Artificial Intelligence applied to improve resilience in the inverse algorithms of Mars wind sensors

ARTIFICIAL INTELLIGENCE APPLIED TO IMPROVE RESILIENCE IN THE INVERSE ALGORITHMS OF MARS WIND SENSORS Bachelor Thesis Submitted to the Faculty of the Escola T` ecnica d’Engiyeria de Telecomunicaci´ o de Barcelona Universitat Polit` ecnica de Catalunya In partial fulfilment of the requirements for the degree in TELECOMMUNICATIONS TECHNOLOGIES AND SERVICES ENGINEERING Written by Oriol Bold´u Nebot Under the direction of Univ. Prof. Dr. Dominguez Pumar, Manuel M. Univ. Prof. Dr. Sayrol Clols, Elisa Barcelona, January 2021 Abstract In recent years, the interest in Mars exploration has increased exponentially due to the attractive desire of setting up the first human settlements in the Red Planet. Great efforts are being made to characterise the evolution and environment of this planet, so far robotic missions lead the field researches. Like any other electronic device, the instruments aboard these rovers have their life deadline and are also sensitive to malfunctions over time. The main goal of this thesis is to design and implement a software, based on artificial neural networks, capable of predicting data values for an out of service wind sensor aboard NASA’s rovers, such as the Curiosity or the InSight lander. To achieve this objective, it is necessary to understand the context and operation of the wind sensors, designed by the UPC-ETSETB. Distinct conditions and situations are described in order to characterise the variables and neural networks proposed. This project demonstrates that it is possible to obtain correlations between variables, which entails that the behaviour of a particular sensor can be predicted by the conduct of the rest. I Resum En aquests ´ultims anys, l’inter`es per l’exploraci´o a Mart ha augmentat exponencialment degut a l’atractiu desig d’establir els primers assentaments humans en el Planeta Vermell. S’estan realitzant grans esfor¸cos per caracteritzar l’evoluci´o i l’ambient d’aquest planeta, fins ara les missions rob`otiques lideren les investigacions de camp. Com qualsevol altre dispositiu electr`onic, els instruments a bord d’aquests r`overs tenen la seva data l´ımit de vida i tamb´e s´on susceptibles a errors al llarg del temps. L’objectiu principal d’aquesta tesi ´es dissenyar i implementar un software, basat en xarxes neuronals artificials, capa¸c de predir dades per un sensor de vent fora de servei a bord de r`overs de la NASA, com el Curiosity o el m`odul d’aterratge InSight. Per aconseguir aquest objectiu, ´es necessari entendre el context i el funcionament dels sensors de vent, dissenyats per la UPCETSETB. Es descriuen diferents condicions i situacions per tal de caracteritzar les variables i xarxes neuronals propostes. Aquest projecte demostra que ´es possible obtenir correlacions entre variables, el que implica que el comportament d’un sensor en particular pugui ser predit mitjan¸cant la conducta de la resta. II Resumen En estos ´ultimos a˜nos, el inter´es por la exploraci´on en Marte ha aumentado exponencialmente debido al atractivo deseo de establecer los primeros asentamientos humanos en el Planeta Rojo. Se est´an realizando grandes esfuerzos para caracterizar la evoluci´on y el ambiente de este planeta, hasta ahora las misiones rob´oticas lideran las investigaciones de campo. Como cualquier otro dispositivo electr´onico, los instrumentos a bordo de estos rovers tienen su fecha l´ımite de vida y son tambi´en susceptibles a errores a lo largo del tiempo. El objetivo principal de esta tesis es dise˜nar e implementar un software, basado en redes neuronales artificiales, capaz de predecir datos para un sensor de viento fuera de servicio a bordo de rovers de la NASA, como el Curiosity o el m´odulo de aterrizaje InSight. Para lograr este objetivo, es necesario comprender el contexto y el funcionamiento de los sensores de viento, dise˜nados por la UPC-ETSETB. Se describen distintas condiciones y situaciones con tal de caracterizar las variables y las redes neuronales propuestas. Este proyecto demuestra que es posible obtener correlaciones entre variables, lo que conlleva que el comportamiento de un sensor en particular pueda ser predicho mediante la conducta del resto. III Acknowledgments First of all, I would like to express my sincere gratitude to the mentors of this thesis, Prof. Manuel M. Dominguez Pumar and Prof. Elisa Sayrol Clols. Thank you for this wonderful opportunity and for the faith you have placed in me. It would not have been possible without your guidance, suggestions and encouragement throughout the entire project. Furthermore, I would like to thank ETSETB-UPC for the academic education and for pushing me to my limits. It has been an experience I will always remember, being part of this school is something unique. To my friends and university colleagues, thank you for your unconditional support, patience and advice during these years. Your energy, attitude and desire to learn have inspired me from day one. Without a shadow of a doubt, I would not be here if it were not in part for your company and friendship. Finally, to my parents, siblings and close family, you have been an essential mainstay throughout my life; your empathy, comfort and moral support have been fundamental to achieve whatever I proposed to. Your philosophy of effort, your spirit of perseverance and your good manners are reflected in who I am now. The following pages below symbolise the fulfilment of four and a half years of effort and hard work that have opened me a passionate world of knowledge and opportunities. Thank you all for making this possible. IV Contents Abstract I Resum II Resumen III Acknowledgments IV Table of contents V List of figures VII List of tables VIII 1 Introduction 1 1.1 Statementofpurpose.................................. 