Nonlinear Finite Impulse Response Research Articles

Gaussian Process based Feedforward Control for Nonlinear Systems with Flexible Tasks: With Application to a Printer with Friction

Feedforward control is essential to achieving good tracking performance in positioning systems. The aim of this paper is to develop an identification strategy for inverse models of systems with nonlinear dynamics of unknown structure using input-output data, which can be used to generate feedforward signals for a-priori unknown tasks. To this end, inverse systems are regarded as noncausal nonlinear finite impulse response (NFIR) systems, and modeled as a Gaussian Process with a stationary kernel function that imposes properties such as smoothness. The approach is validated experimentally on a consumer printer with friction and shown to lead to improved tracking performance with respect to linear feedforward.

Learning low-dimensional separable decompositions of MIMO non-linear systems

We present a new internal structure exploration method developed for the multiple-input multiple-output (MIMO) dynamical systems with finite memory and almost arbitrary non-linear characteristic. The proposed Double Separation Algorithm applies distance correlation screening for pre-selection of those system inputs that contribute to the consecutive outputs and, based on the first-stage inference outcomes, estimates projection coefficients sensitive to the existence of additive system sub-characteristics. In effect, the proposed approach allows for effective exploration of the internal system structure. A numerical experiment on an MIMO nonlinear finite impulse response (NFIR) system illustrates the ability of the proposed approach to indicate which of the system inputs contribute to which of the system outputs. The experiment also illustrates the ability of the approach to detect which of the nonlinear sub-characteristics, recovered in the first stage of the approach, can be separated into a sum of lower-dimensional sub-characteristics.

Fouling Detection in Industrial Heat Exchanger Using Number of Transfer Units Method, Neural Network, and Nonlinear Finite Impulse Response Models

Due to reduced energy efficiency and productivity loss caused by fouled heat exchangers in industrial plants there is an obvious need for detection of fouling formation. Based on continuously measured temperatures and flow rates collected from the refinery plant history database, a semi-empirical number of transfer units (NTU) model and neural network-based models are developed. In order to confirm the reliability of proposed fouling factor calculation, the entire procedure was performed by developing a dynamic nonlinear finite impulse response (NFIR) model. Developed models are intended for fouling detection for industrial shell and tube heat exchangers. The performance criteria of developed models together with residual monitoring indicate that not only neural networks but the NTU and NFIR models effectively detect fouling formation.

Iterative parameter and order identification for fractional‐order nonlinear finite impulse response systems using the key term separation

SummaryThis article considers the parameter estimation for a fractional‐order nonlinear finite impulse response system with colored noise. For the fractional‐order systems, the challenge and difficulty are to identify the order and parameters of the systems simultaneously under colored noise disturbances. In order to reduce the problem of redundant parameter estimation, the output form of the system can be expressed by a linear combination of unknown parameters through the separation of the key term separation. A key term separation auxiliary model gradient‐based iterative algorithm is derived by using the negative gradient search. Meanwhile, to achieve the higher estimation accuracy, we propose a key term separation auxiliary model multiinnovation gradient‐based iterative algorithm by utilizing the multiinnovation theory. Finally, the simulation results test the effectiveness of the proposed algorithms.

Modelling the Influence of Soil Properties on Crop Yields Using a Non-Linear NFIR Model and Laboratory Data

This paper introduces a new non-linear correlation analysis method based on a non-linear finite impulse response (NFIR) model to study and quantify the effects of ten soil properties on crop yield. Two versions of the NFIR model were implemented: NFIR-LN, accounting for both the linear and non-linear variability in the system, and NFIR-L, accounting for linear variability only. The performance of the NFIR models was compared with a non-linear random forest (RF) model, to predict oilseed rape (2013) and wheat (2014) yields in one field at Premslin, Germany. The ten soil properties were used as system inputs, whereas crop yield was the system output. Results demonstrated that the individual and total contribution of the soil properties on crop yield varied throughout the different cropping seasons, weather conditions, and crops. Both the NFIR-LN and RF models outperformed the NFIR-L model and explained up to 55.62% and 50.66% of the yield variation for years 2013 and 2014, respectively. The NFIR-LN and RF models performed equally during yield prediction, although the NFIR-LN model provided more consistent results through the two cropping seasons. Higher phosphorus and potassium contributions to the yield were calculated with the NFIR-LN model, suggesting this method outperforms the RF model.

