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Fault Prognostics of Micro-Electro-Mechanical Systems Using Particle Filtering*
3rd IFAC Workshop on Advanced Maintenance Engineering, Service and Technology 3rd Workshop Advanced Maintenance 3rd IFAC IFAC19-21, Workshop on Advanced Maintenance Engineering, Engineering, Service Service and and Technology Technology October 2016.on Biarritz, France 3rd IFAC19-21, Workshop Advanced Maintenance Engineering, Service and Technology October 2016. Biarritz, France October 19-21, 2016.on Biarritz, France Available online at www.sciencedirect.com October 19-21, 2016. Biarritz, France
ScienceDirect IFAC-PapersOnLine 49-28 (2016) 226–231
Fault Fault Prognostics Prognostics of of Fault Prognostics of Micro-Electro-Mechanical Systems Micro-Electro-Mechanical Systems Micro-Electro-Mechanical Systems Particle Particle Filtering Filtering Particle Filtering ∗ ∗∗
Using Using Using
Haithem Skima ∗ Kamal Medjaher ∗∗ Christophe Varnier ∗∗ ∗ Kamal Medjaher ∗∗ Christophe Varnier ∗ ∗ Haithem Skima ∗ ∗ Haithem Skima Medjaher Christophe Zerhouni Varnier Eugen Dedu Julien Bourgeois and∗∗Noureddine ∗ Kamal ∗ ∗ Haithem Skima Kamal Medjaher Christophe Varnier ∗ ∗∗ ∗ Julien ∗ and Noureddine Eugen Dedu Bourgeois Eugen Dedu ∗ Julien Bourgeois ∗ and Noureddine Zerhouni Zerhouni ∗ Eugen Dedu Julien Bourgeois and Noureddine Zerhouni ∗ FEMTO-ST Institute, UMR CNRS 6174 – UFC / ENSMM ∗ ∗ FEMTO-ST Institute, UMR CNRS 6174 – UFC / ENSMM Institute, UMR CNRS – cUFC / ENSMM 15B av. des Montboucons, 250006174 Besan¸ on, France ∗ FEMTO-ST FEMTO-ST Institute, UMR CNRS – cUFC / ENSMM 15B av. av. des Montboucons, 250006174 Besan¸ on, France France 15B des Montboucons, 25000 Besan¸ con, (e-mail: [email protected]) 15B av. des Montboucons, 25000 Besan¸ c on, France (e-mail: [email protected]) ∗∗ (e-mail: [email protected]) Production Engineering Laboratory (LGP), INP-ENIT ∗∗ (e-mail: [email protected]) ∗∗ Production Engineering Laboratory (LGP), INP-ENIT Engineering Laboratory (LGP), INP-ENIT 47 Av. d’Azereix, 65000 Tarbes, France ∗∗ Production Production Engineering Laboratory (LGP), INP-ENIT 47 Av. d’Azereix, 65000 Tarbes, France 47 (e-mail: Av. d’Azereix, 65000 Tarbes, France [email protected]) 47 (e-mail: Av. d’Azereix, 65000 Tarbes, France (e-mail: [email protected]) [email protected]) (e-mail: [email protected]) Abstract: This paper presents a hybrid prognostics approach for Micro-Electro-Mechanical Abstract: This presents hybrid Micro-Electro-Mechanical Abstract: This paper paper presents a arelies hybrid prognostics approach for Micro-Electro-Mechanical Systems (MEMS). The approach on prognostics two phases: approach an offline for phase for the MEMS and its Abstract: This paper presents arelies hybrid approach Micro-Electro-Mechanical Systems (MEMS). The and approach on prognostics two phases: anprognostics. offline for phase for proposed the MEMS MEMS and its its Systems (MEMS). The approach reliesphase on two phases: an offline phase for the and degradation modeling, an online for its fault The approach Systems (MEMS). The approach relies on two phases: an offline phase for proposed the MEMS and its degradation modeling, and an online for its The approach degradation modeling, and an consisting online phase phase forelectro-thermally its fault fault prognostics. prognostics. The valve. proposed approach is applied to a MEMS device in an actuated In the offline degradation modeling, and an online phase for its fault prognostics. The valve. proposedthe approach is applied to device an actuated is applied to a a MEMS MEMS platform device consisting consisting invalidate an electro-thermally electro-thermally actuatedbehavior valve. In In the offline offline phase, an experimental is built toin the obtained nominal model of the is applied to a MEMS device consisting in an electro-thermally actuated valve. In the offline phase, an experimental platform is the nominal model of phase, anMEMS experimental platform is built built to to validate validate the obtained obtained nominal behavior behavior model of the the targeted and to get its degradation model. This model represents the drifts in a MEMS phase, anMEMS experimental platform is built to validate the obtained nominal behavior model of the targeted to its degradation model. This model represents the drifts in targeted MEMS and and which to get get is itsits degradation model. This model represents the filter drifts algorithm in aa MEMS MEMS physical parameter, compliance. In the online phase, a particle is targeted MEMS and which to get is its degradation model. This model represents the filter drifts algorithm in a MEMS physical parameter, In online phase, aa particle is physical parameter, which is its its compliance. compliance. Inofthe the online phase, particle filterand algorithm is used to perform online parameters estimation the derived degradation model calculate physical parameter, which is its compliance. In the online phase, a particle filterand algorithm is used to online parameters estimation the degradation used to perform perform onlineuseful parameters estimation ofprognostic the derived derived degradation model and calculate calculate the MEMS remaining life. The obtainedof results show themodel effectiveness of the used to perform online parameters estimation of the derived degradation model and calculate the MEMS remaining useful life. The obtained prognostic results show the effectiveness of the MEMS remaining useful life. The obtained prognostic results show the effectiveness of the the proposed approach. the MEMS remaining useful life. The obtained prognostic results show the effectiveness of the proposed proposed approach. approach. proposed approach. © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Prognostics and health management, micro-electro-mechanical system, fault Keywords: and management, Keywords: Prognostics and health health management, micro-electro-mechanical system, system, fault fault prognostics,Prognostics remaining useful life, particle filter. micro-electro-mechanical Keywords: Prognostics and health management, micro-electro-mechanical system, fault prognostics, prognostics, remaining remaining useful useful life, life, particle particle filter. filter. prognostics, remaining useful life, particle filter. 1. INTRODUCTION 1. INTRODUCTION INTRODUCTION 1. 1. INTRODUCTION Micro-Electro-Mechanical Systems (MEMS) are microData HMI Micro-Electro-Mechanical Systemscomponents (MEMS) are are microacquisition Data Micro-Electro-Mechanical Systems (MEMS) microData systems that integrate mechanical using elecHMI HMI acquisition Micro-Electro-Mechanical Systems (MEMS) are microacquisition Data systems that integrate mechanical components using elecelecHMI systems that integrate mechanical components using tricity as source of energy in order to perform measurement acquisition systems that integrate mechanical components using elecData tricity as source of energy in order to perform measurement Decision tricity as source of energy in order to perform measurement PHM functions and/orofoperating in structure having micrometprocessing Data tricity as source energy in in order to perform measurement Data Decision PHM functions and/or operating structure having micrometDecision PHM processing functions and/or In operating in structure micrometprocessing Data ric dimensions. the past few years,having MEMS devices Decision PHM functions and/or operating in structure having micrometprocessing ric dimensions. In the past few years, MEMS devices ric dimensions. In the past few years, MEMS devices Prognostic gained wide-spread acceptance in several industrial segDetection ric dimensions. In the past few MEMS devices Prognostic gained wide-spread acceptance in years, several industrial segDetection Prognostic gained wide-spread acceptance in several industrial segDetection ments including aerospace, automotive, medical and even Prognostic gained wide-spread acceptance in several industrial segDetection ments including aerospace, automotive, medical and even ments including aerospace, automotive, medical and even military applications, where they contribute to important Diagnostic ments including aerospace, automotive, medical and even military applications, where they contribute to important Diagnostic military contributeoftoMEMS important Diagnostic functions.applications, The