SMarble localization in industrial mixing tanks using TDOA and echo data

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SMarble localization in industrial mixing tanks using TDOA and echo data

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By Stefan van der Kolk

GRADUATION REPORT

Submitted to

Hanze University of Applied Science Groningen

in partial fulfillment of the requirements for the degree of

Fulltime Master Sensor System Engineering

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Abstract

Industrial mixing is a field where yearly between 1 billion and 10 billion dollars are lost due to badly mixed batches. The reason for this is that industrial mixing still relies on simplified models that do not take into account the specific conditions within an industrial mixing tank. The main component that contributes to good mixing is turbulence. SMarbles which are small sensor balls can be used to measure this turbulence utilizing the internalIMU. To do this the location of the SMarble has to be linked to a location in the mixing tank. This can be done by using an ultrasonic transducer in the SMarble and hydrophones in the tank. This allows the SMarble location to be determined using time difference of arrival (TDOA). In addition to this echo data is added to be able to determine the height of the SMarble in case the TDOA timings become too similar.

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Declaration

I hereby certify that this report constitutes my own product, that where the language of others is set forth, quotation marks so indicate, and that appropriate credit is given where I have used the language, ideas, expressions or writings of another.

I declare that the report describes original work that has not previously been presented for the award of any other degree of any institution.

Signed,

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List of tables

Table Page

Table 1: Determining starting point for the number of hidden layers 33

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List of figures

Figures page

Figure 2.1: Laminar flow 9

Figure 2.2: Transitional flow 9

Figure 2.3: Vortex occurring at the edge of an airplane wing shown with coloured smoke 10 Figure 2.4: Scalar field representing in temperature in an area 10

Figure 2.5: Turbulent flow 11

Figure 2.6: Dispersion in a mixing tank 11

Figure 2.7: Diffusion of dye 12

Figure 2.8: Scale of segregation 12

Figure 2.9: Intensity of segregation 12 Figure 2.10: Scale of segregation and intensity of segregation combined 13 Figure 2.11: Covariance of variation in mixing process 13 Figure 2.12: Effects of impeller on dispersion and diffusion 13 Figure 2.13: Exposure, Scale and CoV 14

Figure2.14: Vortexing and Swirling 14

Figure 2.15: Baffles preventing vortexing/swirling and promoting turbulence 14

Figure 2.16: SMarbles 15

Figure2.17: SMarble internals containing weight to match density, IMU and Transducer 15

Figure2.18: SMarble localization visualization consisting of 4 hydrophones 16

Figure 2.19: Neural network 19

Figure 2.20: Chart showing most of the possible neural network configurations 20 Figure 2.21: Acoustic signal and resulting transient 21 Figure 2.22: From original signal to onset 22 Figure 2.23: Onset strength and onset peaks 22 Figure 3.1: Visual representation of hydrophone distance calculation 24

Figure 3.2: Propagation of sound 24

Figure 3.3: Sides consisting of the distance to the hydrophone (d), radius (r) and the tank

Radius (tr) the echo propagation path (f) and the hypotenuse of the reference triangle aref 25 Figure 3.4: Reference triangle two with reference line bref which is equal to the tank radius 26 Figure 3.5: Echo propagation from the back wall 27 Figure 3.6: Echo reflection from the bottom 28 Figure 3.7: Echo propagation path in case of no radius 28 Figure 3.8: Echo reflection from the wall 29 Figure 4.1: SMarble 2d polar coordinates 30 Figure 4.2: 3D SMarble visualization in 3d 30 Figure 4.3: Learning rate to high, bounces around the desired value 32 Figure 4.4: Learning rate to low, loss function is not approached in the number of epochs 32 Figure 4.5: Loss function with appropriate learning rate 33 Figure 5.1: R2 values compared to number of hidden layers 34 Figure 5.2: R2 value change per number of layers is increased from 5 to 10 neurons 34 Figure 5.3: R2 value based on neuron increase with increments of 5.3 35

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Figure 5.4: Prediction compared to determined value for 4 hidden layers and 35 neurons 35

1. Rationale

Industrial mixing is a multi-billion euro industry that revolves around mixing substances together to create new substances. The area’s where industrial mixing is most prevalent are the chemical, pharmaceutical, pulp and paper and food industries. The problem with current day industrial mixing however is that industrial mixing as of yet is not a precise art. It is estimated that in the US alone between 1 to 10 billion dollars is lost annually due to badly mixed batches[1]. This problem stems from the fact that currently industrial mixing relies on simplified models that do not convey all the details and discrepancies between mixing processes. To alleviate this problem for the mixing of liquids the proposed solution is using SMarbles to monitor and analyse the mixing process. SMarbles[2] are small sensor motes that are able to measure the direction and the acceleration of flow. Using the data gathered by the SMarbles a more complete model of a mixing process can be established. This enhanced model can then be utilized to get a better understanding of the mixing process. This will lead to optimized mixing protocols which will reduce the amount badly mixed batches which in turn lead to more profit for companies.

The problem however is that creating an accurate model relies on being able to link a certain event to a certain location inside the tank. Currently it is not possible to determine the location of a SMarble inside a mixing tank. This has led to the following research question:

 How can a SMarble be located inside a mixing tank? With the following sub questions:

 What factors affect mixing?

 Which parameters determine if a localization model is suitable?  What localization models exist?

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2. Situational & Theoretical analysis

In this chapter the situational and theoretical analysis is discussed. first in chapter 2.1 the basis of industrial mixing and the effect of turbulent flow is explained. In chapter 2.2 SMarbles and their capabilities are

discussed. In 2.3 the possible localization models are looked at. In chapter 2.4 the proposed localization model is determined. In chapter 2.5 the machine learning methods are discussed. And in chapter 2.6 the method for detecting the onset is shown.

2.1 Industrial mixing

Mixing is the process of combining multiple substances and combining these to create a new substance. The goal is to create out of different components a new homogenous substance where the added substances are evenly distributed throughout the mixture. Industrial mixing can consist of the mixing of solids, liquids or gasses or combinations of these but the focus of this report is on liquids in which the mixing process is for a large part depended on the type of flow[1].

