Failure Prognosis of Embedded Systems Based on Temperature

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Failure Prognosis of Embedded Systems Based onTemperature Drift Assessment

Oussama Djedidi, Mohand Djeziri, Samir Benmoussa

To cite this version:Oussama Djedidi, Mohand Djeziri, Samir Benmoussa. Failure Prognosis of Embedded Systems Basedon Temperature Drift Assessment. IMAACA 2019 – Proceedings of the International Conferenceon Integrated Modeling and Analysis in Applied Control and Automation, 2019, Sep 2019, Lisbon,Portugal. pp.11-16. �hal-02311476�

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FAILURE PROGNOSIS OF EMBEDDED SYSTEMS BASED ON TEMPERATURE DRIFTASSESSMENT

Oussama Djedidi(a), Mohand A. Djeziri(b), Samir Benmoussa(c)

(a)(b)Aix Marseille University, Université de Toulon, CNRS, LIS, SASV, Marseille, France(a)(b)Laboratoire d’Automatique et de Signaux de Annaba (LASA), University Badji Mokhtar Annaba, 23000 Algeria.

(a)[email protected], (b)[email protected], (c)[email protected]

ABSTRACTThe Systems-on-Chip provide a large capacity for calcu-lation and monitoring, so they are increasingly integratedinto risky processes such as aeronautical and power gen-eration systems. However, embedded systems are subjectto degradation caused by wear, that can be acceleratedby the often hostile environment. This paper proposes amethod of failure prognosis of embedded systems basedon the estimation of the temperature drift under referenceoperating conditions, then the modelling of the drift trendusing a support vector regression model. The remaininguseful life is estimated using the integral of the proba-bility density function of the time to failure. Experimen-tal results, evaluated by performance analysis techniques,show the effectiveness of the proposed approach.Keywords : Remaining Useful Life; support vector re-gression; Fault Diagnosis; Systems-on-Ship

1. INTRODUCTIONThe development of computer science and artificial in-telligence has contributed to the gradual replacement ofseveral functions of management and control in systemsat risk by embedded electronic devices. This evolutionmust be accompanied by the development of methods offault diagnosis and failure prognosis to ensure the op-eration of these systems safely and prevent any dam-age or failure. In this context, part of existing workconsider electronic cards as discrete systems integrat-ing several components, and whose functioning dependson proper operation of all the components, assumingthat there is a strong dependence of operation betweeneach component (Steininger 2000). In this caser, thedeveloped fault diagnosis methods are based on causalmodels such as multi-signal flow graph (Deb, Pattipati,Raghavan, Shakeri & Shrestha 1995), information flowmodel (Sheppard 1996), directed graph (Zhang 2005)and the fault tree (Wang, Shi & Wang 2011). A clas-sification and a comparative analysis of existing faultdiagnosis methods applied on multicore processor ar-chitectures are proposed in Gizopoulos, Psarakis, Adve,Ramachandran, Hari, Sorin, Meixner, Biswas & Vera(2011) where four categories are ditinguished: redun-