Nonlinear Finite Impulse Response Estimation using Regularized Neural Networks

Abstract This work presents a new regularization scheme for identifying nonlinear finite impulse response (NFIR) models using artificial neural networks (ANN). Prior knowledge, such as the exponentially decaying nature of an impulse response, is included during the identification using a regularization approach inspired on the well-known regularized linear finite impulse response identification literature. More specifically the sensitivity of the modeled output with respect to the delayed input of the NFIR model is penalized to provide an exponentially decaying prior. The proposed method is illustrated and compared to other ANN regularization schemes on a simulation example.

Optimization-Oriented High Fidelity NFIR Models for Estimating Indicated Torque in Diesel Engines

In this paper, optimization-oriented high fidelity indicated torque models which cover the whole operating regions under both steady-state and transient cycles for heavy-duty vehicles are developed. Two different experiments are performed and their data are merged to be utilized in the training of the models. In the first experiment, all combustion input channels are excited by quadratic chirp signals with different sweeps in their frequency profiles. Different from the first experiment, the engine speed is excited by ramp-hold signals in the second experiment. The estimations of friction, pumping and inertia torques in addition to the torque measured from the engine dynamometer are utilized in the indicated torque calculations. In order to model the calculated indicated torque, a nonlinear finite impulse response (NFIR) model with a single layer sigmoid neural network has been designed. A sensitivity analysis is performed by generating several models with different number of input regressors and neurons. Experimental results show that the majority of the models in a selected wide range of the model parameters are validated with fit accuracies higher than 90 % and 85 % on the World Harmonized Stationary Cycle (WHSC) and the World Harmonic Transient Cycle (WHTC), respectively.

Two-Layer Nonlinear FIR Filter and Unscented Kalman Filter Fusion With Application to Mobile Robot Localization

In this paper, we propose a new state estimator called the two-layer nonlinear finite impulse response (TLNF) filter and adopt this new filter and unscented Kalman filter (UKF) as subfilters to create the fusion TLNF/UK filter. The TLNF filter is constructed with measurements that are redefined by weighting the estimated states acquired through minimizing the cost function based on the Frobenius norm. The efficient iterative form of the TLNF filter is also developed in this paper. Using the fact that the UKF and the TLNF filter each takes a different type of memory structure, the fusion TLNF/UK filter is designed as a robust nonlinear state estimator taking both advantages of each filter. To obtain the best fusion estimates, probabilistic weights are computed based on Bayes’ rule and the likelihood of each filter. Both simulation and experimental results for mobile robot indoor localization have shown that the fusion TLNF/UK filter achieves a higher level of accuracy and robustness under practical situations.

Imaging of Nonlinear and Dynamic Functional Brain Connectivity Based on EEG Recordings With the Application on the Diagnosis of Alzheimer's Disease.

Since age is the most significant risk factor for the development of Alzheimer's disease (AD), it is important to understand the effect of normal ageing on brain network characteristics before we can accurately diagnose the condition based on information derived from resting state electroencephalogram (EEG) recordings, aiming to detect brain network disruption. This article proposes a novel brain functional connectivity imaging method, particularly targeting the contribution of nonlinear dynamics of functional connectivity, on distinguishing participants with AD from healthy controls (HC). We describe a parametric method established upon a Nonlinear Finite Impulse Response model, and a revised orthogonal least squares algorithm used to estimate the linear, nonlinear and combined connectivity between any two EEG channels without fitting a full model. This approach, where linear and non-linear interactions and their spatial distribution and dynamics can be estimated independently, offered us the means to dissect the dynamic brain network disruption in AD from a new perspective and to gain some insight into the dynamic behaviour of brain networks in two age groups (above and below 70) with normal cognitive function. Although linear and stationary connectivity dominates the classification contributions, quantitative results have demonstrated that nonlinear and dynamic connectivity can significantly improve the classification accuracy, barring the group of participants below the age of 70, for resting state EEG recorded during eyes open. The developed approach is generic and can be used as a powerful tool to examine brain network characteristics and disruption in a user friendly and systematic way.

Nonlinear system identification via data augmentation

This paper presents a novel nonparametric approach to the identification of nonlinear dynamical systems. The proposed methodology exploits the potential of manifold learning on an artificially augmented dataset, obtained without running new experiments on the plant. The additional data are employed for approximating the manifold where input regressors lie. The knowledge of the manifold acts as a prior information on the system, that induces a proper regularization term on the identification cost. The new regularization term, as opposite to the standard Tikhonov one, enforces local smoothness of the function along the manifold. A graph-based algorithm tailored to dynamical systems is proposed to generate the augmented dataset. The hyperparameters of the method, along with the order of the system, are estimated from the available data. Numerical results on a benchmark Nonlinear Finite Impulse Response (NFIR) system show that the proposed approach may outperform the state of the art nonparametric methods.

