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This article presents a method to estimate frequency distributions of the parameters associated with the presence of two leaks in a main water pipeline: the locations and the emitter coefficients. Since the method is offline, it can be... more
This article presents a method to estimate frequency distributions of the parameters associated with the presence of two leaks in a main water pipeline: the locations and the emitter coefficients. Since the method is offline, it can be used to locate simultaneous or sequential leaks; the only requirement is that both leaks must be present when the data for diagnosis are acquired. The method requires as input information pressure and flow rate data to be measured at the pipeline boundaries. In a first stage, hydraulic quasi-steady state relations are computed by using the input information. These relations are used to calculate hydraulic and spatial constraints. In a second stage, Monte Carlo simulations are used together with the previously defined restrictions to obtain frequency distributions of the parameters associated with both leaks. To test the feasibility and potentiality of the method, it was implemented and tested in MATLAB with synthetic data.
This article introduces an energy-based approach for modeling water distribution networks with faults. The flow in each network pipeline is described by the rigid water column model (RWC), which can be obtained by assuming that the walls... more
This article introduces an energy-based approach for modeling water distribution networks with faults. The flow in each network pipeline is described by the rigid water column model (RWC), which can be obtained by assuming that the walls of the pipelines are rigid and the flow is incompressible. The key feature of the proposed approach is the modeling of the interactions of the network components (pipelines, faults, and sources), which is done through the use of the graph theory and from an energy point of view. Three examples are given: a pipeline with a partial blockage, a pipeline with a leak, and a pipeline with both faults. The models resulting from this approach can be used for the implementation of realtime applications, for example, for fault diagnosis or for control of valves and pumps in case of faults.
Shipping water events (SWE) occur when incident waves flood and propagate over the deck of maritime structures, usually during extreme wave climate. SWE can cause structural damage, unexpected overloading, human losses or even spills of... more
Shipping water events (SWE) occur when incident waves flood and propagate over the deck of maritime structures, usually during extreme wave climate. SWE can cause structural damage, unexpected overloading, human losses or even spills of products that are harmful to the environment. Therefore, the estimation of variables that help to predict the evolution of these events is highly helpful to lessen catastrophic consequences. In this regard, this work proposes a model-based approach to describe the spatiotemporal evolution of SWE on a fixed structure with a horizontal propagation domain. The approach is based on a model expressed as an advection-difussion equation with space-dependent nonlinear coefficients. To explore the suitability of the model, for characterizing the SWE evolution, its numerical response is compared with elevation data of SWE generated in a channel by incident regular wave trains. For the comparison, the model coefficients were estimated from an experimental data set with the use of an adaptive observer. The results of the comparison show that the response of the model allows to represent the physics of the analyzed SWE in an acceptable way. The advantage of using an adaptive observer for the estimation is that it can be used in further applications where the actual values of varying coefficients could be required in a reasonable computational time.
This article presents a methodology for using data from social networks, specifically from Twitter, to diagnose leaks in drinking water distribution networks. The methodology involves the collection of tweets from citizens reporting... more
This article presents a methodology for using data from social networks, specifically from Twitter, to diagnose leaks in drinking water distribution networks. The methodology involves the collection of tweets from citizens reporting leaks, the extraction of information from the tweets, and the processing of such information to run the diagnosis. To demonstrate the viability of this methodology, 358 Twitter leak reports were collected and analyzed in Mexico City from 1 May to 31 December 2022. From these reports, leak density and probability were calculated, which are metrics that can be used to develop forecasting algorithms, identify root causes, and program repairs. The calculated metrics were compared with those calculated through telephone reports provided by SACMEX, the entity that manages water in Mexico City. Results show that metrics obtained from Twitter and phone reports were highly comparable, indicating the usefulness and reliability of social media data for diagnosing leaks.