2.1.1 Different types of flow

There are three types of flow that exist, laminar, turbulent and transitional. The distinction between these three types of flow can be determined by calculating the Reynolds number. The Reynolds number in cylindrical vessels that are stirred from the centre is defined as[1]:

ℜ=

ρN D

2

μ

=

ρVD

μ

where:

ρ is the density of the fluid in kg/m3

μ is the dynamic viscosity of the fluid in kg/m*s D = the diameter of the agitator in m

N is the rotational speed in m/s V is ND the velocity of the fluid in m/s

Using this equation the Reynolds number for a liquid in a mixing tank can be calculated.

Laminar flow

At a Reynolds number that is generally below 2100 the flow is considered laminar an example of this is shown in figure 2.1. In a laminar flow the viscosity of the fluid is dominant and will damp out small disturbances in the fluid.

Figure 2.1: Laminar flow [3] Transitional flow

At a Reynolds number that is generally between 2100 and 10,000 the flow is considered transitional. This is the stage at which the laminar flow starts to transition towards turbulent flow which this is shown in figure 2.2 Very little is known about transitional flow. This is why often a disparity is made between turbulent and fully turbulent flow where transitional flow falls under turbulent. Which means that at this stage the velocity fluctuates in time and direction and elements such as vortices, sheets, ejections and sweeps start to appear in the flow and scalar fields are quickly dispersed. These elements are explained below.

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Figure 2.2: Transitional flow[3]

Vortices

Vortices are rotations in a fluid that revolve around a centreline. In figure 2.3 an example is shown of a vortex occurring around the tip of an airplane.

Figure 2.3: Vortex occurring at the edge of an airplane wing shown with coloured smoke [6]

Sheets

Sheets occur when there are differences in flow. For example when a liquid moves through a pipe the part of the liquid near the pipe wall will encounter drag which will slow its speed down, whilst the flow towards the middle wants to keep moving at the same speed. This leads to sheets being formed of areas where the speed of the flow differs.

Ejections and sweeps

Because sheets are formed due to a difference in speed this will lead to certain interactions between sheets. Ejections are when a part of the liquid particles move away from the sheet whilst sweeps are when liquid particles move towards a sheet[5].

Scalar fields

Scalar fields describe the difference in area. This could be a difference in temperature, density, pH value etc. the example of a scalar field in 2.4 shows the difference in temperature.

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Figure 2.4: Scalar field representing in temperature in an area [6] Turbulent flow

At a Reynolds number that is generally above 10,000 turbulent or fully turbulent flow occurs. In this state the changes in the velocity and direction are intense enough for inertial forces to overwhelm viscous forces and particles do not follow a clear path, as shown in figure 2.5. This means that the viscosity of the fluid has no effect on the mixing process. Just as in turbulent flow vortices, sheets, ejections and sweeps appear and scalar fields are quickly dispersed.

Figure 2.5: Turbulent flow [3]

Generally the mixing mechanisms that allow for substances to be properly mixed start to occur at transitional to turbulent flow[1].

2.1.2 Mixing mechanisms

The end goal of mixing is to create a homogenous substance out of multiple substances. There are several mechanisms that promote this. These mechanisms are a form of either dispersion or diffusion. Dispersion is the spreading out of large clusters of the two substances. In figure 2.6 the principle of dispersion is shown by the chunks of the red fluid being distributed in the transparent fluid, the substances are being mixed together but the individual molecules are still not yet completely being intermixed.

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Figure 2.6: Dispersion in a mixing tank [7]

Diffusion on the other hand is the spreading out of individual molecules from an area with a high concentration to area’s with a low concentration. This principle is shown below in figure 2.7, this shows a drop of dye being introduced into a liquid. The individual molecules spread out in the liquid until they are homogenously distributed in the liquid and the liquid has a consistent colour. The time it takes for the dye to dissolve into the fluid by diffusion alone would be several minutes.

Figure 2.7: Diffusion of dye [8]

In general these two principles are combined in mixing because dispersion distributes large chunks throughout the mixture which means the diffusion gets sped up because of more contact area and less distance between area’s with low concentration and high concentration.

There are special cases in which diffusion/dispersion takes place are listed below:

 Eddy diffusion also called turbulent diffusion, this consists of the movement of large groups of molecules which are called eddies that swirl around in the fluid. This motion is generally measured as the turbulent velocity fluctuations.

 Convection which is sometimes also called bulk diffusion is dispersion of a substance due to bulk motion. Bulk motion is the movement of large groups of molecules.

 Taylor dispersion is considered a special case of convection . The dispersion in this mechanism occurs due to a mean velocity gradient. An example of this would be laminar flow in a pipe where an axial dispersion occurs due to the parabolic velocity gradient in the pipe[1].

Dispersion is generally called the scale of segregation, which consists of the large scale breakup of chunks of substance without diffusion. This is shown in figure 2.8.

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Figure 2.8: Scale of segregation [1]

Diffusion is expressed as intensity of segregation, which measures the difference between the purest

concentration of substance A and the purest concentration of substance B when this approaches zero it means that the mixture is homogenous. this is shown in figure 2.9.

Figure 2.9: Intensity of segregation [1]

The way scale of segregation (dispersion) and intensity of segregation (diffusion) work together is shown in figure 2.10.

Figure 2.10: Scale of segregation and intensity of segregation combined [1]

The difference between separate substances and a homogenous substance is expressed in the covariance of variation (CoV) below in figure 2.11 this principle is shown. This figure shows that when the substances are still mostly separate the CoV is high, but the more the substances get mixed over time the CoV goes down. When the CoV approaches zero the substances are mixed into a homogenous substance.

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The way the CoV gets reduced in a mixing tank is shown below in figure 2.12. A substance is introduced in the mixing process and each time it passes through the impeller it gets broken up (dispersion) and creating more interfacial area to help with diffusion.

Figure 2.12: Effects of impeller on dispersion and diffusion [8]

In figure 2.13 the scale of the drops (blue), the CoV (red) and the exposure (green) are shown. This graph shows that the drop size goes down in steps where every step is a pass through the impeller. The CoV declines rapidly in the beginning and after this gradually moves towards zero. The exposure shows saw tooth behaviour because the concentration difference goes down, but each pass through the impeller the interfractal area goes up. This starts to drop off as the drops reach their equilibrium size.

