Detection of Sudden Seepage Changes in … Detection of Sudden Seepage Changes in Embankment Dams Carl Nygren Bachelor’s Thesis in Computer Science (15 ECTS credits) Single Subject

Bachelor’s Thesis in Computer Science at Stockholm University, Sweden 2013

Detection of Sudden Seepage Changes in Embankment Dams

Carl Nygren

NADA

Detection of Sudden Seepage Changes in Embankment Dams Carl Nygren

Bachelor’s Thesis in Computer Science (15 ECTS credits) Single Subject Courses Stockholm University year 2013 Supervisor at was Jan-Olov Strömberg, KTH SCI dept. of Mathematics Examiner was Johan Håstad TRITA-CSC-E 2013:028 ISRN-KTH/CSC/E--13/028--SE ISSN-1653-5715 Department of Numerical Analysis and Computer Science KTH CSC SE-100 44 Stockholm, Sweden

Abstract

In 2009 a �bre optic cable with its belonging measuring tools was installedalong the dam toe in Ledinge channel dam. By measuring the temperature inthe cable, any leakage zones can be detected and localized. HydroResearch, acompany that perform measurements and analysis of embankment dams withthe primary purpose to detect and prevent leakage, has a method that detectssudden leakages by �nding sudden changes in the measured temperature.In this bachelor's thesis, three new methods are presented, the sum of sinemethod, the slope comparison method and the �lter method. These methodshave been developed mainly by tests with arti�cial data of leakages. All thethree methods can �nd clear sudden changes in the arti�cial data, but thesum of sine method failed to �nd the smooth unclear temperature change.With the real data, the �lter method did not work at all because of the realdata noise. The two other methods were able to �nd sudden clear changes.

Sammanfattning

Detektering av plötsliga läckageförändringar

i fyllnadsdammar

En �beroptisk kabel med tillhörande mätinstrument installerades 2009 längsdammtån i Ledinge kanaldam. Genom att mäta temperaturen i kabeln kaneventuella läckagezoner upptäckas och lokaliseras. HydroResearch är ett fö-retag som utför mätningar och analyser av fyllnadsdammar med det primärasyftet att upptäcka och förebygga läckage. I skrivande stund har de en metodsom upptäcker plötsliga läckage genom att hitta förändringar i den uppmättatemperaturen. I denna rapport presenteras tre nya modeller, �sum of sine�,�slope comparison� och ��lter�, som har utvecklats huvudsakligen med hjälpav arti�ciell data av läckage. De tre metoderna kan hitta tydliga plötsligaläckage i den arti�ciella datan men �sum of sine� klarar inte av att hitta småförändringar. �Filter� klarade inte att hantera den riktiga datan på grundav den riktiga datans brus. De två andra metoderna lyckades hitta plötsligatydliga förändringar i den riktiga datan.

Preface

This is my Bachelor's thesis in computer science done at the department ofNumerical Analysis and Computer Science (NADA) at Stockholm Univer-sity on behalf of HydroResearch AB. The project was supervised by SamJohansson at HydroResearch and Johan Håstad at the school of ComputerScience and Communication at KTH who also was examiner. The develop-ment phase started in the summer 2012 and lasted until the beginning of theautumn. The completion of the thesis was delayed until spring 2013.

I would like to thank HydroResearch for the opportunity to write this the-sis and for their help, knowledge and o�ce space. I also would like to thankall the others who were involved during the process, Jan-Olov Strömberg atthe department of Mathematics at KTH, Johan Håstad and the others whoread and commented on the thesis.

Contents

1 Introduction 1

1.1 Embankment Dams . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Problem and Purpose . . . . . . . . . . . . . . . . . . . . . . . 21.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Theory 4

2.1 Distributed Temperature Sensing . . . . . . . . . . . . . . . . 42.2 Thermal Processes in Embankment Dams . . . . . . . . . . . 52.3 Curve Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3.1 Nonlinear Least Squares Fitting . . . . . . . . . . . . . 6

3 Method and Analysis 8

3.1 HydroResearch's Current Method . . . . . . . . . . . . . . . . 83.2 Arti�cial Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.3 Real Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.3.1 Temperature Measurements at Ledinge Dam . . . . . . 103.3.2 Chosen Data . . . . . . . . . . . . . . . . . . . . . . . 11

3.4 Evaluation Methods . . . . . . . . . . . . . . . . . . . . . . . 133.4.1 Sum of Sine . . . . . . . . . . . . . . . . . . . . . . . . 133.4.2 Slope Comparison . . . . . . . . . . . . . . . . . . . . . 143.4.3 Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.4.4 Other Methods . . . . . . . . . . . . . . . . . . . . . . 15

4 Results 16

4.1 Arti�cial Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 164.1.1 Sum of Sine . . . . . . . . . . . . . . . . . . . . . . . . 164.1.2 Slope Comparison . . . . . . . . . . . . . . . . . . . . . 184.1.3 Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.2 Real Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.2.1 Sum of Sine . . . . . . . . . . . . . . . . . . . . . . . . 204.2.2 Slope Comparison . . . . . . . . . . . . . . . . . . . . . 22

4.2.3 Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

5 Conclusions 25

6 Discussion 27

References 29

Chapter 1

Introduction

For centuries dams have been used to control water �ow. The earliest damswere made for water supply and irrigation. Today, the stored water has avariety of uses such as electricity production, water supply, �ood preventionand land reclamation. The dams' area of use make them valued by today'ssociety.

