Evaluation of Processor Health within Hierarchical Condition

Monitoring System

Lenka Pavelkov´a and Ladislav Jirsa

Department of Adaptive Systems, Institute of Information Theory and Automation,

Czech Academy of Sciences, Pod Vod´arenskou vˇeˇz´ı 4, Prague, Czech Republic

Keywords:

CPU Usage, Processor Utilisation, Condition Monitoring, Processor Health Evaluation, Bayesian Estimation,

Autoregressive Model, Probabilistic Logic, Binomial Opinion.

Abstract:

This paper proposes an intelligible method for the evaluation of a condition of the central processing unit

(CPU). Proposed method monitors CPU utilisation with respect to user given bounds and provides result in

the form of binomial opinion that serves subsequently for the condition monitoring of an industrial system.

The system in question is described by a hierarchical structure and the examined CPU belongs to the set of its

basic building blocks.

1 INTRODUCTION

Nowadays, fault detection and isolation (FDI) forms

an important part of control systems in engineering

applications (Isermann, 2011). FDI provides an opin-

ion whether the system is in faulty state and indicates

the location and nature of a possible fault. Within

an industrial plant, many possible fault sources ex-

ist, e.g., sensors, actuators, hardware components.

Therefore, monitoring and processing of the system

as a whole is a complex task and it results generally

in a solution tailored for a particular system.

A novel dynamic hierarchical monitoring system

based on probabilistic approach to fault detection is

proposed in (Dedecius and Ettler, 2014). There,

the industrial system of interest is decomposed into

blocks representing individual physical or logical sys-

tem units. For each particular block, a binomial opin-

ion on its condition (health) has to be assessed. These

individual opinions are subsequently combined to ob-

tain the resulting opinion on a total system health.

In this contribution, we focus on an evaluation of

the condition of one particular building block within

above mentioned hierarchical structure, namely cen-

tral processing unit (CPU).

CPU belongs to the most important part of a com-

puter. To evaluate an opinion on its health, the CPU

utilisation U [%] is usually monitored that refers to

a computer’s usage of processing resources. An over-

loaded CPU can slow down a computer unbearably or

a running applications can freeze. On other side, too

low CPU usage could indicate that some application

has been unexpectedly terminated.

Within considered industrial system, only long-

lasting crossing of given bounds indicate possible

troubles. Short overshoots of given boundaries are

acceptable. Therefore, immediate evaluation of a cur-

rent CPU usage provided e.g. by Task Manager in

Windows or htop in Linux is not suitable because

an alarm signalising a bad CPU condition would be

given after each particular bounds crossing.

Many methods and software have been evaluated

that monitor the CPU usage. Some of them serve

merely for observation and possibly for prediction

while others also take an action after CPU overload

detection.

For example, a CPU usage prediction method

based on the linear regression technique is presented

in (Farahnakian et al., 2013). The proposed approach

approximates the short-time future CPU utilization

based on the history of usage. It is employed to

predict over-loading and under-loading of CPU. In

(Wang et al., 2012), Kalman ﬁlter is adapted to es-

timate CPU consumption from observed data. The

paper (Akhtar and Sidek, 2013) proposes method for

maximum CPU utilization using bandwidth alloca-

tion.

To name some software samples, CPU Utilization

Monitor

is a program that provides a means to mon-

itor and log CPU usage for any period of time. The

http://sourceforge.net/projects/cpu-usage-log/

667

Pavelková L. and Jirsa L..

Evaluation of Processor Health within Hierarchical Condition Monitoring System.

DOI: 10.5220/0005578106670671

In Proceedings of the 12th International Conference on Informatics in Control, Automation and Robotics (ANNIIP-2015), pages 667-671

ISBN: 978-989-758-122-9

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

optionally produced log ﬁle is tab delimited and eas-

ily importable e. g. into MS Excel for further trending

and analysis. A software for music production, pro-

gram Reaktor

, monitors CPU usage during its per-

formance. When the CPU load reaches a certain value

limit, Reaktor will shut down audio processing to as-

sure that the system is not frozen by a processor over-

load.

Despite of highly elaborated tools in this ﬁeld

to monitor CPU performance, none is compatible

with a uniﬁed interface of building blocks enabling

a generic modularity.

This paper proposes such a method. The idea is to

combine consistently statements on condition of log-

ical blocks within a hierarchically composed system

using the binomial opinion(Josang, 2008)as the com-

mon interface. This approach is then applicable for

any logical structure provided that condition of each

logical block is described by the binomial opinion.

The evaluation the CPU’s condition is based on an

estimation of U using a probabilistic autoregressive

model and on the evaluation of obtained estimates by

considering user given bounds on CPU usage.

The paper is organised as follows. Section 2.1

introduces basics of hierarchical monitoring system

which comprises CPU as one of its basics parts. Sec-

tion 2.2 presents the model of a CPU usage. The eval-

uation of CPU condition is described in Section 2.3.

Section 2.4 provides an algorithmic summary. Exper-

iments with simulated data are presented in Section 3.

Section 4 concludes the paper.