2 1.2 Requirements and specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Methodologyandprocedure.............................. 3 1.4 Workplan........................................ 4 1.5 Deviations and modifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Context 5 2.1 Marsexploration .................................... 5 2.2 InSightMission..................................... 6 2.2.1 Science ..................................... 7 2.2.2 Temperature and Wind for InSight (TWINS) . . . . . . . . . . . . . . . . 7 3 State of the art 10 3.1 Artificial Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.2 Regressionprediction.................................. 10 3.2.1 Multilayer Perceptron (MLP) . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2.2 Long Short-Term Memory (LSTM) . . . . . . . . . . . . . . . . . . . . . . 11 4 Project development 12 4.1 Dataset......................................... 12 4.1.1 Input/Output variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.2 Design and development of the Neural Network architecture . . . . . . . . . . . . 15 4.3 Prediction from data of two Booms . . . . . . . . . . . . . . . . . . . . . . . . . . 17 4.4 Prediction from data of one Boom . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.5 Prediction of short non-consecutive periods of time . . . . . . . . . . . . . . . . . 19 4.5.1 Prediction of one day in non-consecutive batches . . . . . . . . . . . . . . 19 5 Results 20 5.1 Prediction from data of two Booms . . . . . . . . . . . . . . . . . . . . . . . . . . 20 5.2 Prediction from data of one Boom . . . . . . . . . . . . . . . . . . . . . . . . . . 22 V 5.3 Resultsreport...................................... 23 5.4 Prediction of short non-consecutive periods of time . . . . . . . . . . . . . . . . . 24 5.4.1 Prediction of one day in non-consecutive batches . . . . . . . . . . . . . . 25 6 Budget 26 7 Conclusions 27 References 28 Appendices 30 Appendix A - Prediction from data of two Booms . . . . . . . . . . . . . . . . . . . . . 30 Appendix B - Prediction from data of one Boom . . . . . . . . . . . . . . . . . . . . . 30 Appendix C - Prediction of short non-consecutive periods of time . . . . . . . . . . . 33 Glossary 34 VI List of Figures 1 One InSight’s TWIN Boom. NASA/JPL-Caltech .................. 2 2 Artist rendition of the InSight Lander. NASA/JPL-Caltech ............ 2 3 Workplandiagram. .................................. 4 4 Curiosity’s selfie at a location nicknamed ”Mary Anning”. NASA/JPL-Caltech . 6 5 MEDA equipped in Perseverance Rover. NASA/JPL-Caltech ........... 6 6 InSight’s landing site. NASA/JPL-Caltech ...................... 6 7 TWINS Booms ready to be installed on InSight. CAB/INTA-CSIC ....... 8 8 Lateral view of four hot points (dice) structure. MNT/UPC ............ 9 9 Set up of two WS boards. NASA/JPL-Caltech/[10] ................ 9 10 Model of a simple MLP. NN-SVG/Alex Lenail ................... 11 11 Unrolled LSTM. [22] .................................. 11 12 Matrix correlation of the WS variables. . . . . . . . . . . . . . . . . . . . . . . . 13 13 Four dice array orientation. [10] ........................... 14 14 HLONG from board PCB 2, Boom BPY. . . . . . . . . . . . . . . . . . . . . . . . 14 15 HT RANS from board PCB 2, Boom BPY. . . . . . . . . . . . . . . . . . . . . . . 14 16 LSTMneuralnetwork.................................. 16 17 Proposed model to predict with data from 2 Booms. . . . . . . . . . . . . . . . . 17 18 Proposed model to predict with data from 1 Boom. . . . . . . . . . . . . . . . . . 18 19 (a) Train/Val loss function without P CB3of Boom BPY (2 Booms). (b) North- East die plotted (HCONV 9)............................... 20 20 Prediction of HCONV 9, Boom BPY - P CB3(2Booms). .............. 21 21 Relative error of prediction of HCONV 9, Boom BPY - P CB3(2 Booms). . . . . . 21 22 Detailed period of day 225 for HCONV 9, Boom BPY - P CB3(2 Booms). . . . . . 21 23 Train/Val loss function without P CB3of Boom BPY (1 Boom). . . . . . . . . . 22 24 Prediction of HCONV 9, Boom BPY - P CB3(1Boom)................ 22 25 Relative error of prediction of HCONV 9, Boom BPY - P CB3(1 Boom). . . . . . 22 26 Detailed period of day 225 for HCONV 9, Boom BPY - P CB3(1 Boom). . . . . . 23 27 HCONV 160s prediction of day 334, 2018. . . . . . . . . . . . . . . . . . . . . . . 24 28 Augmented batch of 60s for HCONV 1prediction, Boom BMY - P CB1....... 24 29 Predicted batches collection from HCONV 1, Boom BPY - P CB1. ......... 25 30 Relative error of predicted batches collection from HCONV 1, Boom BPY - P CB1. 25 31 (a) Train/Val loss function without P CB2of Boom BMY (2 Booms). (b) South- West die plotted (HCONV 7)............................... 30 32 Prediction of HCONV 7, Boom BMY - P CB2(2Booms)............... 30 33 Relative error of prediction of HCONV 7, Boom BMY - P CB2(2 Booms). . . . . 30 34 Detailed period of day 168 for the HCONV 7, Boom BMY - P CB2(2 Booms). . . 31 35 Train/Val loss function without PCB2 of Boom BMY (1 Boom). . . . . . . . . . 31 36 Prediction of HCONV 7, Boom BPY - P CB2(1Boom)................ 31 37 Relative error of prediction of HCONV 7, Boom BPY - P CB2(1 Boom). . . . . . 32 38 Detailed period of day 168 for the HCONV 7, Boom BPY - P CB2(1 Boom). . . . 32 39 HCONV 360s prediction of day 349, 2018. . . . . . . . . . . . . . . . . . . . . . . 33 40 Augmented batch of 60s for HCONV 3prediction, Boom BMY - P CB1....... 33 VII List of Tables 1 VariablesfromoneBoom................................ 12 2 Extravariables...................................... 13 3 Dataset split configuration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4P CB3mean relative error (2 Booms). . . . . . . . . . . . . . . . . . . . . . . . . 23 5P CB3mean relative error (1 Boom). . . . . . . . . . . . . . . . . . . . . . . . . . 