most where knownthey applications are military applications, where contributeoftoMEMS important Diagnostic functions. The for most knownthey applications are functions. The most known applications of MEMS gyare accelerometers automotive (airbag) applications, 1. Prognostics and Health Management cycle. functions. The for most known applications of MEMS gyare Fig. accelerometers automotive (airbag) applications, Fig. 1. Prognostics and Health accelerometers for automotive (airbag) applications, gyroscopes for mobiles phones, pressure sensors for engine 1. Prognostics and Health Management Management cycle. cycle. accelerometers for automotive (airbag)sensors applications, gy- Fig. Fig. 1.1)Prognostics andThurston Health Management roscopes for mobiles phones, pressure for engine (Fig. (Lebold and (2001)). It iscycle. a discipline roscopes for mobiles phones, pressure sensors for engine management and micro-mirror arrays for display applicaroscopes for mobiles phones, pressure sensors forapplicaengine (Fig. 1) and Thurston (2001)). It management and micro-mirror micro-mirror arrays for display 1) (Lebold (Lebold andstudy Thurston (2001)). It is is a a discipline discipline that deals with the of failure mechanisms in order management and arrays for display applica- (Fig. tions. Nevertheless, the reliability of MEMS is considered 1) (Lebold andstudy Thurston (2001)). It is a discipline management and micro-mirror arrays for display applica- (Fig. that deals with the of failure mechanisms in order tions. Nevertheless, the reliability of MEMS is considered that deals with the study of failure mechanisms in order to extend the life cycle of systems and to better manage tions. Nevertheless, thetheir reliability of MEMS is considered as a major obstacle for development (Medjaher et al. that deals the withlife thecycle study of failureand mechanisms in order tions. Nevertheless, thetheir reliability of MEMS is considered to extend of systems to better manage as a major obstacle for development (Medjaher et al. to extend the life cycle of systems and to better manage their health. Within the framework of PHM, prognostics is as a major obstacle for their development (Medjaher et al. (2014)). They sufferforfrom numerous failure mechanisms to extend theWithin life cycle of systems of and to better manage as a major obstacle their development (Medjaher et al. their health. the framework PHM, prognostics is (2014)). They suffer from numerous failure mechanisms their health. Within the framework of PHM, prognostics considered as a core activity for applying a good predictive (2014)). They suffer from numerous failure mechanisms which impact their performance, reducefailure their lifetime, and their health. Within the framework of PHM, prognostics is is (2014)). Theytheir suffer from numerous mechanisms considered as a core activity for applying a good predictive which impact performance, reduce their lifetime, and considered as a core activity for applying a good predictive Prognostics is for defined by the PHMpredictive commuwhich impact their performance, reduce lifetime, and maintenance. the availability of systems in which theytheir are used (Huang considered as a core activity applying a good which impact their performance, reduce their lifetime, and Prognostics is defined PHM the availability of systems systems in(2015); which they they are van usedSpengen (Huang maintenance. maintenance. Prognostics is Remaining defined by by the the PHM community as the estimation of the Useful Lifecommu(RUL) the availability of which are used (Huang et al. (2012); Skima et al.in Merlijn maintenance. Prognostics is Remaining defined by the PHM commuthe availability of systems in(2015); which they are van usedSpengen (Huang nity as the estimation of the Useful Life (RUL) et al. (2012); Skima et al. Merlijn nity as the estimation of the Remaining Useful Life (RUL) of physical systems based on their current health state and et al. (2012); Skima et al. (2015); Merlijn van Spengen (2003); Li and Jiang (2008)). This analysis shows the need nity as the estimation of the Remaining Useful Life (RUL) et al. (2012); Skima et al. (2015); Merlijn van Spengen of physical systems based on their current health state and (2003); Li and Jiang (2008)). This analysis shows the need of physical systems based on their current health state their future operating conditions. Prognostics approaches (2003); Li and Jiang (2008)). This analysis shows the need to monitor their behavior, assess their health statethe andneed an- of physical systems based on their current health state and and (2003); Li and Jiang (2008)). Thistheir analysis shows their future operating conditions. Prognostics approaches to monitor their behavior, assess health state and antheir future operating conditions. Prognostics approaches befuture classified into three main approaches (Jardine et al. to monitor their behavior, assess health state and an- can ticipate their failures before theirtheir occurrence. These tasks their operating conditions. Prognostics approaches to monitor their behavior, assess their health state and ancan three (Jardine et ticipate theirbyfailures failures before their theirand occurrence. These tasks tasks (2006); can be be classified classified into three main main approaches (Jardine et al. al. Heng et into al. (2009); Pengapproaches et al. (2010); Medjaher ticipate their before occurrence. These can be done using Prognostics Health Management be classified into three main approaches (Jardine et al. ticipate theirbyfailures before theirand occurrence. These tasks can (2006); Heng et al. (2009); Peng et al. (2010); Medjaher can be done using Prognostics Health Management (2006); Heng et al. (2009); Peng et al. (2010); Medjaher and Zerhouni (2013)): model-based, data-driven and hycan be done by using Prognostics and Health Management (PHM) approaches, and this is the aim of this paper. (2006); Heng et al. (2009); Peng et al. (2010); Medjaher can be done by usingand Prognostics and Health Management and (2013)): model-based, data-driven and (PHM) approaches, this is is the the aim of this this paper. and Zerhouni Zerhouni (2013)): model-based, data-drivenapproach and hyhybrid prognostics approaches. The model-based (PHM) approaches, and this aim of paper. and Zerhouni (2013)): model-based, data-driven and hy(PHM) approaches, and this is the aim of this paper. prognostics approaches. The model-based approach PHM is the combination of seven layers that collectively brid brid prognostics approaches. The model-based approach deals with estimation of the RUL by using mathematical brid prognostics approaches. The model-based approach PHM islinking the combination combination of seven seven layers layers thatmanagement collectively deals PHM the of that collectively of RUL using enableis failure mechanisms with life deals with with estimation estimation of the the RUL by by using mathematical mathematical to formalize physical understanding of a dePHM the combination of seven layers thatmanagement collectively representation deals with estimation of the RUL by using mathematical enableislinking linking failure mechanisms mechanisms with life life enable failure with management representation to formalize physical understanding of a representation toThe formalize physical understanding oftransa dede grading system. data-driven approach aims at enable linking failure mechanisms with management This work has been supported by the R´ egion life Franche-Comt´ e and representation toThe formalize physical understanding oftransa de grading system. data-driven approach aims at This work has been supported by the R´ e gion Franche-Comt´ e and grading system. The data-driven approach aims atvoltage, transwork has beenproject supported by the R´ egion Franche-Comt´ e and forming raw monitoring data (e.g. temperature, theThis ACTION Labex (contract ANR-11-LABX-0001-01). grading system. The data-driven approach aims atvoltage, transThis work has been supported by the R´ egion Franche-Comt´ e and forming the forming raw raw monitoring monitoring data data (e.g. (e.g. temperature, temperature, voltage, the ACTION ACTION Labex Labex project project (contract (contract ANR-11-LABX-0001-01). ANR-11-LABX-0001-01). forming raw monitoring data (e.g. temperature, voltage, the ACTION Labex project (contract ANR-11-LABX-0001-01).
