Prediction Error Method Research Articles

A new reference model-based fixed-structure controller for industrial applications

This paper introduces a new approach to design a fixed-structure controller for those industrial applications, where mathematical model of the plant is not known. The design methodology is composed of two steps. First, black-box system identification is used to obtain a mathematical model of plant and second, a fixed-structure controller is designed based on reference model defined by closed-loop performance. For controller identification, prediction error method (PEM) is considered, which uses the off-line generated input-output inherently noise free data using the reference model. Due to fixed design structure, the controller is independent of plant's order. The proposed approach is tested on a lab-based real-time magnetic levitation system (MLS). The results show effectiveness of the proposed approach with good reference tracking and robustness properties. The proposed approach emerged a lower order controller which is computationally efficient and easy to implement. Compare to other data-driven techniques, inverse mapping of the reference model is not required and the performance versus design/tuning time comparison with conventional proportional integral derivative (PID) controller is also improved.

Recursive system identification for coefficient estimation of continuous-time fractional order systems

Fractional-order calculus has already proven to be effective in order to model diffusive phenomena, such as heat transfer or anomalous mass transfer. This has led to developments of fractional-order transfer function models and, as a consequence, system identification algorithms have been developed to identify the parameters for this type of structures. However, it may be necessary to perform real-time system identification in which the parameters evolve over time while more and more data is acquired. Extensions to recursive identification algorithms are presented for fractional-order transfer functions. Two methods are proposed for recursive estimation of the coefficients of continuous-time fractional order systems: the recursive least squares with state variable filters and the prediction-error method. These two methods are compared with different signal to noise ratio levels through Monte Carlo simulations.

Deep learning with transfer functions: new applications in system identification

Abstract This paper presents a linear dynamical operator described in terms of a rational transfer function, endowed with a well-defined and efficient back-propagation behavior for automatic derivatives computation. The operator enables end-to-end training of structured networks containing linear transfer functions and other differentiable units by exploiting standard deep learning software. Two relevant applications of the operator in system identification are presented. The first one consists in the integration of prediction error methods in deep learning. The dynamical operator is included as the last layer of a neural network in order to obtain the optimal one-step-ahead prediction error. The second one considers identification of general block-oriented models from quantized data. These block-oriented models are constructed by combining linear dynamical operators with static nonlinearities described as standard feed-forward neural networks. A custom loss function corresponding to the log-likelihood of quantized output observations is defined. For gradient-based optimization, the derivatives of the log-likelihood are computed by applying the back-propagation algorithm through the whole network. Two system identification benchmarks are used to show the effectiveness of the proposed methodologies.

Modeling and Validation of a Four‐Tank System for Level Control Process Using Black Box and White Box Model Approaches

Mathematical modeling of a system plays a vital role in controller design, tuning to meet the desired specifications and process parameter optimization. In this paper, different identification algorithms are implemented in the four‐tank system to demonstrate the superiority of the recommended subspace system identification method (Numeric Algorithms for Subspace State Space System Identification [N4SID]) for the different input design. A system identification method was utilized to identify the model of a dynamic system. It is modeled using the First‐Principle Method (FPM), Prediction Error Method (PEM) and Numeric Algorithms for N4SID method. The identification is performed through MATLAB. The plant input and output is acquired through LabVIEW. The developed models are validated with a new dataset based on the model performance specifications: Mean Absolute Error (MAE), Root Mean Squared Error (RMSE) and Best Fit Rate (BFR). The results show that the proposed N4SID method with the amplitude‐modulated pseudorandom binary signal (APRBS) signal is better than the other methods with different inputs. © 2020 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Depth Estimation for Light-Field Images Using Stereo Matching and Convolutional Neural Networks.