This paper describes the implementation of three deterministic algorithms for the attitude estimation of a rigid body in a pragmatic fashion. For that, a tri-axis accelerometer and a tri-axis magnetometer, and a low-cost microcontroller... more
This paper describes the implementation of three deterministic algorithms for the attitude estimation of a rigid body in a pragmatic fashion. For that, a tri-axis accelerometer and a tri-axis magnetometer, and a low-cost microcontroller are used. The algorithms implementation is carried out using MATLAB/Simulink. The proposed methodology allows a fast evaluation of any deterministic algorithm. Then, it aids the subsequent development of embedded implementations. Experimental results validate the proposed methodology.
This paper presents port-Hamiltonian models for describing flow dynamics of incompressible fluids in rigid pipelines with faults. Two types of faults are addressed in this paper: leaks and partial blockages. In order to facilitate the... more
This paper presents port-Hamiltonian models for describing flow dynamics of incompressible fluids in rigid pipelines with faults. Two types of faults are addressed in this paper: leaks and partial blockages. In order to facilitate the understanding of the modeling, the proposed formulation is introduced starting from the analogy between electrical and hydraulic circuits. Thanks to the port-Hamiltonian formalism the models proposed here have a particular structure that makes them plug-in and modular, so that they can be interconnected for building holistic models for faulty water distribution networks.
Green water events may present different features in the initial stage of interaction with the deck of a structure. It is therefore important to investigate the evolution of different types of green water, since not all the events... more
Green water events may present different features in the initial stage of interaction with the deck of a structure. It is therefore important to investigate the evolution of different types of green water, since not all the events interact with the deck at the same time. In this paper, the evolution of three types of green water events (dam-break, plunging-dam-break, and hammer-fist) are studied. The water surface elevations and volumes over the deck in consecutive green water events, generated by incident [wave trains in a wave flume, were analyzed using image-based methods. The results show multiple-valued water surface elevations in the early stage of plunging-dam-break and hammer-fist type events. Detailed experimental measurements of this stage are shown for the first time. The effect of wave steepness on the duration of the events, maximum freeboard exceedance, and volumes were also investigated. Although the hammer-fist type showed high freeboard exceedances, the plunging-dam...
This paper presents a model for describing the flow of a mixture of water and glycerol in pressurized horizontal pipelines. The model is constituted by mass and momentum conservation equations together with experimental formulas for... more
This paper presents a model for describing the flow of a mixture of water and glycerol in pressurized horizontal pipelines. The model is constituted by mass and momentum conservation equations together with experimental formulas for computing both the density and dynamic viscosity of the mixture. The model was programmed in MATLAB to be numerically solved, as well as to simulate flow with different fractions of water and glycerol in leaking pipelines, which could allow to conceive algorithms for diagnosing leaks during the transport of flows with high viscosity. To show the agreement between the model prediction and the actual flow behavior of the mixture, the numerical model solution, for certain boundary conditions, is compared with some data acquired during an experimental test in a laboratory pipeline.
This paper presents a novel method for diagnosing leaks in a pipeline. The method is based on a discrete-space version of a Lienard-type model, which describes the fluid behavior in a pipeline only in terms of the flow rate. This latter... more
This paper presents a novel method for diagnosing leaks in a pipeline. The method is based on a discrete-space version of a Lienard-type model, which describes the fluid behavior in a pipeline only in terms of the flow rate. This latter detail was very useful in designing our method, which was conceived to deal with pipelines solely equipped with flowmeters or in conjunction with pressure sensors, but which are temporarily out of service. The working principle of our methodology is the generation of a set of residuals (each one defined for a specific section of the pipeline) to estimate the position of a leak. The residual near zero will indicate the section where a leak is occurring. The main advantage of our approach is that it does not require pressure measurements, which occurs in most existing methodologies. Thus, to show its potential, we present the results of some tests carried out in simulation.
