Change Point Detection with Applications to Wireless Sensor Networks

UNIVERSITATIS ACTA UPSALIENSIS

Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1777

Change Point Detection with Applications to Wireless Sensor Networks

MARKUS ERIKSSON

ISSN 1651-6214

Dissertation presented at Uppsala University to be publicly examined in Room 80101, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, Friday, 10 May 2019 at 08:30 for the degree of Doctor of Philosophy. The examination will be conducted in English. Faculty examiner: Professor Idris Eckley (Department of Mathematics and Statistics, Lancaster University).

Abstract

Eriksson, M. 2019. Change Point Detection with Applications to Wireless Sensor Networks.

Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1777. 102 pp. Uppsala: Acta Universitatis Upsaliensis. ISBN 978-91-513-0580-6.

In this thesis work we develop a new algorithm for detecting joint changes in statistical behavior of multiple, simultaneously recorded, signals. Such signal analysis is commonly known as multivariate change point (CP) detection (CPD) and is of interest in many scientific and engineering applications.

First we review some of the existing CPD algorithms, where special attention is given to the Bayesian methods. Traditionally, many of the previous works on Bayesian CPD have focused on sampling based methods using Markov Chain Monte Carlo (MCMC). More recent work has shown that it is possible to avoid the computationally expensive MCMC methods by using a technique that is reminiscent of the forward-backward algorithm used for hidden Markov models. We revisit that technique and extend it to a multivariate CPD scenario where subsets of the monitored signals are affected at each CP. The extended algorithm has excellent CPD accuracy, but unfortunately, this fully Bayesian approach quickly becomes intractable when the size of the data set increases.

For large data sets, we propose a two-stage algorithm which, instead of considering all possible combinations of joint CPs as in the fully Bayesian approach, only computes an approximate solution to the most likely combination. In the first stage, the time series are processed in parallel with a univariate CPD algorithm. In the second stage, a dynamic program (DP) is used to search for the combination of joint CPs that best explains the CPs detected by the first stage. The computational efficiency of the second stage is improved by incorporating a pruning condition which reduces the search space of the DP.

To motivate the algorithm, we apply it to measurements of radio channels in factory environments. The analysis shows that certain subsets of radio channels often experiences simultaneous changes in channel gain.

In addition, a detailed statistical study of the radio channel measurements is presented, including empirical evidence that radio channels exhibit statistical dependencies over long time horizons which implies that it is possible to design predictors of future channel conditions.

Keywords: Change Point Detection, Signal Processing, Dynamic Programming

Markus Eriksson, Department of Engineering Sciences, Signals and Systems Group, Box 528, Uppsala University, SE-75120 Uppsala, Sweden.

© Markus Eriksson 2019 ISSN 1651-6214 ISBN 978-91-513-0580-6

urn:nbn:se:uu:diva-377640 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-377640)

Sammanfattning

Denna avhandling handlar om modellering av sekventiell data som innehåller brytpunkter (eng. change points), vilket är punkter i datasekvensen där obser- vationerna genomgår en förändring i statistiska egenskaper. Med data menas en sekvens av observationer av vad som helst som kan mätas eller represen- teras med siffror, till exempel inspelningar av trafikintensitet, opinionsunder- sökningar eller årlig BNP. Sådan data är ofta sorterad efter tid och då kallas sekvensen av observationer för en tidsserie. Om vi vet vad tidsserien represen- terar kan vi i vissa fall ge en intuitiv beskrivning av dess allmänna beteende.

Källan till den intuitionen är ofta förkunskaper om det fenomen som genererar tidsserien. Till exempel, om tidsserien innehåller mätningar av trafikintensitet vet vi att det kommer att finnas trender i sekvensen där trafiken är intensiv under morgon och kväll när folk pendlar till och från jobbet, men mer stilla mellan dessa perioder. Sådana trender ger upphov till beroenden mellan ob- servationerna där observationer som ligger nära varandra i sekvensen antar ungefär samma värden. Statistiska modeller som formaliserar sådana förkun- skaper med hjälp av matematik har attraherat mycket forskningsintresse efter- som modellerna kan vara till stor hjälp när man försöker förutse framtida vär- den av tidsserien. Men när fenomen övervakas över lång tid är det vanligt att de statistiska modellerna bara är giltiga under kortare perioder, och i så fall är det viktigt att identifiera punkter i sekvensen då det statistiska beteendet förändras, alltså att utföra brytpunktsdetektering.

Datorprogram som utför brytpunktsdetektering har använts i en rad olika tillämpningar såsom klimat- och miljöforskning, ekonomi, datornätverk, bi- nomik samt modellering av radiokanaler i industriella trådlösa sensor- och ak- tuatornätverk. Den senare tillämpningen kommer att vara i fokus i detta arbete där vi först utvecklar en ny metod för brytpunktsdetektering i så kallade multi- variata tidsserier, vilket innebär att data består av flera simultant inspelade sig- naler. Den nya metoden används för att studera radiokanaler i fabriksmiljöer.

Den analysen motiveras av att information om vilka kanaler som ofta genomgår samtidiga förändringar i kanalförhållanden kan vara till stor hjälp för att organ- isera trafiken så att dataöverföringen sker så tillförlitligt som möjligt.

Denna avhandling har två delar, där den första delen består av sju inledande kapitel och den andra delen innehåller tre artiklar. Syftet med den första delen är att sätta artiklarna i ett bredare perspektiv och kapitlen är disponerade på följande sätt:

Kapitel 1

I det första kapitlet beskrivs huvudsyftet med avhandlingen: design av algorit-

mer, alltså datorprogram, för brytpunktsdetektering. De viktigaste bestånds-

delarna av sådana algoritmer demonstreras med hjälp av ett fiktivt dataset.

Kapitel 2

Här introduceras industriella trådlösa nätverk och vi beskriver även nyttan med att detektera brytpunkter i radiokanalsmätningar. Kapitlet avslutas med en beskrivning av en mätkampanj där radiomiljöerna i två fabriker uppmättes med hjälp av ett nätverk av trådlösa noder.

Kapitel 3

I detta kapitel ges en översikt av olika metoder för brytpunktsdetektering. My- cket av diskussionen är inriktad på att beskriva för- och nackdelar med de olika metoderna, vilka lättast inses genom en beskrivning av deras underliggande statiska modeller.

Kapitel 4

Här presenterar vi en ny metod för att detektera brytpunkter i multivariata tidsserier där endast en delmängd av de inspelade signalerna påverkas vid varje brytpunkt. Resultaten visar att metoden har god noggrannhet, men tyvärr så är dess praktiska tillämpbarhet begränsad eftersom beräkningstiden växer väldigt snabbt när datamängden ökar. För användare som vill analysera stora dataset föreslår vi istället en betydligt snabbare, men inte lika noggrann, metod och den beskrivs mer detaljerat i artikel II.