There are di�erent type of dams, where embankment dams are the mostcommon type in Sweden. HydroResearch is a company that analyzes mea-surements and evaluates embankment dams to detect and prevent leakage.Sudden seepage changes can be detected by performing temperature mea-surements and analyze temperature changes in the dam.

1.1 Embankment Dams

Filter

CoreFill

Water level

Figure 1.1: Section through an embankment dam.

The core is the central part of the majority of the embankment dams andconsists of material with low permeability (�gure 1.1). The �lter consistsof more permeable material and surrounds the core. It prevent wash outof the �nes from the core and drains the seepage water. The �ll material

1

1.2. PROBLEM AND PURPOSE

consists of soil, gravel and/or rock. It stabilizes and supports the dam. Thepermeability of the core decides the amount of leakage through the dam sinceits material has much lower permeability than the rest of the dam.

Internal erosion is the process inside the dam caused by seepage wheresoil are transported away from the foundation or the core. It leads to ahigher seepage �ow that will potentially increase the speed of the erosion.The internal erosion process can be divided into three di�erent categories.Two of them involve the foundation of the dam where one is when internalerosion occurs from the embankment into the foundation and the other iswhen the internal erosion occurs merely through the foundation. The lastone is internal erosion inside the core. For an extensive illustration of theprocess, refer to [3].

A failure of a dam can cause fatal consequences. The main reasons for em-bankment dam failure are overtopping, internal erosion in the embankmentand internal erosion in the foundation. Damages on dams are mostly detectedby visual inspection. But certain types of damage, such as internal erosion,are harder to detect of natural reasons by visual inspections [5]. Thereforeto prevent failures, surveillance of the dam is needed. The most commonmonitoring systems are measurement of seepage, pressure and measurementof crest, slope and internal movements [6]. Due to their limitations regardingaccuracy and spatial representability other methods have now been recentlyintroduced. One such method is temperature measurements, especially withoptical �bres.

1.2 Problem and Purpose

In some dams conventional leakage detecting systems are not possible to setup due to the environment. In such cases the intention is to completelybe able to replace conventional systems with a DTS system (distributedtemperature sensing, see section 2.1 for more details).

There are several factors that can a�ect the temperature in the damreservoir. On a yearly basis the water temperature has a seasonal variation,up and down similar to a sine curve. Then there are short variations such asweekly changes due to weather conditions and �nally diurnal variation (24 hday and night variation). All these temperature changes can be seen at thedam toe with the installed �bre optic cable if the seepage �ow is high enough.When the seepage is low or non-existent the temperature will be near thegroundwater temperature.

HydroResearch has at the present time, an alert system that detects sud-den leakages. It is based on the seasonal variation (see chapter 3). The

2

1.3. LIMITATIONS

system leaves room for improvement and the purpose with this bachelor'sthesis is to �nd ways to improve the system.

1.3 Limitations

This bachelor's thesis will focus on improvement of the detecting systemfor sudden leakage using temperature data. Other methods such as �owcalculations will not be mentioned.

The tests will mainly be done with arti�cial data. The leakage simulationsare provided by HydroResearch and are not a part of this bachelor's work.The real data used for this thesis has no clear leakage as the arti�cial databut it contains sudden smaller changes. However, a system with the abilityto detect such changes should detect signi�cant changes easily.

3

Chapter 2

Theory

The two �rst sections in this chapter are intended to provide understandingof the measuring technique used to obtain the temperatures along the damand the thermal processes in embankment dams. The last section explainsthe method nonlinear least squares for curve �tting which is used in two ofthe developed evaluation methods.

2.1 Distributed Temperature Sensing

Distributed Temperature Sensing or DTS is a technique that lets the usermeasure temperatures along a �ber optic cable. With today's techniquethe cable can be up to 60km long and measure the temperature with aresolution of 0.01◦C at every meter of the cable. This makes DTS suitablefor monitoring long distances with high precision which is needed in damsurveillance.

anti-Stokes Stokes

Wavelength

Figure 2.1: Raman spectrum.

