Hammerstein-Wiener Model Research Articles

Optimal demand response scheduling of an industrial air separation unit using data-driven dynamic models

Managing electricity demand has become a key consideration in power grid operations. Industrial demand response (DR) is an important component of demand-side management, and electricity-intensive chemical processes can both support power grid operations and derive economic benefits from electricity price fluctuations. For air separation units (ASUs), DR participation calls for frequent production rate changes, over time scales that overlap with the dominant dynamics of the plant. Production scheduling calculations must therefore explicitly consider process dynamics. We introduce a data-driven approach for learning the DR scheduling-relevant dynamics of an industrial ASU from its operational history, and present a dynamic optimization-based DR scheduling framework. We show that a class of low-order Hammerstein-Wiener models can accurately represent the dynamics of the industrial ASU and its model predictive control system. We evaluate the economic benefits of the proposed scheduling framework, and analyze their sensitivity to electricity price uncertainty.

A Hammerstein–Wiener Model for Single-Electron Transistors

This paper proposes a new dynamic behavior model for single-electron transistors (SETs). A comprehensive review of modeling techniques and previous models was carried out aiming to remark the originality of the new proposed technique. Once established that SET is a nonlinear system, five classes of nonlinear models were simulated and compared to each other. Characteristic SET curves obtained using Simulation of Nanostructures were used as benchmark. The mean squared error (mse) was used as metric, and the simulation time was computed for each model. Regarding these two criteria—least mse and least simulation time—the Hammerstein–Wiener model outperformed the others models.

Over parameterisation and optimisation approaches for identification of nonlinear stochastic systems described by Hammerstein-Wiener models

This paper proposes two iterative procedures based on over-parameterisation and optimisation approaches for the identification of nonlinear systems which can be described by Hammerstein-Wiener stochastic models. In this case, the dynamic linear part of the considered system is described by ARMAX mathematical model. The static nonlinear block is approximated by polynomial functions. The first procedure is based on a combination of the prediction error method by using the recursive approximated maximum likelihood estimator (RAML), the singular value decomposition (SVD) approach and the fuzzy techniques in order to estimate the parameters of the considered process. As for the second procedure, it includes an appropriate representation named as generalised orthonormal basis filters (GOBF) in order to reduce the complexity of the considered system. The parametric estimation problem is formulated using the recursive extended least squares (RELS) algorithm incorporated with the singular value decomposition (SVD) and fuzzy techniques in order to segregate the coupled parameters and improve the estimation quality. The validity of the developed approaches is proved by considering a nonlinear hydraulic process simulation.

Over parameterisation and optimisation approaches for identification of nonlinear stochastic systems described by Hammerstein-Wiener models

This paper proposes two iterative procedures based on over-parameterisation and optimisation approaches for the identification of nonlinear systems which can be described by Hammerstein-Wiener stochastic models. In this case, the dynamic linear part of the considered system is described by ARMAX mathematical model. The static nonlinear block is approximated by polynomial functions. The first procedure is based on a combination of the prediction error method by using the recursive approximated maximum likelihood estimator (RAML), the singular value decomposition (SVD) approach and the fuzzy techniques in order to estimate the parameters of the considered process. As for the second procedure, it includes an appropriate representation named as generalised orthonormal basis filters (GOBF) in order to reduce the complexity of the considered system. The parametric estimation problem is formulated using the recursive extended least squares (RELS) algorithm incorporated with the singular value decomposition (SVD) and fuzzy techniques in order to segregate the coupled parameters and improve the estimation quality. The validity of the developed approaches is proved by considering a nonlinear hydraulic process simulation.

