J. L. Martins de Carvalho

An LPV Modeling and Identification Approach to Leakage Detection in High Pressure Natural Gas Transportation Networks

In this paper a new approach to gas leakage detection in high pressure natural gas transportation networks is proposed. The pipeline is modelled as a Linear Parameter Varying (LPV) System driven by the source node massflow with the gas inventory variation in the pipe (linepack variation, proportional to the pressure variation) as the scheduling parameter. The massflow at the offtake node is taken as the system output. The system is identified by the Successive Approximations LPV System Subspace Identification Algorithm which is also described in this paper. The leakage is detected using a Kalman filter where the fault is treated as an augmented state. Given that the gas linepack can be estimated from the massflow balance equation, a differential method is proposed to improve the leakage detector effectiveness. A small section of a gas pipeline crossing Portugal in the direction South to North is used as a case study. LPV models are identified from normal operational data and their accuracy is analyzed. The proposed LPV Kalman filter based methods are compared with a standard mass balance method in a simulated 10% leakage detection scenario. The Differential Kalman Filter method proved to be highly efficient.

Identification of Bilinear Systems Using an Iterative Deterministic-Stochastic Subspace Approach

In this paper we introduce a new identification algorithm for MIMO bilinear systems driven by white noise inputs. The new algorithm is based on a convergent sequence of linear deterministic-stochastic state space approximations, thus considered a Picard based method. The key to the algorithm is the fact that the bilinear terms behave like white noise processes. Using a linear Kalman filter, the bilinear terms can be estimated and combined with the system inputs at each iteration, leading to a linear system which can be identified with a linear-deterministic subspace algorithm such as MOESP, N4SID, or CVA. Furthermore, the model parameters obtained with the new algorithm converge to those of a bilinear model. Finally, the dimensions of the data matrices are comparable to those of a linear subspace algorithm, thus avoiding the curse of dimensionality.

On the Analysis and Design of Robot Manipulators: A Statistical Approach

Abstract A new approach to the analysis and design of robot manipulators is presented. The novel feature resides on a non-standard approach to the modelling problem. Usually, system descriptions are based on a set of differential equations which, due to their nature lead to very precise results and strategies but in general lead to laborious computations. This motivates the need of alternative models based on other mathemati c al concepts . The proposed statistical method is a step in this direction which gives clear guidelines towards the robot kinematic and dynami c optimization . Furthermore, the use of histograms allows not only fast design procedures but above all, the use of experimental data; consequently, complex dynamic modelling exercises can be avoided.

ROBOT MANIPULATOR DYNAMICS — TOWARDS BETTER COMPUTATIONAL ALGORITHMS

Abstract A new robot manipulator inverse dynamics computational algorithm is announced. The novel feature resides in the computations which are a blend of ordinary and Boolean algebra. As such, this method may also be interpreted as a dedicated compiler that optimizes the on-line computing time at expenses of the off-line stage. Nevertheless, the high off-line requirements are alleviated, through the derivation of some general rules that stem from the structure of the robot manipulator equations. In a practical implementation, a computer program based on a Quine-McCluskey truth table simplification method was used and experimented on a 2R robot manipulator. The results show a considerable computational improvement on a conventional sequential machine. Furthermore, they clearly point out new computational parallel architectures, without scheduling problems, and where performance improvement is proportional to the number of processors. Finally, it is observed that the proposed algorithm is not restricted to robot inverse dynamic computations, but is also applicable to kinematic and control computations.

LPV system identification using a separable least squares support vector machines approach