4

2.2. THERMAL PROCESSES IN EMBANKMENT DAMS

Optical �bres are made from a material that is a�ected by thermal e�ects.The temperature creates lattice oscillations in the �bers. When a light sendsthrough the cable, Raman scattering occurs [11]. The light scattered back isthen analyzed. Raman scattering is an inelastic scattering, i.e. a scatteringwhere the frequencies of incident and scattered photons di�er. In the Ramanspectrum, the Stokes and the anti-Stokes can be found (�gure 2.1). Theanti-Stokes wavelength increases with higher temperature while the Stokesis merely temperature sensitive [4]. By comparing the Stokes and the anti-Stokes the temperature can be obtained. The time it takes from the launchof the light till the light scattered back has returned determines the positionwhere the backscattering occurred. Thus the position of the temperature canbe decided [9].

2.2 Thermal Processes in Embankment Dams

The temperature in the upstream reservoir and the air are the factors thatmainly a�ect the temperature in an embankment dam [7]. The air and thereservoir temperature vary seasonally. Due to advection caused by seepage�ow and heat conduction a seasonal temperature variation also occurs withinthe dam (see �gure 2.2).

JOHANSSON and SJÖDAHL 4

3 THERMAL PROCESSES IN DAMS

3.1 General The temperature in an embankment dam depends mainly on the temperature in the air and in the upstream reservoir. These temperatures vary seasonally and create seasonal temperature variation within the dam (see Figure 4) due to advection (caused by seepage flow) and heat conduction.

Advective transportand heat conduction

Heat exchangewith the air

Seasonaltemperaturevariation

vT

Geothermal flow Figure 4 Basic thermal processes in an embankment dam. The seepage flow is normally small in embankment dams (hydraulic conductivity often less than 10-6m/s) and the seasonal temperature variation in the upper part of the dam depends essentially on the air temperature at the surface. The influence from the air decreases with depth, and is less than 1oC for depths in the dam body that exceed 10m. This process must however be considered in small dams with heights less than about 20m, or if measurements are made at the dam toe at shallow depth. In larger dams with heights above 100m the geothermal flow must be considered, as well as the thermal stratification in the reservoir. Temperature acts as a tracer with the seasonal temperature variation as source. Low seepage flows will not affect the thermal condition in the dam, and the temperature will remain constant. At increasing seepage flows the temperature in the dam will begin to vary seasonally. The amplitude of the variation is dependent on seepage flow, the seasonal variation at the inflow boundary, and the distance from the boundary to the measuring point. The thermohydraulic behavior of an embankment dam is complex. It includes such basic thermal processes as heat conduction (from the dam crest and from the foundation due to geothermal flow), advection and radiation. The first two processes are partly coupled to each other because viscosity and density of water are temperature dependent. The problem is further complicated by the variation in material properties in the dam, and the different conditions in the saturated and unsaturated parts of the dam. In order to analyze the problem certain assumptions have generally to be made. The general problem can be studied using coupled transport models (based on FEM or FD). At most dam application with concentrated seepage/leakage a simplified evaluation can be considered. The evaluation method for flow quantification presented below can then be used to evaluate the seepage from temperature measurements in the dam. Measurements at the dam toe can be made in standpipes cc 10-50m, where manual or automated measurements can be performed, preferably on different levels. An optic fibre can also be, buried close to the groundwater level or below, can also be used to measure the temperature all along the dam. Some examples from these different approaches are shown below.

Figure 2.2: Basic thermal process in an embankment dam [7].

When the seepage is small in the dam, which it normally is, the seasonaltemperature variation in the upper part of the dam depends mostly on the airtemperature variations. The air in�uence decreases with depth, and depthsthat exceed 10m has less than 1◦C impact from the air [7]. This process mustbe considered when measurements are made at shallow depth at the dam toeand in smaller dams. In larger dams were height is above 100m, geothermal�ow and the thermal strati�cation in the reservoir must be considered.

5

2.3. CURVE FITTING

With the seasonal temperature variation as a source, temperature canbe seen as a tracer. The thermal condition in the dam will not be a�ectedby low seepage �ow, thus the temperature will remain constant. When theseepage �ow increases, the seasonally temperature variation will become vis-ible. Seepage �ow, the seasonal variation at the in�ow boundary, and thedistance from the boundary to the measuring point are all factors that a�ectthe amplitude of the variation.

With the temperature, calculations can be done to estimate the �ow inthe dam. When sudden �ow changes occur it takes some time before the�ow calculation stabilizes on the new �ow value. Also, the �ow calculationassumes that the temperature only depends on the seepage inside the dam,which is not the case [8]. This makes �ow calculations a bad choice to detectsudden changes rapidly. But the �ow change can be seen directly in thetemperature measurements and therefore is it appropriate to have an alarmdirectly on the temperature.

2.3 Curve Fitting

Curve �tting is the technique of adjusting a curve for best possible �t toa set of data. It can either be interpolation or smoothing, where the �rstmentioned method is to �t the curve exactly through the given data and thesecond one is to �nd a smooth function that approximately �ts the data.