Continuous Prediction for Quality of Experience in Wireless Video Streaming

Due to the rapid development of communication technologies, the requirement of mobile video streaming services is extremely increased in recent years. However, the bandwidth limitation of the wireless network often causes video impairments, such as compression artifacts and rebuffering event, when users are watching online videos. Hence, this problem often causes the reduction of quality of experience (QoE). Predicting the QoE can provide a reference to improve resource allocation strategies, accordingly providing users with a higher quality of video streaming services. In order to predict the impact of video impairment, continuous prediction for the QoE in wireless video streaming is proposed. The input of the predicted model consists of three vectors that characterize frame quality, the state of rebuffering events, and memory effect, respectively, while the output consists of continuous predicted the QoE. The predicted model uses a block-structured nonlinear Hammerstein-Wiener model. The experimental results confirm that our proposed model can effectively predict the continuous QoE for wireless video streaming.

Application of a Nonlinear Hammerstein-Wiener Estimator in the Development and Control of a Magnetorheological Fluid Haptic Device for Robotic Bone Biopsy

A force generator module (FGM) based on magnetorheological fluid (MRF) was developed to provide force-feedback information for applications in tele-robotic bone biopsy procedures. The FGM is capable of rapidly re-producing a wide range of forces that are common in bone biopsy applications. As a result of the nonlinear nature of MRF, developing robust controllers for these mechanisms can be challenging. In this paper, we present a case study motivated by robotic bone biopsy. We use a non-linear Hammerstein-Wiener (H-W) estimator to address this challenge. The case is presented through three studies. First, an experiment to develop design constraints is presented and describes biopsy force measurements for various animal tissues. Required output forces were found to range between <1 N and <50 N. A second study outlines the design of the FGM and presents the experimental characterization of the hysteretic behavior of the MRF. This data is then used as estimators and validators to develop the nonlinear Hammerstein-Wiener (H-W) model of the MRF. Validation experiments found that the H-W model is capable of predicting the behavior of the MRF device with 95% accuracy and can eliminate hysteresis in a closed-loop control system. The third study demonstrates the FGM used in a 1-DOF haptic controller in a simulated robotic bone-biopsy. The H-W control tracked the input signal while compensating for magnetic hysteresis to achieve optimal performance. In conclusion, the MRF-based device can be used in surgical robotic operations that require a high range of force measurements.

Continuous Estimation of the Key Components Content in the Isomerization Process Products

Soft sensors for estimating a fraction of key components in the products of a Low-temperature isomerization process equipped with a deisohexanizer distillation column are developed. Real plant data from the refinery distributed control system (DCS) are used. A considerable attention is paid to data selection, selection of key input variables, data processing and analysis.Dynamic soft sensor models for estimating the fraction of 2,2-Dimethylbutane, 2,3-Dimethylbutane, 2-Methylpentane and 3-Methylpentane in the products of the process are developed based on linear and nonlinear regression techniques. The development of a linear dynamic Finite Impulse Response (FIR), Autoregressive with Exogenous Inputs (ARX), Output Error (OE), as well as Nonlinear Dynamic Autoregressive with Exogenous Inputs (NARX) and Hammerstein-Wiener (HW) models are presented. Developed models were evaluated by validation techniques including Root Mean Square Error (RMSE), Absolute Error (AE), Final Prediction Error (FPE) and FIT coefficients.The results show that the developed soft sensors can reliably estimate the content of key components and thus replace process analysers in the case of failure. This will contribute to the operation stability of the column, the rise in product quality, the reduction in energy consumption as well as the improvement of whole isomerization process. Also, the developed soft sensors can be applied in the Advanced Process Control scheme of the deisohexanizer column.

Double-layered nonlinear model predictive control based on Hammerstein–Wiener model with disturbance rejection

This paper presents the double-layered nonlinear model predictive control method for a continuously stirred tank reactor and a pH neutralization process that are subject to input disturbances and output disturbances at the same time. The nonlinear systems can be described as a Hammerstein -Wiener model. Furthermore, two nonlinear parts of the Hammerstein -Wiener model should be transformed into linear combination of known input and unknown disturbances, respectively. By taking advantage of Kalman filter, disturbances and states can be estimated. The estimated disturbances and states can be considered to calculate steady-state target in steady-state target calculation layer. Moreover, the state feedback control law can be obtained in dynamic control layer. A simple proof for offset-free control is given in the proposed method. The simulation results show that the controlled variable can achieve the offset-free control. It can be seen that the proposed method has better disturbance rejection performance, strong robustness and practical value.