23 6 ProjectBudget...................................... 26 VIII 2 CONTEXT 2.2.1 Science The expression “Sol” is how is used to call the Martian day, which is approximately 40 minutes longer than a day on Earth (24h, 39 min and 35s). A Mars solar day is defined as the amount of time that the planet takes to spin on its axis so that the Sun appears again in the same position in the sky. Due to the greater distance between Mars and Sun compared to the Earth, a Mars tropical year is 668.5921 sols, slightly less than two years on Earth. Only every 26 months (2.16 years), what is called launch window to Mars opens, since is the short period of time when the distance between Earth and Mars is minimum. InSight’s mission is still collecting data after 768 Sols (one Mars year and 99 Sols). This spacecraft defined Sol 0 as the solar day on which the lander touched down on the Martian surface. Once on the Red Planet, InSight unrolled its solar panel, did some needed checks and after 16 minutes first data were arriving on Earth. Despite the lander’s main science operations can not be fully settled until two months after landing, TWINS began collecting data a few days after. [6][2] The InSight Lander carries an advanced equipment of seven principal science instruments, in order to provide key information on the internal structure and composition of Mars, as well as, to carry out a series of surface geophysical investigations. One of the main objectives of this mission is to contribute to a deep understanding of the tectonic activity and meteorite impact rates, which are crucial to characterise the thermal evolution and forces that cause this geology and processes in what was supposed to be an Earth-like planet. This spacecraft carries three primary investigations: Seismic Experiment for Interior Structure (SEIS); Heat Flow and Physical Properties Package (HP3); and Rotation and Interior Structure Experiment (RISE). SEIS is a seismometer protected by a wind and thermal shield, it measures the surface internal vibrations generated by “marsquakes” or meteorite impacts. The second instrument is used to generate pulses of heat through the inner layer of Mars, in order to reveal how much heat or vibrations flows out to surface. RISE is an X-band radio instrument that measures the wobble (rotational dynamics) and deep core properties of Mars, based on the well-known Doppler Shift. Last but not least, these primary investigations are supported by a robotic arm, two cameras and the set of sensors (wind, temperature, pressure and magnetic field) called Auxiliary Payload Sensor Subsystem (APSS). [3][4] 2.2.2 Temperature and Wind for InSight (TWINS) TWINS is part of the complete InSight Lander weather station (APSS). The sensors that form it are very similar to those used in REMS (Curiosity), which were the first Spanish instruments that travelled to Mars. This weather station provides a precise continuous record of pressure, air temperature and winds at the surface of Mars. Consequently, its main purpose is to help and support the SEIS instrument, since the temperature and wind variations measured are removed or subtracted from the SEIS signal, therefore it characterise the influence of the landing site on these measurements. Moreover, TWINS helps to understand the current weather and climate of the Red Planet, provide information about wind speed and direction, essential to investigate atmospheric properties and dynamics or dust devils. 7 2 CONTEXT As mentioned in the introduction of this project, TWINS is comprised of two identical booms placed on diametrically opposite sides of the lander deck and disposed horizontally in such a way that one (Boom BPY) is pointing in the +Y lander axis direction and the other (Boom BMY) in the -Y direction. To understand this setting, it is easy to imagine a horizontal plane above the surface of the InSight’s platform, parallel to the ground, which is created by an axis (Y) aligned with booms and another (X) perpendicular to this, with its centre in the middle of the lander. Both booms are located at 265 mm above the lander main deck and about 1.665 m from the surface of Mars, as it can be seen in Figure 1. This layout is optimised and intended to minimise the effects and perturbations that other elements of the lander can cause on the wind flow, ensuring that measurements are clean wind data for any given wind direction and angle. Figure 7: TWINS Booms ready to be installed on InSight. CAB/INTA-CSIC Each boom is composed of three principal components: Wind Sensors, which are three recording points based on hot film anemometer that are explained in detail in the next paragraph. Air Temperature Sensor (ATS), a small rod made of a low thermal conductivity that obliquely comes out of the bottom of each boom. This rod has three Platinum Resistance Thermometer (PRT) placed on different levels. ATS provide air temperature measurements, and their readings are combined and processed to provide clean wind data despite the thermal contamination from the boom. Finally, the Pressure Sensor (PS), a pressure transducer located in the lander body, where the effects of temperature that corrupt the pressure measurement are minimised. [19][5] The WS mainly record data in a continuous mode, which is based on low-frequency sampling (1Hz), resulting in 1s the physical response time of the sensor to wind perturbations. One wind sensor is a 2D hot film anemometer composed of four hot dice and a separated reference cold point in a transducer Printed Circuit Board (PCB). Moreover, each board has an additional PRT (PT1000) to monitor the board’s temperature and evaluate the conductive thermal losses of the dice. There are three identical PCB around the boom surface, each one oriented at 120ºfrom the next one and connected by a flexible circuit. These dice are assembled in a square configuration as shown in Figure 8, it is used an electro-thermal sigma-delta modulation loop that supplies the required power to each hot die.