Sensors 2013, 13, 587-610; doi:10.3390/s130100587 OPEN ACCESS sensors ISSN 1424-8220 www.mdpi.com/journal/sensors Article A Novel Health Evaluation Strategy for Multifunctional Self-Validating Sensors Zhengguang Shen * and Qi Wang School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China; E-Mail: [email protected] * Author to whom correspondence should be addressed; E-Mail: [email protected]; Tel.: +86-451-8641-5440 (ext. 16); Fax: +86-451-8641-3621 (ext. 812). Received: 15 November 2012; in revised form: 1 January 2013 / Accepted: 2 January 2013 / Published: 4 January 2013 Abstract: The performance evaluation of sensors is very important in actual application. In this paper, a theory based on multi-variable information fusion is studied to evaluate the health level of multifunctional sensors. A novel conception of health reliability degree (HRD) is defined to indicate a quantitative health level, which is different from traditional so-called qualitative fault diagnosis. To evaluate the health condition from both local and global perspectives, the HRD of a single sensitive component at multiple time points and the overall multifunctional sensor at a single time point are defined, respectively. The HRD methodology is emphasized by using multi-variable data fusion technology coupled with a grey comprehensive evaluation method. In this method, to acquire the distinct importance of each sensitive unit and the sensitivity of different time points, the information entropy and analytic hierarchy process method are used, respectively. In order to verify the feasibility of the proposed strategy, a health evaluating experimental system for multifunctional self-validating sensors was designed. The five different health level situations have been discussed. Successful results show that the proposed method is feasible, the HRD could be used to quantitatively indicate the health level and it does have a fast response to the performance changes of multifunctional sensors. Keywords: health evaluation; data fusion; multifunctional self-validating sensor; health reliability degree; grey theory Sensors 2013, 13 588 1. Introduction Multifunctional sensors have drawn more and more attention in modern production, because they can simultaneously detect several different parameters [1–3]. However, a multifunctional sensor will lead to a greater possibility of failure because it has more sensitive components [4]. Once faults occur, major industrial accidents could happen, so their health evaluation is extremely important. Aiming at the above problem, a multifunctional self-validating sensor model was proposed by authors [4,5] and its functional architecture is as shown in Figure 1. It not only includes traditional fault detection, isolation, and recovery (FDIR), but also provides the uncertainty of each measurement. Some previous work has been done [4–9], and this paper will center on the health evaluation to help users comprehend the current health level as well as the future performance degradation trend of multifunctional sensors. Figure 1. Functional architecture of a multifunctional self-validating sensor. The current approach to evaluate the health level of sensors is to use large numbers of experiments. These experimental setups are tested under different environmental parameters, such as temperature, humidity, pressure, power supply. The process is done by humans and it is very labor intensive. Another shortcoming is that humans may not be able to make out the relationships among the multiple variables of the multifunctional sensor. Further, some potential faults could happen too quickly for humans to detect them before they become catastrophic [10]. Most of existing automated methods only provide two health states (typically, healthy and faulty) [11–13], which is essentially a fault diagnosis. However, more detailed health information could not be obtained in this way, and a quantitative health evaluation may emerge as it can directly manifest the health level [10,14,15]. The vibration state is assessed in large capacity rotary machinery by using fusion