The paper presents a novel depth-estimation method for light-field (LF) images based on innovative multi-stereo matching and machine-learning techniques. In the first stage, a novel block-based stereo matching algorithm is employed to compute the initial estimation. The proposed algorithm is specifically designed to operate on any pair of sub-aperture images (SAIs) in the LF image and to compute the pair’s corresponding disparity map. For the central SAI, a disparity fusion technique is proposed to compute the initial disparity map based on all available pairwise disparities. In the second stage, a novel pixel-wise deep-learning (DL)-based method for residual error prediction is employed to further refine the disparity estimation. A novel neural network architecture is proposed based on a new structure of layers. The proposed DL-based method is employed to predict the residual error of the initial estimation and to refine the final disparity map. The experimental results demonstrate the superiority of the proposed framework and reveal that the proposed method achieves an average improvement of in root mean squared error (RMSE), in mean absolute error (MAE), and in structural similarity index (SSIM) over machine-learning-based state-of-the-art methods.

Navigation error prediction for UWAN based on AUV

An underwater acoustical navigation (UWAN) system is widely used on an autonomous underwater vehicle (AUV). The navigation error prediction is of great significance to the design, use, and capability upgrade for the UWAN system. Owing to the trend of faster AUV and the need for higher navigation accuracy, traditional navigation models are mismatched. Besides, they adopt fixed input errors (including measurement errors of sound velocity, time delay, and array position), which are inconsistent with the real complex acoustic channel. As a consequence, the prediction accuracy of the navigation error is greatly reduced. The authors proposed a novel navigation error prediction method for UWAN based on AUV. Firstly, they established the acoustical navigation model for moving AUV and deduced the error prediction formula. Secondly, considering the complex underwater acoustic channel, they applied the variable error models as the inputs of the prediction formula. Finally, simulations and experiments in different situations verified the effectiveness of the proposed method. The method will provide effective theoretical support for the performance evaluation of the UWAN system based on moving AUV.

Feedback identification of conductance-based models

This paper applies the classical prediction error method (PEM) to the estimation of nonlinear discrete-time models of neuronal systems subject to input-additive noise. While the nonlinear system exhibits excitability, bifurcations, and limit-cycle oscillations, we prove consistency of the parameter estimation procedure under output feedback. Hence, this paper provides a rigorous framework for the application of conventional nonlinear system identification methods to discrete-time stochastic neuronal systems. The main result exploits the elementary property that conductance-based models of neurons have an exponentially contracting inverse dynamics. This property is implied by the voltage-clamp experiment, which has been the fundamental modeling experiment of neurons ever since the pioneering work of Hodgkin and Huxley.

Robust Estimation of Wiener Models in the Presence of Outliers Using the VB Approach

This article is concerned with the identification of a Wiener model, which is a widely used block-oriented nonlinear model. The identification of the Wiener model in the presence of outliers and process noises has not been well studied to date. We propose a graphical model to describe the Wiener process, where the outliers are modeled by Student's <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$t\text{-}$</tex-math></inline-formula> distribution. Due to the negative effects of the nonlinearity and latent variables on parameter estimation, the model is estimated using a variational Bayesian approach. We propose an effective method to approximate the posterior distributions of the latent variables. As a result, a new method for Wiener model identification is proposed. Compared with the straightforward maximum-likelihood estimation and the classical prediction error method, the proposed method is more robust and provides more accurate parameter estimates. The proposed method is used to identify the temperature dynamic of the phase-change cooling module of the high-performance chip.

A critical evaluation of the Jones models and the industry approach for the estimation of discretionary accruals

ABSTRACT We critically examine two important methodological issues related to the estimation of discretionary accruals: the Jones models and the industry approach, both of which are considered the norms in the earnings management studies. We document that the original Jones models are the regression-through-the-origin (RTO) models. The RTO Jones models unduly overstate the significance of PPE and R2, produce inconsistent coefficients and non-zero mean discretionary accruals. If we include the intercept in the models, then they lack power. We show that the RTO Jones models are theoretically flawed while their non-RTO variations are empirically flawed. We also address the issue of using the industry approach as a sole approach for the estimation of discretionary accruals. We document that the CFO approach outperforms the industry approach. Lastly, we document that the prediction error method outperforms the estimation error method in detecting earnings management.