dant execution approaches which exploit the inherentreplication of processor cores and threads in a multicoreprocessor architecture (Aggarwal & Ranganathan 2007,LaFrieda, Ipek, Martínez & Manohar 2007, Mukherjee,Kontz & Reinhardt 2002), periodic Built-In Self-Test(BIST) approaches which advocate leveraging the built-in test mechanisms of processors traditionally used formanufacturing testing (Shyam, Constantinides, Phadke,Bertacco & Austin 2006, Foutris, Psarakis, Gizopoulos,Apostolakis, Vera & Gonzalez 2010), dynamic verifica-tion approaches (Austin 1999, Meixner, Bauer & Sorin2007), and anomaly detection approaches (Racunas,Constantinides, Manne & Mukherjee 2007, Wang &Patel 2006, Li, Ramachandran, Sahoo, Adve, Adve &Zhou 2008). The results of the comparative study high-light the effectiveness of the dynamic verification ap-proaches in targeting both transient faults, permanentfaults and design bugs.Several methods of failure prognosis have been devel-oped in recent years. They can be classified in threecategories: modal-based (Feng, Kvam & Tang 2016),data-driven (Nguyen, Djeziri, Ananou, Ouladsine &Pinaton 2016), and hybrid approaches that combine phys-ical knowledge with data analysis for failure progno-sis (Benmoussa & Djeziri 2017, Djeziri, Nguyen, Ben-moussa & M’Sirdi 2017). These methods have been ap-plied to electrical systems, mechatronics and renewableenergy systems, but to our knowledge, there has beenno approach applied to processing units. So, we pro-pose in this paper the application of a failure prognosismethod to a processing unit based on the monitoring ofthe temperature drift generated by the SoC under refer-ence conditions of use. The link between the drift of tem-perature and the degradation process is formally demon-strated and found experimentally in several works (Hong& Kim 2010, Djedidi, Djeziri & M’Sirdi 2018), it cantherefore be used as a health index under reference oper-ating conditions. To detect this drift, a reference model,data-driven, is built, then the trend of this drift is mod-elled by a Support-Vector Regression (SVR), and the on-line projection of the estimate up to a predefined maxi-

Proc. of the Int. Conf. on Integrated Modeling and Analysis in Applied Control and Automation, 2019 ISBN 978-88-85741-31-7; Bruzzone, Dauphin-Tanguy and Junco Eds

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mum drift allows the Remaining Useful Life (RUL) pre-diction.This paper is organised as follows: Section 2 is devotedto an overview of the proposed approach. The system,its operation, its inputs and outputs as well as its mod-elling for the estimation of the temperature are describedin Section 3. In Section 4, the HI generation and eval-uation are presented, then the tend modelling method isdescribed in section 5 and the RUL prediction method insection 6. The results obtained are shown and analysedin Section 7, then a conclusion and perspectives are givenin section 8.

2. RUL PREDICTION SCHEMAThe proposed approach is summarised in four steps asillustrated in Fig. 1. The first step is devoted to thetemperature modelling using an Autoregressive-moving-average (ARMAX) model. The second step concerns theHealth Index (HI) generation, which represent the differ-ence between the measured SoC temperature online andthe estimated one. The trend of the temperature drift ismodelled in the third step using a Support Vector Regres-sion (SVR) with a Gaussian kernel. The RUL expectationis then estimated in the fourth step using the time integra-tion of the Probability Density Function (PDF) until thepredefined time-to-failure.

ProcessingUnit Frequency

MOR

TemperatureEstimator

Temperature

HI Generator

^ TTrend Model

HI ( t)

HI ( t+Δt)RUL

PredictorRUL

Figure 1: Overview of the RUL estimation process

3. TEMPERATURE MODELExperimental tests presented in (Hong & Kim 2010),show that the variation of the temperature of a Sytem-on-Chip (SoC) is influenced by two variables: the powerconsumed and the memory intensity (rate of access to theGDDR), and that it is the memory intensity which is themost influential on the variation of the temperature. Thiswork also shows that the power consumed depends on thethermal voltage, and the thermal voltage is a function ofthe temperature, so there is an algebra-differential loopbetween the temperature and the power. Going back thecause-and-effect links between these two variables andthe load, we find that the first common input is the fre-quency. Thus in the model proposed in this paper, theinputs considered are the frequencies of the CPU and theGPU, the Memory Ooccupation Rate (MOR) and the pre-vious temperature of the SoC. The MOR is chosen be-cause the memory intensity is not measurable.To built a temperature estimator taking into ac-count the regression property of the temperature, anautoregressive–moving-average (ARMAX) model is im-plemented. This models use the regression of inputs andprevious outputs, along with the moving average to esti-mate the current output:

y(k) = P1y(k�1)+ ...+Pny(k�n)

+Q1u(k�1)+ ...+Qmu(k�m)

+ e(k)+H1e(k�1)+ ...+Hre(k� r) (1)

Equation (1) is the linear difference equation of an AR-MAX (n,m,r) (Orders of the model), with y(k) being theoutput to compute, u the exogenous (X) variable or sys-tem input, and e is the moving average (MA) variable(Fung, Wong, Ho & Mignolet 2003). In the case of thiswork, temperature TSoC is the output y(k) to be estimated,and the system input is u(k) = [ f1, ..., f4, fGPU ,MOR].