information entropy [14], a health level of the liquid-propellant rocket engine ground-testing bed is given in [10], and a single sensitive component is preliminarily evaluated by using fuzzy set theory in [15]. The notion of quantitative Sensors 2013, 13 589 health evaluation was mainly applied to complicated systems. Further, previous work centered on the health evaluation of single sensitive components and the method was also relatively complicated. Commonly, the correlations of multiple measured parameters are not fully used. From a quantitative point of view, the problem will become far more difficult and the quantitative health level analysis of multifunctional sensor not only involves the health level of each sensitive unit itself, but relates to their distinct weight distribution [16]. In this paper, we extend the traditional qualitative fault detection to quantitative health level evaluation by using multi-variable data fusion coupled with a grey evaluating algorithm [17,18]. It not only can be applied for fault detection, but also for health evaluation of multifunctional sensors. The interrelations of multi-variables can also be fully considered and this provides a health evaluation method from a “local” and “global” perspective. This paper is organized as follows: Section 2 presents the proposed concept of health reliability degree; it is used as a quantitative index for the health condition evaluation of multifunctional sensors, while Section 3 discusses the novel methodology about how to evaluate the health level from asingle sensitive component and the overall multifunctional sensor. Section 4 designs a real experimental system of a multifunctional self-validating sensor and the actual samples of different health levels are used to verify the proposed methodology. Finally, Section 5 offers some concluding remarks and future directions. 2. Definition of Health Reliability Degree The quantitative health levels to reflect sensor performance changes are implemented by using the proposed health reliable degree (HRD). Due to the presence of many more sensitive units, the health evaluation of multifunctional sensor not only includes each single sensitive unit but the overall sensor itself. The research content is shown in Figure 2. Figure 2. Health evaluation content of a multifunctional self-validating sensor. Health levels of a single sensitive unit are different at different time points, so data fusion of multiple time points is needed to achieve the HRD of each sensitive unit as shown in Figure 2. The HRD of different time points can be treated as a tool for fault detection, and it should have fast response to faults. The overall health state of a multifunctional self-validating sensor is related to the importance of all sensitive units at certain time point, so its HRD can be obtained by using multiple Sensors 2013, 13 590 sensitive unit data fusion as shown in Figure 2. Based on the HRD results, four degradation stages of sensor performance are defined and they are health, sub-health, marginal failure and failure. By using historical HRD information, health forecasting for multifunctional self-validating sensors can be done and this will play a more important role in industrial production. This thesis will emphasize the health evaluation aspect, and the health forecasting will be the topic of our next study. The HRD is a comprehensive variable as a quantitative index, which indicates the degree of reliability of the multifunctional sensor and each sensitive unit. Health is an extent of degradation or deviation from an expected state, so the health evaluation is built on the expected health levels. Here, the expected sample can be acquired by calibration. Detailed descriptions about HRD are as follows: 2.1. Inner Meaning The range of HRD is defined between 0 and 1. The state 0 indicates that the multifunction sensor or certain sensitive unit is in catastrophe failure mode, while state 1 is complete health. The different health levels are distributed between these extremes. The greater the value is, the higher the health level is. In this way, more detailed health information can be provided by using the proposed HRD, which benefits the understanding for users. 