Metodo de medicion de combustible en una embarcacion fluvial.

Se expone una forma de mejorar el método de medición de combustible en una embarcación fluvial, específicamente en un remolcador. El marco de referencia sobre el que se basa este artículo, es la estrategia utilizada para establecer la cantidad de combustible presente en los tanques de la embarcación. El método que hasta el momento se viene utilizando, produce un error influenciado por factores de perturbación, como la inclinación y la forma de tanqueo del remolcador. Se buscó desarrollar un método alternativo que redujera el error entre el combustible entregado y el medido en la embarcación. Este nuevo método logró ser independiente de la inclinación sin necesidad de utilizar un inclinómetro o instrumento de medida de ángulos.
Palabras claves: medición de niveles, centroide, punto de sondeo, sensores de presión.
Abstract
This paper exposes a way to improve the method of fuel measurement in a river vessel, specifically a tugboat. The framework of this article is the need of a strategy to establish the amount of fuel volume that is contained in the tanks of the tugboat. The method, that have been used so far, produces errors influenced by disturbance factors such as the inclination and the shape of the tanks of the tugboat. It is needed to develop an alternative method that reduces the error between the fuel which is provided by the suppliers and the measured one in the tugboat. This new method tries to be independent of the inclination of the boat with no need of using a clinometer or instrument of angle measurement.
Key words: level measurement, centroid, test point, pressure sensors.
1 Introducción
El marco de trabajo en el cual surge este método de medida de combustible es el desarrollo de un proyecto en la modalidad universidad--empresa. El proyecto denominado "Sistema de Telemetría para Remolcadores", involucra una empresa del sector carbonero de la región caribe colombiana y la Universidad del Norte como centro de desarrollo tecnológico, y comprende: la construcción de un sistema de adquisición de señales, el desarrollo de un sistema de posicionamiento de la embarcación y la creación de un sistema de gestión de operaciones del remolcador.
La necesidad más importante que la empresa desea suplir con el desarrollo del proyecto, es el monitoreo continuo de la cantidad de galones de combustible en los tanques de los remolcadores, que permita tomar decisiones desde el punto de vista logístico, que apunten a la reducción del rubro correspondiente a gastos operacionales del estado de pérdidas y ganancias. Este proyecto, concebido para el desarrollo de un prototipo, involucra un remolcador con seis tanques de combustible repartidos uniformemente, es decir, tres a cada lado de la embarcación. Si bien los tanques son iguales con respecto a su contraparte del otro lado, los tanques de un flanco del remolcador son diferentes entre sí y no son prismas rectangulares rectos. Adicionalmente, debido a que el medio en el cual el remolcador se encuentra trabajando permite modificaciones en el plano horizontal del marco de referencia de la embarcación, el método de medición del nivel de combustible que se seguía hasta el inicio del proyecto, incluía errores que afectaban la operación logística de la empresa. De esta forma, se desarrolla un método experimental de medición, lo más independiente posible, de inclinaciones proa-popa y estribor-babor.
En la sección (2) se presentan la configuración de los tanques del remolcador que funcionó como prototipo, sus formas, método de medida empleado hasta entonces y los problemas que involucraba.
Posteriormente, en la sección (3), se presentan los conceptos matemáticos que permitieron la búsqueda y desarrollo de un método alternativo, así como la elección de una estrategia de sensado conveniente para el caso particular.
En la sección (4) se presenta un resumen del desarrollo de la estrategia con base en lo expuesto en la sección (3). Finalmente, en la sección (5) se muestran los resultados y conclusiones.
(2) Antecedentes: tanques y sus propiedades, método de medida anterior
El remolcador utilizado para el desarrollo del sistema prototipo, cuenta con dos motores de propulsión, dos generadores eléctricos y seis tanques de almacenamiento de combustible, denominados bodegas. Las bodegas se encuentran repartidas de forma tal que las tres de un flanco sirven al motor y/o generador del lado correspondiente. Las bodegas se denominan, de proa a popa: bodega 1, bodega 2 y bodega 3, adjuntando a la clasificación la palabra estribor o babor, dependiendo de la ubicación del tanque, tal y como se muestra en la figura (1).

Blind deconvolution of the aortic pressure waveform using the Malliavin calculus

1. Introduction

In this paper, we present a new approach to monitor central arterial pressure using the Multichannel Blind Deconvolution (MBD)[1, 2]. A multichannel blind deconvolution problem can be considered as natural extension or generalization of instantaneous Blind Source Separation (BSS) problem [3, 4]. The problem of BSS has received wide attention in various fields such as signal analysis and processing of speech, image [5, 6], and biomedical signals, especially, signal extraction, enhancement, denoising, model reduction, and classification problems [7-9].

The MBD is the technique that allows the estimation of both an unknown input and unknown channel dynamics from only channel outputs. Although one cannot place a sensor [10] to directly measure the input, yet, it may be recovered from the outputs that are simultaneously measured at the multiple branches of the system. The MBD technique distinguishes itself from other techniques that apply a predetermined transfer function [11, 12] to interpret sensor data. The other techniques cannot account for individual differences nor can they account for dynamic changes in the subject's physiologic state.