2.3.1 Nonlinear Least Squares Fitting

Given a function f(x) depending on n parameters f(x;λ1, λ2, ...λn) and aset of m data points (x1, y1), (x2, y2), ..., (xm, ym) where m ≥ n we have theoverdetermined equation system

y1 = f(x1;λ1, λ2, . . . , λn)

y2 = f(x2;λ1, λ2, . . . , λn)

...

ym = f(xm;λ1, λ2, . . . , λn)

We want to �nd the values λ1, . . . , λn that best satisfy the equation system.We choose an initial guess for λi and de�ne

dβi = yi − f(x1;λ1, λ2, . . . , λn)

6

2.3. CURVE FITTING

To reduce dβi to 0, obtain the estimate for the changes dλi

dβi =n∑j=1

∂f

∂λjdλj

∣∣∣xiλλλ

for i = 1, . . . ,m, where λλλ ≡ (λ1, . . . , λn). This is equivalent to

dβββ = AAAdλλλ

where βββ is a vector of dimension m, λλλ is a vector of dimension n and AAA isthe matrix

AAA =

∂f∂λ1

∣∣∣x1λ

· · · ∂f∂λn

∣∣∣x1λ

.... . .

...∂f∂λ1

∣∣∣xmλ

· · · ∂f∂λn

∣∣∣xmλ

Multiply the transpose of AAA to both sides gives

AAATdβββ = (AAATAAA)dλλλ

Set

aaa ≡ AAATAAAbbb ≡ AAATdβββ

then we getaaadλλλ = bbb.

This can be solved for dλλλ and applied to λλλ and a new dβ is calculated. Dothis iteratively until dλλλ is smaller than a chosen constant. The sum of squareresiduals is dβββ ∗ dβββ. The sum of square residuals will hit a local min if theprocedure converges. A properly chosen initial value near the best �t valuewill improve the convergence. [1]

Without the assumptionm ≥ n, aaa would be singular making the equationaaadλλλ = bbb unsolvable. Even with the assumption there are cases where thematrix aaa is singular. MATLAB uses trust-region technique that in shortrestricts the step of dλλλ which avoids a singular aaa. For more information,refer to [2].

7

Chapter 3

Method and Analysis

The development of the alarm methods can be divided into three di�er-ent phases. First, an analysis was made of HydroResearch's current system(see section 3.1) and research was done on other possible approaches of theproblem. The next phase, own methods was developed through testing witharti�cial data of leakage using MATLAB. The arti�cial data was providedby HydroResearch (see section 3.2). The last phase involved adjustments tomake the methods work with real data (see section 3.3) and analysis of thecharacteristics of the di�erent methods.

3.1 HydroResearch's Current Method

HydroResearch's current leakage detection system is based on a comparisonbetween the expected temperature and the real temperature. The expectedtemperature is calculated with a sine approximation of 100 measured datapoints starting from a year ago to the current time. A sine curve is in manycases a good approximation of the temperature curve in a dam [5]. But athigh latitudes as in the northern part of Sweden, the sine curve is a roughapproximation. There the temperature curve will �atten towards zero at thewinter season and in the summer the shape will be more like a triangularwave. Therefore a large di�erence can occur between the calculated temper-ature and the real temperature without defections on the dam. This meansthat the alarm threshold must be set relatively high to avoid false alarm.

3.2 Arti�cial Data

In 2011, Hydroresearch performed temperature simulations with sudden leak-age changes. The model was a 8 m high dyke (wall to control water level) with

8

3.3. REAL DATA

the optical �bers located just downstream the toe. This model was basedon a dam in the southern part of Sweden. A sinusoidal water temperaturewas found to be appropriate. The boundary conditions for the simulationsare water and air temperature and pressure determined by reservoir waterlevel and downstream water level. Those are time dependent so a transientsolution is needed. COMSOL with the Subsurface Module was used for thesimulations.

Figure 3.1: Model used in the temperature simulations with hydraulic con-ductivities log K [8].

Leakage increase during 10 days was simulated at di�erent time of the yearby changing the hydraulic conductivity zone of the core (�gure 3.1). Thesechanges increased the �ow from 7.65∗10−6m3s−1m−1 to 28.2∗10−6m3s−1m−1.As seen in �gure 3.2 the temperature change is signi�cant for all simulationsdespite a small seepage (about 3 centiliters per second and meter dam).

Figure 3.2: Simulated temperatures for dam where defect starts at di�erentdates [8].

3.3 Real Data

Measuring temperatures with �bre optic cables is a newly developed tech-nique resulting in a smaller number of dams with longer time periods of data.Ledinge dam is one of those dams.

9

3.3. REAL DATA

3.3.1 Temperature Measurements at Ledinge Dam

Ledinge dam, �gure 3.3, is located in Ångermanälven in central Sweden.Its power plant started to operate in 1982. The dyke has a total length ofapproximately 4500 m and has a maximum height of 12.5 m.

Figure 3.3: Ledinge Embankment Dam and Intake [10].