2.2. Extended Meaning By using the HRD result, the four performance degradation stages of multifunctional sensor are defined as Health State (HS), Sub-Health State (SH), Marginal Failure State (MF), and Failure State (FS) respectively. Four classes of health levels are represented correspondingly. Here, the four stages can be also taken as the health features of a single sensitive unit. Further, the relationship between HRD and health degradation stages is defined in Table 1. Table 1. Relationship between HRD and health degradation stages. HRD Health stages 1 [0.9, 1.0] HS 2 [0.7,0.9) SH 3 [0.2,0.7) MF 4 [0.0, 0.2) FS HS: The multifunctional sensor is very healthy. Each sensitive unit is also healthy and their measured data are nearly close to the true value. SH: The multifunctional sensor is in sub-health and this is a state between HS and MF. The outputs of certain sensitive unit may fluctuate around their true values but within the normal ranges, so it is reliable to some extent. Commonly, it most situations multifunctional sensors are in HS or SH. MF: The multifunctional sensor is nearly a failure. A few sensitive units are faulty, and their measured data have deviated from their true values, but none have deviated completely. Therefore, it is unreliable unless fault recovery is performed, which is also a topic of our future research. FS: The multifunctional sensor is invalid. Most of sensitive units are faulty and the measurements have completely deviated from their true values, so it is totally unreliable. Sensors 2013, 13 591 2.3. Computation of HRD The above four classes of health features are treated as four evaluating criteria of the grey evaluating model, and then their corresponding attached parameters are obtained. The computation of HRD can be further implemented by using the multi-variable data fusion of these parameters. In order to get the local and global HRD, the data fusion of a single sensitive unit among different time points and a single time point among multiple sensitive units are both needed, as shown in Figure 2. From the above analysis, the four attached parameters are the key to the computation of HRD. From Table 1, the attached degree of four evaluating criteria can be represented in a simplified way as shown in Figure 3. When the belonging relationship degree (BRD) to a certain criterion is the value 1, the current state is at its corresponding degradation stage. When the BRD is the value 0, the current state is completely not at its corresponding degradation stage. Other BRDs would decrease with the changes of HRD. To simplify the health evaluation problem, the decrease is assumed to be linear. Figure 3. Relationship between BRD and HRD. The computation of HRD involves mapping multiple variables, so acquiring such a clear formula to express the complex mapping is difficult. As one of the most promising technologies in computing, the back-propagation neural network (BPNN) is suitable to solve the health level problem. The input layer, hidden layer and output layer are included in BPNN and the formula of HRD is obtained by using the Matlab Neural Network ToolBox. The number of input layer nerve cells is n (n = 4) because we have four attached parameters brd , brd , brd , and brd , output layer cell m is 1 because of one desired HS SH MF FS HRD, and hidden layer has 10 cells according to experience formula n+m+a(a∈[1,10]), wherein a equals 7). The transfer function of the hidden layer is tansig ( f (x)=2/(1+e−2x)−1) and the output 1 layer is purelin ( f (x)= x), and the Levenberg-Marquardt optimization based trainlm is selected as 2 the training function because it is the fastest back-propagation algorithm in the toolbox. The BPNN structure is shown in Figure 4, wherein the W , b represents the weight vector and threshold vector 1 1 between input and hidden layer respectively, and corresponding W , b between hidden and output layer. 