Modeling of monetary and credit system indicators of the Russian Federation in multidirectional scenarios of oil market dynamics

The purpose of research – to build mathematical models that describe interrelationships between the key market indicators, significant for the Russian economy, and macroeconomic indicators of the monetary system. Materials and methods. In this study, we applied methods of model description, mostly used in control theory, meant for technical engineering, such as linear discrete transfer functions, space-state models and nonlinear Hammerstein-Wiener models. To identify these models, we used System Identification Toolbox from Matlab software package, mostly used for mechanical systems’ analysis. Based on the known input and output signals, a mathematical model was estimated. Time series of macroeconomic and market indicators for the period from January 10, 2008 to January 10, 2018 were used for identification. Results. Two prediction models were designed in this work. The first model describes a sequential transfer from the oil price and dollar- to-ruble exchange rate to the gross domestic product, then to M2 and then to loans. Dependencies between economic parameters are described by linear discrete transfer functions. There is only one difference in the second model’s general structure: the sequence of the last two transitions from the gross domestic product to loans, and then to M2. In addition, nonlinear Hammerstein-Wiener models describe last two transitions in the second model. As a result, predictions for macroeconomic indicators’ trends were given on different time horizons: three, seven and twelve years and with two differently directed scenarios of the oil market. The conclusion. Despite close values in the models accuracy estimation, they give similar results for matching scenarios, but different growth rates in general, in the forecast. Such a result in scenarios shows, that a sharp fall in oil prices has a stronger impact on given macroeconomic and market indicators, which, in its turn, shows the capability of the models to make correct trend predictions. In further studies, it is possible to move from macroeconomic indicators to their more particular components at meso- and micro levels.

A Nonlinear TSNN Based Model of a Lead Acid Battery

The paper studies a nonlinear model based on time series neural network system (TSNN) to improve the highly nonlinear dynamic model of an automotive lead acid cell battery. Artificial neural network (ANN) take into consideration the dynamic behavior of both input-output variables of the battery charge-discharge processes. The ANN works as a benchmark, its inputs include delays and charging/discharging current values. To train our neural network, we performed a pulse discharge on a lead acid battery to collect experimental data. Results are presented and compared with a nonlinear Hammerstein-Wiener model. The ANN and nonlinear autoregressive exogenous model (NARX) models achieved satisfying results.

An improved method for Wiener–Hammerstein system identification based on the Fractional Approach

This paper develops and analyses a novel method for identifying Wiener–Hammerstein models, i.e. models consisting of two linear dynamic parts with a static non-linearity in between. Starting from the best linear model, which is a consistent estimate of the system dynamics for Gaussian excitation, the identification problem includes the partitioning of the poles and zeros between the two linear parts. This partitioning can be formulated as a discrete optimization problem. The fractional approach considers a relaxation of this problem into a continuous one, by parameterizing the partition of each pole and zero in a fractional way, and carrying out the computations in the frequency domain. In this paper it is shown that the fractional approach becomes ill-conditioned for some configurations of the poles and zeros of the linear dynamic parts, causing identifiability issues. A modification of the original fractional approach is then introduced, based on series expansion of the fractional transfer functions. This modification shares most of the properties of the fractional approach. However, it is shown that it provides an implicit regularization of the identification problem. It addresses the ill-conditioning problem while preserving meaningful statistical properties of the estimation. Furthermore, a lifted formulation of the estimation problem is proposed, which improves the algorithmic performance in the framework of Newton-based methods.