The physiologic state of the cardiovascular (CV) system can be most accurately assessed by using the aortic blood pressure or CAP [7, 13, 14] and flow. However, standard measurement of these signals, such as catheter, entails costly and risky surgical procedures. Therefore, most of the practically applicable methods aim to monitor the CV system based on peripheral circulatory signals, for example, arterial blood pressure at a distant site. Various methods have been developed to relate the peripheral signals to the CV state. These include blind deconvolution [15-17] methods for recovering the CAP signal from the upper-limb arterial blood pressure, and the estimation of CV parameters such as left ventricular elasticity, end diastolic volume, total peripheral resistance (TPR), and mean aortic flow from arterial BP measurement [18, 19]. A chronic challenge of these previous methods is that the dynamics of the CV system, which relates the aortic and peripheral signals, is unknown and time-varying as well. So this problem turns out to be an ill-posed system identification problem because we are asked to identify both the unknown system dynamics and input signal using the output signal measurement alone.

Because of the practical difficulty in measuring the arterial pressure waveform near the heart [13, 15, 20], several mathematical transformation methods have been developed based on a generalized transfer function approach [21, 22]. Over the years many methods have been suggested for blind deconvolution for estimating central aortic pressure and flow [3, 9, 19, 23, 24]. One of the most popular and effective techniques is to assume an FIR model [1] and IIR model [18, 19, 25] for the modulating channels/paths and to estimate the coefficients [26] of this model. Through the inversion of the FIR filter, we get the original source signals. The principal assumption underlying these methods is that the arterial tree properties are constant over time and between individuals. A few methods have therefore been more recently developed towards "individualizing" the transfer function [1, 12, 21 ] relating peripheral artery pressure to central aortic pressure. These methods essentially involve (1) modeling the transfer function [11, 23] with physiologic parameters, (2) estimating a subset of the model parameters [7,15] from the peripheral arterial pressure waveforms and/or other measurements from an individual while assuming values for the remaining parameters, (3) constructing a transfer function based on the estimated and assumed parameter values [26], and(4) applying the transfer function to the measured peripheral arterial pressure waveforms to predict the corresponding central aortic pressure waveform. While these methods attempt to determine a transfer function that is specific to an individual over a particular time period, only a partial individualization is actually obtained. Perhaps, as a result, these methods have found only limited success with results not much, if at all, better than the generalized transfer function approach.

In this paper, we suggest characterizing the channels of the single-input, multi-output system model of the arterial tree by linear and time-variant FIR filters. If we make only one of the FIR filter parameters changing over time, then the problem is handled by the Ito calculus [27,28], while, if we make more than one of the FIR filter parameters changing over time, then the problem could be handled by the Malliavin calculus [29] as we propose in this paper.

This way, the ambiguity in the order of the impulse response is compensated by the time variations of the filter parameters [29-31].

In this paper, we introduce a method that could estimate time-varying parameters/coefficients. It is based on the stochastic calculus of variations (Malliavin calculus) 28, 32-35]. We derive a closed-form expression for the unknown time varying FIR filter parameters by using the Clark-Ocone formula [30]. This will enable us to find a stochastic differential equation (SDE) for each unknown time-varying parameter of the FIR filter. Each SDE is function of PAP and some other unknown deterministic parameters. The unknown deterministic parameters are estimated through Monte Carlo simulation methods.

The proposed method is then applied to noninvasive monitoring of the cardiovascular system of the swine. The arterial network is modeled as a multichannel system where the CAP is the input and pressure profiles measured at different branches of the artery, for example, radial and femoral arteries, are the outputs. The proposed method would allow us to estimate both the waveform of the input pressure and the arterial channel dynamics from outputs obtained with noninvasive sensors placed at different branches of the arterial network. Numerical examples verify the major theoretical results and the feasibility of the method. In Section 2, we describe the blind deconvolution problem, conventional solution methods. In Section 3 we introduce the proposed method based on the Malliavin calculus. In Section 4, we present the results for the reconstruction of single-input CAP from two distant measures outputs PAP. Finally in Section 5, we provide summary and conclusions. The Appendix contains the technical derivations of the proposed method.

2. Problem Formulation

2.1. Multichannel Dynamic Systems

The cardiovascular system is topologically analogous to a multichannel dynamic system. Pressure wave emanating from a common source, the heart, is broadcast and transmitted through the many vascular pathways. Therefore, noninvasive circulatory measurements taken at different locations (as shown in Figure 3) can be treated as multichannel data and processed with an MBD algorithm. Figure 1 illustrates, in a block diagram form, the relation between the central aortic pressure waveform u(t) and the peripheral arterial pressure waveforms [y.sub.i] (t). The arterial channels [h.sub.i](t) relating the common input to each output represent the vascular dynamic properties of different arterial tree paths as characterized by finite impulse responses (FIRs). The main idea is therefore to determine the absolute central aortic pressure waveform within an arbitrary scale factor by mathematically analyzing two or more PAP waveforms or related signals so as to extract their common features. An ancillary idea is to then determine the parameters of the determined central aortic pressure waveform.

We estimate the FIR filter coefficients by the conventional methods in Section 2.2. We introduce our proposed method that is based on Malliavin calculus in Section 3. We will be working in the probability space ([OMEGA], F, P). To simplify the exposure, we shall assume that we have only two measurements outputs of a modulated version of the source signal that are given as

[y.sub.1](t) = [h.sub.1] (t) * tu() + [[epsilon].sub.1](t), (2.1)

[y.sub.2](t) = [h.sub.2] (t) * tu() + [[epsilon].sub.2](t), (2.2)

[FIGURE 1 OMITTED]

where u(t) is the unknown source signal (central AP), [h.sub.1](t) and [h.sub.2](t) are unknown filters (hemodynamic response at time t) or arterial paths, "*" is the convolution operation, [y.sub.1](t) (femoral AP) and [y.sub.2](t)(radial AP) are the observed measurements, and [[epsilon].sub.1](t) and [[epsilon].sub.2](t) are the measurements noise. The objective is to deconvolve [y.sub.1](t) and