Copyright © 2016, 2016 IFAC 226Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2016 IFAC 226 Copyright ©under 2016 responsibility IFAC 226Control. Peer review of International Federation of Automatic Copyright © 2016 IFAC 226 10.1016/j.ifacol.2016.11.039
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etc.) into relevant information to build behavior models including the degradation evolution, which are then used for RUL estimation. Finally, the hybrid approach combines both previous approaches to achieve more accurate RUL estimates. This paper proposes a hybrid prognostics approach for MEMS, with a specific application to an electro-thermally actuated MEMS valve. The approach combines two types of models: a nominal model of the MEMS derived by writing its physical laws, and a degradation model obtained from accelerated life tests conducted on several samples of the same reference of MEMS. The generated prognostic model is then used to estimate the RUL of the MEMS. The paper is structured in six sections. After the introduction, Section 2 discusses the implementation of prognostics for MEMS instead of studying their reliability. Section 3 deals with the proposed approach to estimate the RUL of MEMS. The used prognostics tool is presented in Section 4. Section 5 describes the application of the proposed approach to a MEMS device and presents the obtained results. Finally, Section 6 concludes the paper. 2. TOWARD PROGNOSTICS OF MEMS MEMS devices suffer from various reliability issues. This is confirmed by numerous published works dealing with MEMS reliability. These works concern: 1) testability and characterization of MEMS, 2) identification and understanding of failure mechanisms, 3) design, fabrication and packaging optimization, 4) accelerated life tests to develop predictive reliability models, and 5) statistical studies of failures on a significant number of samples. Improving reliability of MEMS devices has several advantages, such as increasing their lifetime and improving their performance. However, reliability still has some limitations. It is defined as the ability of a system or a product to perform its intended function without failure and within specified performance limits for a specified period of time under stated conditions. Thus, according to this definition, reliability is valid only for given conditions and a period of time. This is the case, for example, for cars which are guaranteed by automobile manufacturers for a period of time in given operating conditions. In this situation, the reliability is estimated without taking into account the specific utilization of each car (e.g. environment conditions, roads quality, frequency of use, etc.). However, in practice, the lifetime should be different from one car to another depending on how and where it is used. In addition to this, reliability models are generally obtained from statistical data on representative samples. These models, which are generic for all the samples, are not updated during the utilization. This means that, once they are estimated, the model reliability parameters still constant while they should change due to the factors mentioned previously. To cope with the above mentioned limitations, one can use PHM. This activity makes use of past, present, and future operating conditions in order to assess the health state of the system, diagnose its faults, update the degradation models parameters, anticipate failures by estimating the RUL and improve decision making to prolong its lifetime. Prognostics is widely applied in industrial systems ranging 227
227
Offline phase
Construction of the nominal behavior model
MEMS device
Accelerated lifetime tests and measurements
Online measurements
Online phase
Health indicator selection
&
Particle filter
Degradation model definition
Estimated model parameters
Health assessment and prediction
≤
RUL estimation
Failure threshold
Fig. 2. Overview of the proposed prognostics approach. from small components (e.g. bearings (Tobon-Mejia et al. (2012)), cutting tools (Javed et al. (2015)), etc.) to complete machines (e.g. turbofans (Mosallam et al. (2014)), mechatronic systems (Medjaher and Zerhouni (2013)), etc.). Although its benefits are well proven, there are few published works addressing fault prognostics of MEMS. To fill this gap, a hybrid prognostics approach for MEMS devices is proposed in the next section. 3. PROGNOSTICS APPROACH The steps of the proposed hybrid prognostics approach are presented in Fig. 2. This approach can be applied on different categories of MEMS at a condition that the following assumptions hold. • The instrumentation needed to monitor the behavior of MEMS (sensors, camera, etc.) is available. • Sufficient knowledge about the studied MEMS is available to derive their nominal behavior models and identify their failure mechanisms which may take place during their utilization. In this work, the approach is applied to an electrothermally actuated valve MEMS (see Section 5.1). It relies on two phases. The first phase is done offline to build the nominal behavior model of the MEMS, select a relevant physical health indicator and derive the MEMS degradation model. The second phase is conducted online and uses the obtained degradation model to predict the MEMS future behavior and calculate its RUL. The steps shown in Fig. 2 can be grouped in three main tasks. (1) Nominal behavior model construction: it is obtained by writing the corresponding physical laws of the targeted MEMS and then validating it experimentally. (2) Degradation model : it is obtained experimentally through accelerated life tests and it is related to drifts in a selected Health Indicator (HI). This HI is a physical parameter, which can be used to track the degradation of the MEMS. (3) Prognostics modeling: prognostics is divided into two main stages: learning and prediction. In the learning stage, the prognostics tool combines the available data with the degradation model to learn the behavior of the system and estimate the parameters of its degradation model. This stage lasts until a prediction is required at time tp . Then, in the prediction stage, the prognostics tool propagates the state of the system and determines at what time the failure threshold (F T ) is reached. Finally, the RUL is calculated as the difference between the failing time Tf and the starting prediction time tp .
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In the offline phase, the evolution of the selected HI is approximated by a mathematical model to define the degradation model. In the online phase, the parameters of this model are unknown and need to be estimated as a part of the prognostics process. To do so, the particle filter algorithm is used as a prognostics tool. It allows handling the non-linearities and non-Gaussian noises (Yin and Zhu (2015)), which are some specificities inherent to MEMS. 4. PROGNOSTICS USING PARTICLE FILTERING 4.1 Particle filtering framework The problem of recursive Bayesian estimation is defined by two equations (Gordon et al. (1993)): the first considers the evolution of the system state {xk , k ∈ N} which is given by: (1) xk = f (xk−1 , λk−1 ) where k is the time step index, f is the transition function from the state xk−1 to the next state xk and {λk−1 , k ∈ N} is the independent identically distributed process noise sequence. The purpose is to recursively estimate xk from measurements introduced by the second equation and which corresponds to the measurement model {zk , k ∈ N}: (2) zk = h(xk , µk ) where k is the time step index, h is the measurement function and {µk , k ∈ N} is the independent identically distributed measurement noise sequence. The aim of the recursive Bayesian estimation problem is to recursively estimate the state of the system by constructing the Probability Density Function (PDF) of the state at time k based on all available information, p(xk |z1:k ). It is assumed that the initial PDF of the state vector, also called the prior, is available (p(x0 |z0 ) = p(x0 )). The PDF p(xk |z1:k ), known as the posterior, can be obtained recursively in two main stages: prediction and update. • Prediction stage: in this stage the state model (Eq. 1) is used to obtain the prior PDF of the state at time k via the Chapman-Kolmogorov equation: p(xk |z1:k−1 ) = p(xk |xk−1 )p(xk−1 |z1:k−1 )dxk−1
(3) • Update stage: when a new measurement zk becomes available, one can update the prior PDF via the Bayes rule: p(zk |xk )p(xk |z1:k−1 ) (4) p(xk |z1:k ) = p(zk |z1:k−1 )
This gives the formal solution to the recursive Bayesian estimation problem. Analytic solutions to this problem are available in a restrictive set of cases, including the Kalman filter, which assumes that the state and measurement models are linear and λk and µk are additive Gaussian noise of known variance. When these assumptions are unreasonable, which is the case in many applications, and the equations (Eq. 3) and (Eq. 4) cannot be solved analytically, approximations are necessary. One of the most used approximate solution for this kind of problem is the particle filtering. The particle filtering solution is a sequential Monte-Carlo method which consists in representing the required posterior PDF by a set of particles with associated weights and
228
computing estimates based on these particles and weights. Different versions of particle filtering are reported in the literature and, for more details, interested readers can refer to the work published by Arulampalam et al. (2002). In this paper, we focus on the Sampling Importance Resampling (SIR) particle filer, which is very commonly used in the prognostics field (see An et al. (2013); Saha and Goebel (2011); Jouin et al. (2014)). To explain the steps of the SIR algorithm, let suppose that at time step k = 0, the initial distribution p(x0 ) is approximated in s the form of a set of Ns samples {xi0 }N i=1 with associated 1 Ns i weights {w0 = Ns }i=1 . Then, the following three steps are repeated until the end of the process. (1) Prediction: a new PDF is obtained by propagating the particles from state k − 1 to state k using the state model (in our case, this corresponds to the degradation model). (2) Update: when a new measurement is available, the likelihood of the particles p(zk |xik ) is computed. This probability shows the degree of matching between the prediction and the measurement. Its calculation allows updating the weight of each particle. (3) Re-sampling: this step appears to avoid a degeneracy of the filter. The basic idea of re-sampling is to eliminate the particles with small weights and duplicate the particles with large weights. The re-sampling step Ns involves generating a new set of particles {xi∗ k }i=1 by re-sampling (with replacement) Ns time from an approximate discrete representation of p(xk |z1:k ). 4.2 Particle filter for fault prognostics In fault prognostics, the SIR particle filter is used in both learning and prediction stages (Fig. 3). In the learning stage, the state of the system and the unknown parameters of its degradation model are estimated. When a prediction is required, at time tp , the posterior PDF given i s by {xip , wpi }N i=1 is propagated until x reaches the failure threshold at Tfi . The RUL PDF is then given by calculating Tfi − tp . Learning stage
Measurement, 𝑧𝑧𝑘𝑘
Prediction stage
Initialize PF parameters
Start prediction at 𝑡𝑡𝑝𝑝
Propose initial population, {𝑥𝑥0 , 𝑤𝑤0 }
Estimate initial population, {𝑥𝑥𝑝𝑝 , 𝑤𝑤𝑝𝑝 }
Propagate particles using state model, 𝑥𝑥𝑘𝑘−1 → 𝑥𝑥𝑘𝑘
Propagate particles using state model, 𝑥𝑥𝑝𝑝+𝑘𝑘−1 → 𝑥𝑥𝑝𝑝+ 𝑘𝑘
Update weights, 𝑤𝑤𝑘𝑘−1 → 𝑤𝑤𝑘𝑘
Weights degenerated ?
Failure Threshold reached ?
No
No Yes Generate RUL PDF
Yes Resample
Fig. 3. SIR particle filter for fault prognostics (adapted from Saha and Goebel (2011)).
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229
Direction of movement Shuttle
Light source
Voltage suppliers
Camera
ᶿ Anchorage
(a)
Hot arms
Anchorage
(b) NI card
Fig. 4. (a) The MEMS valve and (b) schematic view of its actuator. 5. APPLICATION AND RESULTS 5.1 The MEMS and its nominal behavior model
MEMS
Arduino
Anti-vibration table
The targeted device consists of an electro-thermally actuated MEMS valve of DunAn Microstaq, Inc. (DMQ) company (Fig. 4(a)). It is designed to control flow rates or pressure with high precision at ultra-fast time response (<< 100 ms). It is currently being used in a number of applications in air conditioning and refrigeration, hydraulic control and air pressure control. The valve is composed of three silicon layers. The center layer is a movable membrane, the top layer is for electrical connections and the bottom layer is for the three fluid connections ports: common port, normally closed and normally open. The maximum actuation voltage of the valve is 12 V.