[7] The main concept of these dice is to maintain a fixed constant temperature difference concerning the cold die (reference). If an incident gust of wind reaches a die, its internal temperature is modified and is at this point when the thermal sigma-delta loop provides more power in order to reach again the constant difference temperature (delta) established. In other words, wind fluid cools the die, so an injected power is needed to heat it up again and keep a constant predefined temperature difference between the hot and cold die (reference).[15] 8 2 CONTEXT Figure 8: Lateral view of four hot points (dice) structure. MNT/UPC Figure 9: Set up of two WS boards. NASA/JPL- Caltech/[10] For each amount of power added in a die, it is calculated the power or heat dissipated in the air called the convection power. To reach its thermal equilibrium, the power injected to each die has to equal the conduction and radiation power losses plus the power lost by convection to the ambient. The thermal conductance (Gth) of each die is related to the wind speed, and is defined by the following expression: Gth =¯ P ∆T=¯ P Thot −Tair (1) Where: ¯ Pis the convection power of a die. (W) ∆Tis the difference between a hot die and air temperature. (K) Once the thermal conductance has been calculated, the next step is to reach the convection or heat transfer coefficient (Hconv), which is the thermal conductance proportional to one die surface. Hconv =Gth A(2) Where: Gth is the thermal conductance of a die. (W K) Ais the area of a die. (m2) Finally, an algorithm based on a querying look-up table of calibrations obtained through extensive series of WS testing and simulation campaigns, is able to transform this convection coefficient into a wind speed and direction in m s. Therefore, the more convection power, the more thermal conductance and higher the convection coefficient is, which also implies a greater incident wind gust at that specific point. The inverse algorithm also combines the data from all the six InSight’s recording points and determines the wind speed and direction, combining all the PCB boards to conceive a 3D wind image. 9 3 STATE OF THE ART 3 State of the art 3.1 Artificial Neural Networks Artificial Intelligence is a term that can contain a lot of meaning and considerable amounts of definitions. In any case, this increasing technological trend is based on a great variety of what is called artificial neural networks (ANN), which are mathematical and computational models inspired by biological neural networks, in order to emulate the internal operations and characteristics of a human brain. A neural network is constructed by an interconnected group of artificial neurons that multiply the inputs received by internal weights of each neuron or perceptron.[11] The output of a single neuron is derived from a sum of the weighted inputs plus a bias term and then computed by a specific activation function that introduces non-linearities. It is said that a neural network learns in the training period when is able to adjust or estimate its weight and bias parameters, in order to obtain the optimal desired output that minimises the loss function error. Due to the nature of the topic presented in this project, a Supervised Learning paradigm defines the basic concepts of the neural network. It is called supervised learning when the algorithm learns by making predictions on the training data and being corrected by the ground truth (correct answer) of the dataset.[14] Therefore, a mapping function for the known input (x) and output (y) variables is created and the network tries to generate close predictions to unseen input data. During the learning process (epochs/iterations), the fundamental idea is based on the comparison of the obtained and target output in order to keep on modifying the neural network weights to minimise the error and generalise the model. Furthermore, the ANN needed has to identify correlations and the better variables for a correct and accurate prediction. 3.2 Regression prediction As the name itself shows, regression is a technique to find correlations or strong mathematical relationships between a group of variables. Therefore, this statistic method gets conclusions and characteristics of variables over a specific period of time, what makes possible to predict “dependent” variables identified as output (ˆy). Nowadays, many regression procedures are being applied in classification problems, where algorithms try to predict a discrete class label output for a specific input image. Nevertheless, the concept of this project does not correspond to this type of practice, the intention is to predict a continuous quantity of real values for each output. In this case, there is more than one input to find similarities in the behaviour of the data, as well as, more than one variable to predict in the same period of time, so the system and strategy needed are based on a multiple regression prediction. The techniques used in this project are briefly presented hereunder. 