2 2 Sensors 2013, 13 592 Figure 4. BPNN structure to fuse the HRD computing formula. P Y1 W W 4×1 1 10×1 2 10×4 + tangsig 1×10 + purelin Y2 f1 f2 1×1 10×1 1×1 b b 1 2 4 10×1 10 1×1 1 Y =f (W ·P+b ) Y =f (W ·Y +b ) 1 1 1 1 2 2 2 1 2 Input layer Hidden layer Output layer In Figure 2, if the interval of HRD is defined as 0.01, HRDs between 0.05 and 1 can be divided into 95 blocks. If HRD is lower than 0.05, the health state is absolutely in FS. To decrease the number of training samples, the HRDs in FS are taken as zero. In summary, 96 training sample sets are selected, and the computing formula of HRD is then obtained by using the above BPNN. The formula can be written as in Equation (1) and the corresponding weight vectors and threshold vectors are also acquired: HRD= f(brd ,brd ,brd ,brd ) HS SH MF FS (1) = f (W ⋅ f (W ⋅P+b )+b ) 2 2 1 1 1 2 where P=[brd , brd , brd , brd ], b =0.3834, HS SH MF FS 2 ⎡ -1.0005 -1.7882 0.5971 1.1644⎤ ⎡ 2.3165⎤ ⎡ 0.0739⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ 1.0286 -0.0875 -0.2166 -1.5229 -2.5580 0.5939 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ 1.3250 0.1149 -0.7423 -1.2401⎥ ⎢-1.1886⎥ ⎢ 0.3065⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ -1.1204 -0.6091 -1.2331 -1.7552 0.9639 -0.3890 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ 1.4452 1.2573 1.0365 0.4800⎥ ⎢-0.2892⎥ ⎢ 0.0851⎥ W =⎢ ⎥,b =⎢ ⎥,WT =⎢ ⎥ 1 ⎢ 0.9119 -0.7922 -1.4945 1.0284⎥ 1 ⎢ 0.2948⎥ 2 ⎢ 0.0050⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ -1.9908 0.9984 0.3054 0.7746 -1.1430 -0.3522 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ 0.8864 -0.2861 -2.3070 -0.5203⎥ ⎢ 1.1854⎥ ⎢-0.0336⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ -0.3461 -1.6779 1.4637 0.6658 -2.0245 -0.2433 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢⎣ 1.7045 -1.3901 -0.8455 0.4996⎥⎦ ⎢⎣ 2.5613⎥⎦ ⎢⎣-0.0169⎥⎦ The P represents the degree of attached relationship to the criteria HS, SH, MF, and FS respectively. In Equation (1), the key issue of HRD computation is to solve the P and the detailed solution will be discussed in Section 3. 2. 4. Significance Analysis The mapping from actual measured data to the grey health level is implemented by using a grey algorithm while the de-greying process from grey evaluation to specific HRD is accomplished by using the proposed HRD. The definition of HRD has important significance in theory and practice. The HRD is a basis of the health forecast. To predict the future health level of a multifunctional self-validating sensor, the current and past health states need to be understood. By using HRDs of different time points, the historical information could be collected and a time series constructed. The health prediction is done by using the time series analysis method, which benefits the understanding of the performance degradation in the real world. Sensors 2013, 13 593 The health level indicated by the proposed HRD can be directly understood by users and the corresponding precautionary measures can be taken to improve the sensor reliability. Taking the above four degradation stages as an example, if the sensor is in HS and SH, it works normally; the repair or data recovery is needed once it is in MF, and the sensor must be exchanged if it is in FS. The computing method itself of HRD is open or extensible. By using the proposed idea, the evaluating criteria can be extended from four to more classes if necessary, and HRD results may be more concrete. The aim of this study is to present a new thought about health evaluation of multifunctional self-validating sensors. 3. HRD Methodology The grey evaluation method coupled with the above HRD computing process is proposed to develop a new methodology for sensor health assessment. This novel strategy can provide a quantitative health level besides the traditional qualitative results. The corresponding flowchart is shown in Figure 5. The correlation among multiple parameters has been fully considered for the weight distribution of different sensitive units and time points, which is different from the traditional evaluation methods. Figure 5. Flowchart of the HRD methodology. 