Prediction Error Method Research Articles

A linear model for the machine tool assembly error prediction considering roller guide error and gravity-induced deformation

In assembly, error prediction and control according to the error state of the machine parts are the key links to ensuring the accuracy of the entire machine tool. In this study, an assembly error modeling method considering the error of the roller guide and gravity-induced deformation is proposed. First, based on the Hertz contact theory, a nonlinear error propagation model for the roller guide to the moving part is proposed. With this model, the analytical relationship between the straightness error of the guide rail and the errors of the moving part can be established. Then, after the linearization of the guide error model, a machine assembly error model considering the guide error is proposed. This model expresses the linear relationship between the error of the rolling joint surface and the error of the machine tool after the final assembly. Additionally, considering the influence of gravity deformation of structural parts, the gravity deformation is extracted by the finite element analysis method and added to the model by linear superposition. As a result, the model corresponds more with the practical assembly process. Finally, an assembly error prediction method of the precision horizontal machining center is presented, and a case is studied to demonstrate the validity of the proposed model and method.

Variable Parameters Stiffness Identification and Modeling for Positional Compensation of Industrial Robots

Due to the weak stiffness of robot structure, the positional accuracy of industrial robots under load can hardly meet the application requirements of high-precision machining. Predicting and compensating errors by accurate stiffness modeling is an effective method to improve robot positional accuracy. Existing stiffness modeling methods use theoretical kinematic parameters and approximate the joint stiffness to a fixed value, so that the modeling accuracy is poor. Thus, this paper proposes a regular sampling point selection method by space gridding. Then, combining Levenberg-Marquardt kinematics parameter calibration and static joint stiffness identification methods, a comprehensive identification method is proposed to achieve simultaneous identifying of robot kinematics and stiffness parameters. Next, a variable parameter stiffness model could be established, according to the identification results in different workspaces. Finally, a model-based error prediction and compensation method is put forward through online sensing of external load. The error compensation is performed on a KR500 robot, and experimental results verified that the average value of absolute positional errors caused by external load, could be reduced by 44.61%, compared with the traditional compensation method.

Prediction of Power Output of Wind Turbines Using System Identification Techniques

In this paper, a generalized State Space Model for prediction of wind turbine output power has been developed via System Identification techniques. The techniques involved in this paper are the subspace methods, mainly, Numerical algorithms for Subspace State Space System Identification based on advanced linear algebra, and Prediction Error Method that based on iterative optimization. Predicting the power output of wind turbines in general is very useful in many applications, such as online monitoring of wind turbines, increasing the share of wind power from the wind farms to grids, operator training simulations, control system upgrades and so on. In order to attain sufficient accuracy for the model, many influencing inputs are taken into account, which are pitch angle, rotor speed with several other meteorological inputs as humidity, temperature, air pressure and wind speed have been considered in the system identification prediction; the result has shown that each input is sufficient and affects the model accuracy. Furthermore, the effect of model order on simulation accuracy has been investigated. In addition, a comparative study has been conducted between Prediction Error Method and Numerical algorithms for Subspace State Space System Identification methods in terms of complexity, accuracy, and speed of simulation. Simulations have demonstrated each methods’ ability to predict wind power with some slight differences in accuracy and computational requirements.

Stability and weighted sensitivity analysis of robust controller for heat exchanger

This study presents a parametric system identification approach to estimate the dynamics of a chemical plant from experimental data and develops a robust PID controller for the plant. Parametric system identification of the heat exchanger system has been carried out using experimental data and prediction error method. The estimated model of the heat exchanger system is a time-delay model and a robust PID controller for the time-delayed model has been designed considering weighted sensitivity criteria. The mathematical background of parametric system identification, stability analysis, and H∞ weighted sensitivity analysis have been provided in this paper. A graphical plot has been provided to determine the stability region in the (Kp,Ki), (Kp,Kd) and (Ki,Kd) plane. The stability region is a locus dependent on parameters of the controller and frequency, in the parameter plane.

Identification of a quadcopter autopilot system via Box–Jenkins structure

This paper presents a method to precisely model a four rotor unmanned aerial vehicle, widely known as quadcopter autopilot system. Common system identification methods limit quadcopter models into first or second order systems, and do not count for noise characteristics. This leads to poor prediction accuracy of its longitudinal and lateral motion dynamics that ultimately affects the aircraft stabilization during flight and landing. To improve the quality of the estimated models, we utilized a statistically suitable discrete-time linear Box–Jenkins structure to model the plant and noise characteristics of the horizontal subsystems of a quadcopter autopilot system. The models were estimated using flight data acquired when the system were provided with pseudo-random binary sequence input. In this proposed method, by employing the prediction error method and least squares approach, the aircraft dynamics could be modeled up until the fifth order. The normalized root mean square fitness value showed that the predicted model output matches the experimental flight data by 94.72% in the one-step-ahead prediction test, and 84.52% in the infinite-step-ahead prediction test. These prediction results demonstrated an improvement of 52.8% when compared with a first and second order model structures proposed in previous works for the same quadcopter model. The output from this research works confirmed the effectiveness of the proposed method to adequately capture the autopilot dynamics and accurately predict the quadcopter outputs. These would greatly assist in designing robust flight controllers for the autopilot system.