Kapitel 5

I detta kapitel undersöker vi noggrannheten för en approximation som utgör grunden till den metod som presenteras i artikel II. Det visar sig att, så länge som antalet brytpunkter är litet i förhållande till det totala antalet observationer i tidsserien, så kan felen från approximation försummas.

Kapitel 6

Det näst sista kapitlet presenterar en fallstudie som exemplifierar några av de olika typer av tidsserier som kan analyseras med metoderna som beskrivs i kapitel 4 och artikel II.

Kapitel 7

Det sista kapitlet sammanfattar den första delen av avhandlingen.

Den andra delen av avhandlingen består av följande artiklar.

Artikel I

Markus Eriksson och Tomas Olofsson "On Long-Term Statistical Dependences in Channel Gains for Fixed Wireless Links in Factories", IEEE Transactions on Communications, juli 2016

I denna artikel analyserar vi radiokanalsmätningar med hjälp av en metod som identifierar brytpunkter. Vi visar även att det finns statistiska beroenden i kanal kvalite före och efter de identifierade brytpunkterna, vilket antyder att det går att prediktera radiokanaler.

Artikel II

Markus Eriksson och Tomas Olofsson "Computationally Efficient Change Point Detection in Multivariate Time Series", IEEE Transactions on Signal Process- ing, januari 2019

I denna artikel utvecklar vi den approximativa metoden för brytpunktsdetek- tering och jämför dess prestanda med två liknande metoder.

Artikel III

Markus Eriksson och Tomas Olofsson "Multivariate Change Point Detection with Optimality Preserving Pruning", Manuskript.

I det här manuskriptet beskriver vi hur man implementerar metoden från Ar-

tikel II mer effektivt genom att använda så kallade beskärningsmetoder. Vi

presenterar också en detaljerad jämförelsestudie av olika metoder för att de-

tektera brytpunkter i multivariata tidsserier.

Acknowledgment

First and foremost, I would like to express my gratitude to my supervisor Tomas Olofsson. I am grateful for the generous amount of time you have spent on training me and your enthusiasm for the subject has been a great source of inspiration during my years as a PhD student.

I would also like to thank Professor Anders Ahlén for offering me a place in his research group and giving me the opportunity to study the topics that I found interesting. Thank you for always taking the time to discuss ideas.

To my colleagues at the Signals and Systems group, the UNO group and the CoRe group: Thank you for all the intriguing and distracting discussions.

I owe special thanks to Professor Mikael Sternad for keeping my spirit up.

I am very grateful to Professor Paul Fearnhead for inviting me to Lancaster University. During my time there I met a lot of great people and engaged in many interesting research discussions. My office mates at the STOR-i group really made me feel at home.

During this thesis work I have had the privilege to be part of an applied research project and special thanks go to Johan Åkerberg and Thomas Lindh for making that experience incredibly rewarding.

Family and friends make the effort worthwhile. I would like to thank my

mother Inga-Lill, my father Ingemar, and my sister Jenny. You have always

been there for me and I am very fortunate to have you in my life. I owe it all

to you.

List of papers

This thesis is based on the following papers, which are referred to in the text by their Roman numerals.

I Markus Eriksson and Tomas Olofsson "On Long-Term Statistical Dependences in Channel Gains for Fixed Wireless Links in Factories", IEEE Transactions on Communications, July 2016.

II Markus Eriksson and Tomas Olofsson "Computationally Efficient Change Point Detection in Multivariate Time Series", IEEE

Transactions on Signal Processing, January 2019.

III Markus Eriksson and Tomas Olofsson "Multivariate Change Point Detection with Optimality Preserving Pruning", Manuscript.

Reprints were made with permission from the publishers.

Contents

Sammanfattning

iii

Acknowledgment

vi

1 Introduction

15

1.1 Outline of the thesis

20

2 Communication over wireless industrial networks

24

2.1 Background and motivation

24

2.2 Improving the data throughput using JCPD

25

2.2.1 Radios in IWSANs

25

2.2.2 The wireless data transfer

26

2.2.3 Revealing the network hierarchy using JCPD

28

2.3 Switching network state models and closed loop control

32

2.4 Measurement campaigns

33

3 Change point detection

38

3.1 CPD paradigms

39

3.1.1 Likelihood ratio detection

40

3.1.2 Searching for multiple CPs using binary segmentation 41 3.1.3 Criterion-based CPD

42

3.1.4 Hidden Markov models

46

3.2 Bayesian algorithms

47

3.2.1 Bayesian inference

48

3.2.2 CPD using the Bayesian framework

51

3.2.3 Bayesian CPD using MCMC

51

3.2.4 Avoiding the Markov chain in MCMC

52

3.2.5 The perfect simulation algorithm

53

3.2.6 Deciding on the final segmentation

57

3.2.7 On-line algorithms

58

3.3 Subset multivariate change point detection

59

3.3.1 Prior works on SMCPD

59

4 Asymptotically exact Bayesian SMCPD

63

4.1 Notation

63

4.2 The first stage of SMPS

65

4.3 The second stage of SMPS

66

4.4 Illustrative Example

67

4.4.1 Data generation model: Independent normal

distribution

68

4.4.2 Synthetic data

69

4.5 Computational complexity

71

4.6 Discussion

72

5 Approximate expression for the CP posterior

75

5.1 Introductory examples

76

5.2 Loss of information when CPs are approximated as temporally independent

77

6 Case studies

81

6.1 Introduction

81

6.2 Binary observations

82

6.2.1 Data generation model

83

6.2.2 JCPD in binary observations

84

6.3 Pooling property

86

6.4 Gamma distributed observations with varying mean

87

6.4.1 Data generation model

88

6.4.2 Sequential Bayesian estimator

89

6.4.3 Synthetic data

92

6.4.4 Real data

93

7 Conclusions

96

References

98

Nomenclature

a Scalar value

a Vector

a s:t Vector with values between indices s and t [a b] Closed interval between a and b

a ⁰ Transpose

Y \ X Set difference

I Y (y) Identity function which takes value 1 if y ∈ Y, and 0 oth- erwise

O( f (x)) = g(x) k f (x)/g(x)k bounded as x → ∞

P(x) Probability of x. Note that we do not make a distinction between variables and outcomes and that a probability distribution is associated with a random variable through its argument

E(·) Expected value

Acronyms

AR Autoregressive.

BER Bit Error Rate.

BS Binary Segmentation.

CC Change Configuration.

CNV Copy Number Variants.

CP Change Point.

CPD Change Point Detection.

CUSUM Cumulative Sum.

DP Dynamic Programming.

DSSS Direct Sequence Spread Spectrum.

FMCPD Fully Multivariate Change Point Detection.