Using Random forest and Gradient boosting trees to improve wave forecast at a specific location

The main objective is to present alternative algorithms to neural networks when improving sea state forecast by numerical models considering main spectral bulk parameters at a specific location, namely significant wave height, peak wave period and peak wave direction. The two alternatives are random forest and gradient boosting trees. To our knowledge, they have never been used for error prediction method. Therefore, their performances are compared with the performances of the usual choice in the literature: neural networks. We showed that the RMSE of the variables updated with gradient boosting trees and random forest are respectively 20 and 10% lower than the RMSE obtained with neural networks. A secondary objective is to show how to tune the hyperparameter values of machine learning algorithms with Bayesian Optimization. This step is essential when using machine learning algorithms and can improve the results significantly. Indeed, after a fine hyperparameter tuning with Bayesian optimization, gradient boosting trees yielded RMSE values in average 8% to 11% lower for the correction of significant wave height and peak wave period. Lastly, the potential benefits of such corrections in real life application are investigated by computing the extreme wave run-up (R2%) at the study site (Biarritz, France) using the data corrected by the different algorithms. Here again, the corrections made by random forest and gradient boosting trees provide better results than the corrections made by neural networks.

Control oriented data driven linear parameter varying model for proton exchange membrane fuel cell systems

Proton exchange membrane fuel cell systems are widely used to drive vehicles. It is indispensable to establish accurate and simple control oriented model of the system. However, this control oriented model is difficult to build due to the characteristic of strongly nonlinear, coupled and time - varying in proton exchange membrane fuel cell systems. To solve this problem, nonlinear subspace identification method is proposed to discover linear parameter varying model for the proton exchange membrane fuel cell system. The modeling process can be divided into two stages. In the first stage, algebraic transformation method is proposed to transform the nonlinear model to linear parameter varying model. In the second stage, kernel method based subspace identification is presented to identify parameter matrices of the proton exchange membrane fuel cell system. The established model is demonstrated by a 50 kW on board proton exchange membrane fuel cell system under real driving condition. The results show that mean absolute percent error and root mean squared error are as low as 9.6941e−06 and 0.0957, respectively. Therefore, the control oriented model perfectly agrees with real data. Compared with the prediction error method and recursive neural network nonlinear auto - regressive moving average model with exogenous method, modeling accuracy and speed of the proposed method are the best. Moreover, linear control theory can be employed to design controller based on the linear parameter varying model, which greatly simplifies controller design for proton exchange membrane fuel cell systems.

Research on Combination Clock Error Prediction Under Uncertain Predicted Length

Clock error prediction is of vital importance for the distributed netted systems’ regular operation, like netted satellites, netted radars, etc. Aiming at the problem of predicted length could not get beforehand in some conditions, we put forth a combined clock error method under uncertain predicted length. We estimate the predicted length based on the clock error data quality factor in advance. Then, we operate clock error prediction based on the combination method. If the time synchronization has reestablished earlier than the predicted length, we stop prediction immediately. And if time synchronization has not reestablished when the clock error prediction reaches the predicted length, we re-estimate the predicted length and continue prediction until time synchronization reestablishes. From examples analyses, we could get 0.3–0.5 ns around precision for one-day long precision and 0.9–1.1 ns for 2 days and 1.2–1.4 ns for 1 week. Besides, we could conclude that the combination method could flat the differences of the clocks and the difference of sole algorithms, improving the robustness of the algorithm. The combination clock error prediction method could be both applied in satellites’ clock error prediction and in other distributed netted system, especially in the condition that the predicted length could not be known before predicting, being vital to the whole systems’ performance.