10 3 STATE OF THE ART 3.2.1 Multilayer Perceptron (MLP) The multilayer perceptron is one of the first deep neural network schemes ever used, a classical type of feed-forward ANN that make use of the error back-propagation technique to be trained. [17] [8] This class of universal predictor consists on three or more layers of neurons or perceptrons interconnected with each other, which can be divided into the input layer, the hidden layer (distinct levels of abstraction) and the output layer, as illustrated in Figure 10. The input layer plays no computational role but is needed to set the input variables of the network, and the output layer defined the predicted vector of the model. An architecture based on MLP represents a nonlinear mapping and flexible relationship between input and output variables, and allows a simple learning process based on corrections in weights that minimise the output’s error. These networks reduce significantly the computational complexity on time series prediction, they are capable of learning temporal features from data in order to accurate an output estimation based on the set of input variables. Figure 10: Model of a simple MLP. NN-SVG/Alex Lenail 3.2.2 Long Short-Term Memory (LSTM) The Long Short-Term Memory is a recurrent neural network that has the ability to maintain long term memory storage. In other words, the algorithm can learn long term correlations in a sequence, which is useful for time sequence prediction problems. By the addition of a circuit of loops, LSTM is created by memory blocks that work as feedback to the next input layer. Consequently, the network learns from the memory of recent temporal sequences, however, a previous deep knowledge of the behaviour of the data is needed.[22][1] Figure 11: Unrolled LSTM. [22] 11 4 PROJECT DEVELOPMENT 4 Project development 4.1 Data set In order to carry out this research, it has been necessary to count with a huge amount of TWINS data. The dataset used has been provided and filtered by the CAB, which has been in charge of the WS tests and possesses the calibration tables for these. The first information of the dataset is dated from Earth day 334 of 2018 (Sol 559, Martian Year 34) at 19:09:38 UTC (Coordinated Universal Time), what means that the available data starts four days after InSight’s landed, 30th November 2018. The last information of the dataset is from Earth day 263 of 2019 (Sol 177, Martian Year 35), 20th September 2019. Consequently, due to the Insight’s landing site (North Hemisphere) and the duration of a Martian year, the available data characterises the final stages of winter on Mars, the spring and early summer seasons. Each document (.csv) supplied by CAB contains TWINS information of a specific day, with a specific hour interval and a second per sample. Therefore, the first thing that has been done is to assemble together the entire collection of documents to create a single global and unique dataset. Through the python code implemented, the first data processing has been done. Moreover, it has been observed that the global dataset created does not have data (NaN) in every line of time, so all the rows with no data values have been removed from the global dataset, succeeding to a final dataset of 290.135 rows in total. The following tables specify the WS variables used in this project. The first table corresponds to the information of the three boards from a single boom, while the second table defines global data from TWINS. Source Variable Description Boom BMY or Boom BPY PT10001PRT sensor as Tair reference for P CB1 HCONV 1 Convection coefficients from P CB1 HCONV 2 HCONV 3 HCONV 4 PT10002PRT sensor as Tair reference for P CB2 HCONV 5 Convection coefficients from P CB2 HCONV 6 HCONV 7 HCONV 8 PT10003PRT sensor as Tair reference for P CB3 HCONV 9 Convection coefficients from P CB3 HCONV 10 HCONV 11 HCONV 12 Table 1: Variables from one Boom. 12 4 PROJECT DEVELOPMENT Source Variable Description InSight’s clock UTC Time variable in Year-Day|hh:mm:ss format Pressure sensor Pressure General variable of Mars pressure Table 2: Extra variables. It is observed that the largest number of variables that define the global dataset is 32 since it integrates the information of both booms. To carry out an initial study or evaluation of the dependencies and correlations between variables, the plot illustrated in Figure 12 has been generated. Values close to one can be identified in most variables of the matrix, which means that there is a powerful correlation and dependence between them. Therefore, as it has been intuited, these are considered the adequate and suitable variables for the model proposed. Figure 12: Matrix correlation of the WS variables. For a further understanding of variables behavior over time, it is interesting to introduce two relevant variables that result from the combination of the convection coefficient signals. The four dice from a single board can be defined as follows: 13 4 PROJECT DEVELOPMENT Figure 13: Four dice array orientation. [10] HLONG =North −South = (A+D)−(B+C) HT RANS =East −W est = (A+B)−(C+D) The graphs below are a representation of the Longitudinal and Transversal variables over an extended period of time. A higher positive value means more wind speed in that direction, because a higher convection power is described. The same concept can be applied in the HT RANS2signal, where the negative value periods indicate more speed in the two West dice of the board. Likewise, the positive interval of HLONG2that represents a time when the North dice had incident wind. Figure 14: HLON G from board PCB 2, Boom BPY. Figure 15: HT RANS from board PCB 2, Boom BPY. 14 4 PROJECT DEVELOPMENT 4.1.1 Input/Output variables From all the variables from the previous tables that define the dataset, it is important to be clear about the input and output required to achieve the objectives and requirements. When a WS die stops working, the data from the three remaining dice are clearly affected by this event. It is for this reason that, it is considered the whole board as absent, whose convection coefficients are defined as the variables to predict (output). Therefore, the model always has an output dimension of four variables, and the information from the other boards is the necessary input. Throughout this document, different output variables are presented in order to characterise the fall of diverse boards. In