GHQ Gauss-Hermite Quadrature.

HDP Hierarchical Dirichlet Process.

HMM Hidden Markov Model.

i.i.d. Independent and Identically Distributed.

IWSAN Industrial Wireless Sensor and Actuator Network.

JCPD Joint Change Point Detection.

KLD Kullback-Leibler Divergence.

MAP Maximum a posteriori.

MC Monte Carlo.

MCMC Markov Chain Monte Carlo.

ML Maximum Likelihood.

OP Optimal Partitioning.

pdf probability density function.

PRR Packet Reception Rate.

PS Perfect Simulation.

RJMCMC Reversible Jump Markov Chain Monte Carlo.

RR Round Robin.

RSS Received Signal Strength.

SMC Sequential Monte Carlo.

SMCPD Subset Multivariate Change Point Detection.

SMPS Subset Multivariate Perfect Simulation.

SNR Signal to Noise Ratio.

UCPD Univariate Change Point Detection.

1. Introduction

This thesis deals with modeling sequential data containing change points (CPs), which are points in the data sequence where the observations undergo a change in statistical properties. By data we mean a sequence of observations of any- thing that can be measured or represented by numbers, e.g., recordings of traffic intensity, polls, or annual crop yield. Such data is typically ordered by time and then the sequence of observations is referred to as a time series.

If we know what the time series represent, then we will in some cases be able to give an intuitive description of its general behavior. The source of that intuition is often prior knowledge of the phenomenon that generates the time series. As an example, if the time series contain measurements of traffic inten- sity, then we know that there will be trends in the data where the traffic is in- tense during the morning and evening commute, and more quiescent between these periods. Such trends induce dependencies between the observations in the sense that observations that are close in the sequence should have roughly similar values. Developing good statistical models which formalize such prior knowledge using mathematics has attracted a lot of research interest since the models can, for instance, be very helpful when predicting future values of the time series. However, when systems are monitored over long time periods, the statistical model might only be valid for shorter periods, and in this case it becomes important to identify points in time where the statistical behavior change, i.e., to perform CP detection (CPD).

We illustrate the elements of CPD by elaborating on the traffic intensity example. Suppose that a group of researchers is interested in studying traffic intensity and has decided to manually count the number of passing cars on a specific road. The morning rush hour is of particular interest, so between 7AM and 9AM they count the number of cars that pass per minute, and the result- ing time series is illustrated in Figure 1.1. By visual inspection of the figure, two conclusions can immediately be drawn. The first is that there is a natural variability where measurements obtained at different times result in different values. Second, we note that there is a clear change in intensity at around 8AM, but the natural variability makes it difficult to judge exactly where the change occurs. Also, we suspect that the variability between two measure- ments generally increases with their temporal separation since it increases the probability that the traffic intensity has transitioned from the quiescent period to rush hour, or vice versa.

Such behavior is quite common for many types of time series since a se-

quence of observations often can be understood as being generated by some

Time

Number of cars /min

07:30 AM 08:00 AM 08:30 AM 0

1 2 3 4 5 6 7 8 9 10

Figure 1.1. Time series of passing cars.

phenomenon that transitions between different generative modes. In such sce- narios, it is often possible to observe regular behavior in the recorded data, manifested by periodic changes in mean, volatility, or some other statistical property. For instance, it is likely that an increase in traffic intensity will be observable at the same time the following day as well, although individual values will be different. Thus, one motivation for studying observational data is that it can contain valuable information about the mechanisms of the under- lying phenomenon.

Remark 1.1. Detecting CPs in time series might expose periodicities and other types of regular behavior which can be very helpful for either, trying to make sense of the data, or predicting future values of the time series.

In order to search for regularities in data sequences using a computer, the first step is to design an appropriate mathematical model of the sequence. An intuitively appealing structure is to use a model that consists of two compo- nents, where the first component describes the small scale variability in each generative mode and the second component describes the transitions between the different modes. The main building block of such statistical models are random variables and these are governed by certain probability distributions.

As an example, for observations that have been obtained by counting out- comes of events, such as passing cars, the Poisson distribution, Po(ρ), accu- rately model their random behavior, where ρ is a model parameter represent- ing the expected number of passing cars per minute. Thus, if x t denotes the number of cars that passed during the tth minute, then Po(ρ) defines a math- ematical model of the probabilities that specific values of x t will be observed.

We denote this as,

x t ∼ Po(ρ). (1.1)

However, the Poisson distribution is based on an assumption that the ex- pected rate of passing cars is constant for all t, which is not consistent with the fact that the traffic intensity will vary during the day. This leads to the second part of the model where the switching behavior between different generative modes is introduced by letting ρ vary over time, emphasized by writing ρ _t . One option is, for instance, to assume that ρ t abruptly changes value at a set of CPs. Typically, neither the positions of CPs nor the values of ρ _t are known to the researchers beforehand, and to complete the statistical model, they would like to estimate both of them using the observations. Unfortunately, such an estimator is ill-posed since any combination of CPs and values of ρ _t could be responsible for generating the data, for the simple reason that the Poisson dis- tribution assigns non-zero probability to any x _t irrespective of ρ _t . It turns out that this problem can be solved by imposing some model assumption on ρ t , say, requiring that it is piecewise constant between the CPs.

Remark 1.2. Most algorithms compute the estimated positions of CPs by pooling information from two different sources: (i) The recorded observa- tions, and (ii) a model assumption. The objective is then to find the positions of CPs that best explains the observed data, conditioned on the model. This property is key for the CPD problem to have a well defined solution.

Proceeding with our discussion on the elements of CPD, imagine that two other members of the research group were positioned at two other roads, also noting the number of passing cars during the same time period. All three time series are illustrated in Figure 1.2, and we see that Road 2 experienced a si- multaneous increase in traffic intensity with Road 1. Conversely, the traffic intensity on Road 3 was constant, which might be explained by its geograph- ical location where it is not a popular choice for commuting to work. It can, however, be a popular choice in some other scenario, say, getting to the local football stadium. Periodically scheduled games will then induce other types of periodicities in the recorded traffic intensity, potentially affecting a different subset of roads. Thus, the third element of CPD that we treat in this work is expressed in the following remark:

Remark 1.3. Including multiple time series in the signal analysis might open up new and interesting ways of extracting information from the data. For in- stance, transitions between generative modes of the underlying phenomenon might only affect a subset of the monitored time series. Identifying these sub- sets can act as a type of fingerprint where, if we can sort out which subset that is affected at what time, periodicities and other types of temporal patterns might be easier to distinguish.