Throughout, the transposition is marked

′

∗

denotes a set of z-values,

is the value of z at discrete-time instant t ∈ t

∗

{1, 2, . .. , T}, T < ∞,

denotes the estimate of X in time t.

The symbol f denotes probability (density) function

(p(d)f) distinguished by the argument names; no for-

mal distinction is made among a random variable, its

realisation and a pdf argument.

2 CPU USAGE MONITORING

The uniﬁed interface to describea condition of a mon-

itored unit as a block in a structure is linked with the

modelling of CPU load.

http://www.native-instruments.com/en/products/

komplete/synths/reaktor-5/

2.1 Basics of Hierarchical Condition

Monitoring

The examined CPU is a part of the above mentioned

probabilistic FDI system (Dedecius and Ettler, 2014),

where the investigated industrial system is decom-

posed into a set of interconnected individual compo-

nents called basic blocks. To each particular block,

a binomial opinion (1) on its condition has to be as-

signed. The basic blocks are interconnected using

principles of the subjective logic (SL) (Josang, 2008).

In this way, a single opinionon the health of the whole

monitored system is obtained by combining opinions

on the health of the individual basic blocks.

In SL, the representation of uncertain probabili-

ties is based on a belief model. A subjective binomial

opinion expresses a subjective belief of a particular

subject about the truth of proposition including a de-

gree of uncertainty. For x ∈ { 0, 1}, a binomial opin-

ion about the truth of proposition x = 1 is the ordered

quadruplet

= (b, d, u, a) (1)

where

b is the belief of x being true, i. e. b = f(x = 1),

d is the belief of x being false (disbelief), i. e. d =

f(x = 0),

u is the uncertainty, i. e. no opinion on x being true or

false,

a is the base rate (corresponds to a prior information).

These components are interpreted as corresponding

probabilities. They satisfy additivity b + d + u = 1

and it holds b, d, u, a ∈ [0, 1].

The expected value of b is

= b+ au . (2)

Here, we consider non-informative prior, i.e. a = 0.5.

Particularly, belief, disbelief and uncertainty rep-

resent opinion on situation that the processor load is

within the requested bounds.

2.2 Model of CPU Utilisation

A CPU utilisation U

is modelled by the autoregres-

sive model, t ∈ t

∗

f(U

|ψ

, ϑ, r) ≡ N

(ψ

′

ϑ, r) (3)

√

2πr

exp



−

−ψ

′

ϑ)



where

(ψ

′

ϑ, r) means Gaussian pdf with the expected

value ψ

′

ϑ and the noise variance r,

= [U

t−1

, . . . , U

t−n

] is the regression vector con-

sisting of n previous values of U,

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668

ϑ is a vector of unknown regression coefﬁcients of

the length n,

Estimation of the Gaussian model, i.e. estimation

of ϑ and r, is performed using sufﬁcient statistics V

and ν

which update according to

= V

t−1

+ Ψ

′

, (4)

= ν

t−1

+ 1,

where Ψ

= [y

, ψ

′

]

′

and V

, ν

are given by the prior

pdf.

Matrix V

can be decomposed as a product V =

′

DL, where L is a lower triangular matrix with unit

diagonal and D is a diagonal matrix.

The moments of the parameters’ posterior pdfs are

given by

E[ϑ|L, D, ν] = L

−1

dψ

≡

ϑ, (5)

E[r|L, D, ν)] =

ν−2

≡ ˆr. (6)

where L

, L

dψ

, D

are obtained by the following de-

composition of L and D

L =



1 0

dψ



, D =



0 D



. (7)

The point output prediction is

′

. (8)

For computational details, see (K´arn´y et al., 2006).

2.3 Evaluation of CPU Condition

After estimating of CPU usage, it remains to assign

the required opinion on the CPU health. To declare

that CPU is health, CPU utilisation U has to be within

interval

;U). (9)

For the purpose of hierarchical monitoring system de-

scribed in Section 2.1, the information about CPU

health is required in the form of binomial opinion (1).

Direct evaluation based on comparing estimates

ϑ (5)

and respective point predictions

with bounds U

and U does not take into account the admissible oc-

casional crossings of given bounds.

We propose the following procedure that treats

these events. It uses σ conﬁdence intervals given by

boundaries

3σ

′

−3σ, U

3σ

′

+ 3σ (10)

where σ =

√

ˆr is the standard deviation, ˆr is given by

(6).

The values of b, d, u in binomial opinion (1) are

obtained by evaluating of boundaries (10) with re-

spect to user given bounds U

and U (9) according to

the Table 1. When constructing this Table, we tried to

imitate a decision-making of a real technical operator

who examines the estimation results personally. Note

that the value of u expresses user uncertainty concern-

ing his/her opinion.

2.4 Algorithmic Summary

Initialisation

- enter bounds U

, U (9)

- set t = 0 and end time T

On-line Phase

1. t = t + 1

2. measure data U

3. update statistics ν

, V

(4)

4. estimate ϑ, r according to (5), (6)

5. compute boundaries L

3σ

, U

3σ

(10)

6. assign b, d, u based on comparingL

3σ

with

, U according to the Table 1

7. IF t < T, GO TO 1

3 EXPERIMENTS

Experiments with simulated data are presented to il-

lustrate the proposed method of assigning an opinion

on CPU condition. We consider bounds (9) as fol-

lows, U

= 10, U = 90. CPU usage U is modelled by

(3) with n = 2.

