ProceedingsPhysics with

Industry 2017Lorentz Center Leiden, the Netherlands, 20- 24 November

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Proceedings Physics with Industry 2017

Lorentz Center Leiden, the Netherlands, 20-24 November 2017

Colophon

Text Participants and organisation workshop.

Cover photo Foto credit: Supernova Studio’s

Design and production NWO, Utrecht, The Netherlands.

Thanks to The organisation is particularly grateful for the excellent service and facilities of the Lorentz Center, the effort of the senior researchers (from the preparation phase onwards) and the enthusiastic contribution of all participants during the week. The workshop 'Physics with Industry' was organised by NWO in collaboration with the Lorentz Center. The event was funded by the Lorentz Center (which is partly funded by NWO) and the participating companies.

Proceedings Physics with Industry 2017

Table of contents

Introduction

Case 1 : Boskalis

Case 2 : Shell

Case 3 : Soiux CCM

Case 4 : NDW

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Proceedings Physics with Industry 2017

Introduction

Physics with Industry: From looking through metal to travel time accuracy

In the eight edition of the Physics with Industry workshop, 35 researchers worked on five real-world industrial problems during five consecutive days. Shell, Boskalis, Sioux-CCM, Koppert and the National Data Warehouse for Traffic Information (NDW) participated with an industrial case.

The cases were selected by a scientific committee after an open call during which companies could submit a case. The submitted cases ranged from optimizing existing technology to getting a better prediction model to finding new theoretical opportunities to tackle a company problem. All of the case owners were pleased with the results of the week and participating in the workshop helped them to develop their case further. For example Hans Kuppens on the case of Sioux-CCM: "They have, in just one short week, been able to come up with two cost-effective solutions. Through a simple experimental setup and systematic approach they have uncovered the problem of the diffractive optical element and found a SLD on their own initiative. In one word: fantastic! We can now move forward with the presented solutions."

All of the cases were coached by an academic and an industrial supervisor. This guaranteed the scientific quality and the applicability of the solution. The participants enjoyed the workshop due to the scientific challenge but also through experiencing how industrial problems are solved and how companies work. The winning team worked on the Boskalis case and excelled with their original experiment: with candles and two bowls of liquid and gel they tested the acoustical differences and viscosity. They researched echography, heat-transport, calculated the amplitude of lamb waves and microgravity. They managed to provide Boskalis with an advise for a concrete solution that could potentially be used by divers.

The workshop was held from 20 to 24 November 2017 at the Lorentz Center in Leiden, and included a site-visits on 17 November as part of the preparation for the workshop. The project is a joint collaboration between NWO and the Lorentz Center.

These proceedings contain five chapters, one for each company case. The Koppert report is not yet available.

OIL DETECTION BEHIND THE HULL OF SHIP

Physics with Industry 2017 - Boskalis

Team Amin Moradi (LU), Dolf Timmerman (UvA), Gijs Hendriks (RU), Lantian Chang (UT), Maysam

Shabanimotlagh (TUD), Sachin Nair (UT) and Shyama Varier Ramankutty (UvA)

Scientific support

Dr. Deyan Draganov (TUD)

Company support

Roeland Neelissen (Boskalis), Mark Biesheuvel (Boskalis) and Marco Mentink (Smit Salvage B.V.)

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Table of Contents

1. Introduction

2. Solution tree

3. Promising solutions

3.1 Thermal methods

3.2 Acoustic methods

3.2.1 Lamb wave attenuation

3.2.2 Attenuation analysis

3.3 Thermal assisted acoustic

4. Possible solutions for limited situations

4.1 Microgravity

4.2 Radioactivity

5. Extra ideas

6. Conclusions

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1. Introduction

One of the main operations done in Boskalis include emergency response and salvage through SMIT. And often they face several difficulties in this process and move forward solving them. One of the main challenges they face in a ship sinking situation is the safe retraction of oil from the hull of the ship or from other parts, which in most of the cases is made of steel. Currently they tackle this by making holes in the areas of the ship where oil is most likely to be found, check whether it is oil or water behind the hole, and if it is oil then remove it by pumping and if it is water fill the hole and then move on to the next possible spot. This process is repeated until they find the oil. This is a very time consuming and expensive process.

A few years back, Boskalis conducted research to improve this process. They used transducers to measure the acoustic impedance of the substance behind a 2-2.5 mm thick steel to imitate the effect of the hull of ship. A schematic of their set-up is shown on the right side image in the figure given below. It can be seen that there are three different compartments with different levels of air, heavy fuel and water. However, the acoustic impedance of sea water and heavy oil were close enough that this method didn’t prove useful in practice.

The problem we were presented with for this years’ Physics with Industry workshop was to make a case for a possible solution by which you can distinguish the presence of oil or water behind a steel block of thickness around 2.5 mm, without drilling a hole on the steel. Our group started tackling this problem on the first day by ‘brain storming’ all ideas we can come up with. This is presented as a chart or tree in the figure below. We first categorized them into possibilities with and without drilling a hole.

We expanded on the possibilities where we don’t have to drill a hole. In this we have several modes of investigation categorized in terms of the type of signal we could use, which can be acoustic (low and high frequencies and other types), electromagnetic (low and high frequencies), potential fields (gravity and magnetic), particles (radioactivity and cosmic muons) and others. We also listed several physical properties which we probe including heat capacity, attenuation coefficient, viscosity etc.

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2. Solution tree:

Once we were done with our out-of-the-box thinking we started looking more into the practical possibilities of the choices we listed. We discarded several but at the same time we also expanded the choices we thought are practically possible. The figure below shows some of the choices we discarded crossed-out in red and some of the choices highlighted which were promising to proceed the research.

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3. Promising solutions

3.1 Thermal method

Thermal conductivity is a property of material that indicates how well it can conduct heat. The equations describing these are Fourier’s law for heat conduction. In a simplified model, where convection is ignored, the parameters describing the dynamics of heat conduction are: Heat capacity Ck (J/ kg K), thermal conductivity (W / m K) and density ρ (kg). Since the values hereof are variating strongly in the materials we are interested in, using these differences may be a viable way of discriminating the materials.

Table 1 shows the materials in our model system, with the accompanying physical parameters of interest (NB these are typical values, but can depend on the exact composition and circumstances).

Thermal Conducivity k (W / m K)

Heat Capacity Ck

( J / kg K ) Density ρ ( kg / m3 )

Steel ~ 17 0.446 8000

Water ~ 0.591 4.2 1000

Air ~ 0.025 1 1.25

Oil ~ 0.114 2.1 950

Thermal conductivity simulations have been performed on the model system shown in the figure. It consists of a point heat source, which is has a fixed heat input at the surface of a steel plate of 20 mm thick. The side of the heater is surrounded by water, and two temperature probes are fixed at 10 cm distance from the heater. On the backside of the steel plate two different liquids (oil, water or air) are fixed. The temperature response of both probes are determined as a function of time, after applying the heater. The begin temperature of the whole system was set at 278.15 K.