Fig. 5. Overview of the experimental platform.
The actuator used inside the targeted MEMS is an electrothermal actuator. This actuator, presented in Fig. 4(b), is composed of hot arms inclined to the horizontal axis by an angle θ and clamped to the substrate and the freestanding central shuttle. When a voltage difference is applied across the anchor sites, a heat is generated along the beams due to ohmic dissipation. The hot arms expand to push ahead symmetrically on the central part of the actuator (the shuttle). This part moves in the direction shown in Fig. 4(b). The shuttle is connected to the membrane and its movement allows moving the membrane to open or close the fluid ports.
Fig. 6. Time response of the MEMS valve. At 8 V, the membrane moves (image 1) to create an output or an input of the air (circled part). At 0 V, the membrane returns to its initial position (image 2).
The physical modeling of the MEMS behavior leads to a first order model. This model,given by equation 5, is confirmed by the experimental results described in the next subsection. K X(p) = U (p) 1 + τp
(5)
In this equation, X is the output of the system (displacement of the actuator), U is the input (voltage), K is the static gain and τ is the time constant. 5.2 Experimental setup and tests In order to validate the nominal behavior model and perform accelerated lifetime tests to generate the degradation model of the targeted MEMS, we designed and built an experimental platform (Fig. 5). This platform is composed of two ARDUINO devices, two voltage suppliers, supports for the camera and the MEMS, a light source for the camera allowing to see the movement of the membrane inside the MEMS, an air inlet, a pressure regulator, an NI card and a computer for data acquisition. Four MEMS are cycled at each experimental campaign. Each MEMS 229
70 60
Direction of motion
Displacement (µm)
50
Direction of motion
40 30 20 10 0
Movable Membrane 0
0.1
0.2
0.3
1 0.4
2 0.5 Time (s)
0.6
0.7
0.8
0.9
1
is fixed on a support specially designed. To minimize the mechanical vibration, the experimental platform is placed on an anti-vibration table. During the accelerated lifetime tests, the supply voltage is set to 8 V . This value is not too high to not bring up prematurely degradation and not too low to obtain enough displacement. The time response of the MEMS is obtained by using the images taking by the camera and a Matlab image-processing algorithm. Fig. 6 shows an example of an obtained time response of one MEMS valve supplied by a periodic square signal of 8 V magnitude and 1 Hz frequency. This time response is typical of a first order system. By using the Matlab system identification toolbox, the transfer function can be obtained and all the system parameters can be easily identified. The transfer function corresponding to the time response presented in Fig. 6 is given in equation 6 and the identified parameters are given in table 1. 8.02 X(p) = U (p) 1 + 0.052p
(6)
Table 1. Identified parameters. Parameter Displacement Current Static gain Time constant Stiffness Friction coefficient
Symbol D I K τ ks f
Value 65 0.5 8.02 0.052 2.7 × 10 1.4 × 10
2 3
Unit µm A µm/V s N/m Ns/m
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0
20
40 Time (days) MEMS 3
60
20 Displacement Compliance
30
15
20
10
10
5
0
0 100
0
20
40 60 Time (days)
80
Compliance (N/m)
40
50
Displacement Compliance
0
0
20
40 60 Time (days) MEMS 4
0 100
80
80
40
60
30
40
20
20 0
10
Displacement Compliance
0
20
40 60 Time (days)
Compliance (N/m)
0 80
100
Compliance (N/m)
Displacement Compliance
0
MEMS 2
Compliance (N/m)
50
Displacement (µm)
100
Displacement (µm)
Displacement (µm)
MEMS 1
Displacement (µm)
Accelerated lifetime tests consist in cycling continuously four MEMS valves (Fig. 5). They are supplied by a periodic square signal of 8 V magnitude and 1 Hz frequency. The measurements acquisition is the same for all the tested MEMS. For each one of them the following steps are applied: 1) adjust the MEMS below the camera by using a 3D positioner until having a very clear image, 2) get the time response by using a Matlab image-processing algorithm, 3) identify the parameters of the system by using the Matlab system identification toolbox, and 4) store the results in different files in a dedicated computer for later use. Note that, the operating conditions and load were kept constant during the cycling tests.
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Prior to curve fitting task to derive the degradation model, the raw experimental data are smoothed by applying a rloess filter to remove the different peaks and extract a monotonic trend (Fig. 8). Basically, rloess is a robust local regression filter that allocates lower weight to outliers. By using the curve fitting method, the evolution of the HI is approximated by a double exponential model, which represents the degradation model of the MEMS valves: (7) HI(t) = aebt + cedt The four tested MEMS valves have the same shape of the degradation model (Eq. 7), but with different values of the parameters (a, b, c and d). Thus, this model is set as a generic degradation model for the studied MEMS valve.
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5.4 Prognostics results
As explained in Section 3, prognostics is divided into two stages: learning and prediction. During the learning stage, the state of the MEMS (PDF of the HI) at time step k is estimated using the degradation model and the state at time step k − 1. The parameters of the state model are consequently adjusted. This process lasts until a prediction is required at tp . At this time, the estimated PDF of the HI is propagated until it reaches the F T at Tf . The duration between Tf and the starting point of prediction tp gives the PDF of the RUL.
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The RUL estimation of each MEMS requires a definition of a corresponding Fault Threshold (F T ). In this case study, the F T corresponds to the point at which the HI value decreases by 60%. Obviously, this value can be changed depending on the desired performance of the MEMS.
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To get the degradation model of the MEMS, the accelerated lifetime tests remained running for approximately three months, during which the MEMS valves were continuously cycled. During this period, measurements were collected regularly. The decrease in the magnitude of the displacement is related to the degradation in the tested MEMS valves (Fig. 7). Among the defined parameters, the compliance 1/ks (inverse of the stiffness) has the same evolution in time as the displacement (Fig. 7). Therefore, the compliance is selected as the physical HI, which can be used to track the degradation of the MEMS valves. The projection of this HI can be exploited to predict the future behavior of each MEMS valve and calculate its RUL.
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(b) RUL estimation at frequent intervals. Fig. 9. Prognostics results. In the following, only the data of the M EM S 4, with the degradation model parameters a = 4.041.106 , b = 0.0116, c = −4.041.106 and d = 0.0116 are used to perform prognostics.