order to develop the ANN, first it has been necessary to divide the dataset into three common subsets: Train, Validation and Test. The first one, used to fit the model, which is validated at each epoch by data from the second subset. Test subset is the unseen data that is used to evaluate the performance of the model for new data. The split percentage has been defined with the following proportion: Subset Split ratio Number of rows Train 64% 185.686 Validation 16% 46.422 Test 20% 58.027 Table 3: Dataset split configuration. Before introducing the input variables in the model, they have been normalised. Due to the micro-magnitude and positive nature of the convection coefficients, the data modification done has been a standardization, which distributed data in a Gaussian form with zero mean and unit standard deviation or variance. Finally, the predicted values are inversely transformed, recovering the form and range of the original signal. 4.2 Design and development of the Neural Network architecture Due to the short duration of this project, only one neural network model has been established and proved. Nevertheless, two possible candidates models were initially assessed and a performance review was carried out to find out which of the two best fit for the problem. The evaluated models were a multilayer perceptron network, which is the native deep learning network, and also the LSTM algorithm. This last recurrent neural network has been designed as shown in Figure 16. This model takes 60 samples of time as a short batch period of memory with one LSTM layer of 200 neurons. Moreover, it counts with two fully connected layers in order to set an output layer of four variables to predict. Despite this kind of recurrent neural networks are suited to solve time sequence regression problems, they introduce a high level of complexity, and besides, in this case, 60 samples are needed to predict just one single time-step value for each die. Considering this project as a starting point and experimenting better early results with a 15 4 PROJECT DEVELOPMENT MLP network, currently, the LSTM has been put aside perceiving it as a possible solution in future researches. Figure 16: LSTM neural network. Consequently, the MLP network has been the convenience neural network model for this project. The strategy applied suggests one model or software for each PCB to predict. Depending on what WS board is simulated as inoperative, the information to predict has to change. For instance, if PCB 1 from Boom BPY is declared faulty, the predicted/output variables have to be HCONV 1...4, while the input variables are all the others from other boards and booms, except the P T 10001, since the entire board is supposed to be defective. Despite the network architecture is changing (explained in the next sections), the design concept characterise to be the first part of an auto-encoder. [20] The activation function used in the entire collection of neurons is the recent SELU (Scaled Exponential Linear Unit). This function correctly treats positive values and permits higher control over negative values, which is critical in this case due to the standardization of the data. Moreover, SELU has achieved better results than other well-known functions like ReLU or LeakyReLU, providing a faster network convergence and avoiding vanishing gradient problems.[12] Dealing with regression in deep learning entails no activation function for the output layer. Training a neural network is an iterative process that in this case consists of two phases: forward and backpropagation. In the first one, all the training dataset (in batches and shuffled) is passed through the network at each epoch. Once each time-step is estimated, a loss function is calculated by the difference between the prediction made and the ground truth. Moreover, a forward process of validation data quantifies the network behaviour for unseen data. Afterwards, in the second phase, the error calculated before is propagated backwards, which is used by the model to upgrade the weights in order to minimise the loss function. The regression metric employed as a loss function is the MSE (Mean Squared Error). MSE =1 N N X n=1 (YGTn−ˆ YP redn)2(3) Where: YGT is the ground truth value. ˆ YP red is the predicted value. 16 5 RESULTS Figure 26: Detailed period of day 225 for HCONV 9, Boom BPY - P CB3(1 Boom). 5.3 Results report Both models predict correctly the behaviour over time of the convection coefficients. Despite the quick variations and large amount of data, the results obtained are similar to the real values. Moreover, an optimistic quality is that the predicted traces are not limited in terms of values, which means that they can reach the offsets of the ground truth. It is noteworthy that with the information of the other Boom, the global prediction experiments less mean relative error than just predicting with a single Boom data. This fact suggests that the external information of the other Boom helps in some way to the predicted trace precision. Nevertheless, it surprises that carrying out a prediction with significantly less information, the second model achieves a close equivalent result, which implies that probably a volatile variable is missing in the input definition. The main conclusion deduced is that despite the proper tracking of the predictions, both models show resilience to accurately predict long time series with such a distant time gap between training and test data. Faulty board Variable Dice’s mean relative error Board’s mean relative error P CB3 HCONV 93,725% 3,932% HCONV 10 4,242% HCONV 11 3,382% HCONV 12 4,380% Table 4: P CB3mean relative error (2 Booms). Faulty board Variable Dice’s mean relative error Board’s mean relative error P CB3 HCONV 94,417% 4,185% HCONV 10 4,982% HCONV 11 4,083% HCONV 12 3,259% Table 5: P CB3mean relative error (1 Boom). 