Thermal probe set-up

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Probe Oil

Probe Water (isolation)

Probe Oil (isolation)

Heater 1 kW

Isolation In order to reduce the effect of the surrounding water, the same simulations were

done on with the assumption of thermal isolation around the probing side. Result of the simulations with and without isolation are both shown on the right hand figure, the heater power was kept at 1 kW.

Heating power In order to see the influence of the power of the heater on the temperature dynamics,

a set of simulation was run, where instead of a fixed temperature, a fixed input power was used. The graph below shows the temperature after 10 minutes for probes in oil and water side, for input powers of 100, 300, 1000, 3000 and 10000 Watt. The blue line indicates the difference in end temperature between the probes.

0 2000 4000 6000 8000 10000

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Thermal profile results of simulations with input power of 1000 Watt after 10 minutes with water on the outside (left figure) and thermally isolated outside (right figure).

It can be concluded that water removes heat better then oil. This will even be stronger

if convection is taken into account, which will occur in water, but not in oil. So the temperature difference can actually be larger than this. For an implementation of this method it is however important to keep the convection in mind, as warmer liquids may rise and heat the above lying material. A horizontal source / detector system will be a viable solution to this problem.

3.2 Acoustic methods 3.2.1 Lamb wave attenuation:

Ultrasound is sound waves with frequencies higher than the human audible frequency limit (approximately 20 kHz). One of the applications of ultrasound is to detect objects and measure distances. This technique is often used in medicine, but also in the non-destructive testing of products and structures. For the proposed problem we can use ultrasound in different ways. One approach is to estimate the properties of the materials behind the ship hull with the amplitude of the reflected echo signal. The reflection coefficient is dependent on the difference between the acoustic impedance of the steel and the material behind that. This approach was used by Boskalis some years ago, which was not successful. From the table below, the acoustic impedance of the oil is very close to the water, even in the laboratory measurements the difference in the reflection coefficient was not easily distinguished from each other.

Density (kg/m3)

Speed of sound (m/s)

Acoustic Impedance (MRayls)

Viscosity (mm2/s)

Water 1000 1500 1.5 1 Oil 991 1430 1.4 330-380

Steel 7800 5900 46 -

Air 1 300 0.0003 -

Although the acoustic impedance of oil and water are quite similar, but the viscosity

of the oil is significantly higher than water. We want to benefit from that, to measure the attenuation of the ultrasound wave. Therefore we use two ultrasound transducer (as shown in the following figure), and use one of them to generate an excitation pressure, and receive

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the wave with the receiving transducer. By propagation of the wave, an interaction is made via the particle motion of the steel and the fluid on the other. In case of having material with high viscosity, the ultrasound wave is attenuated. Therefore the material with high viscosity can be distinguished from the material with low viscosity.

In solid plates elastic waves can propagate in the plane of the plate. One type of these waves are the Lamb waves whose velocities depend on the frequency (or wavelength) and plate thickness, as well as the elastic properties and the density of the plate material. In the following figure, dispersions curves of free Lamb waves for plates with two different Poisson's ratios are plotted. The x-axis shows the product of angular frequency and plate thickness normalized by the shear wave velocity of the plate, and the y-axis shows the phase velocity of the Lamb wave normalized by the shear wave velocity. For the high frequencies symmetric (S0) and anti-symmetric (A0) modes converge to the Rayleigh wave velocity, which is approximate 92 % of the shear wave velocity. From this table one can obtain the phase velocity of the modes which can propagate in a plate, at a certain excitation frequency and plate thickness.

Dispersions curves of free Lamb waves for two different Poisson's ratios . The x-axis shows the product of angular frequency and plate thickness normalized by the shear wave velocity. The y-axis shows the phase velocity of the Lamb wave normalized by the shear wave velocity. For high frequencies and modes have the Rayleigh wave velocity, approximate 92 % of the shear wave velocity. [Wikipedia]

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Furthermore from the literature, the effect of viscosity of the fluid on the amplitude of the lamb wave propagation for the first symmetric mode is calculated for a 1 mm thick SiC plate loaded with a fluid with different viscosities. For the frequencies below the critical frequency, the viscosity does not have any influence on the attenuation of the wave, but at higher frequencies the wave is attenuated based on the viscosity of the fluid. This figure shows that for the proposed approach, the frequency should be chosen higher than the critical frequency, so that it can influence the lamb waves. This critical frequency is related to the thickness of the steel plate.

Normalized ‘‘viscosity-induced’’ attenuation versus frequency for the lowest-order symmetric mode in a 1-mm-thick immersed SiC plate [1].

In order to test this concept, two similar transducers from Olympus (V305, 5 MHz, 0.5 inch) are employed. With an arbitrary wave generator, a 2 cycle sine pulse is applied to the transmit transducer, and steel plates with different thicknesses are used to test. We tested at two different frequencies of 5 MHz and 1.7 MHz. On the other side of the plate, and in different measurements, air, water, and oil are employer on the steel, and the amplitude of the received signals are compared. A photograph of the measurement setup is shown in the following figure:

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Results, discussion and conclusions:

Table below shows the peak to peak voltage (Vpp) measure for the output signal from our experiment shown in the picture above for two different transducer frequencies:

Vpp in air (mV)

Vpp in water at RT (mV)

Vpp in water at

LT, T~7C (mV)

Vpp in oil at RT (mV)

Vpp in oil at LT (mV)

5 MHz 300 100 80 160 100 (T=7C) 1.7 MHz 2200 400 - 600 600 (T=8C)

Output wave from our experimental set-up for 1.7 MHz which is shown in the figure above showing

the results with (a) air (Vpp 2 V) (b) water (Vpp 400 mV) and (c) oil (Vpp 600 mV) between two transducers.

As can be seen in the table, the peak to peak voltage (Vpp) of water is higher compared to oil at both frequencies and temperature indicating that differences in viscosity and density between oil and water can be used to discriminate between the two liquids. The difference in Vpp in oil between room and low temperature is 60 volts at 5 MHz; while the difference is 0 at 1.7 MHz. The viscosity of oil changes with temperature (table 2), which may indicate that around 1.7 MHz damping by density differences was observed, while at 5 MHz a combination of damping by density and viscosity was observed.

However, these observations have to be investigated more carefully, for example using higher frequencies and other plate thicknesses. Furthermore, the transducer used in this experiment had a matching layer which was designed for water coupling, not for steel coupling. Finally, the transducer surface was positioned directly on the steel plate. However, according to [REF2] ,an angle between the plate and transducer surface might provide improved coupling between the transducer and steel plate since the wave-length in the coupling gel, plexiglass or other material (λs), and the steel plate (λL) are matched. This angle can be calculated by ϴ = arcsin(Cgel/Csteel), with C the speed of sound in the coupling gel/material and steel. See also the figure below [2].