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An example of RUL estimation at 60 days is given in Fig. 9(a). The estimated health indicator is represented with a confidence interval of 95%. The current HI is also drawn to show the difference. The estimated RUL corresponds to the median of the RUL PDF. The median RUL is chosen rather than the mean RUL since it gives early estimates and has better accuracy when more data are available. Note that, in PHM context, it is better to have early estimates rather than late RUL to avoid failures. In order to demonstrate the online estimation of the RUL, the prediction is initiated at regular intervals. Fig. 9(b) shows the estimated RUL at regular intervals compared to the real one. One can clearly see that the accuracy of the RUL estimates increases with time, as more data are available. Furthermore, the real RUL values are within the prediction interval at different time steps. These obtained results demonstrate the accuracy and the significance of the proposed prognostics approach. Note that, the same observations are made for all tested MEMS. 6. CONCLUSION In this paper, a hybrid prognostics approach is proposed. First, before presenting the approach, the necessity of implementing PHM for MEMS devices instead of simply studying their reliability is discussed. After that, a brief presentation of the particle filter algorithm is given. The proposed approach is then applied to an electrothermally actuated MEMS valve. For this purpose, an experimental platform is designed to validate the obtained nominal behavior model of the targeted MEMS, perform accelerated lifetime tests and derive its degradation model. Once the degradation model is obtained, the SIR particle filter is used to perform online prognostics. This tool allowed to estimate the degradation model parameters, predict the future behavior of the MEMS valve and calculate its RUL. The obtained results show the significance of the proposed prognostics approach. As a future work, this approach will be implemented on a real application: a centimeter contact-less distributed MEMS-based conveying surface. This application, conducted in our laboratory, is dedicated for distributed postprognostics decision making and aims at optimizing the utilization of the conveying surface and maintaining a good performance as long as possible. REFERENCES An, D., Choi, J.H., and Kim, N.H. (2013). Prognostics 101: A tutorial for particle filter-based prognostics algorithm using matlab. Reliability Engineering & System Safety, 115, 161–169. Arulampalam, M.S., Maskell, S., Gordon, N., and Clapp, T. (2002). A tutorial on particle filters for online nonlinear/non-gaussian bayesian tracking. Signal Processing, IEEE Transactions on, 50(2), 174–188. Gordon, N.J., Salmond, D.J., and Smith, A.F. (1993). Novel approach to nonlinear/non-gaussian bayesian state estimation. In Radar and Signal Processing, IEE Proceedings F, volume 140, 107–113. IET. Heng, A., Zhang, S., Tan, A.C., and Mathew, J. (2009). Rotating machinery prognostics: state of the art, chal231
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lenges and opportunities. Mechanical Systems and Signal Processing, 23(3), 724–739. Huang, Y., Vasan, A.S.S., Doraiswami, R., Osterman, M., and Pecht, M. (2012). MEMS reliability review. Device and Materials Reliability, IEEE Transactions on, 12, 482–493. Jardine, A.K., Lin, D., and Banjevic, D. (2006). A review on machinery diagnostics and prognostics implementing condition-based maintenance. Mechanical systems and signal processing, 20(7), 1483–1510. Javed, K., Gouriveau, R., Zerhouni, N., and Nectoux, P. (2015). Enabling health monitoring approach based on vibration data for accurate prognostics. Industrial Electronics, IEEE Transactions on, 62(1), 647–656. Jouin, M., Gouriveau, R., Hissel, D., P´era, M.C., and Zerhouni, N. (2014). Prognostics of PEM fuel cell in a particle filtering framework. International Journal of Hydrogen Energy, 39(1), 481–494. Lebold, M. and Thurston, M. (2001). Open standards for condition-based maintenance and prognostic systems. In Maintenance and Reliability Conference (MARCON), 6–9. May. Li, Y. and Jiang, Z. (2008). An overview of reliability and failure mode analysis of microelectromechanical systems (MEMS). In Handbook of performability engineering, 953–966. Medjaher, K., Skima, H., and Zerhouni, N. (2014). Condition assessment and fault prognostics of microelectromechanical systems. Microelectronics Reliability, 54, 143– 151. Medjaher, K. and Zerhouni, N. (2013). Hybrid prognostic method applied to mechatronic systems. The International Journal of Advanced Manufacturing Technology, 69(1-4), 823–834. Merlijn van Spengen, W. (2003). MEMS reliability from a failure mechanisms perspective. Microelectronics Reliability, 43, 1049–1060. Mosallam, A., Medjaher, K., and Zerhouni, N. (2014). Data-driven prognostic method based on bayesian approaches for direct remaining useful life prediction. Journal of Intelligent Manufacturing, 1–12. Peng, Y., Dong, M., and Zuo, M.J. (2010). Current status of machine prognostics in condition-based maintenance: a review. The International Journal of Advanced Manufacturing Technology, 50(1-4), 297–313. Saha, B. and Goebel, K. (2011). Model adaptation for prognostics in a particle filtering framework. International Journal of Prognostics and Health Management Volume 2 (color), 61. Skima, H., Medjaher, K., Varnier, C., Dedu, E., and Bourgeois, J. (2015). Hybrid prognostic approach for microelectro-mechanical systems. In 2015 IEEE Aerospace Conference, 1–8. Tobon-Mejia, D.A., Medjaher, K., Zerhouni, N., and Tripot, G. (2012). A data-driven failure prognostics method based on mixture of gaussians hidden markov models. Reliability, IEEE Transactions on, 61(2), 491– 503. Yin, S. and Zhu, X. (2015). Intelligent particle filter and its application on fault detection of nonlinear system. Industrial Electronics, IEEE Transactions on, 62(6), 3852–3861.
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Fault Fault Prognostics Prognostics of of Fault Prognostics of Micro-Electro-Mechanical Systems Micro-Electro-Mechanical Systems Micro-Electro-Mechanical Systems Particle Particle Filtering Filtering Particle Filtering ∗ ∗∗
Using Using Using
Haithem Skima ∗ Kamal Medjaher ∗∗ Christophe Varnier ∗∗ ∗ Kamal Medjaher ∗∗ Christophe Varnier ∗ ∗ Haithem Skima ∗ ∗ Haithem Skima Medjaher Christophe Zerhouni Varnier Eugen Dedu Julien Bourgeois and∗∗Noureddine ∗ Kamal ∗ ∗ Haithem Skima Kamal Medjaher Christophe Varnier ∗ ∗∗ ∗ Julien ∗ and Noureddine Eugen Dedu Bourgeois Eugen Dedu ∗ Julien Bourgeois ∗ and Noureddine Zerhouni Zerhouni ∗ Eugen Dedu Julien Bourgeois and Noureddine Zerhouni ∗ FEMTO-ST Institute, UMR CNRS 6174 – UFC / ENSMM ∗ ∗ FEMTO-ST Institute, UMR CNRS 6174 – UFC / ENSMM Institute, UMR CNRS – cUFC / ENSMM 15B av. des Montboucons, 250006174 Besan¸ on, France ∗ FEMTO-ST FEMTO-ST Institute, UMR CNRS – cUFC / ENSMM 15B av. av. des Montboucons, 250006174 Besan¸ on, France France 15B des Montboucons, 25000 Besan¸ con, (e-mail: [email protected]) 15B av. des Montboucons, 25000 Besan¸ c on, France (e-mail: [email protected]) ∗∗ (e-mail: [email protected]) Production Engineering Laboratory (LGP), INP-ENIT ∗∗ (e-mail: [email protected]) ∗∗ Production Engineering Laboratory (LGP), INP-ENIT Engineering Laboratory (LGP), INP-ENIT 47 Av. d’Azereix, 65000 Tarbes, France ∗∗ Production Production Engineering Laboratory (LGP), INP-ENIT 47 Av. d’Azereix, 65000 Tarbes, France 47 (e-mail: Av. d’Azereix, 65000 Tarbes, France [email protected]) 47 (e-mail: Av. d’Azereix, 65000 Tarbes, France (e-mail: [email protected]) [email protected]) (e-mail: [email protected]) Abstract: This paper presents a hybrid prognostics approach for Micro-Electro-Mechanical Abstract: This presents hybrid Micro-Electro-Mechanical Abstract: This paper paper presents a arelies hybrid prognostics approach for Micro-Electro-Mechanical Systems (MEMS). The approach on prognostics two phases: approach an offline for phase for the MEMS and its Abstract: This paper presents arelies hybrid approach Micro-Electro-Mechanical Systems (MEMS). The and approach on prognostics two phases: anprognostics. offline for phase for proposed the MEMS MEMS and its its Systems (MEMS). The approach reliesphase on two phases: an offline phase for the and degradation modeling, an online for its fault The approach Systems (MEMS). The approach relies on two phases: an offline phase for proposed the MEMS and its degradation modeling, and an online for its The approach degradation modeling, and an consisting online phase phase forelectro-thermally its fault fault prognostics. prognostics. The valve. proposed approach is applied to a MEMS device in an actuated In the offline degradation modeling, and an online phase for its fault prognostics. The valve. proposedthe approach is applied to device an actuated is applied to a a MEMS MEMS platform device consisting consisting invalidate an electro-thermally electro-thermally actuatedbehavior valve. In In the offline offline phase, an experimental is built toin the obtained nominal model of the is applied to a MEMS device consisting in an electro-thermally actuated valve. In the offline phase, an experimental platform is the nominal model of phase, anMEMS experimental platform is built built to to validate validate the obtained obtained nominal behavior behavior model of the the targeted and to get its degradation model. This model represents the drifts in a MEMS phase, anMEMS experimental platform is built to validate the obtained nominal behavior model of the targeted to its degradation model. This model represents the drifts in targeted MEMS and and which to get get is itsits degradation model. This model represents the filter drifts algorithm in aa MEMS MEMS physical parameter, compliance. In the online phase, a particle is targeted MEMS and which to get is its degradation model. This model represents the filter drifts algorithm in a MEMS physical parameter, In online phase, aa particle is physical parameter, which is its its compliance. compliance. Inofthe the online phase, particle filterand algorithm is used to perform online parameters estimation the derived degradation model calculate physical parameter, which is its compliance. In the online phase, a particle filterand algorithm is used to online parameters estimation the degradation used to perform perform onlineuseful parameters estimation ofprognostic the derived derived degradation model and calculate calculate the MEMS remaining life. The obtainedof results show themodel effectiveness of the used to perform online parameters estimation of the derived degradation model and calculate the MEMS remaining useful life. The obtained prognostic results show the effectiveness of the MEMS remaining useful life. The obtained prognostic results show the effectiveness of the the proposed approach. the MEMS remaining useful life. The obtained prognostic results show the effectiveness of the proposed proposed approach. approach. proposed approach. © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Prognostics and health management, micro-electro-mechanical system, fault Keywords: and management, Keywords: Prognostics and health health management, micro-electro-mechanical system, system, fault fault prognostics,Prognostics remaining useful life, particle filter. micro-electro-mechanical Keywords: Prognostics and health management, micro-electro-mechanical system, fault prognostics, prognostics, remaining remaining useful useful life, life, particle particle filter. filter. prognostics, remaining useful life, particle filter. 