23 5 RESULTS 5.4 Prediction of short non-consecutive periods of time This section presents the results obtained for the prediction of non-consecutive periods, which has been defined as a batch time of 60 seconds. Therefore, the experiment that has been carried out consists on predicting distinct gaps of the same day’s time of P CB1(Boom BMY), in such a way, that the model possesses previous and future events in the training and validation dataset. This concept can be observed in the following figure, where an augmented and single predicted batch is represented between two collections of Train/Val data. Notice that the predicted trace precisely follows the ground truth values, obtaining new data for one faulty batch of the North- East die. Appendix C shows the results of another 60s from a different day and dice variable. Figure 27: HCONV 160s prediction of day 334, 2018. Figure 28: Augmented batch of 60s for HCONV 1prediction, Boom BMY - P CB1. The prediction of short non-consecutive periods has turned out to be more accurate, effective and robust than the other estimates. It is verified that the model is able to learn characteristics from the behaviour of the WS signals of the other boards and also from the previous and future samples of the predicted one. This data interpolation results in a correct prediction of different non-consecutive time periods, which allows obtaining new reliable data for those empty batches and establishing a continuous-time data series. 24 5 RESULTS 5.4.1 Prediction of one day in non-consecutive batches This section presents the results of the collection of predicted gaps that constitute the recorded day 335, 2018. It is displayed the estimation of the North-East die from P CB1, Boom BMY. The results show a great improvement in terms of global accuracy and mean relative error. Therefore, this performance suggests that predicting short non-consecutive periods not only is possible but also provide solid information of a sporadic faulty sensor over one entire day. Finally, it is confirmed that the model carries out a better prediction when is being fitted by nearby facts that characterise the desired intervals. Figure 29: Predicted batches collection from HCONV 1, Boom BPY - P CB1. Figure 30: Relative error of predicted batches collection from HCONV 1, Boom BPY - P CB1. 25 6 BUDGET 6 Budget An overall approach of the direct and indirect costs of the project has been made based on the following premises: •The duration of the project has been four and a half months, 18 weeks and a total of 25 hours per week. •The student is considered a Junior Engineer, whose wage is 9 €per hour. Furthermore, the two professors responsible for the supervision of the project are defined as Senior Engineers with a salary of 25 €per hour, 3 hours per week are assumed. •The UPC (ETSETB) GPU server used in this project has been a free remote service. However, to capture realistic project costs, it is assumed a virtual server GPU (IBM Cloud server and NVIDIA GPU) with a monthly fee of 46,04 €. •A computer, desk, chair and other amortizable material have been acquired for a total price of 1.630,00 €. •Due to the COVID-19 situation, this project has been carried out from home by telematic means. Therefore, the cost of the project assumes a part of the internet and home expenses, which go up to 45€per month. Next table shows the summary of all the costs that materialise throughout the project. The total final cost ascends to 8.812,70 €. Concept Cost Junior Engineer 4.050,00 € Supervision 2.700,00 € Remote GPU Server 230,20 € Amortizable Material 1.630,00 € Home Expenses 202,50 € TOTAL 8.812,70 € Table 6: Project Budget. 26 7 CONCLUSIONS 7 Conclusions The main motive and desire that has remained throughout this project has been the idea of setting the first methods and techniques for this fascinating new research under the care of MNT-UPC group. Despite developing an artificial neural network from scratch has been an ambitious and tough labour, the obtained global results present a positive performance and give an optimistic and promising impression facing towards the future. Through the understanding and representation of the exposed wind sensors, it has been able to characterise the behaviour of its variables over time. Although the results shown represent a general picture of the methods and procedure operations, an exhaustive analysis and conception of the model designed and variables efficiency have been carried out, what provides a great wealth of knowledge and experience for these WS variables. This project demonstrates that it is possible to obtain strong correlations between variables, as well as, to predict the behaviour and specific values of a particular sensor by means of the conduct and information of the remaining. Furthermore, it has been identified that the proposed model has an accurate and successful operation when predicting short periods of time knowing previous and subsequent events. This implies that it is possible to acquire precise predicted data of non-consecutive time batches for the same day. Besides, despite the prediction of long-isolated intervals has been shown to be not so exact, indeed, the trace of the ground truth values is well predicted, which permits to know the behaviour of the sensor in a distant future. For these reasons, it can be concluded that the initial objectives have been completely satisfied and satisfactory exceeds nearly all the initial requirements and specifications. Moreover, not only a model able to predict WS values has been implemented but also a baseline environment and system suitable to new improvements and modifications that allow the continuity of this research has been prepared. As mentioned at the beginning of this thesis, the