For future reference, a time series that consists of scalar observations is

termed a univariate time series. If instead multiple, simultaneously recorded,

Road 3 Road 2

Time

Road 1

Number of cars / min

07:30 AM 08:00 AM 08:30 AM

0 2 4 6 8

0 2 4 6 8

0 2 4 6 8

Figure 1.2. Three time series of passing cars where only Road 1 and Road 2 are affected by the morning rush hour.

signals are available, then the time series is referred to as a multivariate time series. Figure 1.1 and Figure 1.2 are examples of univariate and multivariate time series, respectively. Also, a list of CPs is called a segmentation since it partitions the time series into contiguous segments of homogenous behavior.

Therefore, performing CPD is sometimes referred to as segmenting the time series.

We conclude our presentation of the elements of CPD with a discussion

on model choice. During this thesis work it will turn out that it is fairly

straightforward to compute the most likely positions of CPs conditioned on

a predetermined model structure. However, deciding on which model to use

is sometimes a more intricate problem. So far, the considered time series have

contained CPs that led to clearly visible, abrupt, changes in statistical prop-

erties. A more realistic scenario is illustrated in Figure 1.3 where the traffic

intensity increases gradually from the quiescent period to rush hour. Obvi-

ously, the previously proposed model where ρ _t is piecewise constant between

CPs is no longer consistent with the data and a more appropriate choice would

be to model ρ _t as piecewise linear between the CPs, illustrated by the red line

in the figure. Choosing the right mathematical model is important since it af-

fects our perception of where the CPs are located. As an example, if we apply

a CPD algorithm to the time series in Figure 1.3 conditioned on an assump-

tion that ρ t is piecewise constant, it is likely that the algorithm will introduce

extra CPs to compensate for the poor model fit during the period of slowly

increasing traffic intensity, illustrated by the black line in the figure.

Time

Number of cars /min

07:30 AM 08:00 AM 08:30 AM 0

5 10 15

Figure 1.3. Time series of passing cars where the increase in traffic intensity occurs gradually. The red dashed line indicates the true underlying, piecewise linear, ex- pected number of passing cars. The black dotted line indicates an attempt to fit a piecewise constant function to the data.

Remark 1.4. The model structure should be carefully selected so that there exists some combination of CPs and parameter values that accurately de- scribes the observed data. For a poor choice of model where no values of these unknowns are consistent with the data, the estimated CPs will simply be positioned at the least bad time indices. The problem is exacerbated by the general difficulty of diagnosing a poor model fit.

Remark 1.4 is particularly important in scenarios where the CPD algorithm is used to search for periodicities in the time series since, if the algorithm introduces additional CPs to compensate for the poor model fit, then these erratic estimates may conceal the regularities that are present in the data.

The focus of this thesis work is to explore the above described elements of

CPD and survey some of the existing literature. As in the traffic intensity ex-

ample, we will occasionally demonstrate some aspects of CPD using synthetic

data since it simplifies the discussion compared to using real data. However,

the reason why so much research effort has been directed towards developing

CPD algorithms in recent years is due to their practical applicability for study-

ing real data sets such as, e.g., recordings of human motion [61], the dance of

honey bees [59], maneuvering targets [31], audio [82, 29], and climate data

[81]. Since increasingly many applications are working with multivariate time

series, developing algorithms which detect simultaneously occurring CPs in

such data has been a particularly active research area. The developed algo-

rithms have, for instance, been used to study DNA sequences [6], acoustic

recordings [62], and telecommunications data [7].

Here we will develop a new multivariate CPD algorithm and use it to study measurements of received signal strength (RSS) for transmissions over wire- less channels in an industrial wireless sensor and actuator network (IWSAN).

As will be described in more detail in Chapter 2, the motivation for the analysis is that information on which channels that are likely to undergo simultaneous CPs can be very helpful when organizing the communication in an IWSAN.

Thus, the main contribution of this thesis is a framework for detecting such changes and we will refer to the suggested algorithm as the joint CPD (JCPD) algorithm.

Loosely speaking, the JCPD algorithm can be described as follows: It con- sists of two stages where the first preprocessing stage applies the Bayesian univariate CPD (UCPD) algorithm that was developed in [26], separately to each time series. We refer to the preprocessing algorithm as Perfect Simula- tion (PS). Bayesian estimation methods will be surveyed in Chapter 3, but in short, the Bayesian approach allows us to associate an uncertainty estimate to each detected CP so that, in addition to identifying its most likely position, also identifies other likely alternative positions. Thus, the output from a Bayesian method is more informative compared to CPD methods which only estimate the most likely position of each CP, referred to as a point estimate. It turns out that the uncertainty information is very helpful in the second stage where the output from the analysis of each time series is combined into an estimate of the positions of CPs in all time series using all the available data.

In the second stage, the final estimate of the positions of CPs in all time se- ries is computed by maximizing a segmentation criterion which is a function of the uncertainty estimates computed in the preprocessing stage. This max- imization step is performed by a computationally efficient dynamic program- ming (DP) algorithm. Thus, the main novelty of this work is the combination of two fast algorithms, PS and DP, to solve the notoriously computationally intensive problem of detecting CPs in multivariate time series. The JCPD algorithm can be used to detect CPs in any time series where it is possible to compute, or at least numerically approximate, the likelihoods for the segments of observations between the CPs.

In order to put our proposed JCPD algorithm into perspective, we will dur- ing this work survey other methods that can be used to search for either single or multiple CPs, in univariate or multivariate time series. The discussion will be focused on data that are ordered by time, but the methods extend trivially to scenarios where the observations are ordered by some other covariate infor- mation, such as, e.g., position.

1.1 Outline of the thesis

This thesis has two parts, where the first part consists of seven introductory

chapters and the second part contains three papers. The focus of the first part

is to put the papers in a broader perspective, where we in Chapter 2 aim to make the ideas in Remarks 1.1 and 1.3 more concrete by exemplifying how the output from CPD algorithms can be used in the context of IWSANs. First we introduce IWSANs and describe some previous work on automatic control over wireless networks. Then we motivate the development of statistical mod- els of radio channels and describe why detecting CPs in such data is beneficial when designing IWSANs. The second chapter concludes with a description of a measurement campaign where the radio environments in two factories were measured using a network of wireless sensor nodes. Chapter 3 gives an overview of the literature on CPD where special attention is given to the PS algorithm. Much of the discussion is focused on elaborating on Remark 1.2 by describing different types of CPD algorithms and their model assumptions. In Chapter 4 we extend the PS algorithm to CPD in multivariate time series where only a subset of them is affected at each time of change. The results indicate that the extended algorithm has exemplary CPD accuracy, but unfortunately, the computational cost scales unfavorably with the size of the data set. There- fore, we proceed with the development of the JCPD algorithm where the first step is to propose a new segmentation criterion which is described in Chapter 5. Chapter 6 presents two case studies that exemplify some of the different types of time series that can be analyzed with the PS algorithm and thereby also our proposed JCPD algorithm. We also present the model that has showed the best fit with our RSS data and we demonstrate the improved segmentation performance by comparing it to an alternative model. The alternative model is used in Paper I to segment RSS data, but during the work with Paper III, we found that the model presented in Chapter 6 results in a better segmentation of the time series. This demonstrates the importance of using an appropriate model when searching for CPs, as discussed in Remark 1.4. Sections 6.2.2- 6.3 are focused on the JCPD algorithm and are meant to be read after Paper II.