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Schematic drawing of using a plexiglass wedge to match the wave length of the transmitted wave in the plexiglass wedge (λs = Cgel/f ) and the wavelength of the Lamb mode (λL = CSteel/f); f is the transmit frequency, C is the speed of sound. The wedge angle can be calculated by ϴ = arcsin(Cgel/Csteel). Figure adapted from Nicolas et al. [2].

References: [1] Adnan H. Nayfeh and Peter B. Nagy; Excess attenuation of leaky Lamb waves due to viscousfluid loading; Journal of Acoustical Society of America; Volume 101 (5), 1997.[2] Nicolas Wilkie-Chancellier, Martinez Loïc, Serfaty Stéphane, Griesmar Pascal. Lamb wavesensor for viscous fluids characterization. IEEE Sensors Journal, Institute of Electrical andElectronics Engineers, 2009, 9 (9), pp.1142-1147.

3.2.1 Attenuation analysis:

In medical pulse-echo measurements, an ultrasound pulse (around 5 MHz, 1 cycle) is transmitted into the tissue and the reflected signals are obtained again by the same transducer element. This principle can also be applied to create a 2-D image using a multi-element-array transducer, an example can be seen in figure 1.

In ultrasound imaging of the liver, the attenuation of the ultrasound signal in depth correlates with the fat content in liver. The obtained ultrasound signal attenuates much stronger in a fatty liver compared to a low fat liver (see figure 1).

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Fig. 1: Left - ultrasound image of low fat liver, and ultrasound image of high fat image. High fat livers will results in high attenuation in the ultrasound images compared to low fat livers. Left bottom of each ultrasound image, a microscopic image of a liver biopsy (left low fat, right high fat) is displayed [ref 1]

This principle might also be applied to discriminate between (salty) water and oil: the ultrasound signal is expected to attenuate minimally while in oil it is expected to attenuate more strongly (table 2). A simple pulse-echo experiment by a one element transducer can be used to test this principle. Only one line (A-line) will be obtained and evaluated instead of 2-D image (build by multiple A-lines, figure A). A drawing of the experimental set-up and expected signals can be seen in figure 2.

Table 1: The effect of temperature on the viscosicoty of different types of crude oils; the viscosity of oil, especially heavy oils (low API) increases strongly with temperature.

Table 2: The speeds of sound, viscosity and attenuations (alpha_abs) of different oils. The Specific Gravity of the different oil can be calculated by the API at 60 degree Fahrenheit according to SG = 141.5/(131.5+API). Figures adapted from REF2

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Figuur 2 a) Schemetic drawing of a pulse-echo aquistion into a liquid (blue) through a (steel) plate (red). A pulse is transmitted by the transducer (gray block) into the liquid, and reflections and scattering by particles (echos) is received again by the same transducer. b) An example of an attenuated received signal c) example of an non-attenuated received signal.

Practical issues:

The transmitted pulse and the reflected signals have to pass the steel layer twice. The steel will probably attenuate and block the signal strongly. Consequently, almost no reflected signal is left to analyse and to compare.

Furthermore, it is questionable if water contains enough particles that can cause reflections and scattering of the transmitted signal to create the echo signal. Otherwise, if water contains less or almost non scattering particles compared to oil, the total power of the reflected signal might also be used to discriminate between water and oil.

sSome experiments were conducted to analyse the signal originating from water and coffee (oil was not available at that moment at Technical University Delft). A pulse-echo experiment (5MHz transducer, water matching layer) was performed in a cup of water and coffee (similar as figure 2, without the metal plate.). Coffee was used as it might contain more particle compared to water. The received signals contained very low and noisy (low SNR). It is expected that these results will be even noisier if a metal plate was between the liquid and transducer surfaces. It has to be tested how this signal will look like in oil.

Conclusions: This method might only be applied when the equipment is sensitive enough to get

signal through the metal plate. In that case, oil and water can be distinguished by differences in attenuation, density of reflecting particles or a combination can be used. References: [1] http://www.engineerlive.com/ Understanding the limitations of ultrasonics in cruel oil measurements, Raymond J Kalivoda; petroleum measurement development manager for FMC Techonologies, Erie, Pennsylvania, USA. www. fmctechnologies.com

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[2] Quantitative Ultrasound for Staging of Hepatic Steatosis in Patients on Home ParenteralNutrition Validated with Magnetic Resonance Spectroscopy: A Feasibility Study.Weijers G, Wanten G, Thijssen JM, van der Graaf M, de Korte CL.Ultrasound Med Biol. 2016 Mar;42(3):637-44. doi: 10.1016/j.ultrasmedbio.2015.11.004. Epub 2015Dec 19.http://www.sciencedirect.com/science/article/pii/S0301562915006432?via%3Dihub

3.2.1 Thermal assisted acoustic method:

In the acoustic solution the amount of power that can be transfer to the metal is highly depend on the coupling efficiency which is influenced by the amount of applied force on the transducers, the angle between transducer and metal surface and the roughness of the surface. These parameters can change the signal in an order of magnitude. Since in the acoustic solution need at least two measurements in two different point the coupling efficiency may cause a lot of error.

Temperature dependence of viscosity AFT oil (red line) and water (blue line)

Here, by combining the acoustic and heat propagation solutions we present a method to detect the material behind the wall by one simple measurement. This method is based on the temperature dependence of viscosity of the fluids. Graph above shows the viscosity of oil (red line) dramatically drops by increasing the temperature while the viscosity of water (blue line) does not change compare to the oil. This open a way to detect the material behind the wall by looking at its viscosity changes while its temperature increase. This can be obtain by measuring the attenuation of the Lamb wave in different temperature.

Figure below shows the schematic of a possible set up for this measurement. Just like the acoustic solution, there is two transducers, one to generate the acoustic wave and another one to detect the Lamb waves. The generated wave will shape a Lamp wave that travel through the metal (oil tank wall in this case) and will be detect on the other transducer. Since the attenuation of the lamb wave depends on the viscosity of the material behind the metal and the viscosity of the material vary with temperature, it is possible to monitor the behavior of the viscosity of the material behind the wall in deferent temperature by looking

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at the attenuation of Lamb wave. If the viscosity changes of the liquid behind the wall shows reasonable attenuation (schematic set-up) the liquid behind the wall is oil.

Schematic of the thermal assisted acoustic set up

4. Possible solutions for limited situations

4.1 Microgravity

Gravimeter can be used to detect small changes in the gravitational field caused by the density different of the material. This technique is used in oil industry to detect oil underground. There are few companies has products to do this such as shown in Fig 1 and Fig 2. Here are two examples:

Figure 1. MEMS based Gravimeter from Silicong. The working principle is based on deformation of a cantilever caused by gravity change. http://www.silicong.com/technology.html

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(a) (b) Figure 2. (a) GT-2M Marine Gravimeter. (b) Example of its measurement with a resolution of 480 m. http://www.canadianmicrogravity.com/gt_2m_marine_gravimeter/.