A �bre optic cable with its belonging measuring equipment was installed2009 along the dam toe in Ledinge channel dam, see �gure 3.4. The cablehas the capability of measuring temperature each meter. Most of the cablewas installed at least 1 m below the surface level to place the cable belowthe ground water level. There are no other conventional ways to measure theseepage �ow at the dam.

Figure 3.4: The dashed line shows the placement of the optical �bres.

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3.3. REAL DATA

3.3.2 Chosen Data

The real temperature data used in this thesis were from the period between1st of August 2009 to 15 of August 2011 with six measurements per day.The data was used to test the di�erent methods in this report. The methodswhere tested with 100 points along the dam and three points are presentedin the report. These points were chosen to get the widest possible spread intemperature patterns. One is smooth without sudden changes, and the twoother have changes in di�erent scale and shape. However, Ledinge has nothad any critical increases in water �ow although HydroResearch's currentalarm system alerted in one of the chosen points in summer 2011. The realdata is a veri�cation if the methods can handle the variations in the data andwhat kind of changes the di�erent methods can detect. The placement of thethree points lies between section 2/600 and 2/700 in the dam, see �gure 3.5.

Figure 3.5: The three points represented in the result section are located atmeasure length 3116, 3119 and 3126 in the �bre and they lie between section2/600 and 2/700 on the dashed line. The �gure is enlarged and cut out from�gure 3.4.

Figure 3.6 shows the chosen points. The point at measure length 3126is clean with no short variations. The second point, 3116 has notable small

11

3.3. REAL DATA

changes but none that should be detected. The third point, shows clearerchanges that indicate a higher seepage �ow. These changes are of interest todetect. The other points along the dam are similar to these three points. Analarm method should be able to detect changes in each speci�c point, meaningthat di�erent alarm levels are needed along the dam. For points similar to3126 the method should alert when changes such as in the point at 3119appear. To avoid false alarm, the method should not detect changes such asin point 3116. A method that can detect the changes in the point at 3119and ignore the smaller changes in point 3116 will therefore be appropriatefor points similar to 3126. The same method will work with points similarto 3116, but a slightly higher threshold is preferred.

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Tem

pera

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° C

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Tem

pera

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° C

Temperature at 3126.527



Figure 3.6: Temperature curves of the chosen points. Locations of the pointsfrom top to bottom in the �bre are 3126, 3116 and 3119.

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3.4. EVALUATION METHODS

3.4 Evaluation Methods

The evaluation methods are the developed methods for detecting changes inthe temperature curves. The �rst two methods both includes curve �ttingand comparison between calculated and measured value. The third methodacts as a �lter where the �ltered signal is intended to only view the anomalies.

3.4.1 Sum of Sine

Sum of Sine is a method where a curve is �tted to the temperature dataand when a new point is measured, a comparison between this point andthe �tted curve is made to detect change. The function that is �tted is ofform a0 + a1Sin(a2x + a3) + b1Sin(b2x + b3) + c1Sin(c2x + c3) and the �tmethod is nonlinear least square. 100 points are used for the �t where 60 %is represented in the latest month. The coe�cients have bounds to controlthe shape of the curve. For example, it is appropriate to have one of the sinefunctions with a period of one year, so a2 has the bounds [ 2π355 ,

2π375

] and thetemperature shouldn't vary more than 20 ◦C, so a1 has the bounds [0, 10].The second sine function is limited to have a period of half the �rst sinefunction's period. With this construction the �tted curve will better approx-imate the temperature curve in the real data where the low temperatures inthe winter season last longer than the summer season. The last sine functionhas even shorter period and the amplitude is limited to at most 1. It acts asa �lter for the small short variations so that the alarm threshold can be settighter. Example of the method can be seen in �gure 3.7.

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6

7

8

9

10

11

12

13

Date

Tem

pera

ture

°C

Artificial TempCalc TempAlarm

Figure 3.7: Sum of Sine example. Calc Temp is the temperature calculatedby the Sum of Sine approximation. The calculated temperature has the samevalue as the arti�cial temperature until the sudden change appears. Then thedi�erence between the arti�cial temperature and the calculated temperaturebecomes greater than the set alarm threshold and an alarm occurs.

13


3.4.2 Slope Comparison

Slope comparison is a method where the slope of a line through the lastpoints of the data is compared to the slope of a line through the last pointsof a �tted curve. For the arti�cial data, a sine curve is �tted to temperaturedata covering a year back in time from current point. 100 points are used inthe �tting and they are evenly selected over the past year. The slope of theline through the last two points of the temperature data is compared withthe slope of the line through the corresponding two points of the �tted sinecurve. When a sudden change in temperature occurs, the di�erence betweenthe slopes will increase rapidly, and an alarm occurs. Example of the methodcan be seen in �gure 3.8.

When real data is processed the method above does not work due to thedaily temperature changes. The line through the last two points could havepositive slope in one point and in the next negative slope. Therefore, the lineis instead �tted to data from the last week. The real data requires a sumof two sine functions a0 + a1Sin(a2x + a3) + b1Sin(b2x + b3) to match thetemperature pattern of the data.

