Time-invariant Methods Research Articles

A novel predefined-time noise-tolerant zeroing neural network for solving time-varying generalized linear matrix equations

Due to the time-varying nature of time-varying linear systems, many traditional time-invariant methods cannot solve time-varying linear systems. The emergence of zeroing neural networks (ZNN) has led to a long and intensive development in this field. Researchers have mainly studied or improved the ZNN model for time-varying linear systems in the direction of activation functions and design parameters. This paper proposes a novel modified versatile activation function (MVAF) from the perspective of activation function optimization, and a modified versatile activation function zeroing neural network (MVAFZNN) model for solving time-varying generalized linear matrix equations is constructed. The proposed model converges faster than the versatile activation function zeroing neural network (VAFZNN) model and other ZNN models. Theoretical analysis shows that the MVAFZNN model can solve time-varying systems in a predetermined time. Two numerical experiments verify the validity of the proposed model, and two circuit experiments show that the proposed model can be used to calculate circuit parameters.

Neurocraft: software for microscale brain network dynamics

The brain operates at millisecond timescales but despite of that, the study of its functional networks is approached with time invariant methods. Equally, for a variety of brain conditions treatment is delivered with fixed temporal protocols unable to monitor and follow the rapid progression and therefore the cycles of a disease. To facilitate the understanding of brain network dynamics we developed Neurocraft, a user friendly software suite. Neurocraft features a highly novel signal processing engine fit for tracking evolving network states with superior time and frequency resolution. A variety of analytics like dynamic connectivity maps, force-directed representations and propagation models, allow for the highly selective investigation of transient pathophysiological dynamics. In addition, machine-learning tools enable the unsupervised investigation and selection of key network features at individual and group-levels. For proof of concept, we compared six seizure-free and non seizure-free focal epilepsy patients after resective surgery using Neurocraft. The network features were calculated using 50 intracranial electrodes on average during at least 120 epileptiform discharges lasting less than one second, per patient. Powerful network differences were detected in the pre-operative data of the two patient groups (effect size = 1.27), suggesting the predictive value of dynamic network features. More than one million patients are treated with cardiac and neuro modulation devices that are unable to track the hourly or daily changes in a subject’s disease. Decoding the dynamics of transition from normal to abnormal states may be crucial in the understanding, tracking and treatment of neurological conditions. Neurocraft provides a user-friendly platform for the research of microscale brain dynamics and a stepping stone for the personalised device-based adaptive neuromodulation in real-time.

Fuzzy time series Markov Chain and Fuzzy time series Chen & Hsu for forecasting

Fuzzy time series theory is a concept of artificial intelligence that can use to conduct forecasting technique.. This paper discusses the fuzzy logic concept to develop the base of the fuzzy time series with time invariant and time variant methods. There are several methods of fuzzy time series, including Markov Chain method and Chen and Hsu method. The Markov Chain method combines between the fuzzy time series and the Markov Chain. This merger goals to finest opportunity of the use matrix probability transitions. Chen and Hsu method is based on the historical data difference in conducting forecasting. By using Markov Chain and Chen & Hsu methods, it may achieve forecasting outcomes with a low mistakes rate. To clarify each technique and for comparison further, it is given an example of the relevant issue to be resolved by both methods. The consequences acquired can be compared, so it can be concluded which method is better.

Analysis of dependence structure among investor sentiment, policy uncertainty and international oil prices

The behavioural aspect of finance and economics has an embedded importance in the literature. This paper provides an evidence of the interrelationship of international oil prices with economic policy uncertainty, consumer sentiments and US investor sentiment proxies. To test the underlying dependence structure, we employ time invariant and time-varying copula methods due to dynamic return patterns of our sampled indices. Our analysis reveals an underlying relationship of investor sentiments and economic policy uncertainty with international oil prices not only during normal periods but also in the periods of financial turmoil. Results of our nonlinear causality highlight potential of bidirectional spillover between oil prices and investor sentiment indices across all quantiles. This helps in understanding that a volatile international oil market may have significant impact on investor sentiments and economic policy uncertainty and vice versa. [Received: December 20, 2019; Accepted: June 17, 2020]