The material in these sections are intended for the specialist who is interested in gaining a more detailed knowledge of the JCPD algorithm. For the rest of the discussion in Chapter 6, it is enough if the reader is familiar with the PS algorithm which is described in Chapter 3. Finally, we conclude and discuss the results in Chapter 7.

The second part of the thesis consists of the following papers.

Paper I

Markus Eriksson and Tomas Olofsson "On Long-Term Statistical Dependences in Channel Gains for Fixed Wireless Links in Factories", IEEE Transactions on Communications, July 2016

In this paper we study the radio channel measurements using a UCPD al-

gorithm which outputs point estimates of CPs. By estimating the parameter

vector that is associated with each segment of observations that gets delimited by the CPs, we show that the estimates from adjacent segments are statistically dependent. The strength of the dependencies were measured by the concept of mutual information and we suspect that they are introduced by the repetitive motion of machines in the vicinity of the nodes. Thus, similarly to the discus- sion in Remark 1.1, this result implies that it is possible to design predictors of future values conditioned on the current value.

Paper II

Markus Eriksson and Tomas Olofsson "Computationally Efficient Change Point Detection in Multivariate Time Series", IEEE Transactions on Signal Process- ing, January 2019

In this paper we develop the JCPD algorithm and also demonstrate it using synthetic data. By comparing the JCPD algorithm with two similar methods, we show that it was faster than the alternatives and at least as accurate on all the considered data sets.

Paper III

Markus Eriksson and Tomas Olofsson "Multivariate Change Point Detection with Optimality Preserving Pruning", Manuscript.

In this paper we describe how to implement the JCPD algorithm more effi- ciently by using so-called pruning techniques which limit the search space of the DP algorithm in the second stage. We also demonstrate the practical im- portance of the reduced processing time by applying it to the radio channel measurements where the size of the data set made it impractical to apply the JCPD algorithm in its basic form. Also, in the supporting material we present a detailed comparative study of some of the methods that are available for detecting CPs in multivariate time series. Compared to the study in Paper II, this study includes more algorithms and a greater variety of time series.

To summarize, the contributions of this thesis are:

• A measurement campaign of radio channels in factory environments.

• A detailed statistical study of the radio channel measurements.

• An algorithm for asymptotically exact Bayesian inference of CPs in mul- tivariate time series where a subset of the monitored time series is af- fected at each time of change.

• A computationally more efficient, but approximate, algorithm for detec-

toing simultaneous CPs in multivariate time series.

• A comparative study between different methods for detecting joint CPs in multivariate time series.

• A motivating example from IWSANs where the benefit of detecting CPs in multivariate time series is demonstrated.

Other related, but not included works, are:

Paper IV

Anders Ahlén, Johan Åkerberg, Markus Eriksson, Alf J. Isaksson,

Takuya Iwaki, Karl Henrik Johansson, Steffi Knorn, Thomas Lindh, and Hen- rik Sandberg "Towards Wireless Control in Industrial Process Automation", Submitted to IEEE Control Systems Magazine.

In collaboration with partners from ABB and Iggesund Paperboard, we have worked on wireless control in the process industry. This article presents both theoretical work as well as a proof-of-concept wireless closed loop control implementation on a starch cooker at Iggesund paperboard mill in Sweden.

Patent application

Johan Åkerberg, Markus Eriksson, Tomas Olofsson "Identification of robust

wireless routing paths", No: PCT/EP2018/081022.

2. Communication over wireless industrial networks

One of the motivations for developing CPD algorithms is that they are very useful for studying measurements of radio channels in factory environments.

Here we define the notion of a radio channel, detail its effect on the wireless data transfer, and motivate the analyses that are presented in the included pa- pers where we apply CPD algorithms to radio channel measurements. Finally, we describe two measurement campaigns that were conducted at two different factories during this work.

2.1 Background and motivation

Typical examples of industries with automated manufacturing are steel, paper, automotive, medical, and food. In these applications, machines are used for tasks such as assembling, welding and palletizing. The automated process relies on a timely and reliable communication between the machines, and this communication can be divided into three different categories based on their required update rates [3]:

• Monitoring - Some sensors collect diagnostics which do not require im- mediate intervention. Examples from this category are sensors that mea- sure temperature, vibration and pressure. The update rate of these sen- sors can range from seconds to days.

• Closed loop control - A common scenario is that a large number of sen- sors and actuators, which are referred to as nodes, are deployed at fixed locations inside a factory in order to control some process of interest.

The sensors measure, for instance, temperature, flow, or torque, and the readings are periodically transmitted to a centralized control room. At the control room, the measurements are used to compute new control commands which are then forwarded to the actuators in order to influ- ence the physical process. Typical values of the update rates for these transmissions range from 10-500 milliseconds.

• Interlocking - To ensure safety, much of the machinery use interlocks where a set of conditions need to be satisfied for continued operation.

For instance, proximity sensors can be used to prevent collisions be-

tween moving machines. Interlock communication is sensitive to delays

and the required update rates range from 10-250 milliseconds.

Due to the strong digitalization evolution, there is an increasing interest for replacing the traditional wired communication with wireless. The main incen- tive is that the wireless technology is less costly to install and maintain. In an ordinary process factory, the cost of installing wires has been estimated to be

$200 per meter and as the wires age, they crack and fail which is one of the most common sources of reliability problems [3]. With the advent of IWSANs (industrial wireless sensor and actuator networks), less time will be spent on troubleshooting physical connectors, which is both time and labour intensive.

The wireless technology also offers other advantages, such as increasing the flexibility of the monitoring and control installations which makes it easier to introduce performance enhancements. Further, for certain rotating equipment, a wired solution is unfeasible and these are sometimes left unmonitored.