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5

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15

20

Date

Tem

pera

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°C

Artificial TempSinefitArtificial Temp SlopeSinefit SlopeAlarm

Figure 3.8: Slope Comparison Example. The slope of the sine �t is virtuallyindistinguishable from the slope of the arti�cial data until the sudden changeappears in the end of the graph where a clear di�erence occurs demonstratedby the arti�cial temp slope line and the sine�t slope line in the graph.

3.4.3 Filter

The �lter method di�ers from the other methods in the sense that no curve�tting or approximation is included in this method. This is an algebraicmethod where the idea is to �lter out the sine function from the temperaturedata so that the anomalies can be seen. The method is expected to work wellwith noiseless data as the arti�cial data, but less good with noisy data. To

14


�lter the data, Equation 3.1 is used. It maps simple sine and cosine functionsto a constant. It is a quotient of the �rst and third di�erence. The time-lagis two steps. Example of the method can be seen in �gure 3.9.

|fk+2 − 3fk+1 + 3fk − fk−1|+ |fk+1 − 3fk + 3fk−1 − fk−2||fk+1 − fk|+ |fk − fk−1|

(3.1)

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2

4

6

8

10

12

14

Date

Tem

pera

ture

°C

Artificial TempFiltered SignalAlarm

Figure 3.9: Filter example. When the temperature curve has the sine char-acteristics, the �ltered signal is mapped to a constant. But, when the sinecharacteristics is replaced by something else, the �ltered signal will changeand an alarm occurs.

3.4.4 Other Methods

Some other methods were developed but not presented in the results dueto inter alia malfunction with real data and similarities with the chosenmethods. One method worth mentioning is a curve �tting where the alarmis based on the square error. This method works great with the arti�cialdata where the �tting has a small error until a sudden change appears i.e.a leakage occurs. With the real data provided for the tests this methoddoesn't work at all depending on the noise. The square error is too largeeven without a leakage. The temperature curve also needs to be able to bereproduced with a known function such that the square error remains lowuntil a sudden change appears. If such function is known for a set of datathat is noise free, then this method could be used.

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Chapter 4

Results

This chapter is divided into two parts. The �rst part presents the results ofthe methods with arti�cial data and the second part presents the results ofthe methods with real data. The graphs are the last frame of each simulation.The Sine�t, the slopes and the interpolation points included in some of the�gures therefore represent the sine �t, the slopes and the interpolation pointsof the last calculation.

4.1 Arti�cial Data

The arti�cial data has clear temperature changes and a signi�cant changecan be seen in the amplitude after the defects. However, the leakage increaseis small as stated in section 3.2.

4.1.1 Sum of Sine

The sum of sine method detects two of the three arti�cial cases. The suddenarti�cial temperature change in �gure 4.1 is detected about a month afterthe defect occurs. The more smooth progression seen in �gure 4.2, the sumof sine method misses the leakage change. The last leakage, �gure 4.3, isdetected 8 days after the defection occurs.

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4.1. ARTIFICIAL DATA

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Figure 4.1: Defect on August 4th.

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Figure 4.2: Defect on November 2nd.

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Figure 4.3: Defect on December 2nd.

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Slope comparison detects all of the arti�cial leakages rapidly. However, inthe �rst and third simulation (�gure 4.4 and �gure 4.6) it take some timebefore the sine curve is adapted to the new temperature curve, i.e. the alarmcontinuous a couple of months after the leakage increase was stabilized. Thesmooth change in �gure 4.5 induces only alarms at the defect.

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4.1.3 Filter

The �lter method detects all of the arti�cial leakages nearly instant. Thealarms are continuous until the shape of the curve is a sine wave, see �gure 4.7,4.8 and 4.9.

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4.2. REAL DATA

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4.2 Real Data

The real data has less clear changes than the arti�cial data and there arevirtually no amplitude changes. Thus the leakage �ow changes are evensmaller in the real data than in the arti�cial data.

4.2.1 Sum of Sine

Two di�erent alarm thresholds are represented below, Alarm 0.7 and Alarm1.0. The �rst has a threshold of 0.7◦C between the calculated temperatureand the real temperature, and the other has a threshold of 1.0◦C. The �rstdata set, �gure 4.10, did not give any alarms as expected, the curve has nosudden signi�cant changes. The second data set, �gure 4.11, has more briefchanges, one alarm occurs from Alarm 0.7. In the last data set, �gure 4.12,both the alarm thresholds alert. But still signi�cantly more from Alarm 0.7.

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4.2. REAL DATA

Recalling the properties of a working method in section 3.3.2 one can see thatAlarm 1.0 possesses these properties and will therefore work with curvessimilar to 3126 (�gure 4.10). Alarm 1.0 will also work with temperaturecurves similar to 3116 but a higher threshold should be used so that falsealarms are avoided. Alarm 0.7 is too sensitive.