Figure 2.13: Exposure, Scale and CoV[8]

In addition to this there are three scales on which these principles can take place. Macromixing which consists of the largest scale of motion in the liquid and is in relation to the blend time in a batch system. Mesomixing is on a scale smaller than bulk circulation or the tank diameter At this point molecular and viscous diffusion start to play a role. Micromixing is mixing on the smallest scales of motion (the Kolmogorov scale) and at the final scale of molecular diffusivity (the Batchelor scale). For this project only macro- and messomixing are considered because these are influenced by turbulence whilst on the micromixing scale depends more on interfacial area.

2.1.3 Tank geometry

The focus of this report is on mixing at the macro- and messomixing level this is why only bulk movement (dispersion) is considered. The desired flow is fully turbulent so the viscosity of the fluid is essentially nullified by the inertial forces. This means that a large factor that impacts the mixing process is the geometry of the tank.

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Mixing tanks are mostly cylindrical or rectangular tanks that are generally only a few meters in wide. In cylindrical tanks the liquid that is being mix might start to swirl and vortex as shown in figure 2.14. Baffles are used to prevent this from happening and promote a turbulent environment that enhances the mixing process. This is shown in figure 2.15.

Figure2.14: Vortexing and Swirling [9]

In rectangular tanks the corners provide a similar function although baffles might be utilized here also. The shape of the tank might differ. For example tanks might have a flat bottom, rounded bottom, angled bottom etc. This might have effect on the way the liquid moves through the tank. Models have been created to determine the way the liquid moves in a mixing tank. The problem however is that these models considered standard tank geometries with standardized impellers[10] which means that these models might not fit different tank geometries and setups very well. Being able to optimize a mixing process using data that is gathered from the specific mixing process it tries to improve would be invaluable. SMarbles would be the perfect tool for this.

2.2 SMarbles

SMarbles (shown in figure 2.16) are small sensor motes (around 5 cm in diameter) that are being developed by the Antea Group in conjunction with the University of Eindhoven. SMarbles contain an internal IMU also referred to as the XWM that contain a triaxial gyroscope and a triaxial accelerometer. These sensors can be used to detect the turbulence and the direction the liquid is traveling in a mixing process by detecting changes in direction on the triaxial gyroscope and changes in the direction of acceleration using the triaxial

accelerometer.

Figure 2.16: SMarbles [11]

The weight of the SMarble is able to be adjusted to make it match the specific density of a liquid by adding a weight inside the SMarble as shown in figure 2.17[2]. This allows the SMarble to monitor the movement and turbulence of a specific fluid in a mixing tank at the macro- and messomixing scale. which will provide valuable data that will help in optimizing a specific mixing process.

Figure 2.15: Baffles preventing vortexing/swirling and promoting turbulence [9]

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Figure 2.17: SMarble internals containing weight to match density, IMU and Transducer [2]

The current limitations of the SMarbles however are that the data cannot be transmitted in real time. It can only gather data which can be read out after the SMarble is removed from the mixing tank. Currently the location inside the mixing tank cannot be determined. This means that the measurements of direction of flow and turbulence cannot be linked to a specific location. Having a localization method that would allow the gathered data to be linked to a specific location would be invaluable.

Currently SMarbles can be equipped with an ultrasonic transducer that emits a signal this is used to locate the SMarble in case they get lost in a system [2]. This ultrasonic signal is going to be used as the basis for the localization. This is because an ultrasonic signal does not require the liquid to be transparent and travels at a low enough speed to be easily detected.

To detect the ultrasonic signal hydrophones will be used, these are underwater microphones that will be able to detect the audio signal that the ultrasonic transducer sends out.

2.3 Localization

There are several methods of localization that can be used to determine the location of an SMarble in a 3-dimensional space. These consists of received signal strength indication (RSSI), angle of arrival (AOA), time of arrival (TOA) and time difference of arrival (TDOA)[8]. The dimensions in which this localization takes place is relatively small as the diameter and depth of industrial mixing tanks generally is only a few meters. A visual representation of the localization problem is shown in figure 2.18.

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Figure 2.18: SMarble localization visualization consisting of 4 hydrophones

2.3.1 Received signal strength indication

Received signal strength indication (RSSI) is a localization method that uses the loss of signal strength over a distance. This is done by finding the relation between propagation decay and distance so that the difference in signal strength between the sender and receiver can be used to determine the distance. These distances in relation to multiple receiver locations allow for the origin of the signal to be determined[12].

The attenuation of ultrasonic signals in water can be calculated by the following formulas[13]:

∝= A∗P∗f

2 A = Ca1- Ca2*T + Ca3*T2 - 1.50*10-8*T3 for T ≤ 20 º Celsius Ca1 = 4.937*10-4 Ca2 = 2.59*10-5 Ca3 = 9,11*10-7 A = Cb1- Cb2*T + Cb3*T2 – Cb3 *T3 for T > 20 º Celsius Cb1 = 4.937*10-4 Cb2 = 2.59*10-5 Cb3 = 9,11*10-7 P = 1-3.83*10-2_{*z + 4.9*10}-4_*z2 T = temperature in Celsius f = frequency in kilohertz z = depth in kilometres

Using this formula a frequency of 20khz in water at 20 degrees Celsius and a depth of 1 meter below the surface the reduction in sound level is around 0.088 dB/km which would translate to a reduction of 88*10^-6 dB per meter the outcome is that same for both formulas. The reduction does go up exponentially with the frequency, if the frequency increase by 10 the reduction in db/km will increase by a factor 100. So this method might work for clear water using a high enough frequency. The problem occurs however once density and pH

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are factored into the equation. These factors have a large impact on the attenuation of the ultrasonic signal especially when using higher frequencies. For this reason this method is not really suited[14].

2.3.2 Angle of arrival

Angle of arrival is a localization method that uses the angle at which the signal arrives at different points to calculate the origin of the signal. The angle at which the signal arrives is determined by using an array of receivers at each measuring point. By determining the small differences in arrival time between the individual receivers contained in an array the angle of arrival for that array can be calculated. Using the angles determined at multiple array locations the origin point can be calculated trough triangulation[12].

This method would require multiple hydrophones in an array configuration at each of the measuring points. The distance between the individual hydrophones in this array would be relatively small. In water that is at 20 º Celsius sounds propagates with a speed of 1482 m/s[15] this would mean that determining the difference in angle using a hydrophone array would rely on values in the nana or even picoseconds. This means that the difference in time that is used to calculate the angle would be hard to determine and would require very accurate measuring equipment. For this reason this method is not really feasible.

