C. A. Teixeira

Nonlinear identification of aircraft gas-turbine dynamics

Abstract Identification results for the shaft-speed dynamics of an aircraft gas turbine, under normal operation, are presented. As it has been found that the dynamics vary with the operating point, nonlinear models are employed. Two different approaches are considered: NARX models, and neural network models, namely multilayer perceptrons, radial basis function networks and B-spline networks. A special attention is given to genetic programming, in a multiobjective fashion, to determine the structure of NARMAX and B-spline models.

Non-invasive tissue temperature evaluation during application of therapeutic ultrasound: precise time-spatial non-linear modelling

The potential of thermal therapy’s applications improve with the development of accurate non-invasive time-spatial temperature models. These models should represent the non-linear tissue thermal behaviour and be capable of tracking temperature at both time-instant and spatial point. An in-vitro experiment was developed based on a gel phantom, heated by a therapeutic ultrasound (TUS) device emitting continuously. The heating process was monitored by an imaging ultrasound (IUS) transducer working in pulse-echo mode, placed perpendicularly to the TUS transducer. The IUS RF-lines and temperature values were collected 60 mm distant from the TUS transducer face. Three thermocouples were aligned along the IUS transducer axial direction and across the TUS transducer radial direction (1 cm spaced). Three different TUS intensities were applied. The non-invasive time-spatial evolutionary temperature models were created making use of radial basis functions neural networks (RBFNN). The neural network input information was: the propagation time-delay between RF-line echoes and the past temperature lags from three different medium locations and three different TUS intensities. A total of nine different operating situations were studied. The best RBFNN structures were automatically determined by a multiobjective genetic algorithm, due to the enormous number of possible structures. The RBFNN temperature models were evaluated with data never used in the models, neither at the training or structural selection phases. In order to precisely evaluate the model generalisation performance these data included the nine possible operating situations. The best model presents a maximum absolute error less than 0.5 degrees Celsius (gold-standard value for hyperthermia/diathermia applications). To be mentioned also that the best model presents low computational complexity enabling future real-time implementations. Concluding, a maximum absolute error below the gold-standard value pointed for hyperthermia/diathermia applications was attained. In addition, this methodology does not require a-priori determination of physical constants and mathematical simplifications required for analytical methodologies.

NARX structures for non-invasive temperature estimation in non-homogeneous media

The safe and effective application of thermal therapies are limited by the existence of precise non-invasive temperature estimators. Such estimators would enable a correct power deposition on the region of interest by means of a correct instrumentation control. In multi-layered media, the temperature should be estimated at each layer and especially at the interfaces, where significant temperature changes should occur during therapy. In this work, a non-linear autoregressive structure with exogenous inputs (NARX) was applied to non-invasively estimate temperature in a multi-layered (non-homogeneous) medium, while submitted to physiotherapeutic ultrasound. The NARX structure is composed by a static feed-forward radial basis functions neural network (RBFNN), with external dynamics induced by its inputs. The NARX structure parameters were optimized by means of a multi-objective genetic algorithm. The best attained models reached a maximum absolute error inferior to 0.5degC (proposed threshold in hyperthermia/diathermia) at both the interface and inner layer points, at four radiation intensities. These models present also a small computational complexity as desired for real-time applications. To the best of ours knowledge this is the first non-invasive estimation approach in multi-layered media using ultrasound for both heating and estimation.

Neuro-genetic non-invasive temperature estimation: Intensity and spatial prediction

OBJECTIVES The existence of proper non-invasive temperature estimators is an essential aspect when thermal therapy applications are envisaged. These estimators must be good predictors to enable temperature estimation at different operational situations, providing better control of the therapeutic instrumentation. In this work, radial basis functions artificial neural networks were constructed to access temperature evolution on an ultrasound insonated medium. METHODS The employed models were radial basis functions neural networks with external dynamics induced by their inputs. Both the most suited set of model inputs and number of neurons in the network were found using the multi-objective genetic algorithm. The neural models were validated in two situations: the operating ones, as used in the construction of the network; and in 11 unseen situations. The new data addressed two new spatial locations and a new intensity level, assessing the intensity and space prediction capacity of the proposed model. RESULTS Good performance was obtained during the validation process both in terms of the spatial points considered and whenever the new intensity level was within the range of applied intensities. A maximum absolute error of 0.5 degrees C+/-10% (0.5 degrees C is the gold-standard threshold in hyperthermia/diathermia) was attained with low computationally complex models. CONCLUSION The results confirm that the proposed neuro-genetic approach enables foreseeing temperature propagation, in connection to intensity and space parameters, thus enabling the assessment of different operating situations with proper temperature resolution.

SINGLE BLACK-BOX MODELS FOR TWO-POINT NON-INVASIVE TEMPERATURE PREDICTION

Abstract In this paper the performance of a genetically selected radial basis functions neural network is evaluated for non-invasive two-point temperature estimation in a homogeneous medium, irradiated by therapeutic ultrasound at physiotherapeutic levels. In this work a single neural network was assigned to estimate the temperature profile at the two considered points, and more consistent results were obtained than when considering one model for each point. This result was possible by increasing the model complexity. The best model predicts the temperature from two unseen data sequences during approximately 2 hours, with a maximum absolute error less than 0.5 °C, as desired for a therapeutic temperature estimator.

Temperature modelling of an homogeneous medium using genetically selected RBF (LIC)

Abstract Temperature modelling of human tissue exposed to therapeutic ultrasound is essential for an accurate instrumental assessment and calibration. In this paper punctual temperature modelling of an homogeneous medium, radiated by therapeutic ultrasound, is presented. Two different approaches are considered: a completely nonlinear approach (Radial Basis Functions neural networks (RBF)), and a hybrid (Linear plus nonlinear) approach (Radial Basis Functions neural networks with Linear Input Connections (RBFLIC)). The best-performant Neural Network (NN) structures were obtained using a Multi-Objective Genetic Algorithm (MOGA). The best RBFLIC structure for the applied MOGA parametrisation, presents 28% improvement in the performance of the best RBF structure.

Multi-objective genetic algorithm applied to the structure selection of RBFNN temperature estimators

Temperature modelling of a homogeneous medium, when this medium is radiated by therapeutic ultrasound, is a fundamental step in order to analyse the performance of estimators for in-vivo modelling. In this paper punctual and invasive temperature estimation in a homo-geneous medium is employed. Radial Basis Functions Neural Networks (RBFNNs) are used as estimators. The best fitted RBFNNs are selected using a Multi-objective Genetic Algorithm (MOGA). An absolute average error of 0.0084°C was attained with these estimators.