1. INTRODUCTION 1. INTRODUCTION INTRODUCTION 1. 1. INTRODUCTION Micro-Electro-Mechanical Systems (MEMS) are microData HMI Micro-Electro-Mechanical Systemscomponents (MEMS) are are microacquisition Data Micro-Electro-Mechanical Systems (MEMS) microData systems that integrate mechanical using elecHMI HMI acquisition Micro-Electro-Mechanical Systems (MEMS) are microacquisition Data systems that integrate mechanical components using elecelecHMI systems that integrate mechanical components using tricity as source of energy in order to perform measurement acquisition systems that integrate mechanical components using elecData tricity as source of energy in order to perform measurement Decision tricity as source of energy in order to perform measurement PHM functions and/orofoperating in structure having micrometprocessing Data tricity as source energy in in order to perform measurement Data Decision PHM functions and/or operating structure having micrometDecision PHM processing functions and/or In operating in structure micrometprocessing Data ric dimensions. the past few years,having MEMS devices Decision PHM functions and/or operating in structure having micrometprocessing ric dimensions. In the past few years, MEMS devices ric dimensions. In the past few years, MEMS devices Prognostic gained wide-spread acceptance in several industrial segDetection ric dimensions. In the past few MEMS devices Prognostic gained wide-spread acceptance in years, several industrial segDetection Prognostic gained wide-spread acceptance in several industrial segDetection ments including aerospace, automotive, medical and even Prognostic gained wide-spread acceptance in several industrial segDetection ments including aerospace, automotive, medical and even ments including aerospace, automotive, medical and even military applications, where they contribute to important Diagnostic ments including aerospace, automotive, medical and even military applications, where they contribute to important Diagnostic military contributeoftoMEMS important Diagnostic functions.applications, The most where knownthey applications are military applications, where contributeoftoMEMS important Diagnostic functions. The for most knownthey applications are functions. The most known applications of MEMS gyare accelerometers automotive (airbag) applications, 1. Prognostics and Health Management cycle. functions. The for most known applications of MEMS gyare Fig. accelerometers automotive (airbag) applications, Fig. 1. Prognostics and Health accelerometers for automotive (airbag) applications, gyroscopes for mobiles phones, pressure sensors for engine 1. Prognostics and Health Management Management cycle. cycle. accelerometers for automotive (airbag)sensors applications, gy- Fig. Fig. 1.1)Prognostics andThurston Health Management roscopes for mobiles phones, pressure for engine (Fig. (Lebold and (2001)). It iscycle. a discipline roscopes for mobiles phones, pressure sensors for engine management and micro-mirror arrays for display applicaroscopes for mobiles phones, pressure sensors forapplicaengine (Fig. 1) and Thurston (2001)). It management and micro-mirror micro-mirror arrays for display 1) (Lebold (Lebold andstudy Thurston (2001)). It is is a a discipline discipline that deals with the of failure mechanisms in order management and arrays for display applica- (Fig. tions. Nevertheless, the reliability of MEMS is considered 1) (Lebold andstudy Thurston (2001)). It is a discipline management and micro-mirror arrays for display applica- (Fig. that deals with the of failure mechanisms in order tions. Nevertheless, the reliability of MEMS is considered that deals with the study of failure mechanisms in order to extend the life cycle of systems and to better manage tions. Nevertheless, thetheir reliability of MEMS is considered as a major obstacle for development (Medjaher et al. that deals the withlife thecycle study of failureand mechanisms in order tions. Nevertheless, thetheir reliability of MEMS is considered to extend of systems to better manage as a major obstacle for development (Medjaher et al. to extend the life cycle of systems and to better manage their health. Within the framework of PHM, prognostics is as a major obstacle for their development (Medjaher et al. (2014)). They sufferforfrom numerous failure mechanisms to extend theWithin life cycle of systems of and to better manage as a major obstacle their development (Medjaher et al. their health. the framework PHM, prognostics is (2014)). They suffer from numerous failure mechanisms their health. Within the framework of PHM, prognostics considered as a core activity for applying a good predictive (2014)). They suffer from numerous failure mechanisms which impact their performance, reducefailure their lifetime, and their health. Within the framework of PHM, prognostics is is (2014)). Theytheir suffer from numerous mechanisms considered as a core activity for applying a good predictive which impact performance, reduce their lifetime, and considered as a core activity for applying a good predictive Prognostics is for defined by the PHMpredictive commuwhich impact their performance, reduce lifetime, and maintenance. the availability of systems in which theytheir are used (Huang considered as a core activity applying a good which impact their performance, reduce their lifetime, and Prognostics is defined PHM the availability of systems systems in(2015); which they they are van usedSpengen (Huang maintenance. maintenance. Prognostics is Remaining defined by by the the PHM community as the estimation of the Useful Lifecommu(RUL) the availability of which are used (Huang et al. (2012); Skima et al.in Merlijn maintenance. Prognostics is Remaining defined by the PHM commuthe availability of systems in(2015); which they are van usedSpengen (Huang nity as the estimation of the Useful Life (RUL) et al. (2012); Skima et al. Merlijn nity as the estimation of the Remaining Useful Life (RUL) of physical systems based on their current health state and et al. (2012); Skima et al. (2015); Merlijn van Spengen (2003); Li and Jiang (2008)). This analysis shows the need nity as the estimation of the Remaining Useful Life (RUL) et al. (2012); Skima et al. (2015); Merlijn van Spengen of physical systems based on their current health state and (2003); Li and Jiang (2008)). This analysis shows the need of physical systems based on their current health state their future operating conditions. Prognostics approaches (2003); Li and Jiang (2008)). This analysis shows the need to monitor their behavior, assess their health statethe andneed an- of physical systems based on their current health state and and (2003); Li and Jiang (2008)). Thistheir analysis shows their future operating conditions. Prognostics approaches to monitor their behavior, assess health state and antheir future operating conditions. Prognostics approaches befuture classified into three main approaches (Jardine et al. to monitor their behavior, assess health state and an- can ticipate their failures before theirtheir occurrence. These tasks their operating conditions. Prognostics approaches to monitor their behavior, assess their health state and ancan three (Jardine et ticipate theirbyfailures failures before their theirand occurrence. These tasks tasks (2006); can be be classified classified into three main main approaches (Jardine et al. al. Heng et into al. (2009); Pengapproaches et al. (2010); Medjaher ticipate their before occurrence. These can be done using Prognostics Health Management be classified into three main approaches (Jardine et al. ticipate theirbyfailures before theirand occurrence. These tasks can (2006); Heng et al. (2009); Peng et al. (2010); Medjaher can be done using Prognostics Health Management (2006); Heng et al. (2009); Peng et al. (2010); Medjaher and Zerhouni (2013)): model-based, data-driven and hycan be done by using Prognostics and Health Management (PHM) approaches, and this is the aim of this paper. (2006); Heng et al. (2009); Peng et al. (2010); Medjaher can be done by usingand Prognostics and Health Management and (2013)): model-based, data-driven and (PHM) approaches, this is is the the aim of this this paper. and Zerhouni Zerhouni (2013)): model-based, data-drivenapproach and hyhybrid prognostics approaches. The model-based (PHM) approaches, and this aim of paper. and Zerhouni (2013)): model-based, data-driven and hy(PHM) approaches, and this is the aim of this paper. prognostics approaches. The model-based approach PHM is the combination of seven layers that collectively brid brid prognostics approaches. The model-based approach deals with estimation of the RUL by using mathematical brid prognostics approaches. The model-based approach PHM islinking the combination combination of seven seven layers layers thatmanagement collectively deals PHM the of that collectively of RUL using enableis failure mechanisms with life deals with with estimation estimation of the the RUL by by using mathematical mathematical to formalize physical understanding of a dePHM the combination of seven layers thatmanagement collectively representation deals with estimation of the RUL by using mathematical enableislinking linking failure mechanisms mechanisms with life life enable failure with management representation to formalize physical understanding of a representation toThe formalize physical understanding oftransa dede grading system. data-driven approach aims at enable linking failure mechanisms with management This work has been supported by the R´ egion life Franche-Comt´ e and representation toThe formalize physical understanding oftransa de grading system. data-driven approach aims at This work has been supported by the R´ e gion Franche-Comt´ e and grading system. The data-driven approach aims atvoltage, transwork has beenproject supported by the R´ egion Franche-Comt´ e and forming raw monitoring data (e.g. temperature, theThis ACTION Labex (contract ANR-11-LABX-0001-01). grading system. The data-driven approach aims atvoltage, transThis work has been supported by the R´ egion Franche-Comt´ e and forming the forming raw raw monitoring monitoring data data (e.g. (e.g. temperature, temperature, voltage, the ACTION ACTION Labex Labex project project (contract (contract ANR-11-LABX-0001-01). ANR-11-LABX-0001-01). forming raw monitoring data (e.g. temperature, voltage, the ACTION Labex project (contract ANR-11-LABX-0001-01).