3.1. Establishing the Grey Evaluating Criterions To distinguish the health hierarchy of multifunctional self-validating sensor accurately, four performance degradation stages (HS, SH, MF, and FS) are treated as the grey evaluating criteria sets. 3.2. Determining the Whitening Function of the Grey Model The actual outputs of each sensitive unit have a mapping to the above four evaluating criteria sets. Some statistical researches on the multifunctional self-validating sensor have been done. It is a fact, that if a certain sensitive unit is not in FS, the measured outputs are closer to the true values, the grey BRD will become higher, and so will be the corresponding health level. The fact can be expressed in a Sensors 2013, 13 594 more simplified way as shown in Figure 6. The BRD is 1 if the measurement x is within the allowed fluctuation range, while BRD decreases linearly if the x is outside the permitted range. Figure 6. Relationship between BRD and measured value x. In application, the true value is difficult to obtain, its best estimation value μ can be acquired by HS using modern machine learning technology, for example, the data fusion result of multiple self-validating sensors or the mean value under health state can be taken as the best evaluated value. The allowed fluctuating interval is [μ −m1 Δ, μ +m1 Δ] if the BRD belongs to grey set HS. In a similar way, the HS 11 HS 12 grey intervals of other two grey sets SH and MF are defined as [μ −m2 Δ, μ -m2 Δ] and HS 11 HS 12 [μ +m2 Δ, μ +m2 Δ], [μ −m3 Δ,μ −m3 Δ] and [μ +m3 Δ, μ +m3 Δ] respectively. Here, the HS 21 HS 22 HS 11 HS 12 HS 21 HS 22 grey interval of grey sets SH and MF is symmetric. In Figure 6, there is a premise that the sensitive unit is not faulty and the outputs are not completely unbelievable, so the above idea id only suitable for the evaluating criteria HS, SH and MF. The FS is under faults, so the continual use of the same idea is improper. The measurement x is completely unreliable if it is beyond the baseline μ −m4 Δ (or smaller than μ −m4 Δ) and μ +m4 Δ HS 11 HS 11 HS 12 (or greater than μ +m4 Δ) as shown in Figure 6. If a certain sensitive unit is faulty, the BRDs under HS 12 FS will undoubtedly become 1. Based on the above failure feature analysis, an upside-down trapezium is chosen as the whitening function under FS, as shown in red curve of Figure 6. In summary, the whitening function of four grey sets can be written in Equations (2–5) respectively: ⎧0 x<μ −m4 Δ or x>μ +m4 Δ HS 11 HS 12 ⎪ ⎪ 1 [x−(μ −m4 Δ)] μ −m4 Δ≤x<μ −m1 Δ f (x)=⎪⎨m411Δ−m111Δ HS 11 HS 11 HS 11 (2) HS ⎪1 μ −m1 Δ≤x<μ +m1 Δ HS 11 HS 12 ⎪− 1 [x−(μ +m4 Δ)] μ +m1 Δ≤x<μ +m4 Δ ⎪⎩ m412Δ−m112Δ HS 12 HS 12 HS 12 ⎧ 0 x<μ −m4 Δ or x>μ +m4 Δ ⎪ HS 11 HS 12 ⎪ 1 [x−(μ −m4 Δ)] μ −m4 Δ≤x<μ −m2 Δ ⎪m411Δ−m211Δ HS 11 HS 11 HS 11 ⎪1 μ −m2 Δ≤x<μ −m2 Δ ⎪ HS 11 HS 12 f (x)=⎪⎨ or μ +m2 Δ≤x<μ +m2 Δ (3) SH HS 21 HS 22 ⎪ − 1 (x−μ ) μ −m2 Δ≤x<μ ⎪ m212Δ HS HS 12 HS ⎪ 1 [x−(μ +m2 Δ)] μ ≤x<μ +m2 Δ ⎪⎪m221Δ HS 21 HS HS 21 ⎪− 1 [x−(μ +m4 Δ)] μ +m2 Δ≤x<μ +m4 Δ ⎩ m412Δ−m222Δ HS 12 HS 22 HS 12 Sensors 2013, 13 595 ⎧ 0 x<μ −m4 Δ or x>μ +m4 Δ ⎪ HS 11 HS 12 ⎪ 1 [x−(μ −m4 Δ)] μ −m4 Δ≤x<μ −m3 Δ ⎪m411Δ−m311Δ HS 11 HS 11 HS 11 ⎪1 μ −m3 Δ≤x<μ −m3 Δ ⎪ HS 11 HS 12 f (x)=⎪⎨ or μ +m3 Δ≤x<μ +m3 Δ (4) MF HS 21 HS 22 ⎪ − 1 (x−μ ) μ −m3 Δ≤x<μ ⎪ m312Δ HS HS 12 HS ⎪ 1 [x−(μ +m3 Δ)] μ ≤x<μ +m3 Δ ⎪⎪m321Δ HS 21 HS HS 21 ⎪− 1 [x−(μ +m4 Δ)] μ +m3 Δ≤x<μ +m4 Δ ⎩ m412Δ−m322Δ HS 12 HS 22 HS 12 ⎧1 x<μ −m4 Δ or x>μ +m4 Δ HS 11 HS 12 ⎪ ⎪− 1 [x−(μ −m3 Δ)] μ −m4 Δ≤x<μ −m3 Δ f (x)=⎪⎨ m411Δ−m311Δ HS 11 HS 11 HS 11 (5) FS ⎪0 μ −m3 Δ≤x<μ +m3 Δ HS 11 HS 22 ⎪ 1 [x−(μ +m3 Δ)] μ +m3 Δ≤x<μ +m4 Δ ⎪⎩m412Δ−m322Δ HS 22 HS 22 HS 12 The matrix form of some parameters in Equations (2–5) can be represented as: ⎡m2 m2 ⎤ ⎡m3 m3 ⎤ M1 =⎡⎣m111 m112⎤⎦, M2 =⎢⎢⎣m211 m212⎥⎥⎦, M3 =⎢⎢⎣m311 m312⎥⎥⎦, M4 =⎡⎣m411 m412⎤⎦ 21 22 21 22 The degree of the deviation from the best estimation μ is assumed to be symmetrically distributed, HS which could avoid more parameter settings. The parameter Δ itself is only a base-level. Taking a temperature sensitive unit for example, if the best estimation value is 20 °C, and the base-level standard Δ is 0.01, the grey interval of HS would become [0.1, 0.1] when M is defined as [10, 10]. 