4. HEALTH INDEX GENERATIONIn this work, the HI is generated by comparing the mea-sured temperature with a reference one estimated by themodel of normal operation presented above. This choiceis motivated by the fact that this approach is well suitedto detect a progressive deviation of the temperature driftfrom its value in normal operation. The HI is calculatedby the following equation:

HI = (Testm(t)�Tmeas(t))/Testm(t) (2)

The launch of the drift trend model for RUL predictionbegins when a drift start is detected. To do so, HI is eval-uated by a statistical method after analysing the data dis-tribution. As the raw HI is normally distributed aroundits mean values, 99% of the data are inside the envelopedelimited by the positive and negative value of mean plusthree times the standard deviation. This property is usedto calculate the normal operation thresholds.Since the drift trend information is contained in the HIaverage and in order to reduce the false alarm rate, theraw HI is processed to extract its moving average HIm.The averaged residual HIm and the normal operatingthresholds are expressed as follows:

8>>><

>>>:

HIm =1n

n

Âi=1

HI ,

th+HI = kHIm +3⇥sHIk ,

th�HI =�kHIm +3⇥sHIk

(3)

sHI is the standard deviation of the HI signal.

5. TREND MODELLINGThe long-term prediction of the evolution of a variablewhose dynamics are unknown and complex, such as theSoC ageing process, can not be done by linear modelslike the ARMA or ARMAX . For efficient prediction it isnecessary to choose a model that supports nonlinear dy-namics and variations of initial conditions. In this con-text, two tools stand out and are widely used, neural net-works and SVR. In this work we choose the SVM as thistool is more suitable for unsupervised learning cases. The


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expression of the prediction by SVR at a step of the evo-lution of the health index is given as follows:

HI(k+1) =N�1

Â[i=(m�1)t+1]

a⇤i K(HI(i),HI(k))+b⇤ (4)

where a⇤i are Lagrange multipliers and t the delay. The

standard SVR toolbox is used without making any spe-cial changes to the prediction of temporal overlays. Thefree parameters, C, e , the size of the kernel (Gaussian),and the dipping dimension m are selected from a com-prehensive search in the parameter space to optimize theperformance of the prediction on the validation set. Theavailable N observations are therefore shared betweentwo sets of training and validation of respective sizes Neand Nv. Values for which the prediction error at a stepon the validation set is minimal are retained for the fi-nal prediction. Once the parameters are fixed, we readthe prediction using all the N observations available. Thepredictions at several steps, ie, for the values (k � N +1),are realized by the ration of the prediction at one step, us-ing the estimated vectors HI(k) at the previous iterationsand not the observations themselves.

6. RUL ESTIMATIONIn this case study, the RUL is expressed as the expectationof the remaining time for HI to reach the threshold T hpand given as follows:

Zt j = inf�

x : HI�t + x) T hp

��HI(t) > T hp�

(5)

RUL(t j) = E�

Zt j

(6)

The Probability Density Function (PDF) of Zt j is ex-pressed as follows:

pd fZt j(x) =

�(T hp �HI(t j))p2.p.x3.s2

.e�

0

@⇣

T hp�HI(t j)�µt j .x⌘2

2.x.s2

1

A

(7)

Thus, RULt j =R +•

0 pd fZt j(x)xdx. The confidence inter-

val from 5% to 95% probability is [RUL�t j ,RUL+

t j ] whereR RUL�t j

0 pd f (x)dx = 0.05 andR RUL+

t j0 pd f (x)dx = 0.95.

7. APPLICATIONThe development board used in this case study is shownin Fig 2. This device can run on Linux and Android, andis equipped with a ARM Cortex-A9 core processor and acore with 1 giga-byte of RAM. This card is not equippedwith sensors to measure the power consumed, so an ex-ternal ammeter and an oscilloscope are used to measurethe power consumed (see Fig 2).