2.3.3 Time of arrival

Time of arrival (TOA) is a method that uses the time it takes for a signal to travel from the sender to the receiver to estimate position. This works by having the time the signal is sent being encoded in the signal. This is then compared to the time at which the receiver receives the signal. This time can then be related to the

propagation speed of the signal which translates to a distance travelled. Using multiple receivers (three in case of a 3d space) the relation between the distances can be found and the origin of the signal can be

calculated[12].

At this point the SMarbles are not yet able to send information through the ultrasonic signal this means that the time of sending cannot be conveyed to the receivers. Another issue that this presents is the fact that it would require the SMarbles and the sender to have clocks with exactly the same timing. This is especially true because the localization needs to be done on a cm scale. This would be very hard to accomplish because generally clocks tend to drift over time. Meaning that small time differences would occur which would make accurate

positioning impossible. This could be alleviated by using a synchronization signal, but this would further complicate this localization method. So this method is not desirable.

2.3.4 Time difference of arrival

Time difference of arrival (TDOA) is a method where the difference is determined between a set of receivers compared to one reference receiver (one reference with three receivers to relate to that reference for a 3d space). The difference between the reference receiver detecting the signal and the other receivers detecting the signal together with the propagation speed of the signal allow for the location of the origin signal to be determined[12].

This method would work for the localization of SMarbles because it only needs the SMarbles to be able to send a signal and four hydrophones to detect this signal. The hydrophones can all be connected to the same

processor so they all function on the same clock which means timing differences will not occur. This makes this method of localization the optimal choice for determining the location of a SMarble in a mixing tank.

2.4 Proposed TDOA configuration

The proposed configuration consists of four hydrophones to be able to localize in three dimensions. It would be desirable that Hydrophones do not interfere with flow inside the tank. This is because the reason of the localization is to get insight into the flow and turbulence inside the mixing process using SMarbles. So the Hydrophones should be flush with the wall of the tank to minimize the impact on movement of liquids in the tank. Because TDOA relies on the difference in timing between signals the distance between the hydrophones should be made as big as possible so that the maximum difference in timing can be achieved. In a cylindrical tank this can be done by placing the hydrophones at 90 degree or 0.5 pi intervals to get the maximum difference in distance.

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Because the tank geometry used in this project is a cylindrical tank a problem is presented. This problem is that when a signal is transmitted from the centre of the tank the travel distance to each microphone is equal. This means that the signal will arrive at all hydrophones simultaneously so the difference between the reference and the three receiver hydrophones becomes zero. In this case there would be no information with which the height of the SMarble can be determined. The proposed solution for this is to utilize the timing of the first echo received by each hydrophone. This is because even when the SMarble is located at the point where the distance to all hydrophones is the same the distance the echo travels is still dependent on the depth of the SMarble. This allows for height to be determined.

The limitation of using echo signals however is that the timing of the echoes are based on the geometry of the tank. The echo timings themselves will show a linear relation. This can be captured in a formula but different tank geometry might make the echo signal propagate differently. Creating a formula that captures this relation would be hard and would make it very specific to a tank with a cylindrical geometry without baffles. Which would bring back the problem that currently the mixing process can only be analysed with standard models[1] [5]. In addition to this there might be tank geometries that would be impossible to relate in a single formula or method.

The proposed solution for this is using machine learning to find the relation between the TODA and echo data and the location inside the mixing tank.

2.5 Machine learning

Machine learning is a field in the realm of artificial intelligence that is based around using algorithms and statistical models to have a computer system perform a specific task or operation without being explicitly told how. This can be done unsupervised or supervised. In unsupervised machine learning the algorithm is given a set of data and it will cluster this data into groups based on certain features. The desired outputs are not shown to the machine learning algorithm and it finds the features on its own.

Supervised learning is done by providing a machine learning algorithm with a set of training data where the inputs and the outputs are known. The machine learning algorithm iterates over this data and tries to find the relation between the input and the output. The number of iterations is often referred to as epochs. When this is successfully done new data can be introduced from which the outputs are not know and the machine learning algorithm is then able to give a prediction of what the output should be.

Because the goal is to relate the TDOA and echo timings to the location of the SMarble in the tank supervised learning will be used. There are multiple methods of supervised learning that exist but most of these are only suitable for classification and not for predicting continues values The method that is able to provide a

continuous value is using a neural network. Neural networks have shown that they can be used as a method for localization. In one example a feedforward neural network was used to implement in near field sound source localization. The reason neural networks where used here was because solving hyperbolic equations is a costly procedure and certain uncertainties due to noise and reverberation where present in the data. By using a neural network these problems could be negated[16]. Another example is using a neural network to deal with

measurement errors like no line of sight and synchronisation errors and still get an accurate measurement out using the neural network[17]. These methods show that neural networks can be used to find relations in between TDOA data and other factors. This relation can then be saved and used to determine the position using new data. The alternative to this would be creating a hyperbolic equation that includes the echo data. This would be very time consuming and hard to do and is more costly when using it in a practical setting compared to a neural network[16].

2.5.1 Neural Network

A neural network consists of three main layers, the input layer where the inputs to the system are given. The output layer where the calculated outputs are located and a hidden layer. Between these layers connections are formed between all the neurons. An example of this is shown in figure 2.19.

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Figure 2.19: [18] Neural network

The hidden layer can consist of multiple neuron layers. The individual neurons and connections between them have weights. The way a neural network learns is by training it using a training dataset. In this training dataset the inputs and the outputs are known. The neural network iterates over this dataset and predicts an output. This output is compared to the output given In the dataset and the difference is calculated using a method of stochastic gradient decent. The goal is to get the difference between the predicted output and the output given in the dataset as close to zero as possible. This is done by back propagation [19], this is adjusting the weights of the neurons and connections based on the error between the known output and the predicted output. The intent is to try and make the error value approach zero so the known output and the predicted output are the same. When the value is close to zero the model is considered properly trained and should be able to accurately predict the output of new data from which the output is not known[20]. This is tested by using testing data, which is usually a percentage of the training data that has deliberately not been shown to the neural network. From this data the output is known but the output is not shown to the neural network. Using this testing data

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the accuracy on new data can be determined. There are many types of neural networks that exist an overview is

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Figure 2.20: Chart showing most of the possible neural network configurations [21]

The topology of a neural network is generally established by trial and error, by trying a different number of models consisting of different setups of layers and neurons and comparing these to try and get the model that gives the most accurate result. [22].