3.1 Data with Outliers

We simulate the set of Us that meets given bounds

(U, U) including two outliers. The simulated data

with highlighted estimates of σ-intervals are in the

upper part of Figure 1. The assigned ω (1) is in its

bottom part.

3.2 Constantly Changing Data

We simulate monotonically changing U with a ﬂat

maximum that is greater than the upper bound

The simulated data with highlighted estimates of σ-

intervals are depicted in the upper part of Figure 2.

The assigned ω (1) is in its bottom part. Figure 3

shows a zoomed part of Figure 2.

EvaluationofProcessorHealthwithinHierarchicalConditionMonitoringSystem

669

Table 1: Assignment of b, d, u (1) depending on L

3σ

and U

3σ

(10).

3σ

∈ h0, U) L

3σ

∈ hU;Ui L

3σ

∈ (U;100i

3σ

∈ h0, U) U

3σ

∈ hU;Ui U

3σ

∈ (U;100i U

3σ

∈ hU;Ui U

3σ

∈ (U;100i U

3σ

∈(U;100i

b 0 0.5 0 1 0.5 0

d 1 0 0 0 0 1

u 0 0.5 1 0 0.5 0

50 100 150 200

time

data, bounds, L

, U

0 50 100 150 200

0.2

0.4

0.6

0.8

time

u, b, d

Figure 1: Simulated data with outliers: On top: CPU us-

age (circles) with highlighted boundary

U (9) (dashed line)

and L

3σ

, U

3σ

(10) (full line). Below: The course of b (thin

line), d (thick line), u (dashed line) in ω (1) according to

Table 1.

3.3 Discussion

A binomial opinion ω = (b, d,u, a) on the CPU con-

dition, see (1), was evaluated. The components of the

binomial opinion are interpreted as probabilities that

the monitoredblock operates correctly (b), incorrectly

(d) or there is an uncertainty about it (u). We used two

types of simulated data.

The experiments show that single overshoots in-

crease temporarily an uncertainty u in ω but they do

not inﬂuence the disbelief d.

50 100 150 200

100

time

data, bounds, L

, U

0 50 100 150 200

0.2

0.4

0.6

0.8

time

u, b, d

Figure 2: Simulated data: On top: CPU usage (circles)

with highlighted boundary

U (9) (dashed line) and L

3σ

(10) (full line). Below: The course of b (thin line), d (thick

line), u (dashed line) in ω (1) according to Table 1.

Concerning the permanent crossing of

U, the dis-

belief d in ω is set only after both L

3σ

and U

3σ

(10)

are outside the requiredarea, which indicates the CPU

overload. Otherwise, uncertainty u is increased only.

These results are in the accordance with con-

clusions that might be reached by the operator, i.e.

when one of the σ-bounds is outside the required

area (U

, U) and the other one is inside, then opera-

tor could be uncertain about the CPU condition.

Use of the Gaussian noise may cause that the

boundaries of the 3σ conﬁdence interval exceed the

physically meaningful set [0%, 100%]. This property

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670

150 155 160 165 170 175 180

time

data, bounds, L

, U

150 155 160 165 170 175 180

0.2

0.4

0.6

0.8

time

u, b, d

Figure 3: Simulated data - zoomed part of Figure 2: On

top: CPU usage (circles) with highlighted boundary

U (9)

(dashed line) and L

3σ

, U

3σ

(10) (full line). Below: The

course of b (thin line), d (thick line), u (dashed line) in ω

(1) according to Table 1.

is practically not relevant because the boundaries of

interest are U

and U.

4 CONCLUDING REMARKS

This paper proposes a straightforward method for

evaluation of the CPU condition that is expressed in

the form of binomial opinion, including uncertainty.

The binomial opinion plays a role of a uniﬁed inter-

face of building blocks that can be organized in a log-

ical structure. The proposed method uses an autore-

gressive probabilisticmodel for modelling CPU usage

U. The parameters of this model are continuously es-

timated and 3σ intervals are constructed around the

point output predictions. Boundaries of these inter-

vals are compared with required CPU usage bounds

and U. In this way, a binomial opinion on CPU

condition is easily inferred using the assignment ta-

ble. This table is constructed in accordance with the

way of operator’s decision-making. This opinion can

be directly used within hierarchical condition mon-

itoring (Dedecius and Ettler, 2014) where CPU be-

longs to set of basic building blocks.

Future works can focus on proposing of a func-

tion that assigns b, d, u continuously, depending on

the distance between boundaries of 3σ intervals and

bounds U, U. The proposed assignment table might

be in fact too rough in some cases because the as-

signment of b, d, u switches between several discrete

values. Models with bounded noise can be taken into

consideration as well.

ACKNOWLEDGEMENTS

The research project is supported by the grant M

SMT

7D12004 (E!7262 ProDisMon).

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