1 3.3. Computing Grey Sample Evaluating (GSE) Matrix By using the above established whitening functions of different evaluating criteria, the GSE matrix can be obtained. The computation of HRD includes a single sensitive unit and the overall multifunctional self-validating sensor, and their meanings are provided here. The GSE matrix of a single sensitive unit at multiple time points is denoted as GSE = (gse ) (j = i ijk m×n 1, 2, …, m; k = 1, 2, …, n) as shown in Equation (6): I I (cid:34) I 1 2 n T ⎡a a (cid:34) a ⎤ 1 i11 i12 i1n T ⎢a a (cid:34) a ⎥ (6) GSE = 2 ⎢ i21 i22 i2n⎥ i (cid:35) ⎢ (cid:35) (cid:35) (cid:35) ⎥ ⎢ ⎥ T ⎣a a (cid:34) a ⎦ m im1 im2 imn where i represents the certain sensitive unit, T (j = 1, 2, …, m) is the different time point, and j I (k = 1, 2, …, n) is the evaluating criterion, it refers to the HS, SH, MF, FS in this paper. k The GSE matrix of multiple sensitive unit at single time point can be expressed as GSE = (gse ) j ijk m×n (i = 1, 2, …, m; k = 1, 2, …, n) as shown in Equation (7): I I (cid:34) I 1 2 n S ⎡a a (cid:34) a ⎤ 1 1j1 1j2 1jn ⎢ ⎥ GSE =S2 ⎢a2j1 a2j2 (cid:34) a2jn⎥ (7) j (cid:35) ⎢ (cid:35) (cid:35) (cid:35) ⎥ ⎢ ⎥ Sm ⎢⎣amj1 amj2 (cid:34) amjn⎥⎦ Sensors 2013, 13 596 where j represents the time point, S ( i = 1, 2, …, m) indicates all the sensitive units of the i multifunctional sensor, and I (k = 1, 2, …, n) is still the evaluating criterion. k 3.4. Deciding Weights The analytic hierarchy process (AHP) [19–22] and objective information entropy [23] are the common methods used to decide weights. As for the HRD of a single sensitive unit at multiple time points, its outputs will change with the passage of time, such as the drift fault. The arbitrary pair-wise comparison among the time points is unavoidable, so the AHP is very suitable to amplify the importance of certain time point, for example, the moment when a fault occurs brings larger weight. As for HRD of the overall multifunctional self-validating sensor, the health evaluation assignment is implemented at a single time point, and the comparison among multiple time points is meaningless. It only needs the objective weight of each sensitive unit to indicate its information importance, which can be well expressed by using the information entropy method. Detailed application in sensor health evaluation is as follows. 3.4.1. Computing the Weights of Different Time Points by Using AHP Before the further computation of HRD, the guideline of computing weights is proposed as follows: Guideline: The farther the output of a certain sensitive unit i deviates from its best estimation μ at HS certain time point j, the greater the measured value x brings importance to this sensitive unit. If the measurement at certain time point is closer to FS, its sensitivity will be higher. In this way, the sensitivity of different time points is expressed by the weight W = (w , w , …, w , …, w ) and its i i1 i2 ij im calculation process is as follows: Firstly, based on the proposed guideline, the scaling value d of sensitive unit i at time point j is ij defined as: d = x −μ(HS) ij ij ij (8) where x is the actual output of sensitive unit i at the time point j, μ (HS) is its best estimation. Then ij ij the scaling values d = ( d , d ,…, d ,…, d ) of sensitive unit i could be derived and m is the number i i1 i2 ij im of time points. In Equation (8), the d becomes greater if the difference between the actual value and μ (HS) is ij ij larger. In other words, if the measured value is closer to the FS, the corresponding time point is of greater importance, which conforms to the above guideline. Secondly, construct the comparison matrix CM in which each element is used to compare with i others as shown in Equation (9). Its physical meaning is a relative importance comparison between two arbitrary time points: ⎡d d d ⎤ i1 i1 (cid:34) i1 ⎢ ⎥ d d d ⎢ i1 i2 im ⎥ ⎢d d d ⎥ ⎢ i2 i2 (cid:34) i2 ⎥ CMi =⎢di1 di2 dim ⎥ (9) ⎢ (cid:35) (cid:35) (cid:34) (cid:35) ⎥ ⎢ ⎥ ⎢d d d ⎥ im im (cid:34) im ⎢⎣d d d ⎥⎦ i1 i2 im