Analysis of dependence structure among investor sentiment, policy uncertainty and international oil prices

The behavioural aspect of finance and economics has an embedded importance in the literature. This paper provides an evidence of the interrelationship of international oil prices with economic policy uncertainty, consumer sentiments and US investor sentiment proxies. To test the underlying dependence structure, we employ time invariant and time-varying copula methods due to dynamic return patterns of our sampled indices. Our analysis reveals an underlying relationship of investor sentiments and economic policy uncertainty with international oil prices not only during normal periods but also in the periods of financial turmoil. Results of our nonlinear causality highlight potential of bidirectional spillover between oil prices and investor sentiment indices across all quantiles. This helps in understanding that a volatile international oil market may have significant impact on investor sentiments and economic policy uncertainty and vice versa. [Received: December 20, 2019; Accepted: June 17, 2020]

Linear parameter-varying subspace identification: A unified framework

In this paper, we establish a unified framework for subspace identification (SID) of linear parameter-varying (LPV) systems to estimate LPV state–space (SS) models in innovation form. This framework enables us to derive novel LPV SID schemes that are extensions of existing linear time-invariant (LTI) methods. More specifically, we derive the open-loop, closed-loop, and predictor-based data-equations (input–output surrogate forms of the SS representation) by systematically establishing an LPV subspace identification theory. We also show the additional challenges of the LPV setting compared to the LTI case. Based on the data-equations, several methods are proposed to estimate LPV-SS models based on a maximum-likelihood or a realization based argument. Furthermore, the established theoretical framework for the LPV subspace identification problem allows us to lower the number of to-be-estimated parameters and to overcome dimensionality problems of the involved matrices, leading to a decrease in the computational complexity of LPV SIDs in general. To the authors’ knowledge, this paper is the first in-depth examination of the LPV subspace identification problem. The effectiveness of the proposed subspace identification methods are demonstrated and compared with existing methods in a Monte Carlo study of identifying a benchmark MIMO LPV system.

A dynamic model and performance analysis of a stepped rotary flow control valve

The hydraulic independent metering is an advanced actuator driving technique that allows the implementation of advanced control algorithms or methods. The main concept of independent metering is to control hydraulic actuators ports, which are the meter-in and meter-out, separately. In this article, a novel stepped rotary type valve has been developed for embedding in hydraulic independent metering systems, instead of conventional types such as poppet and spool. The insertion leads to developing different and novel control techniques, which require software-in-the-loop simulation and hardware-in-the-loop simulation of the proposed system. The paper explores the dynamic representation of this valve and defines its own performance limitations. This includes the development of a linear model comprising its two main subparts which are the stepper motor and the rotary orifice. Consequently, the linear time-invariant methods are used to explore the performance of the valve by considering the effect of different parameters namely the pressure drop, friction coefficient, damping coefficient, and bristle coefficient.

Manual Control with Pursuit Displays: New Insights, New Models, New Issues

Mathematical control models are widely used in tuning manual control systems and understanding human performance. The most common model, the crossover model, is severely limited, however, in describing realistic human control behaviour in relevant control tasks as it is only valid for tracking with a compensatory display. This paper first discusses the state-of-the-art in modelling human control in tracking with pursuit displays. It is shown that, although both tasks seem very similar, the separate presentation of target and system output signals allows operators to adopt a huge variety in control strategies, which makes the development of a universal model for pursuit control a challenge. Two recent models are then described which can act as precursors to such a universal model. Third, system identification choices and issues are discussed for pursuit tracking tasks. Finally, it is argued that it is inevitable that time-varying rather than time-invariant methods are needed to properly describe human behaviour in the pursuit tracking task, as skilled operators will learn to characterize the probabilistic nature of the task, which cannot be captured in a single, linear, time-invariant model.