Low-order Nonlinear Finite-Impulse Response Soft Sensors for Ionic Electroactive Actuators Based on Deep Learning

This paper introduces a soft sensor (SS) for the estimation of the deflection of a polymeric mechanical actuator. The actuator is based on ionic polymer-metal composites (IPMCs). Applications of IPMCs have been proposed in fields such as robotics, surgery, and aerospace, to mention the most interesting ones. In such application fields, both the complexity and the size of the actuating system are of chief importance. An SS can be, therefore, preferred to hardware measuring the actuator output, for estimating the actuator motion. Also, low-order models are of interest to limit the computational load, which can be a constraint in real-time applications. To this aim, several data-driven nonlinear finite-impulse response (NFIR) models have been investigated. Data, used for the model identification, have been acquired, in controlled environmental conditions, by using swept signals as the input to the IPMC actuator. Linear and nonlinear models, based on principal component analysis, shallow, and deep neural networks (NNs), have been investigated, for different model orders. The best results have been obtained by an SS based on a fifth-order NFIR model, implemented by a deep belief NN.

Non‐linear FIR smoothing filter for systems with a modelling error and its application to the DR/GPS integrated navigation

Infinite impulse response (IIR) filter generally used in estimation, positioning, etc. has problems in that, when there is a modeling error even if the system is completely observable, the estimates may converge to incorrect values or the varying values cannot be estimated quickly. The finite impulse response (FIR) filter, which has been investigated as a method to solve this problem, has faster estimation performance than the IIR filter in the presence of modelling error, but there is a limit to the convergence characteristic of the state variables. In this paper, a non-linear FIR smoothing (NFS) filter is proposed to overcome the limitation of the state variable convergence characteristic of the FIR filter. The proposed NFS filter adds the smoothing concept to the modified receding horizon Kalman FIR filter. In order to verify the performance of the NFS filter, this filter is applied to a delay-tolerant integrated navigation system using magnetic compass (MC) of which error is difficult to be modelled accurately. If an un-modeled jump or ramp error occurs in the MC measurement, it shows that the NFS filter can estimate the measurement error more accurately than the FIR filter as well as the IIR filter through a simulation.

YAPAY ARI KOLONİSİ ALGORİTMASI İLE OPTİMİZE EDİLEN HAMMERSTEIN MODEL KULLANARAK SİSTEMLERİN KİMLİKLENDİRİLMESİ

Hammerstein model is formed by cascade of linear and nonlinear parts. In literature, memoryless polynomial nonlinear (MPN) model for nonlinear part and finite impulse response (FIR) model or infinite impulse response (IIR) model for linear part are mostly preferred for Hammerstein models. This paper different from the studies in literature, focuses on the success of Hammerstein block model that Second Order Volterra (SOV) is preferred instead of MPN as nonlinear part. In this context , a new Hammerstein model is presented which is obtained by cascade form of a nonlinear SOV and a linear FIR model. In simulations, different types of system are identified by proposed Hammerstein model which is optimized with ABC (artificial bee colony) algorithm. The simulation results reveal effectiveness and robustness of the proposed model with ABC algorithm.

Nonlinear FIR Identification with Model Order Reduction Steiglitz-McBride

In system identification, many structures and approaches have been proposed to deal with systems with non-linear behavior. When applicable, the prediction error method, analogously to the linear case, requires minimizing a cost function that is non-convex in general. The issue with non-convexity is more problematic for non-linear models, not only due to the increased complexity of the model, but also because methods to provide consistent initialization points may not be available for many model structures. In this paper, we consider a non-linear rational finite impulse response model. We observe how the prediction error method requires minimizing a non-convex cost function, and propose a three-step least-squares algorithm as an alternative procedure. This procedure is an extension of the Model Order Reduction Steiglitz-McBride method, which is asymptotically efficient in open loop for linear models. We perform a simulation study to illustrate the applicability and performance of the method, which suggests that it is asymptotically efficient.

Comparing Models of Spontaneous Variations, Maneuvers and Indexes to Assess Dynamic Cerebral Autoregulation.