2.2 Improving the data throughput using JCPD

In addition to the benefits of IWSANs, the inherent limitations associated with this technology give rise to several challenging research problems. The main problem is that communication between two nodes can not be guaranteed and the nodes will generally need to collaborate in order to establish communica- tion between all nodes in an IWSAN. For instance, the control room, which we refer to as the sink, might not be within direct communication range with some of the nodes and the data must be forwarded by intermediate relaying nodes. A transmission that has been relayed by at least one intermediate node is referred to as a multi-hop transmission and an algorithm that organizes the multi-hop transmissions is referred to as a routing protocol. Extensive research efforts have been directed towards designing routing protocols that achieve a timely and reliable data transfer, and even if successful deployments have been demonstrated [86], the technology is still in the development stage. Below we describe how the JCPD algorithm can be used to make better, more robust, routing decisions. First we give a more detailed description of the problem where each node will experience time varying data throughput to its neigh- bors due to variability in the associated radio channels. Then we survey some of the methods for routing the packets through the network so that they reach their end destination even when the data throughput varies. Finally, we de- scribe how the JCPD algorithm can be used to improve the routing decisions, resulting in a more reliable data transfer.

2.2.1 Radios in IWSANs

The nodes in IWSANs generally combine three different technologies: a mi-

crocontroller, a radio transceiver, and sensing/actuating capabilities. When a

node has produced new data, such as a sensor measurement or a control com-

mand, it is stored as a sequence of binary digits, or bits. To transmit that

data to some other part of the network, the radio on the node is responsible for transforming the bit sequence into a physical signal. In this thesis work we use radios compliant to the IEEE 802.15.4 standard [4] which is a popular choice for IWSANs [3]. These radios are specifically designed to have a low power consumption which allows the nodes to be deployed for months or years be- fore their batteries need to be replaced. Another distinguishing feature is the use of direct sequence spread spectrum (DSSS) modulation which increases the robustness to interference from other nearby networks [36]. Also, the data rate is 250 kbit/s which is relatively low compared to other standards, such as 802.11 (WLAN) or 802.15.1 (Bluetooth). Transmitting at a high rate has not been a priority in IWSANs since the data packets are small and the challenge is instead to transmit these reliably.

2.2.2 The wireless data transfer

When a radio signal is transmitted, the emitted radio waves spread into the surroundings of the transmitter. Much like echoing sound waves, reflecting objects in the vicinity of the nodes illuminate the receiver with radio waves that arrive with different attenuation and delay. At some spatial locations, the reflections will interfere constructively, and at other locations, they will inter- fere destructively. Thus, the transmitter establishes a spatial field of varying signal strength and the receivers ability to decode the transmission will depend on its location within the field. Typically, factory environments are cluttered with overhead cranes, conveyor belts, pumps and robots, all acting as radio reflectors. Much of this equipment is moving which cause the spatial field to vary over time. Also, the activity is typically recurrent where, for example, a robot may activate in order to complete some specific task and then halt and wait for the next cycle. Hence, even if both the transmitter and the receiver are positioned at fixed locations, the activity in their vicinity will cause a tempo- ral variability of the received signal strength. This variability is typically less volatile compared to mobile communication where the nodes are moving, but a fixed wireless link can still go from reliable to disconnected as a result of the movement of some large object.

Much of the analysis in this thesis work is focused on studying the link variability in factory environments using measurements of channel gain, h, which is defined as the ratio between the power of the received signal, R, and the power of the transmitted signal, T , i.e.,

h = R

T . (2.1)

Thus, h relates two quantities that are of particular interest in digital commu-

nication. Intuitively, the received signal power is one of the components that

determine the receivers ability to decode the received message and the trans-

mitted signal power determines the energy expenditure of the transmitter.

On the receiver side, the received data packet consists of a sequence of bits.

The rate at which received bits differ from the corresponding transmitted bits is referred to as the bit error rate (BER), which depends on both R, and the power of the background noise. ¹ Specifically, the BER is a function of the received signal to noise ratio (SNR), γ, which is defined as,

γ = R

N , (2.2)

where N is the power of the background noise. The probability of a successful transmission increases with increasing γ, and the exact relationship depends on the transmission technique being used. For 802.15.4 radios, which use offset quadrature phase shift keying modulation and DSSS, the resulting BER is given by [2],

β (γ) = 1 30

∑ 16 j=2

( −1) ^j

 16 j



e ^−20γ ( 1− j

). (2.3) Since the BER is determined by both R and N, modeling these quantities is of general interest in the literature on IWSANs. Here we focus on model- ing the variability in R caused by the radio channel, and this phenomenon is commonly known as fading.

There is a vast body of prior works that have fitted statistical models to measurements of fading channels, see, e.g., [67, 79] and references therein.

Some works have found that certain probability distributions accurately model the observed variability, and these are referenced in Paper I. However, most studies have used measurements from a relatively short time span, typically seconds or minutes. Recent studies have showed that when IWSANs are de- ployed over longer time periods, say hours or days, the statistical properties of the radio channels are only piecewise stationary and may change abruptly [2, 60]. In [60], the authors recorded measurements of RSS (received sig- nal strength) for 16-20 hours at three different factories and concluded that conventional single fading distributions are insufficient for modeling the data.

Instead they proposed using a so-called mixture component model. Also, they found that the number of components in the mixture increases with the length of the observation interval and that a semi-Markov chain can be used to model the temporal switching behavior between the components.

An example of a radio channel exerting such a regime switching behavior is illustrated in Figure 2.1, which shows the measured RSS, in dBm, ² between two nodes deployed inside a paperboard mill. The transmitter was sending packets every second using a fixed transmit power and the long term volatility

1

The noise can consist of thermal noise, background noise, and interference. These noise sources will collectively be referred to as background noise.

2

This means that the power is expressed in decibels relative to 1 mW. See Appendix 2.A for

more details on the RSS measurements.

in RSS was most probably caused by a crane in the ceiling that was moving paper rolls from one position to another.

Time [h]

RSS [dBm]

0 2 4 6 8 10 12 14 16

−85

−80

−75

−70

−65

−60

−55

−50

−45

−40

Figure 2.1. Measured RSS between two nodes at fixed locations at the Iggesund pa- perboard mill in Sweden. The transmitting node was using a fixed transmit power and the observed volatility of the received signal strength was thus caused by the time varying radio environment.

When a network of nodes is deployed inside a factory, it is common that the repositioning of radio reflecting objects will cause simultaneous changes in signal strength for several of the radio channels in the network. This is illus- trated in Figure 2.2 which shows RSS measurements for six channels inside the mentioned paperboard mill. In the figure, there are clear signs of regular behavior in the RSS data. For instance, each channel switch between volatile and more quiescent periods, illustrated by the red and green background col- ors, respectively. These periods overlap relatively well for channels 1-4, and the same behavior can be seen for channels 5 and 6. Next we describe the benefit of identifying which channels that are likely to undergo simultaneous changes.