Time-variant fatigue reliability assessment of welded joints based on the PHI2 and response surface methods

A time-variant fatigue reliability assessment model for welded joints subjected to stochastic loading is presented. The PHI2 method, which allows one to solve time-variant problems using time-invariant methods, provides the framework of the model. A sophisticated fatigue crack growth model that is capable of taking the residual stress effect into account is employed to compute crack sizes at different times under stochastic loading. The crack sizes are explicitly represented by response surface models. Limit state functions are formulated based on combined fracture criteria, which consider both brittle and ductile fracture, and the response surface models. The time-variant fatigue reliability of a T-plate welded joint with an edge crack located at the weld toe is assessed. It appears that results from the time-invariant fatigue reliability assessment may be too optimistic. The weld induced residual stress effects are considered based on the stress intensity factor due to residual stress. Its effects on the crack size and time-variant fatigue reliability are significant and cannot be ignored.

Seismic data two-step recovery approach combining sparsity-promoting and hyperbolic Radon transform methods

In current research of seismic data recovery problems, the sparsity-promoting method usually produces an insufficient recovery result at the locations of null traces. The HRT (hyperbolic Radon transform) method can be applied to problems of seismic data recovery with approximately hyperbolic events. Influenced by deviations of hyperbolic characteristics between real and ideal travel-time curves, some spurious events are usually introduced and the recovery effect of intermediate and far-offset traces is worse than that of near-offset traces. Sparsity-promoting recovery is primarily dependent on the sparsity of seismic data in the sparse transform domain (i.e. on the local waveform characteristics), whereas HRT recovery is severely affected by the global characteristics of the seismic events. Inspired by the above conclusion, a two-step recovery approach combining sparsity-promoting and time-invariant HRT methods is proposed, which is based on both local and global characteristics of the seismic data. Two implementation strategies are presented in detail, and the selection criteria of the relevant strategies is also discussed. Numerical examples of synthetic and real data verify that the new approach can achieve a better recovery effect by simultaneously overcoming the shortcomings of sparsity-promoting recovery and HRT recovery.

Performance and Risk Assessment of Soil-Structure Interaction Systems Based on Finite Element Reliability Methods

In the context of performance-based earthquake engineering, reliability method has been of significant importance in performance and risk assessment of structures or soil-structure interaction (SSI) systems. The finite element (FE) reliability method combines FE analysis with state-of-the-art methods in reliability analysis and has been employed increasingly to estimate the probability of occurrence of failure events corresponding to various hazard levels (e.g., earthquakes with various intensity). In this paper, crucial components for FE reliability analysis are reviewed and summarized. Furthermore, recent advances in both time invariant and time variant reliability analysis methods for realistic nonlinear SSI systems are presented and applied to a two-dimensional two story building on layered soil. Various time invariant reliability analysis methods are applied, including the first-order reliability method (FORM), importance sampling method, and orthogonal plane sampling (OPS) method. For time variant reliability analysis, an upper bound of the failure probability is obtained from numerical integration of the mean outcrossing rate (MOCR). The MOCR is computed by using FORM analysis and OPS analysis. Results by different FE reliability methods are compared in terms of accuracy and computational cost. This paper provides valuable insights for reliability based probabilistic performance and risk assessment of SSI systems.

Consideration of Gyroscopic Effect in Fault Detection and Isolation for Unbalance Excited Rotor Systems

Fault detection and isolation (FDI) in rotor systems often faces the problem that the system dynamics is dependent on the rotor rotary frequency because of the gyroscopic effect. In unbalance excited rotor systems, the continuously distributed unbalances are hard to be determined or estimated accurately. The unbalance forces as disturbances make fault detection more complicated. The aim of this paper is to develop linear time invariant (LTI) FDI methods (i.e., with constant parameters) for rotor systems under consideration of gyroscopic effect and disturbances. Two approaches to describe the gyroscopic effect, that is, as unknown inputs and as model uncertainties, are investigated. Based on these two approaches, FDI methods are developed and the results are compared regarding the resulting FDI performances. Results are obtained by the application in a rotor test rig. Restrictions for the application of these methods are discussed.