This work deals with the hydraulic gradient estimation in real-time of a transport pipeline computational model by considering a slightly compressible fluid and slightly deformable conduit walls. Since the hydraulic gradient (J(Q)) caused... more
This work deals with the hydraulic gradient estimation in real-time of a transport pipeline computational model by considering a slightly compressible fluid and slightly deformable conduit walls. Since the hydraulic gradient (J(Q)) caused by the friction phenomenon in a pipeline plays an important role in the system's behavior, and this function is affected by fluid properties' deviations, environmental disturbances and conduit deteriorations, it is proposed that the on-line estimation of J(Q) could be part of a monitoring system. The proposition can be applied to obtain computational models of a line with a junction and assumes only measurements of pressure and flow rate at the ends of the conduit and the junction outflow. The generic form of the gradient function J(Q) is a second-order polynomial with coefficients that involve indirectly pipe roughness, the transversal area of the conduit, fluid viscosity and elements connected to the line. The extended Kalman filter (EKF)...
This work addresses the estimation of two interrelated parameters of the fluid flow in pipes. First, a numerical and experimental evaluation of some proposed methods to compute the friction factor in turbulent regime is presented. Special... more
This work addresses the estimation of two interrelated parameters of the fluid flow in pipes. First, a numerical and experimental evaluation of some proposed methods to compute the friction factor in turbulent regime is presented. Special attention is given to an explicit solution obtained through the Lambert W-function. Subsequently, a method to estimate the roughness coefficient using nonlinear optimization techniques is proposed, which then allows determining the friction factor from it. Numerical tests were performed for a wide range of operating points of a pipeline. In order to validate the proposed approach, experimental analysis was carried out on a pipeline pilot-plant. The results show the applicability and effectiveness of the proposed method.
This chapter presents the implementation of optimization algorithms to build auxiliary signals that can be injected as inputs into a pipeline in order to estimate—by using state observers—physical parameters such as the friction or the... more
This chapter presents the implementation of optimization algorithms to build auxiliary signals that can be injected as inputs into a pipeline in order to estimate—by using state observers—physical parameters such as the friction or the wave speed. For the design of the state observers, we propose to incorporate the parameters to be estimated into the state vector of Lienard-type models of a pipeline such that the observers can be constructed from the modified models. The proposed optimization algorithms guarantee a prescribed observability degree of the modified models by building an optimal input for the identification. The optimality of the input is defined with respect to the minimization of the input energy, whereas the observability through a lower bound for the observability Gramian, which is constructed from the Lienard-type models of the pipeline. The proposed approach to construct auxiliary inputs was experimentally tested by using real data obtained from a laboratory pipeline.
This article presents an approach based on a state observer to calibrate the Hazen-Williams (HW) equation, which is widely used to model the head loss in a pipeline. To perform the calibration process, the approach requires a record over... more
This article presents an approach based on a state observer to calibrate the Hazen-Williams (HW) equation, which is widely used to model the head loss in a pipeline. To perform the calibration process, the approach requires a record over time of the flow rate, which can be taken in any coordinate along the pipeline, and a record of the pressure taken at the inlet. Specifically, the proposed approach allows estimating both the roughness coefficient involved in the HW equation and the hydraulic head at the pipeline outlet. The closure of this contribution presents some results involving data that were collected during experiments in a physical model. Such results show the feasibility of implementing the proposed approach.
This paper presents a novel non-invasive monitoring method, based on a Liénard-type model (LTM) to diagnose single and sequential leaks in liquid pipelines. The LTM describes the fluid behavior in a pipeline and is given only in terms of... more
This paper presents a novel non-invasive monitoring method, based on a Liénard-type model (LTM) to diagnose single and sequential leaks in liquid pipelines. The LTM describes the fluid behavior in a pipeline and is given only in terms of the flow rate. Our method was conceived to be applied in pipelines mono-instrumented with flowmeters or in conjunction with pressure sensors that are temporarily unavailable. The approach conception starts with the discretization of the LTM spatial domain into a prescribed number of sections. Such discretization is performed to obtain a lumped model capable of providing a solution (an internal flow rate) for every section. From this lumped model, a set of algebraic equations (known as residuals) are deduced as the difference between the internal discrete flows and the nominal flow (the mean of the flow rate calculated before the leak). Once the residuals are calculated a principal component analysis (PCA) is carried out to detect a leak occurrence. ...