Predictive control of thermal state of blast furnace

The work describes the structure of the model for predictive control of the thermal state of a blast furnace. The proposed model contains the following input parameters: coke rate; theoretical combustion temperature, comprising: natural gas consumption, blasting temperature, humidity, oxygen, blast furnace cooling water; blast furnace gas utilization rate. The output parameter is the cast iron temperature. The results for determining the cast iron temperature were obtained following the identification using the Hammerstein-Wiener model. The result of solving the cast iron temperature stabilization problem was provided for the calculated values of process parameters of the target area of the respective blast furnace operation mode.

Simultaneous Self-Sensing of Displacement and Force for Soft Dielectric Elastomer Actuators

This paper presents a novel self-sensing method for soft actuators based on dielectric elastomer (DE) membranes. The proposed self-sensing scheme permits the reconstruction of both membrane force and displacement during actuation, based on voltage and current measurements only. The simultaneous self-sensing of displacement and force allows one to implement interaction control strategies without the need for additional electro-mechanical transducers. To achieve this goal, an online estimation algorithm based on recursive least squares is implemented to reconstruct the membrane capacitance from voltage and current measurements. Subsequently, mathematical models are developed to relate the capacitance to membrane displacement and force. Several modeling approaches are compared, ranging from physics-based to black box ones (i.e., Hammerstein–Wiener models and neural networks), in order to evaluate which strategy maximizes the estimation accuracy. After discussing the complete self-sensing algorithm, experimental validation is performed on a prototype consisting of a cone DE membrane.

Nonlinear system identification of the reduction nickel oxide smelting process in electric arc furnace

As the title implies the article describes the nonlinear system identification of the reduction smelting process of nickel oxide in electric arc furnaces. It is suggested that for operational control ratio of components of the charge must be solved the problem of determining the qualitative composition of the melt in real time. The use of 0th harmonic of phase voltage AC furnace as an indirect measure of the melt composition is proposed. Brief description of the mechanism of occurrence and nature of the non-zero 0th harmonic of the AC voltage of the arc is given. It is shown that value of 0th harmonic of the arc voltage is not function of electrical parameters but depends of the material composition of the melt. Processed industrial data are given. Hammerstein-Wiener model is used for description of the dependence of 0th harmonic of the furnace voltage from the technical parameters of melting furnace: the melt composition and current. Recommendations are given about the practical use of the model.

Nonlinear modeling of the relationship between reagent dosage and flotation froth surface image by Hammerstein-Wiener model

Due to the frequent and random disturbances to flotation banks, reagent dosages are frequently changed to stabilize the flotation process at a desired level to obtain an expected grade and recovery. It is widely accepted that the froth surface after a reagent change is the essential process output, corresponding to reagent dosages for a current chemical condition (that also can be characterized by the froth surface). Based on this causal relationship, the froth surface can be controlled to any expected stable state by changing reagent dosage. Therefore, a Hammerstein-Wiener based causal model that models bubble size distribution (the image feature used to characterize froth appearance) and reagent dosage as a nonlinear relationship was developed. Since existing watershed algorithms are ineffective in segmenting the highly reflective zinc bubble images, a novel illumination modeling-based marker watershed method was proposed. A log-normal distribution model was used to fit the bubble size distribution, and then a nonlinear model between bubble size distribution and reagent dosage was approximated by a wavelet-based Hammerstein-Wiener model. The proposed methods have been validated through comparative experiments for a lead–zinc flotation plant in China.