Doing this it should be possible to create a neural network that is able to accurately convey the relation between the TDOA and echo inputs and the localization data. To train the neural network a dataset needs to be created that contains sufficient points. This is because a larger data set helps prevent overfitting. Overfitting occurs when the dataset used is too small and only the relations present in the training set are considered by the network. The way this can generally be detected is when the predictions of the model on the training data that it has previous seen are very accurate, but when the test data is introduced the accuracy goes down by a significant amount[22]. To prevent this a large enough dataset should be created that is able to have enough data points so that overfitting doesn’t occur. A larger dataset would also mean more points inside the mixing tank identified and would result in less uncertainty when predicating a point in the tank that is not contained in the training data. The machine learning will be done in the Python language since this contains a lot of standard libraries for this purpose.

To create a large enough dataset a model of a the TDOA and echo propagation times in a mixing tank will be created. This is done because getting data in a real world setting would be unfeasible because a neural network required thousands of datapoints to find the relation between input and output. This does make the neural network model specific for a certain kind of tank. To make the neural network work for a specific tank geometry this model can be used to pretrain the neural network [22]. This is a technique where the neural network is presented with a dataset that conveys the general relation that is sought. After this the neural network can continue to be trained on data gathered from the specific tank geometry. Because the neural network has gotten a rough idea of what the data should look like due to pretraining the amount of training data needed to make it specific for a particular tank geometry becomes a lot less.

To determine the timings of ultrasonic signal inside the mixing tank accuracy the onset of the signal needs to be determined.

2 .6 Onset detection

The start of an acoustic signal is described in the attack, the transient and the onset. The attack is the time interval over which the signal increases. The transient is the area over which a signal evolves quickly. This can either be a sudden increase or a sudden decrease. The onset is the specific point chosen to mark the start of the transient. These principles are shown below in figure 2.21.

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For an accurate localization algorithm it is important to be able to correctly and consistently detect the onset of a signal. This is done by identifying the transients. The problem with this is that audio signals are additive which means that signals might superimpose on each other and audio signals are also oscillatory. This means that the transient cannot be detected by simply differentiating the signal in the time domain. So the onset detection is done by using an intermediate signal that in a simplified form represents the logical structure of the original signal. This is mostly referred to as a detection function or novelty function. Figure 2.22 shows how most onset detection algorithms bring the original signal down to a detection function and from this determine the onset[23].

Figure 2.22: From original signal to onset [23]

There are several ways the onset can be detected, one of these ways is to split up the signal in different frequency bands. This might require some pre-processing to make the signal applicable to certain applications. Ways this can be done is for example slicing the spectrogram of the signal into spectrum strips and recognizing the onset of a signal by detecting a sudden onset in energy. Another way the onset can be detected is using transient and steady state separation this is generally used in the modelling of music signals[18]. In python the librosa library[24] is available. This library Is originally intended to transcribe the onset in music. It detects the onset by first calculating thresholded spectral flux operation over a spectrogram and puts this in a one dimensional array that represents the increase in spectral energy for each frame. This is represented by the blue line in figure 2.23. Using this it determines the peak positions from the onset strength curve by determining the local maxima. [25]

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3. Conceptual model

In this chapter the conceptual model is discussed. In chapter 3.1 the mixing tanks specifications are given. In chapter 3.2 the TDOA propagation model is determined. In chapter 3.3 the echo propagation calculations are shown. In chapter 3.4 the machine learning model is determined.

3.1 Mixing tank specifications

Because the focus of this project is on the localization of SMarbles in a mixing tank a general mixing tank is considered in this report as the basis of this localization method. This is a cylindrical tank with a flat bottom that does not contain baffles or a impeller and is filled with normal tap water at room temperature (20 degrees Celsius). Because it is a cylindrical tank the coordinate system that is going to be used is also a cylindrical coordinate system consisting of a radius (r), a height (z) and an angle (theta). This coordinate system is chosen because in a cylindrical tank without baffles the forces and conditions on the liquid are going to be equal in the same radius. Because of this the angle (theta) data is considered less important. It is important to note that the intention is to make sure to have the localization method also be applicable to other tank geometries.

3.2 TDOA propagation model

The model of the tank used in this simulation is a tank with a 5 meter radius and a 5 meter depth. For a mixing tank this is quite large but the increased size will make for a bigger difference between the timings of the TDOA and echo timings which will make it easier to detect the difference. But the simulation is created in such a way that the radius and depth of the tank can easily be changed. The hydrophones are located at the same height. This is done to make the height detection solely rely on the echo signals. In this model the Hydrophones are located 90 degrees apart and simulated to be flush with the tank wall. The SMarble is given a radius, height and angle value that indicate its location inside the tank. To determine the propagation times to the hydrophone the distance from the simulated SMarble and the hydrophone needs to be determined. This is done in two parts by basic trigonometry by dividing the 3d plane into a plane x,y plane and a y,z plane. First the distance to the hydrophone is calculated in the x,y plane with the following formula:

distance

_xy

=

√

r

_sm2

+

r

_tank2

−

2∗r

_sm

∗

t

_tank

∗cos ⁡(angle

_hyd

−

angl e

_sm

)

Where:

rsm= SMarble radius from the centre in meters

rtank = tank radius in meters

anglehyd = angle of the hydrophone in radians

anglesm = angle SMarble in radians

This formula allows finding the length of the 3rd_{side of a triangle when 2 sides and an angle between them is}

known. After this is calculated the distance to the hydrophone in the 3d plane (d) can be determined by using the distancexy in the Pythagorean theorem shown below. This is because the depth or z value of the SMarble is

always at a right angle on the radius of the SMarble. This principle is shown below in figure 3.1.

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Figure 3.1: Visual representation of hydrophone distance calculation

When the distance to the hydrophone is determined the time can be calculated by dividing the travelled distance by the propagation speed of sound in water. At 20 degrees Celsius this is 1482 m/s. This then provides the time it takes for the sound signal to travel. To turn this into TDOA timings the time it takes the signal to propagate to the reference hydrophone is subtracted from time it takes the signal to travel to the receiving hydrophones. This provides the TDOA timings and can be used to calculate the timings for all positions in the tank.

3.3 Echo propagation calculation

A simulation of the first echo is created to simulate the propagation time of echoes. The underlying assumption of this is that sound propagates as a sphere in a 3d space. This principle is represented in 2d below in figure 3.2 with circles.