A new model has been established in order to represent one-phase water flow transients in pipeline systems. This model is based on a system of hyperbolic partial differential equations solved via the orthogonal collocation method. An... more
A new model has been established in order to represent one-phase water flow transients in pipeline systems. This model is based on a system of hyperbolic partial differential equations solved via the orthogonal collocation method. An observer can be designed from this model in order to estimate the unsteady friction when a transient event occurs in the pipeline. The Extended Kalman filter is chosen as an observer for this estimation. The observer and the model response are tested and compared respectively with experimental data obtained from a pilot water pipeline.
Abstract This article presents a procedure, which is formulated in three stages, to simplify the problem of localizing a single leak in a pipeline with multiple branches. The first two stages involve the fulfillment of generic conditions... more
Abstract This article presents a procedure, which is formulated in three stages, to simplify the problem of localizing a single leak in a pipeline with multiple branches. The first two stages involve the fulfillment of generic conditions deduced from head loss and flow rate balances for detecting and locating the specific section where the leak is present. The fulfillment of these conditions allows finding the analytical expression for the leak localization, which is the goal of the third stage. The key point of the procedure is the search for the section where the leak is found, which is based on a search for similarity between two types of models that depend, respectively, on measured and estimated hydraulic variables. To support the generality of the analytical expression for the leak localization, it is used to derive previously reported particular expressions for localizing leaks in single-branch pipes. The simplicity of the procedure is demonstrated by numerical simulations. Its performance under real conditions is demonstrated with field data of a 60-km long LPG pipeline in which the correct section with abnormal events is determined, despite uncertain data.
This article introduces an on-line fault diagnosis (FD) system to detect and recognize open-phase faults in switched reluctance motors (SRMs). Both tasks, detection and recognition, are based on functions built with the same information... more
This article introduces an on-line fault diagnosis (FD) system to detect and recognize open-phase faults in switched reluctance motors (SRMs). Both tasks, detection and recognition, are based on functions built with the same information but from different sources. Specifically, these functions are constructed from bus current measurement provided by a sensor and from the estimate of such a current provided by an extended Kalman filter (EKF) that performs the estimation from only rotor angular position measurements. In short, the FD system only requires two measurements for employment: bus current and angular position. In order to show its efficacy, results from numerical simulations (performed in a virtual test bench) are presented. Specifically, these simulations involve the dynamics of the SRM, including the magnetic phenomena caused by the analyzed faults. The motor dynamics were obtained with finite element simulations, which guarantee results close to the actual ones.
We study a high-viscosity two-phase flow through an analysis of the corresponding pressure signals. In particular, we investigate the flow of a glycerin–air mixture moving through a horizontal pipeline with a U-section installed midway... more
We study a high-viscosity two-phase flow through an analysis of the corresponding pressure signals. In particular, we investigate the flow of a glycerin–air mixture moving through a horizontal pipeline with a U-section installed midway along the pipe. Different combinations of liquid and air mass flow rates are experimentally tested. Then, we examine the moments of the statistical distributions obtained from the resulting pressure time series, in order to highlight the significant dynamical traits of the flow. Finally, we propose a novel correlation with two dimensionless parameters: the Euler number and a mass-flow-rate ratio to predict the pressure gradient in high-viscosity two-phase flow. Distinctive variations of the pressure gradients are observed in each section of the pipeline, which suggest that the local flow dynamics must not be disregarded in favor of global considerations.
