,U3}) and they can divide into the test-point voltages (v1j, v2j, v3j) corresponding to four components of the respective 500 parameters. In the experimental process of the fault diagnosis, for 2000 groups of sampling data of the test-point voltages(v1j, v2j, v3j,), 1964 groups are diagnosed that the “&”operating results of component parameter ranges basically accord with the ranges of the measured component parameters. The diagnosis rate is 98.2%. D. Analysis of Experimental Results In table 7 the diagnostic model S-FCDM compares with the other two fault diagnosis model for the diagnosis ranges and the advantages and disadvantages. The advantages of the diagnostic model S-FCDM are that 1) the model implements the conceptual soft classification of test-point voltage intervals based on the qualitative concept-characteristic values of cloud model theory. 2) The range of fault component parameters and test-point voltage intervals associate with qualitative concepts one by one to achieve complete descriptions of
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TABLE IV. The language values of test-point voltage qualitative concepts The characteristic values of test-point voltage qualitative concepts The test-point voltage intervals The range of component parameters
THE TEST-POINT VOLTAGE CONCEPT TABLE OF TEST-POINT 1
Voltage higher
hig her
characteristic value
91. 22
Voltage interval
[5,4 .1]
hi gh
Parameter range Fault concept
Voltage low
(52.01,8.87,0.05)
(21.00,6.62,0.06)
(1.00,0.63,0.02)
[5,4.1] (0,117]
[4.1,3.3] (117,288]
[3.2,1.8] (288,999]
[1.7,0.19] (999,14041]
[0.18,0.054] (14041,50000)
norm al
74 .0 8 [4. 1, 3. 3]
Voltage lower
(74.08,6.17,0.08)
. FAULT CATEGORY CONCEPT TABLE OF THE TEST CIRCUIT
Test-point voltage u1
Language value
Voltage normal
(91.22,7.46,0.12)
TABLE V. Test-point
Voltage high
lo w
[3.2,1 .8]
21 .0 0 [1. 7, 0. 19 ]
…
…
52.01
Test-point voltage u2 low er 1.00 [0.1 8,0. 054]
Test-point voltage u3
hi gh
norm al
lo w
low er
high er
hi gh
norma l
lo w
lowe r
61 .5 7
41.00
21. 00
1.44
92.2 2
72 .0 0
51.51
20. 00
1.00
[2. 7, 2. 0]
[1. 9, 1. 4]
[1.3,0 .9]
[0. 89, 0.1 4]
[0.1 3,0. 029]
[3.1, 2.6]
[2. 5, 2. 0]
[1.9,1 .1]
[1. 0,0 .15 ]
[0.14 ,0.03 3]
…
…
…
…
…
…
…
…
…
…
The language values of fault category concepts
…
…
fc1 fc2 …
1 0 …
0 1 …
0 0 …
0 0 …
0 0 …
1 0 …
0 1 …
0 0 …
0 0 …
0 0 …
1 0 …
0 1 …
0 0 …
0 0 …
0 0 …
Category 1 Category 2 …
fcq
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
Category q
TABLE VI.
Components R1 R2 R3 R4
…
hi gh er 86 .9 1
THE “&”OPERATING RESULTS OF COMPONENT PARAMETER RANGES CORRESPONDING TO THE TEST-POINT QUALITATIVE CONCEPT “VOLTAGE LOW” component parameter ranges corresponding to specific qualitative concepts of test points N1[voltage low] N2[voltage low] N3[voltage low] (117,288] (198,531] (108,306] NULL NULL NULL NULL NULL NULL NULL NULL NULL TABLE VII. Diagnosis method
Reference[17]
using ui
j 1
j
as
Diagnosis range Hard and soft fault
character for fault location of NN Reference[9]
This paper
using voltage intervals of test points as character for fault location of FNN The test-point voltage values are converted to qualitative concepts indicated by the characteristic values of cloud model for fault location
Hard and soft fault
Hard and soft fault
fault states in analog circuits based on Pspice simulation method. 3) In light of the fault category concept table, the qualitative concepts of the test-point voltages, intervals of voltages, the ranges of component parameters are corresponded with fault category concept items one-to-one to diagnose faults of analog circuits fast and the concept representation conforms to human's subjective thinking. Therefore the diagnosis model S-FCDM in fault location and diagnosis of analog circuit boards has practical applications.
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(108,288)(Resistance small,