The interpolation points in the �gures below are the points used to �tthe sum of sine function.

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Figure 4.10: Temperature at measure length 3126 in �bre.

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4.2. REAL DATA

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Two alarm thresholds are represented below. The alarm controls the dif-ference between the calculated slope and the real slope, and the di�erentthresholds appearing below are |ktemp − kcalc| > 0.5 and |ktemp − kcalc| > 0.3,Alarm 0.5 and Alarm 0.3. The slope comparison detects nothing in the �rstreal data set (�gure 4.13). In the second and third (�gure 4.14 and �g-ure 4.15), the Alarm 0.3 detects sudden changes both in the temperaturedrop in autumn 2010 and in the temperature rise in spring 2011. The morebounded Alarm 0.5 only alerts in the last data set in the temperature rise,spring 2011. In similarity to Alarm 1.0 in Sum of Sine, Alarm 0.5 ignores thesmaller changes in 3116 and detects the clearer changes in 3119 which makesthe method workable with temperature curves similar to 3126. Alarm 0.3 istoo sensitive.

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4.2. REAL DATA

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4.2. REAL DATA

4.2.3 Filter

Only one point is presented to view the instability of the �lter function withreal data. The small but existing diurnal variations make the �lter unstableand impossible to use with real data as seen in �gure 4.16.

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Chapter 5

Conclusions

The �lter method is the best of the three to detect changes in the arti�cialdata. But with real data, the method is too unstable to be interpreted. Inorder to operate it needs data that normally is exactly formed as a sine curve.This makes the method unusable with real data.

The sum of sine method detects the clear changes in the arti�cial data.In the real data, it �nds sudden changes and the di�erent thresholds on thealarm makes the method capture di�erent number of changes.

The slope comparison method detects the simulated changes early. Withthe real data, the changes are detected, but not as fast as with the arti�cialdata. This is due to the di�erence between the design of the method for realdata and for arti�cial data described in subsection 3.4.2.

With a dam that has a smooth temperature curve with small or non-existent weekly changes, the slope comparison method will be a good choice.In such case, the alarm threshold can be set small so that changes are detectedrapidly. However, in a dam where the weekly temperature changes originallyare more prevalent, the sum of sine method would be best suited. In suchcase, the slope comparison would be hard to modify so that it distinguishesthe allowed changes from the not allowed ones.

The di�erent alarm levels for sum of sine and slope comparison presentedin the real data section in results shows that the two methods can be adaptedto capture di�erent rates of changes in the temperature data. This is animportant feature as it makes it possible to adapt the methods for di�erentusers and di�erent points along a dam. For example, the changes at measurelength 3116 are interesting to detect for an analyst who wants to see allthe changes and compare points along the dam. Then the slope comparisonmethod with its lower threshold could be used to achieve this.

For the owner of the dam, the higher threshold on both the methodscould be used at points where the temperature curve is similar to 3126. The

25

same thresholds can be used for measure length 3116 although slightly higherthresholds are preferable to avoid false alarm. But for temperature curvessimilar to 3119 clearer changes such as in the arti�cial data are of importance,because we already know that the smaller changes exist in such points. Theresults of the arti�cial data show that this can be accomplished with datawithout noise. The methods should be able to detect the same changes as inthe arti�cial data but with the noise from the real data. However, it cannotbe said for sure that the two methods can achieve this without triggering falsealarms, but by setting a higher threshold, smaller changes can be avoided andthe clearer changes should still trigger the alarm.

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Chapter 6

Discussion

To detect changes in the real data the slope comparison method is the best.But as mentioned in the conclusion, all the small changes are not interestingto alert in all cases. With Alarm 1.0 on sum of sine and Alarm 0.5 on slopecomparison, both the methods alert only in the point 3119, however not in thesame moment. I.e. the data with more obvious changes emits similar alarmfor both the methods. With the more narrow alarm threshold set on boththe methods (sum of sine with Alarm 0.7 and slope comparison with alarm0.3) an interesting pattern occurs. Comparing �gure 4.12 and �gure 4.15 onecan see that in the temperature rise, starting in late April, both the methodsalert at about the same time. But, the slope comparison method alerts acouple of days earlier at all points.

To make the alarm more accurate, the boundaries of the coe�cient onthe sum of sine function can be changed. For example, if you have a coupleof years measured temperature data of a dam and clearly can see a patternof the temperature change, then the boundaries of the coe�cients can bemodi�ed so that the shape of the �tted curve is limited to the same patternas the temperature data. With such stable pattern, the alarm threshold canbe set narrow, and changes in temperature pattern will be detected rapidly.