The purpose of this paper is to provide a structural review of the progress made on the detection and localization of leaks in pipelines by using approaches based on the Kalman filter. To the best of the author’s knowledge, this is the... more
The purpose of this paper is to provide a structural review of the progress made on the detection and localization of leaks in pipelines by using approaches based on the Kalman filter. To the best of the author’s knowledge, this is the first review on the topic. In particular, it is the first to try to draw the attention of the leak detection community to the important contributions that use the Kalman filter as the core of a computational pipeline monitoring system. Without being exhaustive, the paper gathers the results from different research groups such that these are presented in a unified fashion. For this reason, a classification of the current approaches based on the Kalman filter is proposed. For each of the existing approaches within this classification, the basic concepts, theoretical results, and relations with the other procedures are discussed in detail. The review starts with a short summary of essential ideas about state observers. Then, a brief history of the use of...
The success of the analysis and design of a Water Network (WN) is strongly dependent on the veracity of the data and a priori knowledge used in the model calibration of the network. This fact motivates this paper in which an off-line... more
The success of the analysis and design of a Water Network (WN) is strongly dependent on the veracity of the data and a priori knowledge used in the model calibration of the network. This fact motivates this paper in which an off-line approach to verify datasets acquired from WN is proposed. This approach allows the data separation of abnormal and normal events without requiring high expertise for a large raw database. The core of the approach is an unsupervised classification tool that does not require the features of the different events to be identified. The proposal is applied to datasets acquired from a Mexican water management utility located in the center part of Mexico. The datasets are pre-processed to be synchronized since they were recorded and sent with different and irregular sampling times to a web platform. The pressures and flow-rate conforming the datasets correspond to the dates between 25 June 2019 @ 00:00 and 25 September 2019 @ 00:00. The District Metered Area (D...
We characterize the long-term development of high-viscosity gas–liquid intermittent flows by means of a detrended fluctuation analysis (DFA). To this end, the pressures measured at different locations along an ad hoc experimental flow... more
We characterize the long-term development of high-viscosity gas–liquid intermittent flows by means of a detrended fluctuation analysis (DFA). To this end, the pressures measured at different locations along an ad hoc experimental flow line are compared. We then analyze the relevant time-series to determine the evolution of the various kinds of intermittent flow patterns associated with the mixtures under consideration. Although no pattern transitions are observed in the presence of high-viscosity mixtures, we show that the dynamical attributes of each kind of intermittence evolves from one point to another within the transport system. The analysis indicates that the loss of a long-range correlation between the pressure responses are due to the discharge processes.
The purpose of this paper is to provide a structural review of the progress made on detection and localization of leaks in pipelines by using approaches based on the Kalman filter. This is, to the best of our knowledge, the first review... more
The purpose of this paper is to provide a structural review of the progress made on detection and localization of leaks in pipelines by using approaches based on the Kalman filter. This is, to the best of our knowledge, the first review on the t opic. In particular, it is the first to try to draw the attention of the leak detection community to the important contributions that use the Kalman filter as the core of a computational pipeline monitoring system. Without being exhaustive, we try to gather the results from different research groups and present them in a unified fashion. For this reason, we propose a classification of the current approaches based on the Kalman filter. For each of the existing approaches within this classification, the basic concepts, fundamental results, and relations with the other approaches are discussed in detail. The review starts from a short summary of basic concepts about state observers. Then, a brief history of the use of the Kalman filter for diag...
This work presents the modeling and simulation of a hydraulic network with four nodes and two branches that form a two-level water distribution system. It also proposes a distribution of hydraulic valves that allows emulating a leak using... more
This work presents the modeling and simulation of a hydraulic network with four nodes and two branches that form a two-level water distribution system. It also proposes a distribution of hydraulic valves that allows emulating a leak using a valve and different network configurations, e.g., simple ducts, closed networks and branched networks. The network is modeled in the steady state considering turbulent flow. Numerical experiments are performed, and the results show that the proposed network is useful for the design of leakage diagnosis and control algorithms in different configurations and leakage scenarios.