There are a two concerns about this technique. First, this technique it commonly used for geological object, thus the resolution may not high enough to distinguish different parts of a ship. For example the resolution in Fig.2 (b) is not good enough. Second, the density of the oil used in ship can be small, equal or larger than the density of sea water. This means the application of this technique need some pre-knowledge about the density of oil used on ship. And it can only be used when the density different is sufficiently large.

The way to answer this two questions will be contact the companies who sell or use gravimeters. The knowledge of whether they can distinguish water from oil and the minimal detectable size is needed to proceed the possibility studies.

4.2 Radioactivity

Radioactive decay (also known as nuclear decay or radioactivity) is the process by which an unstable atomic nucleus loses energy by emitting radiation. Since the radioactive elements are exist in oil it may be possible to detect the oil in a sunk ship tank by monitoring the radioactive radiation around the ship. There are several type of radioactive decay such as Alpha particle, Beta particle and gamma ray. Although Alpha and Beta particles cannot travel in long distance (around 20 cm in air) and those will be bloke by the oil tank’s wall, Gamma ray can be still detected around the ship. Since the radioactive pollutions in the oil are deferent, depend where the oil come from and how it has been transported and also the radioactive element in seawater vary in different region of the world, this method need is not an easy and cheap way to detect the oil.

Reference:

5. Extra ideas

5.1 Muon scattering tomography Muon tomography is an imaging technique where the incoming and outgoing

trajectories of muons are detected. Charged particles (in this case muons) crossing a material

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are deflected (and decelerated). The deviation angle roughly follows a Guassian distribution with mean =0 and r.m.s value given by:

where p is muon momentum, X material thickness, X0 the radiation length (~ 1/Z). Linear scattering density is given by:

This method has been shown to be useful in finding elements of higher atomic number and can be done in a relatively short time (~ 7 minutes). However, in our case the distribution of heavy elements present in sea water and oil are not well known and may not be uniform in all parts of the world. Also, the experimental set-up is not handy enough to use it in a situation like in the case of ship sinking. Due to these restrictions on the available set-up’s we have at this time, decision was taken to discard further research on the applicability of this technique in detecting oil and water in the tank of a sunken ship.

References: [1] http://www.pd.infn.it/~checchia/Siena2016.pdf[2] M. Benettoni et al., 2013 JINST 8 P12007[3] K. N. Borozdin et al., Nature 422, 277 (2003)[4] Wikipedia – section on muon scattering tomography in Muon tomography

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5. Conclusions

It can be concluded that thermal assisted acoustics is a promising direction to further investigate. Thermal assisted acoustics is the powerful combination of viscosity detection by lamb waves and heat conductivity. In practice, a diver positions a transmit and a receive transducer with a fixed spacing on the steel hull of the ship and start the measurements to detect the signal intensity of the lamb wave. Thereafter, the diver heats up (according to heat capacity calculations) the steel plate between the two transducers to also the liquid behind the plate. Next, the measurement will be repeated. If the signal intensity of the lamb wave increases, since the viscosity decreases by increased temperatures, the liquid will be most-likely to be oil; if the intensity remains the same, it will be water or air.

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Sorting carbon particles: running on hydrogen, building

on carbon

Authors Artem Ivashko (LU), Irana Denissen (UT), Sudeep Maheshwari (TUD), Teofil Minea (TUe), Ido Niesen (UvA), Vivek Sinha (UvA)and Chao Zhou (UT)

Company representative and scientific guidance -Cor van Kruijsdijk (Shell) and Ilja Voets (TUe)

Company: Shell

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1. Situation / background

Driven by recent technological advances and the need to minimize anthropogenic global warming, it is expected that

the near-future will see a shift towards renewable energy sources, such as wind and solar, as the main sources of

energy. These sources employ electrons as their energy carriers. Since electric energy is not easily stored, nor readily

applicable for high-power industrial applications, there is a need for complementary dense energy carriers. A

promising carbon-free candidate is hydrogen, which, among other methods such as water splitting, can be produced

by splitting abundantly available methane into hydrogen and carbon using pyrolysis. In this process, most of the

carbon is seen as an unwanted by-product. However, certain valuable carbon structures such as carbon nanotubes may

form during the pyrolysis. Developing a low-cost and scalable process to separate and extract the nanotubes from the

carbon by-product may lead to stronger and more environment friendly manufacturing products, and in the process

make methane splitting more economically viable.

2. Problem description / scientific challengeCurrent processes that produce the solid carbon as a side product yield a variety of carbon particle sizes and

morphologies. Optimising the processes to increase the yield of the more valuable forms of carbon is in its infancy.

To speed up the development of this technology we are turning to high throughput experimentation. The current

bottle neck lies in sorting and characterizing the produced carbon particles.

3. Research questionHow can we separate a batch of carbonaceous nano-particles based on size, shape and morphology?

4. Proposed SolutionsOur solution consists of two parts: A mechanical sorting of the carbon particles followed by a chemical separation of

the carbon nanotubes (CNTs) from the amorphous carbon (AC) bulk. For mechanically pre-sorting the carbon

particles obtained from the methane pyrolysis based on their shape and size, we suggest a combination of three

complementary methods: sieving, centrifugation, and magnetic separation using a ferro-fluid. In the sieving part, we

use a two-stage technique described in [1]. During stage one the carbon particles are flushed through a sieve with a

mesh size ranging from 1 – 100 µm. The carrier liquid is subjected to low-frequency mechanical oscillations to

prevent the clogging of particles into the sieve pores. Ultimately, a layer of larger particles builds up against the sieve

pores, which are rinsed periodically by reversing the fluid flow (stage two), after which we repeat the whole

procedure. By sequencing sieves with different pore-sizes, we can split the original carbonaceous powder into several

bins each containing carbon particles of similar smallest cross-section. Sieving can be done on both lab and industrial

scale.

The centrifugation method is a well-established sorting technique [2], which is widely used in for example

microbiology. By immersing the carbon powder in a liquid and then rotating the system with high angular velocity

(~10,000 rpm), particles of different diameters start to move with different radial velocities, separating the particles

based on their surface areas (and to a lesser extent on their shape and density). We propose to use centrifugation on a

lab-scale for the initial experiments.

The final pre-sorting method is magneto-hydraulic dynamic separation. We immerse the carbon particles in a

ferro-fluid. Applying a strongly-varying magnetic field to a ferro-fluid creates an effective buoyancy gradient for the

carbon particles, sorting the particles based on their surface area. A quick calculation for carbon particles (of sizes in

between 1 to 100 µm) shows that a permanent magnet can realize the sorting with acceptable resolution (e.g. into four

bins corresponding to 0-25, 25-50, 50-75, and 75 and above µm). Even higher resolutions can be achieved with a

superconducting magnet, but at increased costs.