Figure 3.2: Propagation of sound

The blue lines in figure 3.2 represent the propagation of the original signal to the hydrophone. The green lines represent the propagation of the echo. In this picture it is shown that the original signal arrives at t=5 whilst the echo that propagates after it hits the edge of the tank arrives at the hydrophone at t=6. This propagation of the

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echo signal can be calculated using the presumption that the fastest path the echo can take is when it hits the wall at the middle of the distance to the hydrophone. This allows for the use of trigonometry to solve the distance calculation . The basis of these calculations are the known variables of the mixing tank used in the simulation. These are the radius (r) in which the SMarble is located. The tank radius (tr) and the distance from the SMarble to the hydrophone (d). The calculations are explained in 2d but the principle can be converted to a 3d by ‘tilting’ the plane by compensating the tank radius (tr) and distance to hydrophone (d)with the depth value using the Pythagorean theorem. Because the angle of the echo is the same as the entry angle the assumption can be made that the sides of the centre point of the echo is in the middle of the distance to the hydrophone (d) where the centreline (e) is perpendicular to line d and the echo propagation path creates two triangles each with a side f. this is shown in figure 3.3.

Figure 3.3: Sides consisting of the distance to the hydrophone (d), radius (r) and the tank radius (tr) the echo propagation path (f) and the hypotenuse of the reference triangle aref

In this triangle consisting of side f, 0.5 side d and the centreline only the value of side d is known. To find the values of the other sides the angles have to be determined using a reference triangle. This reference triangle consists of a hypotenuse (aref) that goes from the center of the tank to the middle of d, the radius (r) and 0.5d.

In this triangle sides 0.5 (d) and side (r) are known. Side (a ref) needs to be calculated. But before that can be done first the angle between r and d needs to be found. Because this angle is the same in the known triangle the angle can be easily calculated using the cosine law:

angle

rd

=arccos ⁡

(

r

2

+

d

2

−

tr

2

2 rd

)

After this angle is calculated the side (a ref) can be calculated using cosine law:

a

ref

=(0.5 d )

2

+

r

2

−2(0.5 d)∗r

2

∗cos ⁡(angle

rd

)

Using this information the angle between (a ref) and (d) can also be calculated using the cosine law:

angle

_aref_d

=arccos ⁡

(

a

ref 2

+(0.5 d)

2

−

r

2

2 a

ref

(0.5 d)

)

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Figure 3.4: Reference triangle two with reference line bref which is equal to the tank radius

This reference triangle utilizes the fact that the distance to the echo point is the same as the tank radius when drawing a triangle from the centre (line bref). The length of side (aref) was calculated using the previous reference

triangle. Because side (e) is perpendicular to side (d) the angle is 90 degrees. So the angle between side (e) and side (aref) is equal to anglearef_d + 90.

Knowing two sides and an angle the length of side (e) can be determined using the sine law:

sin ⁡( A)

a

=

sin ⁡(B)

b

=

sin ⁡(C )

c

sin ⁡(angle

e_tr

)

a

_ref

=

sin ⁡(angle

e_aref

)

b

_ref

=

sin ⁡(angle

bre f_aref

)

e

First calculate the angle between e and bref

sin

₍

angle

ebref

)

=

sin

₍

angle a e angle

_aref_e

₎

b

_ref

∗

a

ref

Knowing the angle between side e and bref the length of e can be calculated.

e=

a

ref

∗sin

(

angle

abref

)

sin(tr angle

ebref

)

knowing side (e) and side (0.5d) using the Pythagorean theorem the hypotenuse of the echo triangle (f) can be calculated.

f =

_√

(0.5 d )

2

+

e

2

Because the echo propagation path was divided in two square triangles of the same size the total echo propagation path of the echo signal is 2f. Because the relations are kept within the dimensions of the triangles. These calculations can be used for all hydrophones. The only value that changes is the value of side d.

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3.3.1 Echo propagation from wall behind the SMarble

In some cases the propagation of the echo by bouncing from the wall behind the SMarble might be faster which is something that also needs to be taken into account. This only counts for the half of the circle opposite to the hydrophone. This is calculated by extending the radius at which the SMarble is located to the edge of the tank . The distance is calculated by creating a triangle with the distance to the wall (wd) + radius(r) as one side, the distance from the echo point to the hydrophone (f) and the radius. This is shown below in figure 3.7.

Figure 3.5: Echo propagation from the back wall

Because the fastest path makes the echo signal propagate straight towards the wall from the SMarble radius (r) and the distance of the SMarble to the wall (wd) this distance combined is equal to the tank radius. The between sides tr and r (anglesm ) is known because this is one of the parameters that determines the SMarble

location. This allows for the value of side f to be found using the cosine law and the total value of the echo propagation path to be determined.

r +wd=tr

f =trz

2

+

tr

2

−2 trz∗tr∗cos ⁡(angle

_sm

)

This means that the total distance the echo signal takes is equal to the distance to the wall (wd) + side f.

Because the cylinder is symmetrical distance f will stay the same irrelevant of which side of the tank it reflects off. So for values over 180 degrees the value is equal to 360 - anglesm.

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Figure 3.6: Echo reflection from the bottom

In this figure the green line represents the path the echo takes when it bounces off the bottom of the tank. To calculate the distance of the SMarble to the bottom of the tank is added to the total tank depth. The distance ot the hydrophone is the distance (x,y) value calculated in 3.2. This creates a square triangle where the

hypotenuse is the same length as the green echo path. This allows the distance to be calculated using the Pythagorean theorem.

tank depth+distance

f =

_√

(

¿

bottom)

2

+(

distance [ x , y ])

2

3.3.2 Edge conditions

There are some edge conditions that need to be taken into account. These are mainly conditions where one of the angles in the previous calculations becomes 180 degrees which leads to calculation errors. One of these is when the radius is zero which means there would be no angle between side r and side d in which case the following occurs shown in figure 3.7:

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In this case the distance to the hydrophone is 2 times the tank radius because from the tank centre to the edge of the tank is equal to the tank radius and the angle for each square triangle is the same. The same applies when the SMarble is located directly in front of a hydrophone which means the echo signal is able to bounce off the back wall towards the hydrophone. This is shown in figure 3.8

Figure3.8: Echo reflection from the wall

Here the distance to the wall is added to the tank diameter to create a square triangle where the hypotenuse is the same length as the green echo propagation path. This is also able to be solved with the Pythagorean theorem.