In this article, an algorithm to identify LPV State Space models for both continuous-time and discrete-time systems is proposed. The LPV state space system is in the Companion Reachable Canonical Form. The output vector coefficients are linear combinations of a set of a possibly infinite number of nonlinear basis functions dependent on the scheduling signal, the state matrix is either time invariant or a linear combination of a finite number of basis functions of the scheduling signal and the input vector is time invariant. This model structure, although simple, can describe accurately the behaviour of many nonlinear SISO systems by an adequate choice of the scheduling signal. It also partially solves the problems of structural bias caused by inaccurate selection of the basis functions and high variance of the estimates due to over-parameterisation. The use of an infinite number of basis functions in the output vector increases the flexibility to describe complex functions and makes it possible to learn the underlying dependencies of these coefficients from the data. A Least Squares Support Vector Machine (LS-SVM) approach is used to address the infinite dimension of the output coefficients. Since there is a linear dependence of the output on the output vector coefficients and, on the other hand, the LS-SVM solution is a nonlinear function of the state and input matrix coefficients, the LPV system is identified by minimising a quadratic function of the output function in a reduced parameter space; the minimisation of the error is performed by a separable approach where the parameters of the fixed matrices are calculated using a gradient method. The derivatives required by this algorithm are the output of either an LTI or an LPV (in the case of a time-varying SS matrix) system, that need to be simulated at every iteration. The effectiveness of the algorithm is assessed on several simulated examples.

Identification of a Benchmark Wiener-Hammerstein System by Bilinear and Hammerstein-Bilinear Models

Abstract In this paper the Wiener-Hammerstein system proposed as a benchmark for the SYSID 2009 benchmark session is identified as a bilinear discrete system. The bilinear approximation relies on both facts that the Wiener-Hammerstein system can be described by a Volterra series which can be approximated by bilinear systems. The identification is performed with an iterative bilinear subspace identification algorithm previously proposed by the authors. In order to increase accuracy, polynomial static nonlinearities are added to the bilinear model input. These Hammerstein type bilinear models are then identified using the same iterative subspace identification algorithm.

Indirect continuous-time system identification—A subspace downsampling approach

This article presents a new indirect identification method for continuous-time systems able to resolve the problem of fast sampling. To do this, a Subspace IDentification Down-Sampling (SIDDS) approach that takes into consideration the intermediate sampling instants of the input signal is proposed. This is done by partitioning the data set into m subsets, where m is the downsampling factor. Then, the discrete-time model is identified using a based subspace identification discrete-time algorithm where the data subsets are fused into a single one. Using the algebraic properties of the system, some of the parameters of the continuous-time model are directly estimated. A procedure that secures a prescribed number of zeros for the continuous-time model is used during the estimation process. The algorithms performance is illustrated through an example of fast sampling, where its performance is compared with the direct methods implemented in Contsid.

A lumped transfer function model for High Pressure Gas Pipelines

In this paper a lumped transfer function (TF) model is derived for High Pressure Natural Gas Pipelines. Departing from a nonlinear partial differential equation (PDE) model a high order continuous state space (SS) linear model is obtained using a finite difference method. An infinite order TF is calculated from the SS representation and finally is approximated by a compact non-rational function. This model is compared with SIMONE®, a commercial simulator of gas transport and distribution, using a case study, and both exhibit a similar accuracy.

Gas pipelines LPV modelling and identification for leakage detection

A new approach to gas leakage detection in high pressure distribution networks is proposed, where the pipeline is modelled as a Linear Parameter Varying (LPV) System driven by the source node mass flow with the pressure as the scheduling parameter, and the system output as the mass flow at the offtake. Using a recently proposed successive approximations LPV system subspace identification algorithm, the pipeline is thus identified from operational data. The leak is detected using a Kalman filter where the fault is treated as an augmented state. The effectiveness of this method is illustrated with an example with a mixture of real and simulated data.

A new insight to the matrices extraction in a MOESP type subspace identification algorithm

In this paper we analyse the estimates of the matrices produced by the non-biased deterministic-stochastic subspace identification algorithms (NBDSSI) proposed by Van Overschee and De Moor (1996). First, an alternate expression is derived for the A and C estimates. It is shown that the Chiuso and Picci result (Chiuso and Picci 2004) stating that the A and C estimates delivered by this algorithm robust version and by the Verhaegens MOESP (Verhaegen and Dewilde 1992a, Verhaegen and Dewilde 1992b, Verhaegen 1993, Verhaegen 1994) are equal, can be obtained from this expression. An alternative approach for the estimation of matrices B and D in subspace identification is also described. It is shown that the least squares approach for the estimation of these matrices estimation can be just expressed as an orthogonal projection of the future outputs on a lower dimension subspace in the orthogonal complement of the column space of the extended observability matrix. Since this subspace has a dimension equal to the number of outputs, a simpler and numerically more efficient (but equally accurate) new subspace algorithm is provided.