Soft sensors model optimization and application for the refinery real-time prediction of toluene content

ABSTRACTIndustrial facilities nowadays show an increasing need for continuous measurements, monitoring and controlling many process variables. The on-line process analyzers, being the key indicators of process and product quality, are often unavailable or malfunction. This paper describes development of soft sensor models based on the real plant data that could replace an on-line analyzer when it is unavailable, or to monitor and diagnose an analyzer’s performance. Soft sensors for continuous toluene content estimation based on the real aromatic plant data are developed. The autoregressive model with exogenous inputs, output error, the nonlinear autoregressive model consisted of exogenous inputs and Hammerstein–Wiener models were developed. In case of complex real-plant processes a large number of model regressors and coefficients need to be optimized. To overcome an exhaustive trial-and-error procedure of optimal model regressor order determination, differential evolution optimization method is applied. In general, the proposed approach could be, of interest for the development of dynamic polynomial identification models. The performance of the models are validated on the real-plant data.

Control-oriented modeling of geothermal borefield thermal dynamics through Hammerstein-Wiener models

Abstract Geothermal energy is considered a clean and sustainable form of renewable energy, that can be exploited directly or indirectly by means of specific devices. Ground-coupled heat pumps are widely used systems to obtain this energy. Control of ground-coupled heat pump systems, where thermal energy is extracted or injected from and to a geothermal borefield, is important for optimal geothermal energy use in the building sector and smart grids. Model-based control of such systems is potentially an optimal solution but this requires control-oriented models for the borefield thermal dynamics, which is quite complicated due to thermal interactions between the boreholes, large-scale nonlinear system dynamics, transient surface boundary conditions, etc. In this paper, we propose and demonstrate the successful identification of these complex dynamics through simple and well-structured nonlinear Hammerstein-Wiener models, which can be used in some advanced convex model-based control algorithms. The results are validated for different borefield configurations and parameters with reference to a detailed finite-element borefield thermal model. Finally, a set of advanced convex model-based control methods are shortly described where Hammerstein-Wiener models can be used as control models.

Maximum Likelihood identification of Wiener-Hammerstein system with process noise

The Wiener-Hammerstein model is a block-oriented model consisting of two linear blocks and a static nonlinearity in the middle. We address the identification problem of this model, when a disturbance affects the input of the non-linearity, i.e. process noise. For this case, a Maximum Likelihood estimator is derived, which delivers a consistent estimate of the model parameters. In the presence of process noise, in fact, a standard Prediction Error Method normally leads to biased results. The Maximum Likelihood estimate is then used together with the Best Linear Approximation of the system, in order to implement a complete identification scheme when the parametrization of the linear blocks is not known a priori. The computation of the likelihood function requires numerical integration, which is solved by Monte Carlo and Metropolis-Hastings techniques. Numerical examples show the effectiveness of the identification scheme.

Modeling and Identification of Ultra-Wideband Analog Multipliers

Analog multipliers are employed in many applications. In conventional RF front ends, for example, they are widely used for frequency conversion tasks. In noncoherent energy detectors or autocorrelation receivers, they multiply the (broadband) input signal by itself to achieve a down-conversion. Unfortunately, there exist no ideal hardware realizations of such devices, hence multipliers inevitably create undesired signal content at their output. To be able to deal with these effects or correct for them, we need to be able to model and identify realistic RF multipliers. This paper proposes and validates a multiple-input single-output Wiener–Hammerstein model for ultra-wideband (UWB) analog multipliers. The structure of the proposed model gives insight in the distortions created. It thus provides the possibility to study the realistic behavior of systems involving those multipliers, e.g., the influence of undesired nonlinear signal content onto noncoherent UWB receivers. A comparison of the model performance is shown with respect to measurements and circuit simulations.

Extremum seeking based on a Hammerstein-Wiener representation

This study is concerned with the development of an extremum seeking (ES) strategy based on recursive least square (RLS) for on-line estimation, and a regression model in the form of a Hammerstein-Wiener model. RLS usually provides a faster convergence than the classical bank of filter estimators, and the consideration of process dynamics allows to take account for the phase-shift and attenuation occurring when increasing the frequency of the dither signal. The resulting ES scheme achieves very significant improvement in convergence speed, as illustrated with a numerical example, and a more realistic application to micro-algae cultures in a photo-bioreactor in simulation.