2.2.3 Revealing the network hierarchy using JCPD

The measurement campaigns that are described in the following section were

conducted in collaboration with experts working in the field of wireless au-

tomatic control. One of the big challenges in this application is designing

routing protocols, which achieve a reliable data transfer even in the presence

of time varying throughput on individual radio channels. More specifically,

the multi-hop transmissions need to be organized so that each packet reliably

reaches its intended destination by propagation along a sequence of interme-

x

x

x

x

x

Time [s]

x

RSS measurements [dBm]

0 100 200 300 400 500 600 700 800

−84

−73

−62

−88

−80

−71

−82

−78

−73

−80

−75

−69

−87

−77

−66

−70

−65

−59

Figure 2.2. Time series of recorded RSS in a network of wireless sensor nodes de- ployed inside a paperboard mill in Iggesund, Sweden. Volatile channel behavior is marked by red and quiescent behavior is marked by green.

diate relaying nodes, which is referred to as a path. To this end, a common technique is to introduce multi-path redundancy by either, transmitting repli- cas of the same packet over different paths, or transmitting each packet over one primary path where the packet is rerouted to an alternative path in case of a transmission failure on any of the traversed channels [54, 9].

In either case, it is desirable that the network is self-configuring in the sense that the paths are selected automatically. For this purpose, most of the de- veloped routing protocols for IWSANs include a neighbor discovery process which, simply put, estimates a ’map’ of the positions of the nodes in the net- work. The map is then used to route packets so that each time a transmission is forwarded by an intermediate node, the packet gets ’closer’ to its end destina- tion. The distance metric in this map is typically not based on spatial distance but rather on some radio propagation metric such as signal strength.

In this section we shortly describe a few approaches for generating such maps and how the JCPD algorithm can be incorporated into this process in order to generate a more informative map, resulting in better routing decisions.

To illustrate the process, we focus on the uplink communication where the

sensors are sending packets to the sink node. In this case, the map can be

stored in the form of a hierarchical tree structure where the sink is the root

node which is connected to its neighboring nodes with weighted edges, or

links, that encode the associated distances. Those neighbors are connected to their neighbors, and so forth, where the sensors are leaf nodes to the tree. First we describe some of the methods for generating the tree structure.

Estimating the network hierarchy

A simple method for generating the tree structure is to use the notion of short- est path where each link between a pair of nodes is assigned a length, or weight [11]. Naturally, the choice of length metric affects the behavior of the rout- ing protocol. Here we imagine a scenario where RSS is used as length metric, which is a quite common choice that has been used in several works on routing algorithms for IWSANs [86, 74]. This choice can for instance be motivated by the study in [51] which showed that for modern radio chips, such as the CC2420 [43] used in this work, measured RSS is a good predictor of packet reception rate (PRR) and it is also reciprocal, i.e., identical in both directions of a link.

The length of a path through the network is given by the sum of the lengths of the traversed links. For node i, the length of the shortest path to the sink, D _i , is given by,

D i = min

j∈N

(d i, j + D j ), (2.4) where d i, j is the length between node i and node j, and N i is the set of neigh- boring nodes which are within direct communication range of the ith node. We assume that the computations are structured in such a way so that all relevant D _j are available when D _i is computed using (2.4). This recursion is initiated at the sink where we set i = 0 and D 0 = 0, and these values can then be used to compute the shortest path for all nodes that are within direct communication range of the sink. For the ith node, the neighboring node that achieves the minimum in (2.4) is referred to as the parent of the ith node. Hence, comput- ing (2.4) is referred to as parent selection. Also, the set of links, or the path, that achieves D i is referred to as the shortest path.

Note that, the parent selection process in (2.4) results in a network with- out multi-path redundancy since each node only selects one neighbor to send packets to. A simple method to introduce redundancy is to instead use the parent selection mechanism in Algorithm 1 below, where each node in the network selects M parent nodes. Since a large M results in more redundancy, it is tempting to set M to a high value so that each node uses many, potentially all, of its neighbors to relay the packets. However, according to the experts that assisted in our gathering of measurement data, a large M will lead to a lot of overhead transmissions which consumes valuable network resources, see [86]. Therefore, it is desirable to keep M small and instead carefully select each parent so that the benefits from the multi-path diversity is maximized.

Such a parsimonious parent selection algorithm is, for instance, obtained if

all the selected paths are node-disjoint, meaning that they do not share inter-

mediate relaying nodes [12]. Figure 2.3 illustrates the concept of node-disjoint

M = /0;

for m = 1,...,M do p = argmin

j∈N

\M

d i, j + D j (2.5)

D ^m _i = d i,p + D p ; M = M ∪ p;

end D _i = D ¹ _i ;

Algorithm 1: Pseudocode for multi-path parent selection on the ith node.

The algorithm is an extension of the parent selection algorithm in (2.4). The list of the M best parents is stored in M and the distance associated with the mth parent is D ^m _i . Note that the last line sets the length of the shortest path for the ith node to the length of the path defined by its best neighbor.

paths where node 1 has selected three such paths to the sink S. The idea is that if the paths do not share intermediate nodes, the probabilities of successfully communicating over the different paths will be independent. However, in fac-

Figure 2.3. Illustration of a two hop network where node 1 has three node-disjoint paths to the sink.

tory environments where large metal objects are moving, several links might be affected by the repositioning of one single object, which induces depen- dence in link quality between the neighbors. This behavior was illustrated in Figure 2.2. For the example network in Figure 2.3, if a single event affects the quality of the links from node 1 to nodes 2 and 3, then these link qualities become dependent. In the extreme case, if the event disconnects the links to nodes 2 and 3, then the only path left goes through node 4. Thus, correla- tions in link quality among the selected paths reduce the gain from multi-path redundancy.

Identification of robust wireless routing paths using JCPD

To make our proposed solution concrete, imagine a scenario where some algo-

rithm has detected a behavior where node 1 often experiences a sudden drop

in link quality to nodes 2 and 3. Then, if we assume that node 1 is to select

M = 2 nodes as parents, then the robust choice is to either select nodes 2 and

4 or nodes 3 and 4 since these choices results in paths that drop packets inde- pendently of each other. In Paper III we use the JCPD algorithm to detect such regular behavior.

2.3 Switching network state models and closed loop control

The idea of improving routing decisions by using CP models of the radio en- vironment is not new. The works in [50] and [64] considered closed loop control over multi-hop networks where such CP models were used to organize the multi-hop transmissions so that the performance of the control loop was maximized. In these works, relevant properties of the radio environment, e.g., the PRR (packet reception rate) for each channel, were summarized by a net- work state variable, ρ t , which was assumed to undergo abrupt changes. The evolution of the state variable was modeled as a Markov chain

..., ρ _t−1 , ρ _t , ρ _t+1 , ... (2.6) meaning that the transition probabilities to the next state only depend on the current state, i.e.,

P(ρ _t+1 |ρ t , ..., ρ ₁ ) = P(ρ _t+1 |ρ t ). (2.7) Altogether, this results in a switching network state model and this model can be motivated by the RSS measurements in Figure 2.2 which exhibit such a switching behavior.