Magnetic sorting with ferro-fluid has been developed and proven to work for the industrial electronic waste

separation. This way, gold, silver, copper, aluminum, PVC, polystyrene, etc. have been separated successfully within

a single-stage process from electronic waste. The advantages of magnetic sorting over centrifugal sorting are the

continuous throughput, very good scalability, and adjustable resolution. We therefore propose to use this method on

industrial scale. However, it should be noted that the method has not yet been demonstrated to work for carbon

particles, so a lab-scale trial is needed. Another disadvantage of this system is its complexity and commercial

unavailability.

After the powder particles have been sorted on the basis of shape and size, we apply separation techniques to

extract the useful materials, namely CNTs from the AC. The AC has a preference towards adsorption of electrons

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while the CNTs preferentially interact strongly with positively charged ions. This selective adsorption of ions stems

from the difference in the electronic properties of CNTs and AC. This difference in property can be utilized for

selective dissolution of CNTs/AC in a polar media. For example, in a salt solution that furnishes large amounts of

ions in the solution phase, CNTs will preferentially interact with the cations and will dissolve readily in the solution.

On the other hand, if the bulk particle containing CNTs and AC together is supplied with electrons, the electrons will

preferably go to the AC leading to its spontaneous dissolution and consequent precipitation of CNTs.

Scheme 1: proposed process flow diagram for separation of CNTs from bulk AC.

Based on this property difference we selected the following three methods for chemical separation of CNTs from AC:

1. Treatment with a solution of Sodium-Naphthalide (NaNp) in Dimethylacetamide (DMAc) [3] 2. Electrochemical

separation [4] 3. Na/NH3 in Dimethylformamide (DMF) [5]. Figure-SI-1 (see appendix) summarizes the working

principle behind methods 1 – 3. Chemical separation in DMAc solution using NaNp has relatively higher yields in

comparison to methods 2 and 31 and is intrinsically scalable in an industrial setting. The electrochemical separation

involves supplying current to the bulk particles at the cathode and thereby selectively charging the AC phase leading

to its dissolution. Using lower voltages, this method can be applied as a pre-purification step before method 1 to

decrease the AC phase and thereby maximizing overall yield. Once the CNTs are separated from the AC phase, a

further size-based separation of CNTs can be performed using method 2. Scheme-1 summarizes the proposed process

flow for chemical separation.

5. Suggestions for next stepsExploration of spectroscopy based methods for lab-scale non-destructve (for the bulk particle) diagnostics for CNT

content shoud be deisgned and developed. In addition, next steps could follow in the form of a lab scale set-up to

design and optimize the suggested process flow. The stage 1, which involves a mechanical pre-sorting can be initiated

with the help of already existing centrufugation set-up. Since the next step involves chemical/electrochemical

separation steps where presence of protic solvents can be a complication, some trials can be made with the liquid used

for centrifugation based separation. In the next step the chemical separation using NaNp/DMAc set-up can be tested

for yields with the bulk particles under consideration. The literature results are mainly reported on particles with high

amount (~90%) CNTs and relatively lower amounts of AC. In the case at hand these proportions are reversed and

therefore extra trials may be required. Use of electrochemcial purification methods under low voltage situations to

perform a pre-purification can be tested. The exact prarmaters for charge density based tuning in the Na/NH3/DMF

based approach can be found by trial experiments for further chemical separation of CNTs. Moreover, the yield of

Na/NH3/DMF based separation can be found by trial experiments as this value is not currently reported in literature.

Once the distribution of CNT content is known the pyrolysis process can be further optimized for production of

unformly sized particles and the first step of separation can be completely avoided leading to further simplification of

the process.

1 The yield from method 3 is not clearly described in literature. Since this method involves selective

dissolution of large sized particles in solution phase, we expect that some amount of CNTs may be lost to

solution and expect the yield to be relatively lower than in Method 1.

26

6. Appendix: Pictures

Approach followed during the workshop week

Possible solutions that did not make it

7. References:[1] Clogging-free microfluidics for continuous size-based separation of microparticles. Y. Yoon, S. Kim, J. Lee, J. Choi, R. Kim, S. Lee, O. Sul, S.

Leea, Sci Rep. 2016; 6: 26531. DOI: 10.1038/srep26531

[2] Classification of particles by centrifugal separator and analysis of the fluid behavior. T. Yamamoto, T. Shinya, K. Fukui, H. Yoshida, Advanced

Powder Technology, Volume 22, Issue 2, March 2011, Pages 294-299. DOI: https://doi.org/10.1016/j.apt.2010.12.009

[3] A one-step route to solubilised, purified or functionalised single-walled carbon nanotubes. A. J. Clancy, J. Melbourne and M. S. P. Shaffer, J.

Mater. Chem. A, 2015, 3, 16708. DOI: 10.1039/c5ta03561a

[4] Systematic comparison of conventional and reductive single-walled carbon nanotube purifications. A. J. Clancy, E. R. White, H. H. Tay, H. C.

Yau, M. S.P. Shaffer, Carbon 108 (2016) 423e432. DOI: http://dx.doi.org/10.1016/j.carbon.2016.07.034

[5] Trajectory of the Selective Dissolution of Charged Single-Walled Carbon Nanotubes. D. J. Buckley, S. A. Hodge, M. De Marco, S. Hu, D. B.

Anthony, P. L. Cullen, Kevin McKeigue, Neal T. Skipper, M. S. P. Shaffer, and C. A. Howard, J. Phys. Chem. C 2017, 121, 21703−21712. DOI:

10.1021/acs.jpcc.7b06553

27

Appendix:

Selection of chemical separation method: Different physical and/or chemical techniques can be employed for extracting CNTs from the

amorphous bulk. All of these techniques essentially employ the difference between physical/chemical

properties of CNT versus the AC. This difference of properties can be intrinsic property difference

between the CNTs and the AC, or could be induced externally. Among chemical separation methods,

several methods that harness reactivity of CNTs with inorganic acids are reported in literature. Chemical

reaction of CNTs with acids suffer from problems of low yields, can cause irreversible damage to CNTs

and are not scalable for industrial applications. Physical purification methods that often employ

selective adsorption of CNTs on solid surfaces also suffer from similar drawbacks.

The approaches that did not specifically work include (for detailed study see reference [4] in main

text):

1. HCl purification

2. H2O2/HCl purification

3. HNO3 purification

4. Air purification

5. Water vapour purification

For more pictures refer to the power-point presentation attached with the report.

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Approach followed during the workshop week Monday:

1. Get to know each other and each other's expertise.

2. Make sure that we all understand the research question.

3. Compose a list of methods we could possibly use to separate and characterize the carbon

particles.