Copyright © 2016, 2016 IFAC 226Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2016 IFAC 226 Copyright ©under 2016 responsibility IFAC 226Control. Peer review of International Federation of Automatic Copyright © 2016 IFAC 226 10.1016/j.ifacol.2016.11.039
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etc.) into relevant information to build behavior models including the degradation evolution, which are then used for RUL estimation. Finally, the hybrid approach combines both previous approaches to achieve more accurate RUL estimates. This paper proposes a hybrid prognostics approach for MEMS, with a specific application to an electro-thermally actuated MEMS valve. The approach combines two types of models: a nominal model of the MEMS derived by writing its physical laws, and a degradation model obtained from accelerated life tests conducted on several samples of the same reference of MEMS. The generated prognostic model is then used to estimate the RUL of the MEMS. The paper is structured in six sections. After the introduction, Section 2 discusses the implementation of prognostics for MEMS instead of studying their reliability. Section 3 deals with the proposed approach to estimate the RUL of MEMS. The used prognostics tool is presented in Section 4. Section 5 describes the application of the proposed approach to a MEMS device and presents the obtained results. Finally, Section 6 concludes the paper. 2. TOWARD PROGNOSTICS OF MEMS MEMS devices suffer from various reliability issues. This is confirmed by numerous published works dealing with MEMS reliability. These works concern: 1) testability and characterization of MEMS, 2) identification and understanding of failure mechanisms, 3) design, fabrication and packaging optimization, 4) accelerated life tests to develop predictive reliability models, and 5) statistical studies of failures on a significant number of samples. Improving reliability of MEMS devices has several advantages, such as increasing their lifetime and improving their performance. However, reliability still has some limitations. It is defined as the ability of a system or a product to perform its intended function without failure and within specified performance limits for a specified period of time under stated conditions. Thus, according to this definition, reliability is valid only for given conditions and a period of time. This is the case, for example, for cars which are guaranteed by automobile manufacturers for a period of time in given operating conditions. In this situation, the reliability is estimated without taking into account the specific utilization of each car (e.g. environment conditions, roads quality, frequency of use, etc.). However, in practice, the lifetime should be different from one car to another depending on how and where it is used. In addition to this, reliability models are generally obtained from statistical data on representative samples. These models, which are generic for all the samples, are not updated during the utilization. This means that, once they are estimated, the model reliability parameters still constant while they should change due to the factors mentioned previously. To cope with the above mentioned limitations, one can use PHM. This activity makes use of past, present, and future operating conditions in order to assess the health state of the system, diagnose its faults, update the degradation models parameters, anticipate failures by estimating the RUL and improve decision making to prolong its lifetime. Prognostics is widely applied in industrial systems ranging 227
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Construction of the nominal behavior model
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Health indicator selection
&
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Fig. 2. Overview of the proposed prognostics approach. from small components (e.g. bearings (Tobon-Mejia et al. (2012)), cutting tools (Javed et al. (2015)), etc.) to complete machines (e.g. turbofans (Mosallam et al. (2014)), mechatronic systems (Medjaher and Zerhouni (2013)), etc.). Although its benefits are well proven, there are few published works addressing fault prognostics of MEMS. To fill this gap, a hybrid prognostics approach for MEMS devices is proposed in the next section. 3. PROGNOSTICS APPROACH The steps of the proposed hybrid prognostics approach are presented in Fig. 2. This approach can be applied on different categories of MEMS at a condition that the following assumptions hold. • The instrumentation needed to monitor the behavior of MEMS (sensors, camera, etc.) is available. • Sufficient knowledge about the studied MEMS is available to derive their nominal behavior models and identify their failure mechanisms which may take place during their utilization. In this work, the approach is applied to an electrothermally actuated valve MEMS (see Section 5.1). It relies on two phases. The first phase is done offline to build the nominal behavior model of the MEMS, select a relevant physical health indicator and derive the MEMS degradation model. The second phase is conducted online and uses the obtained degradation model to predict the MEMS future behavior and calculate its RUL. The steps shown in Fig. 2 can be grouped in three main tasks. (1) Nominal behavior model construction: it is obtained by writing the corresponding physical laws of the targeted MEMS and then validating it experimentally. (2) Degradation model : it is obtained experimentally through accelerated life tests and it is related to drifts in a selected Health Indicator (HI). This HI is a physical parameter, which can be used to track the degradation of the MEMS. (3) Prognostics modeling: prognostics is divided into two main stages: learning and prediction. In the learning stage, the prognostics tool combines the available data with the degradation model to learn the behavior of the system and estimate the parameters of its degradation model. This stage lasts until a prediction is required at time tp . Then, in the prediction stage, the prognostics tool propagates the state of the system and determines at what time the failure threshold (F T ) is reached. Finally, the RUL is calculated as the difference between the failing time Tf and the starting prediction time tp .
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In the offline phase, the evolution of the selected HI is approximated by a mathematical model to define the degradation model. In the online phase, the parameters of this model are unknown and need to be estimated as a part of the prognostics process. To do so, the particle filter algorithm is used as a prognostics tool. It allows handling the non-linearities and non-Gaussian noises (Yin and Zhu (2015)), which are some specificities inherent to MEMS. 4. PROGNOSTICS USING PARTICLE FILTERING 4.1 Particle filtering framework The problem of recursive Bayesian estimation is defined by two equations (Gordon et al. (1993)): the first considers the evolution of the system state {xk , k ∈ N} which is given by: (1) xk = f (xk−1 , λk−1 ) where k is the time step index, f is the transition function from the state xk−1 to the next state xk and {λk−1 , k ∈ N} is the independent identically distributed process noise sequence. The purpose is to recursively estimate xk from measurements introduced by the second equation and which corresponds to the measurement model {zk , k ∈ N}: (2) zk = h(xk , µk ) where k is the time step index, h is the measurement function and {µk , k ∈ N} is the independent identically distributed measurement noise sequence. The aim of the recursive Bayesian estimation problem is to recursively estimate the state of the system by constructing the Probability Density Function (PDF) of the state at time k based on all available information, p(xk |z1:k ). It is assumed that the initial PDF of the state vector, also called the prior, is available (p(x0 |z0 ) = p(x0 )). The PDF p(xk |z1:k ), known as the posterior, can be obtained recursively in two main stages: prediction and update. • Prediction stage: in this stage the state model (Eq. 1) is used to obtain the prior PDF of the state at time k via the Chapman-Kolmogorov equation: p(xk |z1:k−1 ) = p(xk |xk−1 )p(xk−1 |z1:k−1 )dxk−1
(3) • Update stage: when a new measurement zk becomes available, one can update the prior PDF via the Bayes rule: p(zk |xk )p(xk |z1:k−1 ) (4) p(xk |z1:k ) = p(zk |z1:k−1 )
This gives the formal solution to the recursive Bayesian estimation problem. Analytic solutions to this problem are available in a restrictive set of cases, including the Kalman filter, which assumes that the state and measurement models are linear and λk and µk are additive Gaussian noise of known variance. When these assumptions are unreasonable, which is the case in many applications, and the equations (Eq. 3) and (Eq. 4) cannot be solved analytically, approximations are necessary. One of the most used approximate solution for this kind of problem is the particle filtering. The particle filtering solution is a sequential Monte-Carlo method which consists in representing the required posterior PDF by a set of particles with associated weights and
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computing estimates based on these particles and weights. Different versions of particle filtering are reported in the literature and, for more details, interested readers can refer to the work published by Arulampalam et al. (2002). In this paper, we focus on the Sampling Importance Resampling (SIR) particle filer, which is very commonly used in the prognostics field (see An et al. (2013); Saha and Goebel (2011); Jouin et al. (2014)). To explain the steps of the SIR algorithm, let suppose that at time step k = 0, the initial distribution p(x0 ) is approximated in s the form of a set of Ns samples {xi0 }N i=1 with associated 1 Ns i weights {w0 = Ns }i=1 . Then, the following three steps are repeated until the end of the process. (1) Prediction: a new PDF is obtained by propagating the particles from state k − 1 to state k using the state model (in our case, this corresponds to the degradation model). (2) Update: when a new measurement is available, the likelihood of the particles p(zk |xik ) is computed. This probability shows the degree of matching between the prediction and the measurement. Its calculation allows updating the weight of each particle. (3) Re-sampling: this step appears to avoid a degeneracy of the filter. The basic idea of re-sampling is to eliminate the particles with small weights and duplicate the particles with large weights. The re-sampling step Ns involves generating a new set of particles {xi∗ k }i=1 by re-sampling (with replacement) Ns time from an approximate discrete representation of p(xk |z1:k ). 4.2 Particle filter for fault prognostics In fault prognostics, the SIR particle filter is used in both learning and prediction stages (Fig. 3). In the learning stage, the state of the system and the unknown parameters of its degradation model are estimated. When a prediction is required, at time tp , the posterior PDF given i s by {xip , wpi }N i=1 is propagated until x reaches the failure threshold at Tfi . The RUL PDF is then given by calculating Tfi − tp . Learning stage
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Fig. 3. SIR particle filter for fault prognostics (adapted from Saha and Goebel (2011)).