Estimation of jump Box–Jenkins models

Jump Box–Jenkins (BJ) models are a collection of a finite set of linear dynamical submodels in BJ form that switch over time, according to a Markov chain. This paper addresses the problem of maximum-a-posteriori estimation of jump BJ models from a given training input/output dataset. The proposed solution method estimates the coefficients of the BJ submodels, the state transition probabilities of the Markov chain regulating the switching of operating modes, and the corresponding mode sequence hidden in the dataset. In particular, the posterior distribution of all the unknown variables characterizing the jump BJ model is derived and then maximized using a coordinate ascent algorithm. The resulting estimation algorithm alternates between Gauss–Newton optimization of the coefficients of the BJ submodels, a method derived based on an instance of prediction error methods tailored to BJ models with switching coefficients, and approximated dynamic programming for optimization of the sequence of active modes. The quality of the proposed estimation approach is evaluated on a numerical example based on synthetic data and in a case study related to segmentation of honeybee dances.

Design of hierarchical control strategies for biological wastewater treatment plants to reduce operational costs

In this research, hierarchical control strategies are developed for biological wastewater treatment plants (WWTPs) to reduce the operational expenses. The benchmark simulation model no. 1 (BSM1) is used as the working platform which is developed based on activated sludge model no. 1 (ASM1) to control dissolved oxygen in aerobic reactors and nitrate levels in anoxic reactors. Fractional PI (FPI) controllers are designed at the lower level and model predictive control (MPC) and a fuzzy controller are designed at higher level in order to achieve enhanced set-point tracking. Initially, linear state space model is developed around the operating point using prediction-error method for lower level. For identification of the higher level model, the lower level control loop is closed in a feedback sense with the designed controller. Based on the identified model in the higher level, the controllers are designed. This paper presents two combinations of hierarchical control strategies: FPI-Fuzzy and FPI-MPC. It is observed that FPI controller at the lower level and MPC controller at the higher level results in better plant performance with better set-point tracking with reduced operational costs. It is observed that FPI-Fuzzy control strategy results in better EQI of 7041.7 for storm weather condition which also resulted in 48% reduction in total nitrogen violations and FPI-MPC results in better OCI of 17119.6 and this strategy resulted in nearly 38% reduction in total nitrogen violations. A significant improvement in the plant performance is observed for dry and rain weather conditions as well.

A Non-Delay Error Compensation Method for Dual-Driving Gantry-Type Machine Tool

The drive at the center of gravity (DCG) principle has been adopted in computer numerical control (CNC) machines and industrial robots that require heavy-duty and quick feeds. Using this principle requires accurate corrections of positioning errors. Conventional error compensation methods may cause vibrations and unstable control performances due to the delay between compensation and motor motion. This paper proposes a new method to reduce the positioning errors of the dual-driving gantry-type machine tool (DDGTMT), namely, a typical DCG-principle-based machine tool. An error prediction method is proposed to characterize errors online. An algorithm is proposed to quickly and accurately compensate the errors of the DDGTMT. Experiment results verify that the non-delay error compensation method proposed in this paper can effectively improve the accuracy of the DDGTMT.

Recursive Bias-Correction Method for Identification of Piecewise Affine Output-Error Models

Learning PieceWise Affine Output-Error (PWA-OE) models from data requires to estimate a finite set of affine output-error sub-models as well as a partition of the regressors space over which the sub-models are defined. For an output-error type noise structure, the algorithms based on ordinary least squares (LS) fail to compute a consistent estimate of the sub-model parameters. On the other hand, the prediction error methods (PEMs) provide a consistent parameter estimate, however, they require to solve a non-convex optimization problem for which the numerical algorithms may get trapped in a local minimum, leading to inaccurate estimates. In this letter, we propose a recursive bias-correction scheme for identifying PWA-OE models, retaining the computational efficiency of the standard LS algorithms while providing a consistent estimate of the sub-model parameters, under suitable assumptions. The proposed approach allows one to recursively update the estimates of the sub-models parameters and to cluster the regressors. Linear multi-category techniques are then employed to estimate a partition of the regressor space based on the estimated clusters. The performance of the proposed algorithm is demonstrated via an academic example.