Tuesday:

1. Organize our list of methods into an issue-tree to make sure we have not missed anything.

2. Group the methods based on which particle property they use to separate the carbon particles

(i.e. mass, size, nanotube content).

3. For each group, pick the method that we expect is least expensive and easily scalable to

industrial size. Result: a two-step process consisting of (A) sorting the carbon particles and

(B) chemically separating then carbon nanotubes from the remaining (amorphous) carbon

material.

4. Take the methods from the previous step to create and prepare short presentation for the next

day, and discuss with our scientific supervisor.

Wednesday:

1. Give 5min presentation.

2. Divide the group into two subgroups (for the sorting and separation steps) to do a literature

study to figure out the details behind the proposed methods.

Thursday:

1. Finish the aforementioned literature studies.

2. Split the group into three: (general overview, sorting and separating), and let each group

create their part of the slides for the final presentation on Friday.

3. Discuss the slides with our industrial supervisor, and implement his input.

4. Practice presentation.

5. Team members that will not present on Friday write up the final report, and the presenting

team members go home and rest.

Friday (planned):

1. Well-rested team member give presentation.

2. Win the award for best presentation.

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Figure 1, the schematic diagram of 3D scanning from the DOE. An incident laser beam with a certain intensity and phase profile is illuminated on the DOE. The phase profile (usually etched to multi-levels profile) on the DOE pattern diffracts the beam that is projected to a far-field screen.

Speckle reduction in 3D teeth reconstruction

Adam Taylor (TUe), Aditya Kulkarni(TUD), Chuan Chen(RUMC), Dejan Davidovikj(TUD), Najmeh Sadegh(ARCNL), Sander Blok (LU), Weichun Zhang(LU), Martin Caldarola (LU) - guidance: Nandini Bhattacharya (TUD) - company: Marnix Tas, Hans Kuppens.

Introduction Clay bite are conventionally used to duplicate a 3-D shape of teeth, which is uncomfortable for

patients and clinicians. As an alternative approach, Sioux CCM has designed a scanning device for 3D mapping of teeth that can replace the use of the clay bite. In this scanning device, a laser line grid is projected onto the teeth surface that the deformed line pattern can be recorded by an integrated camera. The 3D shape of teeth can be reconstructed from the deformed lines pattern based on the so-called triangulation technique.

The fidelity of the 3D mapping is directly related to the accuracy in determining the position of the lines in the acquired image. This depends on i) the quality of the projected lines and ii) noise in the acquisition stemming from the roughness of the target surface, also called speckle. The main problem currently lies in the sharpness and the uniformity of the projected light, which also appears to have a noisy, “wiggly” shape.

Figure 1 shows the proposed 3D scanning set up composed by three components: laser source, diffraction optical element (DOE) and the screen, emulating the teeth. The source of the low pattern quality was narrowed down to the DOE and the target surface. Various strategies were proposed to improve the line quality, such as improving the DOE, modulating the laser source wavelength, decreasing the coherence of the light source, changing the DOE filling factor and fast speckle disturbance. Possible solutions were explored and evaluated through either experiment or numerical modeling. To quantify the sharpness of the lines, an algorithm was used to assess the uncertainty in determining the center of a projected line. The details of this algorithm are described in Appendix C.

Methodology The DOE is manufactured by

etching multiple discrete phase levels (see figure 1). The number of discretization levels has an influence in the final pattern. We evaluated this effect by synthesizing DOE designs with a variable number of discrete steps using the Gerchberg-Saxton algorithm. We then quantified the precision based on the deviation of the lines position for each design.

Since interference is an inherent phenomenon of coherent light, the speckles are expected to be substantially suppressed by reducing the coherence of the light source. To experimentally show the effectiveness of incoherent light

source, a non-coherent white light source was filtered using a bandpass filter of (with a bandwidth of 100 nm) and central wavelength of 470 nm. The resulting pattern was then compared to that of the coherent one. In addition, the beam was collimated before the DOE to observe the effect of collimation

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and beam size (with a iris of variable size) by measuring the pattern created on a screen with a second lens. In the appendix we give more details about all our experiments.

To quantify the performance of the explored methods, we fitted the line’s crossing profile of the stripe pattern with a Gaussian function and extracted the center. The standard deviation of the extracted center was chosen to quantify the pattern’s accuracy.

Another possible solutions we discussed but did not fully explore are: mechanically vibrate an optical element with a frequency much higher than the integration time of the camera, blurring out the speckle pattern and modulating the wavelength of the laser.

Results and Discussion For the DOE design optimization we evaluated the performance of different discretization levels,

obtaining a dramatic drop in the standard deviation when the number of levels is increased, as it can be seen in figure 2(a). We observed a ten-times reduction when we go from 2 to 8 levels. From the information of SILIOS optics (a micro-optics company in French), the price of 8 phases pattern is 160 euros per piece, and the price of 2 phases one is 60 euros per piece, which makes this a viable improvement for the device that does not require any change to the design.

Figure 2. Results. (a) Effect of discretization steps in the DOE. Standard deviation of the determination of the center of the line for different discretization steps. We observe a dramatic drop in the first few steps. The dashed line shows the continuous case. (b) Effect of the illumination source coherence. We show the line pattern obtained with a laser diode source (top) and incoherent blue light (bottom). (c) Effect of the illumination area on the DOE. We changed the spot size on the DOE, from small (top) to complete illumination (bottom).

In figure 2(b) we show the comparison of the experimental stripe patterns obtained with a coherent laser diode and incoherent light blue light. Although the use of incoherent light source broadens the line, the obtained accuracy in estimating the center is 5 higher. By using incoherent light source, we expect that the speckle created by the teeth will also be dramatically reduced. For implementation , we propose to replace the laser diode by a bright incoherent source such as a superluminescence diode.

In figure 2(c) we show the effect of the DOE illumination area on the pattern quality. We observe that the line pattern is better for a completely illuminated DOE. Thus we recommend to modify the design of the optical system in the device head to produce a collimated beam that completely illuminates the DOE and then focus the pattern onto the target by a second lens.

In summary, our simulations and experiment show that the use of a better DOE with full illumination in combination with an incoherent light source will suppress the noise speckle leading to an increased resolution for the 3D reconstruction.

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Appendix A: The effect of defocus

The DOE is optimized using the Gerchberg-Saxton algorithm for a perfectly focussed beam. Inversely, this means that if the system is in perfect focus, the projected pattern is defined most clearly. When defocusing the system, the pattern is blurred. Moreover, as the projected pattern is created by light rays with different phases, as these rays start to overlap,

interference occurs, as shown in the figure below. The red regions show regions of interference occurring. This has a profound impact on the projected pattern. Regions with opposite phase that previously had no overlap, now do so and produce regions with destructive interference, deteriorating the visual clarity of the pattern.