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Fig. 4. (a) The MEMS valve and (b) schematic view of its actuator. 5. APPLICATION AND RESULTS 5.1 The MEMS and its nominal behavior model
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The targeted device consists of an electro-thermally actuated MEMS valve of DunAn Microstaq, Inc. (DMQ) company (Fig. 4(a)). It is designed to control flow rates or pressure with high precision at ultra-fast time response (<< 100 ms). It is currently being used in a number of applications in air conditioning and refrigeration, hydraulic control and air pressure control. The valve is composed of three silicon layers. The center layer is a movable membrane, the top layer is for electrical connections and the bottom layer is for the three fluid connections ports: common port, normally closed and normally open. The maximum actuation voltage of the valve is 12 V.
Fig. 5. Overview of the experimental platform.
The actuator used inside the targeted MEMS is an electrothermal actuator. This actuator, presented in Fig. 4(b), is composed of hot arms inclined to the horizontal axis by an angle θ and clamped to the substrate and the freestanding central shuttle. When a voltage difference is applied across the anchor sites, a heat is generated along the beams due to ohmic dissipation. The hot arms expand to push ahead symmetrically on the central part of the actuator (the shuttle). This part moves in the direction shown in Fig. 4(b). The shuttle is connected to the membrane and its movement allows moving the membrane to open or close the fluid ports.
Fig. 6. Time response of the MEMS valve. At 8 V, the membrane moves (image 1) to create an output or an input of the air (circled part). At 0 V, the membrane returns to its initial position (image 2).
The physical modeling of the MEMS behavior leads to a first order model. This model,given by equation 5, is confirmed by the experimental results described in the next subsection. K X(p) = U (p) 1 + τp
(5)
In this equation, X is the output of the system (displacement of the actuator), U is the input (voltage), K is the static gain and τ is the time constant. 5.2 Experimental setup and tests In order to validate the nominal behavior model and perform accelerated lifetime tests to generate the degradation model of the targeted MEMS, we designed and built an experimental platform (Fig. 5). This platform is composed of two ARDUINO devices, two voltage suppliers, supports for the camera and the MEMS, a light source for the camera allowing to see the movement of the membrane inside the MEMS, an air inlet, a pressure regulator, an NI card and a computer for data acquisition. Four MEMS are cycled at each experimental campaign. Each MEMS 229
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is fixed on a support specially designed. To minimize the mechanical vibration, the experimental platform is placed on an anti-vibration table. During the accelerated lifetime tests, the supply voltage is set to 8 V . This value is not too high to not bring up prematurely degradation and not too low to obtain enough displacement. The time response of the MEMS is obtained by using the images taking by the camera and a Matlab image-processing algorithm. Fig. 6 shows an example of an obtained time response of one MEMS valve supplied by a periodic square signal of 8 V magnitude and 1 Hz frequency. This time response is typical of a first order system. By using the Matlab system identification toolbox, the transfer function can be obtained and all the system parameters can be easily identified. The transfer function corresponding to the time response presented in Fig. 6 is given in equation 6 and the identified parameters are given in table 1. 8.02 X(p) = U (p) 1 + 0.052p
(6)
Table 1. Identified parameters. Parameter Displacement Current Static gain Time constant Stiffness Friction coefficient
Symbol D I K τ ks f
Value 65 0.5 8.02 0.052 2.7 × 10 1.4 × 10
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Accelerated lifetime tests consist in cycling continuously four MEMS valves (Fig. 5). They are supplied by a periodic square signal of 8 V magnitude and 1 Hz frequency. The measurements acquisition is the same for all the tested MEMS. For each one of them the following steps are applied: 1) adjust the MEMS below the camera by using a 3D positioner until having a very clear image, 2) get the time response by using a Matlab image-processing algorithm, 3) identify the parameters of the system by using the Matlab system identification toolbox, and 4) store the results in different files in a dedicated computer for later use. Note that, the operating conditions and load were kept constant during the cycling tests.
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Fig. 7. Displacement and compliance as functions of time.
Prior to curve fitting task to derive the degradation model, the raw experimental data are smoothed by applying a rloess filter to remove the different peaks and extract a monotonic trend (Fig. 8). Basically, rloess is a robust local regression filter that allocates lower weight to outliers. By using the curve fitting method, the evolution of the HI is approximated by a double exponential model, which represents the degradation model of the MEMS valves: (7) HI(t) = aebt + cedt The four tested MEMS valves have the same shape of the degradation model (Eq. 7), but with different values of the parameters (a, b, c and d). Thus, this model is set as a generic degradation model for the studied MEMS valve.
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5.4 Prognostics results
As explained in Section 3, prognostics is divided into two stages: learning and prediction. During the learning stage, the state of the MEMS (PDF of the HI) at time step k is estimated using the degradation model and the state at time step k − 1. The parameters of the state model are consequently adjusted. This process lasts until a prediction is required at tp . At this time, the estimated PDF of the HI is propagated until it reaches the F T at Tf . The duration between Tf and the starting point of prediction tp gives the PDF of the RUL.
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To get the degradation model of the MEMS, the accelerated lifetime tests remained running for approximately three months, during which the MEMS valves were continuously cycled. During this period, measurements were collected regularly. The decrease in the magnitude of the displacement is related to the degradation in the tested MEMS valves (Fig. 7). Among the defined parameters, the compliance 1/ks (inverse of the stiffness) has the same evolution in time as the displacement (Fig. 7). Therefore, the compliance is selected as the physical HI, which can be used to track the degradation of the MEMS valves. The projection of this HI can be exploited to predict the future behavior of each MEMS valve and calculate its RUL.
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(b) RUL estimation at frequent intervals. Fig. 9. Prognostics results. In the following, only the data of the M EM S 4, with the degradation model parameters a = 4.041.106 , b = 0.0116, c = −4.041.106 and d = 0.0116 are used to perform prognostics.
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An example of RUL estimation at 60 days is given in Fig. 9(a). The estimated health indicator is represented with a confidence interval of 95%. The current HI is also drawn to show the difference. The estimated RUL corresponds to the median of the RUL PDF. The median RUL is chosen rather than the mean RUL since it gives early estimates and has better accuracy when more data are available. Note that, in PHM context, it is better to have early estimates rather than late RUL to avoid failures. In order to demonstrate the online estimation of the RUL, the prediction is initiated at regular intervals. Fig. 9(b) shows the estimated RUL at regular intervals compared to the real one. One can clearly see that the accuracy of the RUL estimates increases with time, as more data are available. Furthermore, the real RUL values are within the prediction interval at different time steps. These obtained results demonstrate the accuracy and the significance of the proposed prognostics approach. Note that, the same observations are made for all tested MEMS. 6. CONCLUSION In this paper, a hybrid prognostics approach is proposed. First, before presenting the approach, the necessity of implementing PHM for MEMS devices instead of simply studying their reliability is discussed. After that, a brief presentation of the particle filter algorithm is given. The proposed approach is then applied to an electrothermally actuated MEMS valve. For this purpose, an experimental platform is designed to validate the obtained nominal behavior model of the targeted MEMS, perform accelerated lifetime tests and derive its degradation model. Once the degradation model is obtained, the SIR particle filter is used to perform online prognostics. This tool allowed to estimate the degradation model parameters, predict the future behavior of the MEMS valve and calculate its RUL. The obtained results show the significance of the proposed prognostics approach. As a future work, this approach will be implemented on a real application: a centimeter contact-less distributed MEMS-based conveying surface. This application, conducted in our laboratory, is dedicated for distributed postprognostics decision making and aims at optimizing the utilization of the conveying surface and maintaining a good performance as long as possible. REFERENCES An, D., Choi, J.H., and Kim, N.H. (2013). Prognostics 101: A tutorial for particle filter-based prognostics algorithm using matlab. Reliability Engineering & System Safety, 115, 161–169. Arulampalam, M.S., Maskell, S., Gordon, N., and Clapp, T. (2002). A tutorial on particle filters for online nonlinear/non-gaussian bayesian tracking. Signal Processing, IEEE Transactions on, 50(2), 174–188. Gordon, N.J., Salmond, D.J., and Smith, A.F. (1993). Novel approach to nonlinear/non-gaussian bayesian state estimation. In Radar and Signal Processing, IEE Proceedings F, volume 140, 107–113. IET. Heng, A., Zhang, S., Tan, A.C., and Mathew, J. (2009). Rotating machinery prognostics: state of the art, chal231
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