¿

√

(2∗tank

_radius

)

2

+(

sm

_z

)

2

3.4 Artificial neural network

At this point there is no set method to determine the design of a neural network. This is mainly because the design is dependent on the application. So this has to be determined through experimentation But there are some general guidelines to take into account. For example the input layer consists of the features that the output will be related to it is important to select these features well because if the inputs are unreliable so will be the output. A smaller amount of inputs means a better performance but still enough input features are needed to be able to accurately relate the inputs to the outputs[26].

As for the hidden layers in a neural network, they are not required for a neural network to function. But a neural network that does not contain a hidden layer can only deal with linearly separable data [27]. To deal with data that is nonlinear separable one or more hidden layers need to be added to the neural network. A greater quantity of hidden layers will in general improve the closeness of fit of the model. But using a smaller number of hidden layers improve the neural networks ability to extrapolation capabilities of the model. Allowing it to more effectively classify unseen data. Another point to take into account that the higher the order of the problem space the number of hidden layers should also become higher.

As for the number of nodes within the hidden layers more nodes mean an increase training time whilst less nodes mean less feature detectors. To many nodes would also increase the chance of overfitting. Overfitting is when the neural network in essence is able to “memorize” the training data, which leads to a very low squared error on the training data, but when tested on previously unseen data the squared error becomes very high[28]. In addition to this, after a certain number of nodes the accuracy of the model does not significantly increase anymore. Taking these factors into account is important to create an accurate model.

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4. Conceptual model

4.1 Dataset creation

The first step is to model the mixing tank and the SMarble within it in python. This is done by defining a tank in radius and height and establishing a coordinate system. In this case the coordinate system starts at hydrophone one, which is also the reference hydrophone. The other detection hydrophones are spaced 90 degrees apart in the tank. This is shown in figure 4.1 The tank is considered to be completely filled with water and the

hydrophones are placed 10 cm below the water level at a height (z) of 4.9 meters with the reference hydrophone 10cm below this to prevent signals from above getting the exact same time as the signals from below. This model is represented visually in figure 4.1

Figure 4.1: SMarble 2d polar coordinates

Using this model an algorithm is developed to create a dataset using the calculations determined in chapters 3.2 and 3.3. The main parameters that can be changed in this algorithm are the tank radius, tank depth location of the hydrophones and the step size for the radius, height and angle value. The amount of data points the algorithm creates is dependent on the step size of the radius, height and angle.

4.2 Machine learning

Because creating a neural network revolves around a lot of different parameters the goal is to find an optimal neural network that is able to solve the relation between the TDOA and echo data and the location inside the mixing tank using trial and error. The main data points that are going to be used are the TDOA + Echo data as inputs and the radius and height as output. The angle information is included in the dataset but will not be utilized because the start point of this is arbitrary and during the rotation the angle jumps from ~360 to 0 which will make it hard for the neural network to interpret this which would require making the model more complex and increase the amount of neurons/hidden layers which will in turn increase learning time. Because the turbulence is the same at the same radius and height the angle data does not provide enough additional information to make it worth the increased complexity and training time. This is mainly because the timeframe to create this model is limited.

4.2.1 Determining the model

The neural network library chosen is the Tensorflow[29]. This is an opensource machine learning library for python and java, in this application the python version will be used. Tensorflow includes a lot of standard machine learning methods. One of these is the Keras library that has been included in Tensorflow. This is the library that is used to create the neural network[30]. The way the optimal neural network is going to be determined is by calculating at the R squared value.

R

2

₌₁₋

Explained Variation

TotalVariation

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This is a statistical measure that represents the proportion of variance that can be explained by independent variables in a regression model. Values below 0.7 indicate that there is weak statistical relation between the input and output, values above 0.85 indicate there is a strong statistical relation between the input and output And also by looking at the loss value and the validation loss value. This value should be as low as possible since it represents the error between the predicted output and the known output. If this approaches one it means that the prediction matches the known output and the model is accurate.

The dataset to be used it is loaded and first split in input and output values. From the total dataset 20 percent of the data is excluded from the training dataset and put in a testing dataset. The training dataset is used to train the neural network from this dataset the input and output values are given to the neural network so it can try and find a relation between these. The testing dataset is kept separate so that this is data the neural network has not seen before. This is done so that when the neural network is asked to predict the location using only input data R2_{score can be calculated for both. If there is a big discrepancy between the training data,}

that the neural network has already seen, and the testing data which is unseen it indicates that the model is overfitting.

For the neural network an optimal model has to be found. This is done because a balance has to be determined between accuracy and the time it takes to train the model. Make the neural network consists of too few layers/neurons and it is not accurate enough. Make the neural network to big and it will take a lot of time to train. Because at this point finding the optimal neural network configuration is based on trial and error the determination of the optimal neural network consists of three stages. First the number of layers needs to be determined. After this the number of neurons per layer and finally the optimal learning rate to get to the desired accuracy. The activation function that is going to be used is the rectified linear unit (relu)[32]. This is because this function is computationally efficient and is able to work well with most kinds of data. The number of epochs is set at 1000 because this is large enough to get a properly trained model, but small enough that it does not take too much time to run. because this is a large At this point determining a neural network is based on trial and error. In table 4.1 the points that help with determining the amount of layers are shown.

Table 3: Determining starting point for the number of hidden layers [33]

Hidden layers Result

none Neural network can only represent linearly separable functions or decisions

One The neural network is able to approximate any function that contains continuous values from one finite space to another finite space.

Two

Is able to represent an arbitrary decision boundary to arbitrary accuracy

Three or more The added layers are able to learn the complex relations between the other layers. (like automatic feature engineering).

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In addition to this to be able to get a start point of the number of neurons inside these hidden layers the points shown in table 4.2 need to be taken into account.

Table 4: Points for determining starting neurons in neural network determination[33]

The amount of hidden neurons should be between the amount of neurons in the input layer and in the output layer

The amount of hidden neurons should be 2/3 the size of the input layer plus the number of neurons in the output layer.

The number of neurons should be less then twice the size of the input layer.

Using the information given in these tables the starting point for the neural network determination where the input layer has 7 neurons (3 TDOA timings and 4 echo signals) and the output layer has 2 neurons (radius and the height). The other parameter that needs to be determined int addition to the layers and the neurons is the learning rate.