To study this effect, we calculated a projected pattern in an ad-hoc fashion using the Gerchberg-Saxton algorithm, and convoluted the image (including phase information) with a Gaussian beam profile with varying width. The result is shown below.

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This figure shows the projected pattern convoluted with a Gaussian function of increasing width, simulating the defocusing effect. The width of the Gaussian is increased from top left to bottom right. The bottom right shows the image with the most defocus. It can be clearly seen that defocusing greatly deteriorates the line quality. Due to time constraints, no quantitative analysis was done on the image. It is however possible to optimize the defocused pattern by using it as a reference and feeding it back into the Gerchberg-Saxton algorithm. We did this, and the result is shown below.

This figure shows the defocus-optimized pattern for increasing defocus (going from top left to bottom right, the colormap shows different colors for the different pictures due to improper normalization of the algorithm). It can be clearly seen that optimizing the pattern for defocus improves the pattern visibility. Using a defocus-optimized pattern does not necessarily improve the projected image, as increasing the focus with this pattern will again change the pattern. To study this, we generated a maximum defocus-optimized phase-plate (DOE, the one seen in the bottom right of the previous figure) and used this to generate projected patterns with different defocus. The result is seen below. This figure shows the pattern generated by a defocus-optimized phase plate using decreasing focus. The top left figure shows maximum focus, and it can be seen that the image quality is the worst. Increasing defocus now seemingly increases the quality of the image, instead of decreasing it. However, it might be that this is only an effect of visual interpretation, as quantitative analysis might prove differently. These results show that improving the DOE not always improves the image quality, and using a two-dimensional DOE in the first place might be the wrong approach to the problem.

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34

Appendix B: experimental set-ups

Figure 1-a shows a schematic layout of the set-up similar to that used in 3D-scanner except the blue laser is replaced by a coherent red laser.In figure 1-b, a photo of the recorded pattern is shown.

non-coherent experiment

A diagram of the set-up used to study the effect of incoherent light on the pattern is presented in figure 2-a. the laser was replaced with a noncoherent white light source and then was filtered using a blue filter with central wavelength of 470 nm and 100 nm bandwidth.The recorded pattern related to this set-up is shown in figure 2-c which is compared the pattern when coherent light is used as the illuminating source in figure 2-b.

Beam size experiment

figure 3-a shows the condition when different areas of DOE was illuminated using a diaphragm along with the recorded patterns for 4 different diaphragm diameters in figures 3-b to 3-e. The light source was a coherent, He:Ne laser and the beam was also collimated before entering DOE. We illuminate the DOE with collimated laser beams of different sizes and look at the diffraction patterns. The localization accuracy increases with increasing beam size and is the best when the entire surface of the DOE is illuminated.

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36

Appendix C: Quantifying sharpness

The quality of the lines, both in the experiments and in the theoretical analysis, was gauged using the algorithm outlined in Figure C1. The algorithm’s working principle relies on

the way that the lines are being detected in the actual device. The top panel of Figure C1 shows an isolated line from a pattern resulting from a 2-

step, binary DOE generated using the Gerchberg-Saxton algorithm. A 5-pixel moving average window is taken along the 1000-pixel long line (x-direction). For each step, the average profile is extracted and fitted with a Gaussian. Examples of such fitting are shown in panels a-c, for regions marked with the white boxes in the top panel. The yellow curves in panels a-c represent the Gaussian fits. Subsequently, the mean value of each Gaussian is extracted and appended to a vector. This mean value is the perceived center of the line at each point along its length (purple points in panels a-c).

The bottom panel shows the extracted center of the line as a function of position along the x-axis (purple line). The quality of the line is then gauged as the standard deviation (σ) of this curve, since the uncertainty in determining the center of the line is directly related to the variance of the means along its length. For comparison, a curve of the extracted center of a line generated using a continuous (ideal) DOE is plotted in the bottom panel (blue curve). It can be seen that the DOE discretization results in almost two orders of magnitude deterioration of the performance of the system. The values of the variance for both curves are shown on the left side of the bottom panel.

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Figure C1. Top: a line pattern generated using a 2-step discretized DOE. Panels a-c: averaged 5-pixel windows of the line shown in the top panel in the regions marked with the white boxes. The yellow curves represent Gaussian fits to each of the curves. Bottom: Mean values of the fitted Gaussians along the length of the curve for a 2-step DOE (purple curve) and for a continuous DOE (blue curve). The panel on the right shows the value distribution of the purple curve, illustrating the extraction of the quality of the line (σ).

38

Travel Time Reliability

Nationale Database Wegverkeersgegevens (NDW)

Desciption of company case

Situation / background

For many people traveling by car is a daily routine, and often a stressful one too. A road trip is

usually planned according to the expected travel time (μ), which is constituted of the free flow travel

time (TTff) plus additional travel time. The latter includes predictable variations (think of rush hours

vs. non-rush hours) as well as unpredictable variations (e.g. car accidents). Knowing the estimated

time of arrival is certainly useful, but in practice road users would also like to know about the travel

time reliability, which depends on the unpredictable variations. It would be useful to know by what

time one should depart in order to be, say, 95% certain to arrive on time for an appointment.

Examples of reliability measures are the buffer index (BI) and planning time index (PTI), respectively

defined as:

𝐵𝐼 =𝑇𝑇95%−𝜇

𝜇, 𝑃𝑇𝐼 =

𝑇𝑇95%

𝑇𝑇ff,

where TT95% denotes the 95% percentile travel time. Several agencies in the United States have

recently started using these measures to improve traffic management (Federal Highway

Administration, 2005).

The Nationale Database Wegverkeersgegevens (NDW) is an alliance of various Dutch road

authorities, which collects and distributes traffic flow data of the Netherlands. The NDW would like to

provide reliability measures to reduce traffic jams and limit CO2 emissions. Moreover, smaller

uncertainties in travel times and less congestion also reduce stress levels of the road users.

The NDW obtains data on travel times from various authorities in a number of different ways, such as

through GPS information from smartphone users – this is called floating car data (FCD), as well as

through loop detectors embedded in the road that rely on electromagnetic induction. The data

collected by the NDW, both real-time and historic, is publicly available and used by routing software

such as Google Maps and TomTom.

Problem description / scientific challenge

The NDW has provided travel time data (FCD and loop detector data) averaged per minute per road

segment for a 4.7 km trajectory of the A1 highway that runs from Voorthuizen to Barneveld. The

main challenge is to define and calculate a reliability measure at the segment level that can be used

to calculate efficiently and effectively the travel time reliability for the whole trajectory. This is highly

nontrivial, as for example travel time percentiles pertaining to segments cannot be straightforwardly

used to obtain percentiles for a combination of segments. For this reason, the BI and PTI per

segment may not be used to obtain those measures for the full trajectory. For our calculations, we

thus need to resort to other measures, such as the variance of the travel time. The variance is

additive, at least when travel times of segments can be treated as independent stochastic variables.