There are several approaches how to pick which data points to be used ina curve �tting. One way is to choose all the points in a given range. If thereis a lot of data in that range, one data point will not make great impact, ifany at all, when added to the �tting data. Therefore it can be a good idea tochoose some of the data in the given range. To make the sum of sine methodwork with the real data, majority of the points is selected from the latestmonth. The real data has small fast changes that should not be alerted andto prevent alerts to occur, majority of the data must be from the last monthto make the �tted curve most dependent on the last month. Unlike the sumof sine method, the slope comparison method uses data uniformly selected

27

over the past year. The �tted function for the slope comparison method isadapted to the year changes in temperature. To �lter the small changes notwanted to be detected, the line �tting uses a week of data to calculate thetemperature trend.

The small but existing diurnal variations in temperature and the tem-perature changes caused by weather variations make the slope comparisonmethod used for the arti�cial data unusable for real data as mentioned in sub-section 3.4.2. For example, in the spring when the temperature is rising,temperature dips can occur. A negative slope will appear, but the calcu-lated slope will not be negative in spring, and an alarm will occur despite noleakage. Therefore, the modi�cation is necessary to make the method usablewith real data.

To make the slope comparison method more sensitive in situations wherethe temperature curve is smoother, the �tting period for the line can betruncated. This may be a good idea with dams that have small or no shortertemperature changes due to weathering and other in�uencing factors exceptthe seasonal changes.

Another approach than monitoring the time dimension is to focus on thespatial dimension. When a seepage increase occurs, it is highly unlikely thatthe same increase occurs along the entire dam at the same time. A spatialmonitoring system could check the di�erence between max and min temper-ature of one point and its adjacent points and do this for each point alongthe dam to detect anomalies. Unlike the other methods presented in thereport, this method would just need one measurement to operate. However,this would only work if the dam normally has small temperature variationbetween the adjacent points.

Di�erent dams have di�erent temperature behavior as well as di�erent partsof a long dam. It is important to do a extensive research of the dams beforethe choice of alarm is made. The above mentioned modi�cations of thedi�erent methods can make the alarm more accurate but it demands carefulanalysis of the temperature data. Both the sum of sine method and theslope comparison method require one year of temperature data to work, butat least two years of data is preferable to see that the yearly temperaturepattern recurs. If one can see that the pattern repeats itself, the boundariesof the �tted curve can be set narrower to have more control of the curve'sbehavior which makes the method more robust.

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References

[1] Douglas Bates. Nonlinear regression analysis and its applications. Wiley,New York, 1988. ISBN 0471816434.

[2] A.R. Conn, N.I.M. Gould, and P.L. Toint. Trust Region Methods. MPS-SIAM Series on Optimization. Society for Industrial and Applied Math-ematics, 1987. ISBN 9780898714609.

[3] R. Fell and J-J. Fry. The state of the art of assessing the likelihood ofinternal erosion of embankment dams, water retaining structures andtheir foundations. In Internal erosion of dams and their foundations.Taylor & Francis, 2007. ISBN 9780415437240.

[4] L. Ho�mann, M.S. Müller, S. Krämer, M. Giebel, G. Schwotzer, andT. Wieduwilt. Applications of �bre optic temperature measurement.Proc. Estonian Acad. Sci. Eng, 13(4):363�378, 2007.

[5] S. Johansson. Seepage monitoring in embankment dams. Royal Instituteof Technology, Stockholm, 1997. ISBN 9171707921. Doctorial Thesis.

[6] S. Johansson. Detection of internal erosion in embankment dams �possible methods in theory and practice. Key Note lecture, Proceedings-Stability and Breaching of Embankment Dams, 2004.

[7] S. Johansson and P. Sjödahl. Downstream seepage detection using tem-perature measurements and visual inspection � monitoring experiencesfrom røsvatn �eld test dam and large embankment dams in sweden. InProc. Intl. Seminar on Stability and Breaching of Embankment Dams,page 21, 2004.

[8] S. Johansson and P Sjödahl. Numerical modeling of seepage and tem-perature for internal erosion detection in embankment dams. In 11thICOLD Benchmark Workshop on Numerical Analysis of Dams, 2011.

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REFERENCES

[9] J.S. Selker, L. Thévenaz, H. Huwald, A. Mallet, W. Luxemburg, N. VanDe Giesen, M. Stejskal, J. Zeman, M. Westho�, and M.B. Parlange. Dis-tributed �ber-optic temperature sensing for hydrologic systems. WaterResources Research, 42(12):W12202, 2006.

[10] P. Sjödahl, S. Johansson, and P. Westerberg. Experience from two em-bankment dams equipped with on-line seepage monitoring system basedon distributed temperature sensing using optical �bres. In 24th ICOLDCongress in Kyoto, Q.95-R.28, 2012.

[11] J.J. Smolen and A. van der Spek. Distributed temperature sensing � adts primer for oil & gas production. Shell International Exploration andProduction: The Hague, The Netherlands, 2003.

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Detection of Sudden Seepage Changes in … Detection of Sudden Seepage Changes in Embankment Dams Carl Nygren Bachelor’s Thesis in Computer Science (15 ECTS credits) Single Subject