The principal aim of a spectral observer is twofold: the reconstruction of a signal of time via state estimation and the decomposition of such a signal into the frequencies that make it up. This paper proposes a novel spectral observer... more
The principal aim of a spectral observer is twofold: the reconstruction of a signal of time via state estimation and the decomposition of such a signal into the frequencies that make it up. This paper proposes a novel spectral observer with an adjustable constant gain for reconstructing a given signal by means of the recursive identification of the coefficients of a Fourier series. The reconstruction or estimation of a signal in the context of this work means to find the coefficients of a linear combination of sines a cosines that fits a signal such that it can be reproduced. The design procedure of the spectral observer is presented along with the following applications: (1) the reconstruction of a simple periodical signal, (2) the approximation of both a square and a triangular signal, (3) the edge detection in signals by using the Fourier coefficients and (4) the fitting of the historical Bitcoin market data from 2014-12-01 to 2018-01-08.
This chapter presents a successful leak diagnosis for a real pipeline. The diagnosis was performed on the water pipeline West 5 located in Guadalajara City, Mexico, which is supervised by Inter-Municipal System of Potable Water and Sewage... more
This chapter presents a successful leak diagnosis for a real pipeline. The diagnosis was performed on the water pipeline West 5 located in Guadalajara City, Mexico, which is supervised by Inter-Municipal System of Potable Water and Sewage (SIAPA). Herein, the authors try to highlight those difficulties that arise when facing a real leak problem, especially if the fluid line is not monitored online or records of the flow rate and pressure are not available. By considering that only one leak is present in the system and by using the pipeline configuration information provided by the SIAPA staff, a discrete-time extended Kalman filter, used as a state observer, was designed in order to isolate the leak. The final decision about the leak location was based on the results of four different database analyses in which three showed a similar tendency.
This paper presents a formal analysis of the pressure wave propagation along a pipeline to locate possible leaks. More specifically, this paper studies the step response of a pipeline when a downstream valve is closed to associate... more
This paper presents a formal analysis of the pressure wave propagation along a pipeline to locate possible leaks. More specifically, this paper studies the step response of a pipeline when a downstream valve is closed to associate leaks' parameters (magnitude and position) with their effects on the pressure wave, such as the diversion and dissipation of the wave energy. The analysis starts with a matrix formulation (in the Laplace domain) to represent the behavior of a pipeline with a leak. Subsequently, boundary and initial conditions are imposed on the formulation in order to obtain the downstream pressure when a downstream valve is closed. Before converting the pressure response expression from the Laplace to the time domain, it is expanded into a series of exponential terms with negative exponents. The resulting transient expression is a sum of step functions with arguments that depend on time, the length of the pipeline, the wave speed and the leak position. From these arguments and the amplitude of the steps, the position and the magnitude of the leak can be determined.
This paper highlights how fluid flow in a pipeline can be represented as a nonlinear model of so-called Liénard type. It is then shown how the structure of this model is suitable for the design of algorithms to identify parameters of a... more
This paper highlights how fluid flow in a pipeline can be represented as a nonlinear model of so-called Liénard type. It is then shown how the structure of this model is suitable for the design of algorithms to identify parameters of a pipeline or estimate unmeasurable states. This approach is illustrated by simulation results, for instance showing how to estimate the Darcy-Weisbach friction coefficient or the fluid acceleration.
This article proposes an approach to synchronize a class of unidimensional spatiotemporal chaotic systems using exponential nonlinear observers. The article focuses on generalized synchronization with parameter mismatching and a... more
This article proposes an approach to synchronize a class of unidimensional spatiotemporal chaotic systems using exponential nonlinear observers. The article focuses on generalized synchronization with parameter mismatching and a unidirectional master–slave topology. The approach involves the conception of two different nonlinear observers to estimate the unknown parameters of a master system, such that the estimated parameters can be injected into a controller to synchronize the slave with the master. To illustrate the proposed approach, an example based on the Gray–Scott equations that exposes the synchronization and the observer conception is presented.