calculation of velocity-angle for wind predicted values has not been possible to obtain, due to the lack of time and the dependence on third parties required to receive feedback on the quality of the results in m/s. However, this project has concluded with a compilation of distinct files (predicted and real values) ready to be sent and evaluated by the CAB-CSIC. The short-term future developments depend on this feedback and evaluation of the results processed to velocity magnitude. In addition, once this analysis has been done, it will be planned a data migration or transfer of all the software and environment to MNT-UPC group, to be useful for incoming papers or thesis, which would propose innovative models that improve the results obtained until now. For long-term studies, it would be significant to apply the methods and concepts proposed in the context of Perseverance (February 2021), which has a higher amount of information and WS on board. 27 References References [1] Anusri Pampari Abhishek Narwekar. Recurrent neural networks architectures. https:// slazebni.cs.illinois.edu/spring17/lec20 rnn.pdf, 2016. [Online] Accessed: 15 December 2020. [2] Michael Allison and NASA Goddard Institute for Space Studies Robert Schmunk. Mars24 sunclock — time on mars. https://www.giss.nasa.gov/tools/mars24/help/notes.html, 2020. [Online] Accessed: 8 December 2020. [3] W Bruce Banerdt, Suzanne E Smrekar, Don Banfield, Domenico Giardini, Matthew Golombek, Catherine L Johnson, Philippe Lognonn´e, Aymeric Spiga, Tilman Spohn, Cl´ement Perrin, et al. Initial results from the insight mission on mars. Nature Geoscience, pages 1–7, 2020. [4] WB Banerdt, S Smrekar, L Alkalai, T Hoffman, R Warwick, K Hurst, W Folkner, P Lognonn´e, T Spohn, S Asmar, et al. Insight: an integrated exploration of the interior of mars. LPI, (1659):2838, 2012. [5] Luis Mora Sotomayor (CAB). Twins and ps data products sis. https://atmos.nmsu.edu/ PDS/data/PDS4/InSight/twins bundle/document/twinspsdp sis issue9.pdf, 2020. [Online] Accessed: 18 November 2020. [6] Royal Observatory (Greenwich) Dhara Patel. How long is a day on mars? https://www.rmg.co.uk/discover/explore/how-long-day-on-mars, 2018. [Online] Accessed: 8 December 2020. [7] M Dom´ınguez, V Jim´enez, J Ricart, L Kowalski, J Torres, S Navarro, J Romeral, and L Casta˜ner. A hot film anemometer for the martian atmosphere. Planetary and Space Science, 56(8):1169–1179, 2008. [8] Matt W Gardner and SR Dorling. Artificial neural networks (the multilayer perceptron)—a review of applications in the atmospheric sciences. Atmospheric environment, 32(14-15):2627–2636, 1998. [9] M Golombek, NH Warner, JA Grant, E Hauber, V Ansan, CM Weitz, N Williams, C Charalambous, SA Wilson, A DeMott, et al. Geology of the insight landing site on mars. Nature communications, 11(1):1–11, 2020. [10] J G´omez-Elvira, C Armiens, L Casta˜ner, M Dom´ınguez, M Genzer, Francisco G´omez, R Haberle, A-M Harri, V Jim´enez, H Kahanp¨a¨a, et al. Rems: The environmental sensor suite for the mars science laboratory rover. Space science reviews, 170(1-4):583–640, 2012. [11] Neha Gupta. Artificial neural network. Network and Complex Systems, 3(1):24–28, 2013. [12] Casper Hansen. Activation functions explained - gelu, selu, elu, relu and more. https: //mlfromscratch.com/activation-functions-explained/#/, 2019. [Online] Accessed: 24 November 2020. [13] Bruce M Jakosky and Christopher S Edwards. Inventory of co2 available for terraforming mars. Nature astronomy, 2(8):634–639, 2018. [14] Tammy Jiang, Jaimie L Gradus, and Anthony J Rosellini. Supervised machine learning: a brief primer. Behavior Therapy, 51(5):675–687, 2020. [15] Lukasz Kowalski. Contribution to advanced hot wire wind sensing. PhD thesis, UPC Barcelona, 2016. Research in Electronic Engineering. 28 References [16] NASA/JPL-Caltech. Mars insight mission. https://mars.nasa.gov/insight/, 2018. [Online] Accessed: 2 December 2020. [17] YQ Ni and M Li. Wind pressure data reconstruction using neural network techniques: A comparison between bpnn and grnn. Measurement, 88:468–476, 2016. [18] GR Osinski, CS Cockell, A Pontefract, and HM Sapers. The role of meteorite impacts in the origin of life. Astrobiology, 20(9):1121–1149, 2020. [19] Aymeric Spiga, Don Banfield, Nicholas A Teanby, Fran¸cois Forget, Antoine Lucas, Balthasar Kenda, Jose Antonio Rodriguez Manfredi, Rudolf Widmer-Schnidrig, Naomi Murdoch, Mark T Lemmon, et al. Atmospheric science with insight. Space Science Reviews, 214(7):109, 2018. [20] Li Tian, Guorui Li, and Cong Wang. A data reconstruction algorithm based on neural network for compressed sensing. In 2017 Fifth International Conference on Advanced Cloud and Big Data (CBD), pages 291–295. IEEE, 2017. [21] Colin F Wilson. Measurement of wind on the surface of Mars. PhD thesis, University of Oxford, 2003. [22] Hangxia Zhou, Yujin Zhang, Lingfan Yang, Qian Liu, Ke Yan, and Yang Du. Shortterm photovoltaic power forecasting based on long short term memory neural network and attention mechanism. IEEE Access, 7:78063–78074, 2019. 29 Appendices Appendices Appendix A - Prediction from data of two Booms For Boom BMY, the South-West die has been chosen to display the results obtained. (a) (b) Figure 31: (a) Train/Val loss function without P CB2of Boom BMY (2 Booms). (b) South-West die plotted (HCONV 7). Figure 32: Prediction of HCONV 7, Boom BMY - P CB2(2 Booms). Figure 33: Relative error of prediction of HCONV 7, Boom BMY - P CB2(2 Booms). 30 Appendices Figure 34: Detailed period of day 168 for the HCONV 7, Boom BMY - P CB2(2 Booms). Appendix B - Prediction from data of one Boom Figure 35: Train/Val loss function without PCB2 of Boom BMY (1 Boom). Figure 36: Prediction of HCONV 7, Boom BPY - P CB2(1 Boom). Hello, here is some text without a meaning. 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