Identification of stochastic nonlinear models using optimal estimating functions

The first part of the paper examines the asymptotic properties of linear prediction error method estimators, which were recently suggested for the identification of nonlinear stochastic dynamical models. It is shown that their accuracy depends not only on how the model is parameterized, but also on the shape of the unknown distribution of the data. Therefore, it is not obvious in general which linear prediction error method should be preferred. In the second part, the estimating functions approach is introduced and used to construct estimators that are asymptotically optimal with respect to a specific class of estimators. These estimators rely on partial probabilistic parametric models, and therefore neither require the computations of the likelihood function nor any marginalization integrals. The convergence and consistency of the proposed estimators are established under standard regularity and identifiability assumptions akin to those of prediction error methods. The paper is concluded by several numerical simulation examples.

Active Disturbance Rejection Control of Boiler Forced Draft System: A Data-Driven Practice

Boiler forced draft systems play a critical role in maintaining power plant safety and efficiency. However, their control is notoriously intractable in terms of modelling difficulty, multiple disturbances and severe noise. To this end, this paper develops a data-driven paradigm by combining some popular data analytics methods in both modelling and control. First, singular value decomposition (SVD) is utilized for data classification, which further cooperates with back propagation (BP) neural network to de-noise the measurements. Second, prediction error method (PEM) is used to analyze the historical data and identify the dynamic model, whose responses agree well with the actual plant data. Third, by estimating the lumped disturbances via the real-time data, active disturbance rejection control (ADRC) is employed to control the forced draft system, whose stability is analyzed in the frequency domain. Simulation results demonstrate the efficiency and superiority of the proposed method over proportional-integral-differential (PID) controller and model predictive controller, depicting a promising prospect in the future industry practice.

Model Reference Robust Adaptive Control of Control Element Drive Mechanism in a Nuclear Power Plant

In the nuclear power plant, the control element drive mechanism (CEDM: A type of solenoid actuators) is used to insert nuclear fuel rods into the core to regulate the neutron absorption within the reactor. The control environment is full of uncertainty and disturbance, and the CEDM is supposed to cope with the varying conditions in the reactor. In this paper, a model reference adaptive control (MRAC) of CEDM is investigated. The existing MRAC scheme that assumes the known system order is first extended to the system with unknown high-frequency gain and output disturbance, and then the extended version is applied to the control problem of CEDM. A simplified relationship between the input voltage and the magnetic force of the CEDM is established based on Kirchhoff’s voltage law and the magnetic co-energy theory. The system order of the plant is identified by the prediction error method using experimental input/output data: A 3rd order linear model with three poles and two zeros turns out to be the best model for control. Based on this model, a 3rd order reference model is selected, and an adaptive control law with s-modified adaptation laws is designed under output disturbance. The performance of the proposed control law is compared with a well-tuned PI controller and the conventional MRAC. The superiority of the proposed method is also demonstrated in an abnormal condition. Simulation and experiment results are provided.

Prediction Error Identification Method for Continuous-time Systems Having Multiple Unknown Time Delays

This paper shows a continuous-time prediction error method for the identification of Multiple Input Single Output (MISO) Continuous-Time (CT) systems with multiple unknown time delays. The proposed algorithm entails the simultaneous estimation of both process parameters and multiple unknown time delays. Indeed, it minimizes the prediction error using the Levenberg-Marquardt (LM) optimization method with derivatives of the objective function with respect to the parameters including the multiple unknown time delays. An analysis is then presented which proves the convergence of the algorithm, and robustness issues are discussed as well. Finally, to verify the analysis and to demonstrate the feasibility of the algorithm, we present some of the simulation results which were carried out.