Early detection of rotating stallin axial flow compressors via deterministic learning:detectability analysis

Rotating stall and surge are two violent unstable phenomena of an aero-engine compressor.The early detection of rotating stall is a critical and difficult issue in the operation of a compressor.Recently,a deterministic learning based stall inception detection approach(SIDA)has been developed for modeling and detecting stall inception in aero-engine compressors.This paper considers the derivation of analytical results on the detection capabilities for the SIDA based on deterministic learning.First,by utilizing the input/output stability of the residual system,a detectability condition of the SIDA is presented,and how to choose the parameters of the diagnostic system is also analyzed.Second,based on the relationship between NN approximation capabilities and radial basis function(RBF)network structures,the influence of RBF network structures on the performance properties of the SIDA is analyzed.Finally,a simulation study is presented,in which the Mansoux-C2 compressor model is utilized to verify the effectiveness of the proposed SIDA.

Electrocardiogram(ECG) pattern modeling and recognition via deterministic learning

A method for electrocardiogram （ECG） pattern modeling and recognition via deterministic learning theory is presented in this paper. Instead of recognizing ECG signals beat-to-beat, each ECG signal which contains a number of heartbeats is recognized. The method is based entirely on the temporal features （i.e., the dynamics） of ECG patterns, which contains complete information of ECG patterns. A dynamical model is employed to demonstrate the method, which is capable of generating synthetic ECG signals. Based on the dynamical model, the method is shown in the following two phases： the identification （training） phase and the recognition （test） phase. In the identification phase, the dynamics of ECG patterns is accurately modeled and expressed as constant RBF neural weights through the deterministic learning. In the recognition phase, the modeling results are used for ECG pattern recognition. The main feature of the proposed method is that the dynamics of ECG patterns is accurately modeled and is used for ECG pattern recognition. Experimental studies using the Physikalisch-Technische Bundesanstalt （PTB） database are included to demonstrate the effectiveness of the approach.

Fault detection for nonlinear discrete-time systems via deterministic learning

Recently, an approach for the rapid detection of small oscillation faults based on deterministic learning theory was proposed for continuous-time systems. In this paper, a fault detection scheme is proposed for a class of nonlinear discrete-time systems via deterministic learning. By using a discrete-time extension of deterministic learning algorithm, the general fault functions （i.e., the internal dynamics） underlying normal and fault modes of nonlinear discrete-time systems are locally-accurately approximated by discrete-time dynamical radial basis function （RBF） networks. Then, a bank of estimators with the obtained knowledge of system dynamics embedded is constructed, and a set of residuals are obtained and used to measure the differences between the dynamics of the monitored system and the dynamics of the trained systems. A fault detection decision scheme is presented according to the smallest residual principle, i.e., the occurrence of a fault can be detected in a discrete-time setting by comparing the magnitude of residuals. The fault detectability analysis is carried out and the upper bound of detection time is derived. A simulation example is given to illustrate the effectiveness of the proposed scheme.

Deterministic learning of completely resonant nonlinear wave systems with Dirichlet boundary conditions

In this paper, we investigate the approximation of completely resonant nonlinear wave systems via deter- ministic learning. The plants are distributed parameter systems （DPS） describing homogeneous and isotropic elastic vibrat- ing strings with fixed endpoints. The purpose of the paper is to approximate the infinite-dimensional dynamics, rather than the parameters of the wave systems. To solve the problem, the wave systems are first transformed into finite-dimensional dynamical systems described by ordinary differential equation （ODE）. The properties of the finite-dimensional systems, including the convergence of the solution, as well as the dominance of partial system dynamics according to point-wise measurements, are analyzed. Based on the properties, second, by using the deterministic learning algorithm, an approxi- mately accurate neural network （NN） approximation of the the finite-dimensional system dynamics is achieved in a local region along the recurrent trajectories. Simulation studies are included to demonstrate the effectiveness of the proposed approach.

Dynamical pattern recognition for univariate time series and its application to an axial compressor

In this paper, a learning and recognition approach is proposed for univariate time series composed of output measurements of general nonlinear dynamical systems. Firstly, a class of dynamical systems in the canonical form is derived to describe the univariate time series by introducing coordinate transformation. An observer-based deterministic learning technique is then adopted to achieve dynamical modeling of the associated transformed systems of the training univariate time series, and the modeling results in the form of radial basis function network (RBFN) models are stored in a pattern library. Subsequently, multiple observer-based dynamical estimators containing the RBFN models in the pattern library are constructed for a test univariate time series, and a recognition decision scheme is proposed by the derived recognition indicator. On this basis, more concise recognition conditions are provided, which is beneficial for verifying the recognition results. Finally, simulation studies on the Rossler system and aero-engine stall warning verify the effectiveness of the proposed approach.

Learning from NN output feedback control of nonlinear systems in Brunovsky canonical form

In this paper, we investigate the learning issue in the adaptive neural network （NN） output feedback control of nonlinear systems in Brunovsky canonical form with unknown affine term. With only output measurements, a high-gain observer （HGO） is employed to estimate the derivatives of the system output which may be associated with the generation of peaking phenomenon. The adverse effect of peaking on learning and its elimination strategies are analyzed. When the gain of HGO is chosen too high, it may cause the failure of learning from the unknown closed-loop system dynamics. Hence, the gain of HGO is not chosen too high to relieve peaking and guarantee the accuracy of the estimated system states. Then, learning from the unknown closed-loop system dynamics can be achieved. When repeating the same or similar control tasks, a neural learning controller is presented which can effectively recall and reuse the learned knowledge to guarantee the output tracking performance. Finally, simulation results demonstrate the effectiveness of the proposed scheme.