Closed-loop fluid flow control using a low dimensional model

This paper is devoted to the problem of defining a control strategy to minimize the drag of a bluff body in a 2-D cross-flow. A reduced model is obtained using a robust statistical reduction approach and an optimal orbit in the phase space is determined using an open-loop control strategy. This open-loop control law is inexpensive to derive as it relies on a reduced order model. Since the deviations from the optimal orbit are meant to remain small, the non-linear flow model can be linearized around the orbit at each time. To compensate for the deviations, a closed-loop control is applied. The design of a robust controller is difficult due to the large number of state space variables, conflicting specifications and parameter uncertainties. Further, the model is a time-varying process, so that Linear Time Invariant design methods cannot be directly applied.

Time-varying Methods for Characterizing Nonstationary Dynamics of Physiological Systems

Accurate and early diagnosis of various diseases and pathological conditions require analysis techniques that can capture time-varying (TV) dynamics. In the pursuit of promising TV signal processing methods applicable to real-time clinical monitoring applications, nonstationary spectral techniques are of great significance. We present two potential practical applications of such techniques in quantifying TV physiological dynamics concealed in photoplethysmography (PPG) signals: early detection of blood-volume loss using a nonparametric approach known as variable frequency complex demodulation (VFCDM), and accurate detection of abrupt changes in respiratory rates using a parametric approach known as combined optimal parameter search and multiple mode particle filtering (COPS-MPF). The VFCDM technique has been tested using ear-PPG signals in two study models: mechanically ventilated patients undergoing surgery in operating room settings and spontaneously breathing conscious healthy subjects subjected to lower body negative pressure (LBNP) in laboratory settings. Extraction of respiratory rates has been tested using COPS-MPF technique in finger-PPG signals collected from healthy volunteers with abrupt changes in respiratory rate ranging from 0.1 to 0.4 Hz. VFCDM method showed promise to detect the blood loss noninvasively in mechanical ventilated patients well before blood losses become apparent to the physician. In spontaneously breathing subjects during LBNP experiments, the early detection and quantification of blood loss was possible at 40% of LBNP tolerance. COPS-MPF showed high accuracy in detecting the constant as well as sudden changes in respiratory rates as compared to other time-invariant methods. Integration of such robust algorithms into pulse oximeter device may have significant impact in real-time clinical monitoring and point-of-care healthcare settings.

METHODS FOR SEISMIC RISK ANALYSIS: STATE OF THE ART VERSUS ADVANCED STATE OF THE PRACTICE

The core of the paper consists of the illustration of a method for seismic reliability analysis of non-linear structures. The method, which is a development over a recent previous proposal, is quite comprehensive in scope since it includes consideration of randomness in the input, in the mechanical properties of the structure and in the limit-state, or capacity, conditions. Essentially, the problem is formulated as the out-crossing of the response process out of a (scalar) safe threshold, and this problem is solved by time-invariant FORM methods. An application to an idealised five-storey building demonstrates the salient theoretical and computational features of the method. The new approach is presented in a broader framework, which involves a discussion on present trends and capabilities in the area of probabilistic seismic design. For the sake of this discussion, two approaches just appeared in the literature are outlined, which are less demanding from a theoretical standpoint, and hence closer to engineering practice, but also less general in scope. It is argued that their introduction on code-assisted design would be feasible immediately with obvious advantages, while approaches of more rigorous nature would be given some more time to mature and to become more accessible to professional use.