Before the algorithms in [50, 64] can be applied, the user needs to specify a set of parameters associated with the network state process. This set contains the following parameters: (i) the PRR for each channel in each network state, (ii) the total number of network states, (iii) a distribution over state durations, i.e., the temporal separation between two CPs, and (iv) the state transition probabilities. In [50], the authors proposed two approaches for setting these parameters. The first approach was to view them as tuning parameters where the user first observes the machines on the factory floor and then manually translates these observations into the mentioned parameter values. In cases where the factory floor is cluttered with moving machinery, their effect on the radio environment might not be intuitively clear which complicates the man- ual approach. The second proposed approach was to estimate the network state parameters from measurements of the radio environment. Clearly, the second approach is preferable, but the authors did not outline such an estimation al- gorithm.

To summarize, a preprocessing algorithm that estimates the parameters

( i) − (iv) would simplify the practical implementation of the algorithms out-

lined in [50] and [64]. The JCPD algorithm proposed in this work is well

suited for this purpose, but before we elaborate on this, we point out three key

properties of such a preprocessing algorithm: (a) In order to treat collective changes in channel behavior, the preprocessing algorithm needs to be multi- variate and support simultaneous CPD in the monitored channels. Similarly to the discussion on fingerprinting in Remark 1.3, an event on the factory floor might only affect some of the channels in the network and the preprocessing algorithm must therefore identify which subset that is impacted at each CP.

(b) Even if the monitored channels show dependencies such as joint changes, their behavior between the CPs might be very different. Thus, recalling the discussion in Remarks 1.2 and 1.4, it is important that the chosen model struc- ture is flexible enough to explain different inter CP behavior. The resulting segmentation might otherwise lead to erroneous CP estimates, as was illus- trated in Figure 1.3. In Section 6.4 we present a model which has showed an excellent fit with our RSS measurements. (c) The preprocessing algorithm needs to support detection of a broad range of changes in statistical properties, such as changes in mean, variance, or both.

In Paper III we demonstrate that the JCPD algorithm fulfills the properties ( a)−(c) and the output can either be used in combination with the above men- tioned wireless control algorithms for inference of (i)−(iv), or for some other subsequent algorithm since models of radio channels is of general interest in the literature on IWSANs [72, 77].

2.4 Measurement campaigns

The RSS measurements that are studied in this work were obtained from three different factories, one rolling mill, one paperboard mill and one flotation plant, all located in Sweden. As discussed hitherto, radio channels in these environments behave differently compared to, for instance, office buildings, due to the open areas and the large amount of metal machinery. Therefore, it is important to specifically study the statistical behavior of radio channels in factories, but since these sites have restricted access, relatively few such stud- ies exist. Even fewer works have considered the long term temporal behavior of the wireless channels in these environments.

The data set that is studied in this thesis work consists of channel measure-

ments where some recordings span up to 96 hours. The measurements have

been obtained in two different measurement campaigns, where the author only

was involved in the second campaign. The first campaign involved all three of

the mentioned sites and the focus was to gather measurements of radio chan-

nels in order to characterize their individual behavior. To this end, packets

were transmitted every second using a National Instruments signal generator

and a set of nodes were deployed at fixed locations in order to record the RSS

of the incoming transmissions. The gathered data set thus consisted of time

series of channel gain for the links between the signal generator and each node.

The second measurement campaign was conducted at the rolling mill and

the paperboard mill, and the focus was to gather measurements that could be

used to study the joint behavior of radio channels. Instead of using a dedi-

cated signal generator, all nodes in the network transmitted packets in a syn-

chronized fashion. That way, all pairwise links in the network were sampled

at regular intervals. Details on the factory environments and the measurement

set-up that was used in the second campaign are given in Appendix 2.A.

Appendix 2.A The second measurement campaign

During the measurement periods, the factories were fully equipped and opera- tional. Also, in order to mimic a realistic network control scenario, the nodes were deployed in the vicinity to machines in positions where sensors normally would be placed. The distances between the nodes varied between three and approximately fifty meters.

Paperboard mill, Iggesund

Iggesunds Bruk is a paperboard mill that produces pulp and paperboard. The radio channel measurements were conducted in the coating kitchen where two fully automated starch cookers produce coating for the paperboard. The equip- ment in this part of the production line consisted of conveyor belts, pumps, and canisters. Most of the equipment were covered in metal casings and the number of moving reflectors was limited. Movement in the vicinity of the wireless nodes mostly consisted of passing personnel that were conducting maintenance or monitoring related tasks. Figure 2.4 shows a photo of the de- ployment area.

Figure 2.4. Deployment area at the paperboard mill.

Rolling mill, Sandviken

The rolling mill in Sandviken produces steel products. The radio channel measurements were conducted along a subsection of the production line which heats and shapes the steel. This part of the production line is automated using a large number of moving machinery, such as conveyor belts and overhead cranes. The need for human intervention is limited so personnel seldom pass this area. The deployment area is depicted in Figure 2.5.

Measurement apparatus for radio channels in a mesh network

To simultaneously monitor the channels between all pairs of nodes in the net-

work, the general idea was to periodically initiate a network-wide measure-

ment round where the nodes transmitted packets in short succession. One

such measurement round is schematically illustrated in Figure 2.6 where, after

the round has been completed, each node has a list of, almost, simultaneous

measurements of channel gains to its neighbors. During the work with the

Figure 2.5. Deployment area at the rolling mill.

measurement set-up, the following two main practical problems were identi- fied:

1. Initiating the burst of transmissions during the measurement round re- quired that the clocks on the nodes were carefully synchronized.

2. When the network was deployed over long time periods, the nodes gen- erate a significant amount of data which could not be stored on their limited onboard memory.

Below we describe the hardware and the software that was used to obtain the measurements and how the mentioned practical problems were solved.

Figure 2.6. Illustration of one measurement round for a network of three nodes, num- bered 1,2, and 3. When the round has been completed, each node has a list where the ith element is the recorded RSS, in dBm, of the incoming transmission from the ith node.

Measurement hardware

The network consisted of 20 Zolertia Z1 wireless sensor nodes [88] which were equipped with the IEEE 802.15.4 compliant CC2420 radio. This radio operate at the 2.4 GHz ISM (industrial, scientific and medical) band which is shared between a range of different technologies, such as WiFi and microwave ovens. The CC2420 can transmit at 16 different channels, which are labeled 11-26 and ordered by ascending center frequency. In this thesis work, all transmissions were done at channel 26, which is the channel that has the least amount of overlap with WiFi transmissions [56].

During the experiments, the radios were set to their maximum transmit

power of 0 dBm. By using a fixed transmit power, the RSS acts as a mea-

sure of the channel gain between the nodes. For each received packet, the

CC2420 reported a RSS value which was computed as the average received