The learning rate determines how big the adjustments are that the model makes after each iteration over the dataset. If this learning rate is to high it might appear that the model is not becoming more accurate but that might be because it is not able to take small enough steps to reach the optimal solution (loss) this is shown in figure 4.3. Here there is a lot of noise in the blue (training loss) and red (validation loss) lines because they are not able to get to the optimal value due to a to high learning rate. When the learning rate is to low it will not be able to get to the solution within the set amount of epochs this is shown in figure 4.4. In figure 4.5 a learning rate is shown that quickly converges on the optimal loss value.

Figure 4.3: Learning rate to high, bounces around the desired value

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Figure 4.5: Loss function with appropriate learning rate

The way the optimal value can be approached quicker is to first train a model with a relatively high learning rate to have it quickly converge on the optimal model and safe this model. Then to load this model and continue training with a lower learning rate to try and get it as close as possible to the optimal solution

Using these three parameters the start conditions for determining the neural network can be determined from which through trial and error the optimal model can be determined. The number of layers will start at one layer because the TDOA and echo data are continuous values in a finite space. The number of neurons in the hidden layer is chosen to start at 5. This is because its equal to 2/3 the input layer plus the output layer and is between the number of neurons of the input and output layers. The learning rate is at first set to 0.01 this is to get relatively fast convergence on the optimal value and it will highlight the differences the amount of layers or neurons make pretty well.

5. Research results

5.1 Dataset creation

The dataset is created using python. The dataset is based on a tank with a radius of 5 meters and a depth of 5 meters. These values are chosen because they are still relatively in the realm industrial mixing tanks but the distances are still far enough apart so the timings will be relatively distinguishable. The datapoints are determined at intervals. The values chosen for these intervals are 0.1m for the radius, 0.1m for height and 5 degrees for the angle. This leads to a dataset containing 300.000 location points and corresponding TDOA and echo timings that can be used to train a neural network. This data is saved in a csv file. The code is included in appendix I.

5.2 Determining optimal Neural network model

As stated in chapter 4.2 determining the neural network model is based on trial and error. The code created for this is shown in appendix II. The start setup consists of one hidden layer that contains 5 neurons with a learning rate of 0.01 using the rectified linear unit (relu) activation function and this model is created in Tensorflow using the Keras library. The first step is to start by increasing the number of layers within the model to see if this improves the R2_{value. Because the initialization of the neurons is random each run was performed 3 times and}

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Figure 5.1: R2_{values compared to number of hidden layers}

In this figure it is shown that at around 4 hidden layers consisting of 5 neurons the optimal R2_{value is archived}

of 0.84 and stays relatively the same from 4 to 7 layers and starts to decrease after that. For this reason four hidden layers are chosen as the number used in this model.

The next part was determining the number of neurons in these hidden layers. The first thing done is to see if increasing individual layers have more effect then increasing the size of all of them. In figure 5.2 R2_{value is}

shown when each layer is increased from 5 to 10 neurons starting with the layer closest to the input. With the starting point being all layers having 5 neurons to the end point al layers having 10 neurons.

Figure 5.2: R2_{value change per number of layers is increased from 5 to 10 neurons}

Repeating this experiment in the opposite order where first he hidden layer closest to the output layer is increased shows similar results. This means that increasing all the neurons has the most effect on the R2_value.

Using this information the neurons in the layers where increase in increments of 5 to see the effect. This is shown in figure 5.3.

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5 10 15 20 25 30 35 40 45 50 0.75 0.8 0.85 0.9 0.95 1

R2 value based on neurons in hidden layers

R^train R^test Neurons R 2 v al u e Figure 5.3: R2

value based on neuron increase with increments of 5.3

This shows that the R2_{value rises quickly when increased from 5 to 10. But from 20 neurons per layer onward}

the increase stays is a lot more shallow. Further tests up to 180 neurons did not show a significant increase past 35 neurons so this amount is chosen for the hidden layers. Mainly because more layers would increase the training time and the slight increase would be offset by having to spend more time training.

Using this model the learning rate is adapted to try and get the R2_{value and the loss as small as possible by}

training the model and then decreasing the learning rate. So the model consisting of four layers with 35 neurons is first trained using a learning rate of 0.01 and trained for 1000 epochs. After this the learning rate is decreased to 0.000001 and trained for another 1000 epochs to try and get closer to the optimal value. Doing this the R2_{value increased to 0.977 for the training set and 0.939 for the testing set with a loss function of}

0.05001. Below in figure 5.4 100 datapoints are shown for the radius (r) and height (z) values for the training and test datasets with the original value in blue and the predicted value in red.

Figure 5.4: Prediction compared to determined value for 4 hidden layers and 35 neurons

Here it shows that the neural network is able to determine the radius with a relatively good accuracy as the red line follows the blue line almost perfectly for both the training and the test data. For the height however the

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the predicted output the error in the radius is in the 10 cm range, which is equal to the steps in the created dataset which where set at 0.1m.

6. Ethical considerations

Being able to get detailed information from the mixing process utilizing SMarbles that are able to be localized inside a mixing process would allow these mixing processes to be improved. This would lead to less badly mixed batches and a reduction in materials needed and waste produced which would be helpful for the carrying capacity of the planet.

As for looking at the technical components used in localization the main consideration would be the ultrasonic signal. There is an indication that ultrasonic signals might be harmful to humans when exposed over a long time at levels over 80dB in intensity and that at levels of 150 dB it starts to produce heat in organic materials which might be something to take into account if the ultrasonic signal reaches that level [34].

7. Conclusions and Recommendations

The main research question for this report is “How can a SMarble be located inside a mixing tank?” The answer to this question is that with the current implementation of the SMarble only the time difference of arrival method of localization would be suitable to be implemented. The problem with this is that the height data would get lost when the SMarble gets towards the centre of the hydrophone setup. This can alleviated by using the timing of the first echo. This is because the distance the echo travels is an indicator of the depth of the SMarble. To solve this relation a neural network can be used.

The recommendations would be to keep improving the neural network. The accuracy at this point is not that great and could be improved but it shows promise that a neural network can be used to get the height information. Also the creation of a dataset that contains real measured values from inside an industrial mixing tank would help improve the model more to a real world scenario.

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SMarble localization in industrial mixing tanks using TDOA and echo data