ORDER BISPECTRUM: A NEW TOOL FOR RECIPROCATED MACHINE CONDITION MONITORING

Vibrations and sounds generated by reciprocated machines or by their parts strongly depend on the rotation speed of the main shaft of the tested reciprocating system. At the testing or at common performance of the reciprocated machines, their rotation speed is usually changing. With regard to this fact, signals produced by reciprocating machines are non-stationary ones. Therefore, conventional time-invariant methods of their spectral or bispectral analysis are frequently unable to provide meaningful results. In order to solve this problem in the field of polyspectral signal analysis, the order bispectrum analysis is proposed in this contribution. This approach is based on the bispectrum estimation from the signal which is a function of the angle of roll of the main shaft of reciprocated machine. A digital representation of this signal can be obtained by resampling of the signal conveniently sampled in the time domain. The advantages of the order bispectrum application in comparison with that of the conventional bispectrum approach is illustrated based on the example of an engine set classification.

Control of General Dynamic Systems With Periodically Varying Parameters Via Liapunov-Floquet Transformation

A new technique in the design of controllers for linear dynamic systems with periodically varying coefficients is presented. The idea is to utilize the well-known Liapunov-Floquet (L-F) transformation such that the original time-varying system can be reduced to a form suitable for the application of standard time-invariant methods of control theory. For this purpose, a procedure for computing the L-F matrices for general linear periodic systems is outlined. In this procedure, the state transition matrices are expressed in terms of Chebyshev polynomials which permits the computation of L-F matrices as explicit functions of time. Further, it is shown that controllers can be designed in the transformed domain via full state or observer based feedback using principles of pole placement and optimal control theory. The effectiveness of the proposed technique is demonstrated through two examples. The first example belongs to the class of commutative systems while in the second example a triple inverted pendulum subjected to a periodic follower load is considered. It is found that both types of controllers can be successfully designed.

On stabilization of nonlinear systems with enlarged domain of attraction

This paper presents a systematic procedure to design a control law that guarantees asymptotic stability of an equilibrium with an enlarged domain of attraction for a class of nonlinear systems. To this end, we use a natural extension of well-known linear time-invariant transformation methods to write the system in controller canonical form with a forcing term. The control law is implemented in two steps, first we calculate a nonlinear state feedback that cancels the nonlinear terms of the unforced system, so that for the resulting system a suitable Lyapunov function candidate is available. Then, we add a linear state feedback that stabilizes the equilibrium and maximizes its domain of attraction. Interestingly enough, the latter maximization problem reduces to a classical, linear time invariant H∞ minimization problem. An example is given to illustrate the procedure.

A time-varying analysis method for rapid transitions in speech

A linear predictive coding (LPC) model based on time-dependent poles which has yielded promising results when applied to synthetic data is applied to real speech data. The data are processed pitch-synchronously using a simple procedure to identify regions of the data that best fit the model. The maximum-likelihood technique, which has been found to be robust in the presence of noise, is used to estimate the parameters. Resulting formant estimates for several diphthongs are presented. The algorithm tracks the formants well, both in stable regions and in regions of transition. This ability to track formant variation within analysis intervals is a definite advantage over traditional LPC. Results from speech data involving final stop consonants are presented. Rapid changes, particularly in the first and second formants, in the region immediately prior to the stop are detected. Such abrupt transitions are often not detected by traditional time-invariant methods. >

Deconvolution in microcalorimetry and an application to mass-varying systems

The behaviour of the calorimetric response in continuous injection devices, which are well suited for measurement of excess partial molar enthalpies at different concentrations, is analysed by means of heat transport models. Signal analysis of the thermal response gives the enthalpy values at very low concentrations. We establish an operating routine for the identification of the time-varying device, and a generalized deconvolution procedure to obtain, with high accuracy, the power released in the calorimeter as a function of time. The main features considered are the changes in sensitivity and dynamic properties of the experimental system due to the injection of one component in the mixture. A formal decomposition of the heat transport equations shows that typically time-invariant methods are able to deal with deconvolution in non-invariant systems.