Although the variance might be best to work with as a reliability measure, it is not easily understood

39

by a nontechnical audience – it is important that travel time reliability can be communicated to as

many road users as possible.

Research question (try to formulate one single, concrete question)

What is an effective and clear reliability measure for the travel time of a trajectory that can be

calculated based on individual travel times of segments?

Solution(s)

To calculate the travel time reliability for a trajectory we rely on the individual travel times of its

segments. Since the ‘scalability’ property for percentiles is rather limited, we propose to use

variances (or, equivalently, standard deviations).

Although the standard deviation (σ) can be effectively used in the calculations, it is not a good

reliability measure to communicate to road users. However, we find that for our trajectory as a

whole, σ can actually easily be translated to TT95%. We find that this percentile corresponds in good

approximation to μ + 1.92σ.1 The coefficient of 1.92 turns out to be independent of the day of the

week. As a result, from σ we can compute BI or PTI, both of which can be easily communicated to

road users.

Suggestions for next steps

In an attempt to combine the variances of the segments, we did not manage to go beyond the

instantaneous approximation (see below). For high amounts of traffic this turned out to overestimate

the true variance. In future work it would be interesting to see if a proper implementation of time

evolution across segments would give a variance from the segments approach that matches the true

variance of the full trajectory, for all days of the week.

One could also look into the so-called Copula method for summing the segments (Chen et al., 2017).

Approach followed during the workshop week

To calculate the variance (Var) of the travel time for a trajectory consisting of n segments, we can

use that

Var(∑ 𝑡𝑖𝑛𝑖=1 ) = ∑ Var(𝑡𝑖) +𝑛

𝑖=1 ∑ Cov(𝑡𝑖 , 𝑡𝑗)𝑖≠𝑗 ,

where ti denotes the travel time pertaining to segment i. In our computation of the total variance we

adopted the instantaneous approximation (i.e. we ignored time evolution across the segments upon

summing them together). When the amount of traffic is low the instantaneous approximation is

justified, which we explicitly verified for the Sundays. For uncorrelated variables the off-diagonal

terms of the covariance matrix Cov(ti,tj) vanish, so that the total variance is simply the sum of the

individual variances pertaining to the segments. In this case, as it turns out, the resulting variance

from the segments approach turns out to underestimate the true variance of the full trajectory. As

the travel times for the segments are clearly not independent, the covariance matrix in our case is

nonzero. Taking into account correlations between segments, the resulting variance from the

segments approach turns out to overestimate the true variance in rush hours probably due to the

limited validity of the instantaneous approximation.

1 Recall that for a normal distribution TT95% corresponds to μ + 1.65σ.

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To estimate the 𝑁𝑡ℎ percentile 𝑝𝑁 from 𝜎, it was modeled as 𝑝𝑁 = 𝜇 + 𝑐(𝑁) ⋅ 𝜎. A least squares approach

was used to find the best value of 𝑐(𝑁). This method turns out to give an error less then 10%, for N

between the 50th and the 95th percentile.

Group members

Bram Bet(UU), Tom van Daal(TUe), Peter Dieleman(AMOLF), Sonia El Hedri(NIKHEF), Leon van

der Graaff(TUD), Nick Plantz(UU), Jorinde van de Vis(NIKHEF), Marco Zaro(NIKHEF)

Company representatives: Edoardo Felici, Remco Gilbers, Marlous Hovestad, Marthe Uenk - Telgen

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Appendix

In this appendix we provide a selection of plots, which support claims made in the main text.

Figure 1: Travel time as a function of time during the morning for different days during the week (from

FCD).

Figure 2: Frequency of travel times for a single segment. All days (in the month of October) and times

during the day are taken into account (from FCD).

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Figure 3: Average velocity of westbound traffic obtained from FCD data over the A1 highway trajectory on

October 20th between 7:30 and 7:45 am.

Figure 4: Average velocity of westbound traffic obtained from FCD data over the A1 highway trajectory on

October 27th between 7:30 and 7:45 am. Figure shows the onset of a traffic jam, propagating to the east.

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Figure 5: The mean travel time from FCD across the full trajectory as a function of time during the morning

(for all days combined). Both the true means as well as the means obtained by the segments approach are

shown.

Figure 6: The standard deviation of the travel time from FCD across the full trajectory as a function of time

during the morning (for all days combined). Both the true standard deviations as well as the standard

deviations obtained by the segments approach are shown.

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Figure 7: The standard deviation of the travel time from FCD across the full trajectory as a function of time

on Monday mornings. Here, as in Figure 6, the true standard deviations as well as the standard deviations

obtained by the segments approach are shown. Additionally, we also plot the total standard deviation

obtained by summing all the elements of the covariance matrix, computed assuming instantaneous travel

times.

Figure 8: The standard deviation of the travel time from FCD across the full trajectory as a function of time

on Sunday mornings. Here, as in Figure 6, the true standard deviations as well as the standard deviations

obtained by the segments approach are shown. Additionally, we also plot the total standard deviation

obtained by summing all the elements of the covariance matrix, computed assuming instantaneous travel

times.

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Figure 9: The standard deviation of the travel time from FCD across the full trajectory as a function of time

on Monday mornings. As in Figure 8, we show the true standard deviations and the standard deviations

obtained by using the segment approach with and without the covariance matrix. We also show that the true

standard deviation is roughly proportional to the result obtained assuming no correlations between the

different segments.

Figure 10: The total travel time over the whole trajectory on Monday, October 2nd as a function of the time

during the morning. The blue line represents the true travel time while the red line represents the travel time

obtained in the instantaneous approximation, by summing the travel times of all the segments, all evaluated

at the same time of the day.

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Figure 11: The total travel time over the whole trajectory on Sunday, October 1st as a function of the time

during the morning. The blue line represents the real travel time while the red line represents the travel time

obtained in the instantaneous approximation by summing the travel times of all the segments, all evaluated

at the same time of the day.

Figure 12: Finding the value 𝑐(𝑁) which gives the best estimation of the 𝑁𝑡ℎ percentile modeled as 𝑝𝑁 = 𝜇 +

𝑐(𝑁) ⋅ 𝜎. For this solution, FCD from the morning peak (6 am to 9 pm) of working days of October 2017,

grouped in time windows of 15 minutes was used.

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Figure 13: Plot of the error between the estimated percentile 𝜇 + 𝑐(𝑁) ⋅ 𝜎 and the actual percentiles 𝑝𝑁 for all

working days in October 2017. Between the 50th and 95th percentile, this error is below 10% except for two

exceptional cases.

Figure 14: A histogram of the travel time as function of the time of the day, grouped in time windows of 15

minutes. FCD based on working days of October 2017. Overlaid, a line showing the mean (yellow), the 95th

percentile (green) and the estimated 95th percentile (𝜇 + 1.92 𝜎).

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49