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Research Interests:

And 67 more

This book focuses on the analysis and design of advanced techniques for on-line automatic computational monitoring of pipelines and pipe networks. It discusses how to improve the systems’ security considering mathematical models of the... more
This book focuses on the analysis and design of advanced techniques for on-line automatic computational monitoring of pipelines and pipe networks. It discusses how to improve the systems’ security considering mathematical models of the flow, historical flow rate and pressure data, with the main goal of reducing the number of sensors installed along a pipeline. The techniques presented in the book have been implemented in digital systems to enhance the abilities of the pipeline network’s operators in recognizing anomalies. A real leak scenario in a Mexican water pipeline is used to illustrate the benefits of these techniques in locating the position of a leak. Intended for an interdisciplinary audience, the book addresses researchers and professionals in the areas of mechanical, civil and control engineering. It covers topics on fluid mechanics, instrumentation, automatic control, signal processing, computing, construction and diagnostic technologies.
Research Interests:
Resumen: Los objetivos de un observador espectral son dos: la reconstrucción de una señal variante en el tiempo y la descomposición de dicha señal en las frecuencias que la componen. Un observador espectral puede ser catalogado como un... more
Resumen: Los objetivos de un observador espectral son dos: la reconstrucción de una señal variante en el tiempo y la descomposición de dicha señal en las frecuencias que la componen. Un observador espectral puede ser catalogado como un algoritmo en línea para el análisis tempo-frecuencial de señales, ya que es un método con el que se puede calcular la transformada de Fourier de una señal conforme se tiene información sobre ella, es decir, sin tener la señal completa. La contribución principal de este trabajo es la presentación de un observador espectral de alta ganancia para reconstruir señales con variaciones de frecuencia en el tiempo mediante la estimación de los coeficientes de una serie de Fourier finita en forma exponencial. El procedimiento de diseño del observador espectral se presenta junto con dos ejemplos de aplicación, así como un análisis comparativo entre el observador espectral de alta ganancia y un método bastante conocido para el análisis tempo-frecuencial: la transformada de Fourier de tiempo reducido.
Research Interests:
The principal aim of a spectral observer is twofold: the reconstruction of a signal of time via state estimation and the decomposition of such a signal into the frequencies that make it up. This paper proposes a novel spectral observer... more
The principal aim of a spectral observer is twofold: the reconstruction of a signal of time via state estimation and the decomposition of such a signal into the frequencies that make it up. This paper proposes a novel spectral observer with an adjustable constant gain for reconstructing a given signal by means of the recursive identification of the coefficients of a Fourier series. The reconstruction or estimation of a signal in the context of this work means to find the coefficients of a linear combination of sines a cosines that fits a signal such that it can be reproduced. The design procedure of the spectral observer is presented along with the following applications: (1) the reconstruction of a simple periodical signal, (2) the approximation of both a square and a triangular signal, (3) the edge detection in signals by using the Fourier coefficients and (4) the fitting of the historical Bitcoin market data from 2014-12-01 to 2018-01-08.
Research Interests:
Spectral Methods, Fourier and Wavelet Processing, Fourier Theory, Spectral Theory, Fourier Analysis, and 30 more
This presentation is about the conference article "Nonlinear estimation of a power law for the friction in a pipeline". The main goal of this article is the introduction of a new algorithm to continuously estimate the energy dissipation... more
This presentation is about the conference article "Nonlinear estimation of a power law for the friction in a pipeline". The main goal of this article is the introduction of a new algorithm to continuously estimate the energy dissipation in a pipeline, i.e. the total head loss, without  the knowledge of the relative roughness and the real length of a pipeline. The principal contribution of this article are: (1) A power law to represent the total head loss in a pipeline. (2) A simple method to estimate in real-time such a power law, including the exponent, with the following characteristics: (A) It is based on nonlinear state observers. (B) It only requires two pressure head recordings and a flow rate measurement. (C) It performs the estimation in short-time.
Research Interests:
System Identification, Pipeline, Water Distribution Systems, Parameter estimation, Nonlinear System Identification and Control, and 19 more