Figure 2: Overview of the application support includingthe development board, the display and the monitoringsystem.

In addition to the real SoC, a SoC simulator, developedand validated with real data in (Djedidi et al. 2018) is em-bedded in the monitoring system. The prediction algo-rithm proposed in this paper is validated using two typesof degradation data: the first type are simulation data gen-erated by the simulator. The second type is experimentaldata obtained on the real SoC over 4 years of use, thesedata are increased by data generated by the simulator toachieve the total failure. In This application case, thetotal failure is considered when the temperature drift isabout 10 � �C.

7.1. Validation of the diagnosis moduleTo validate the diagnostic part of the proposed approach,the algorithms for generating HI, moving-average filter-ing and generating normal operating thresholds are im-plemented in the supervisor. The results obtained areshown in Fig 3) for the normal operation and in Fig 4)for the case of degradation beginning emulated by over-heating the SoC using a light projector of 1000W .

7.2. Validation of the prognosis moduleTo validate the prediction model of the temperature drift,a SoC temperature drift was generated using the simula-tor. The result of the prediction is given in Fig 5. TheSVM model inputs are the actual values of the drift. Theresult of RUL prediction follows the performance of thedegradation prediction, and the real is estimated accu-rately. This first test shows that when the prediction isdone over a short-time (with a permanent update of themeasured drift) the result is very satisfactory with a neg-ligible prediction error.In the second test, it is assumed that the profile of HI isavailable until the time t = 3000h. From this moment, theinputs of the trend model are the values of HI estimatedby the same model at the previous instants. The resultsare given in the Fig 6.The results show that when the prediction is done in themedium term, the estimation error of the RUL is moreimportant but remains acceptable as it represents 5,17%of the real RUL.


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800 820 840 860

Time (s)

-0.04

-0.02

0

0.02

0.04

Tem

pera

ture

resi

duals

r T

(a)

800 820 840 860

Time (s)

-0.01

0

0.01

Ave

raged r

esi

duals

r m

T (b)

800 820 840 860

Time (s)

-1

0

1

Norm

aliz

ed r

esi

duals

R

T (c)

Figure 18: Temperature residuals assessment in normal operation. (a): Raw residuals.(b): Averaged Residuals. (c): Normalized residuals.

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Figure 3: Health index profile in normal operation. (a):Raw HI, (b): Filtered HI, (c): Normalised HI

In the last test, we assume that HI’s profile is availableuntil t = 2500h. From this moment, the inputs of thetrend prediction model are the values of HI estimated bythe model at the previous instants. The results are givenin the Fig 7.The results show that when the prediction is long-term,the estimation error of the RUL is larger but is still ac-ceptable as it represents 8% of the real RUL.

8. CONCLUSION

In this work, a generic method of failure prognosis ofSoC is proposed in two major steps. The first step con-cerns the modelling of the SoC temperature and the gen-eration of a health index characterising the SoC degrada-tion process. This index is the drift of the temperaturewhich represents the difference between the temperaturegenerated by the SoC and a temperature reference gener-ated by the ARMAX model. The second step is a prog-nostic one that concerns the estimation of the evolution ofthe short-term, medium-term and long-term temperaturedrift using a Support Vector Regression model. The RULis estimated in this work using the PDF integration ofthe times to failure. The results obtained show the effec-tiveness of the proposed method on important prognostichorizons.

Figure 24: Evolution of the residuals rT , rmT and RT in the presence of overheating. Thealarm generated at t = 190 s.

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Figure 4: Health index profile at the beginning of thedegradation. (a): Raw HI, (b): Filtered HI, (c): Nor-malized HI

0 1 2 3 4 5 6 7Time (h) 107

-2

0

2

4

6

8

10

12

14

Deg

rada

tion

(°C

)

Real HIPredicted HI

Figure 5: Degradation-trend and RUL prediction usingone-step SVR model from the raw HI

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0 1 2 3 4 5 6 7Time (h 107

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Failure Prognosis of Embedded Systems Based on Temperature