We analyzed the performance of linear and nonlinear models to assess dynamic cerebral autoregulation (dCA) from spontaneous variations in healthy subjects and compared it with the use of two known maneuvers to abruptly change arterial blood pressure (BP): thigh cuffs and sit-to-stand. Cerebral blood flow velocity and BP were measured simultaneously at rest and while the maneuvers were performed in 20 healthy subjects. To analyze the spontaneous variations, we implemented two types of models using support vector machine (SVM): linear and nonlinear finite impulse response models. The classic autoregulation index (ARI) and the more recently proposed model-free ARI (mfARI) were used as measures of dCA. An ANOVA analysis was applied to compare the different methods and the coefficient of variation was calculated to evaluate their variability. There are differences between indexes, but not between models and maneuvers. The mfARI index with the sit-to-stand maneuver shows the least variability. Support vector machine modeling of spontaneous variation with the mfARI index could be used for the assessment of dCA as an alternative to maneuvers to introduce large BP fluctuations.

Tracking Nonlinear Correlation for Complex Dynamic Systems Using a Windowed Error Reduction Ratio Method

Studying complex dynamic systems is usually very challenging due to limited prior knowledge and high complexity of relationships between interconnected components. Current methods either are like a “black box” that is difficult to understand and relate back to the underlying system or have limited universality and applicability due to too many assumptions. This paper proposes a time-varying Nonlinear Finite Impulse Response model to estimate the multiple features of correlation among measurements including direction, strength, significance, latency, correlation type, and nonlinearity. The dynamic behaviours of correlation are tracked through a sliding window approach based on the Blackman window rather than the simple truncation by a Rectangular window. This method is particularly useful for a system that has very little prior knowledge and the interaction between measurements is nonlinear, time-varying, rapidly changing, or of short duration. Simulation results suggest that the proposed tracking approach significantly reduces the sensitivity of correlation estimation against the window size. Such a method will improve the applicability and robustness of correlation analysis for complex systems. A real application to environmental changing data demonstrates the potential of the proposed method by revealing and characterising hidden information contained within measurements, which is usually “invisible” for conventional methods.

System identification using Hammerstein model optimized with differential evolution algorithm

This paper aims to improve Hammerstein model for system identification area. Hammerstein model block structure is formed by cascade of linear and nonlinear parts. In literature, memoryless polynomial nonlinear (MPN) model for nonlinear part and finite impulse response (FIR) model or infinite impulse response (IIR) model for linear part are mostly preferred for Hammerstein models. In this study, a Hammerstein model is presented which is obtained by cascade form of a nonlinear second order volterra (SOV) and a linear FIR model. In addition, proposed Hammerstein model is optimized with differential evolution algorithm (DEA). In simulations, different types of systems are identified by proposed Hammerstein model. Also, performance of the proposed model is compared with different model performances. In conclusion it can be said that the main benefit of this study is that simulation results reveal the effectiveness and robustness of the proposed model.

System identification application using Hammerstein model

Generally, memoryless polynomial nonlinear model for nonlinear part and finite impulse response (FIR) model or infinite impulse response model for linear part are preferred in Hammerstein models in literature. In this paper, system identification applications of Hammerstein model that is cascade of nonlinear second order volterra and linear FIR model are studied. Recursive least square algorithm is used to identify the proposed Hammerstein model parameters. Furthermore, the results are compared to identify the success of proposed Hammerstein model and different types of models.

Self-recovering extended Kalman filtering algorithm based on model-based diagnosis and resetting using an assisting FIR filter

This paper proposes a new intelligent filtering algorithm called the self-recovering extended Kalman filter (SREKF). In the SREKF algorithm, the EKF׳s failure or abnormal operation is automatically diagnosed using an intelligence algorithm for model-based diagnosis. When the failure is diagnosed, an assisting filter, a nonlinear finite impulse response (FIR) filter, is operated. Using the output of the nonlinear FIR filter, the EKF is reset and rebooted. In this way, the SREKF can self-recover from failures. The effectiveness and performance of the proposed SREKF are demonstrated through two applications – the frequency estimation and the indoor human localization.

Weighted average extended FIR filter bank to manage the horizon size in nonlinear FIR filtering

In this paper, we propose a novel approach to manage the horizon size in nonlinear finite impulse response (FIR) filtering. The proposed approach is to perform state estimation through a bank of FIR filters called a weighted average extended FIR filter bank (WAEFFB). In the WAEFFB, the state estimate is obtained by weighting the average of multiple estimates from a bank of extended FIR filters that uses different horizon sizes. The horizon sizes used for the WAEFFB are adjusted constantly by maximizing the likelihood function. We show through simulations that the WAEFFB yields better results than the conventional approach that uses a constant (i.e., fixed) horizon size.