Controller design for the closed loop system with non-interaction condition

ABSTRACT For some complex systems with several controlled variables and with interaction between these controlled variables, one complex mathematical model is established to include lots of elements in the control matrix. In order to reduce the number of elements in the control matrix and increase real-time property in designing the unknown controllers, an idea of non-interaction property is introduced to simplify our mentioned closed loop system with many variables. To achieve the non-interaction property, some conditions are derived to guarantee one controlled input only influences one output. Based on this simplified model, the prediction error method coming from system identification field is applied to design the optimal controllers. The advantage of our prediction error method is that the optimal controller is a constant ratio of two polynomials. Finally one simulation example confirms our theoretical results.

An Adaptive Kinematic Filter Extended by the Additionally Measured Velocity or Acceleration

A previously described adaptive-gain tracking filter with the position only measurements is extended to models with additionally measured velocity or acceleration. The devised filter adapts the full matrix gain, copes with sensors cross-correlation, and improves the position-only prototype. By using a prediction error method, the adaptive gain always follows the Kalman gain. The filter proves efficient in scenarios with piecewise constant acceleration.

Adaptive Feedback Cancellation in Hearing Aids Based on Orthonormal Basis Functions With Prediction-Error Method Based Prewhitening

Acoustic feedback is a persistent problem in hearing aids, which limits the achievable amplification and may severely degrade the sound quality by producing howling artifacts. A potential approach to feedback cancellation is to estimate the feedback path utilizing an adaptive filter. However, estimation of the feedback path suffers a large model error, known as the bias, due to the correlation between the loudspeaker and source signals. A prediction-error method (PEM) based prewhitening filter has been widely utilized to reduce the bias. This approach, however, requires a large number of adaptive parameters, thus increasing the computational complexity, reducing the convergence rate, and limiting the added stable gain. We introduce an adaptive feedback cancellation (AFC) algorithm derived based on the orthonormal basis functions (OBFs) for closed-loop identification of the feedback path by minimizing the prediction error. The OBFs are defined by a set of fixed poles and a small number of adaptive tap-output weights. We study two methods for obtaining the fixed poles, an inherently stable least-squares method and a log-scale frequency resolution method. The poles are then embedded as the a priori information into the algorithm. The proposed algorithm is extensively evaluated with speech and music source signals and with sudden changes in the feedback path. The experimental results show that the proposed method significantly increases the added stable gain, accelerates the convergence rate, and enhances the sound quality compared to state-of-the-art, while requiring far fewer adaptive parameters which leads to reduced computational complexity.

Enforcing stability through ellipsoidal inner approximations in the indirect approach for continuous-time system identification

Recently, a new indirect approach method for continuous-time system identification has been proposed that provides complete freedom on the number of poles and zeros of the linear and time-invariant continuous-time model structure. However, this procedure has reliability issues, as it may deliver unstable estimates even if the initialisation model and true system are stable. In this paper, we propose a method to overcome this problem. By generating ellipsoids that contain parameter vectors whose coefficients yield stable polynomials, we introduce a convex constraint in the indirect prediction error method formulation, and show that the proposed method enjoys optimal asymptotic properties while being robust in small and noisy data set scenarios. The effectiveness of the novel method is tested through extensive simulations.

Real-Time System Identification Using Deep Learning for Linear Processes With Application to Unmanned Aerial Vehicles

This paper proposes a novel parametric identification approach for linear systems using Deep Learning (DL) and the Modified Relay Feedback Test (MRFT). The proposed methodology utilizes MRFT to reveal distinguishing frequencies about an unknown process; which are then passed to a trained DL model to identify the underlying process parameters. The presented approach guarantees stability and performance in the identification and control phases respectively, and requires few seconds of observation data to infer the dynamic system parameters. Quadrotor Unmanned Aerial Vehicle (UAV) attitude and altitude dynamics were used in simulation and experimentation to verify the presented methodology. Results show the effectiveness and real-time capabilities of the proposed approach, which outperforms the conventional Prediction Error Method in terms of accuracy, robustness to biases, computational efficiency and data requirements.

Consistent identification of dynamic networks subject to white noise using Weighted Null-Space Fitting

Identification of dynamic networks has been a flourishing area in recent years. However, there are few contributions addressing the problem of simultaneously identifying all modules in a network of given structure. In principle the prediction error method can handle such problems but this methods suffers from well known issues with local minima and how to find initial parameter values. Weighted Null-Space Fitting is a multi-step least-squares method and in this contribution we extend this method to rational linear dynamic networks of arbitrary topology with modules subject to white noise disturbances. We show that WNSF reaches the performance of PEM initialized at the true parameter values for a fairly complex network, suggesting consistency and asymptotic efficiency of the proposed method.

Constrained Subspace Method for the Identification of Structured State-Space Models (COSMOS)

In this article, a unified identification framework called constrained subspace method for structured state-space models (COSMOS) is presented, where the structure is defined by a user-specified linear or polynomial parametrization. The new approach operates directly from the input and output data, which differs from the traditional two-step method that first obtains a state-space realization followed by the system-parameter estimation. The new identification framework relies on a subspace inspired linear regression problem which may not yield a consistent estimate in the presence of process noise. To alleviate this problem, the linear regression formulation is imposed by structured and low-rank constraints in terms of a finite set of system Markov parameters and the user specified model parameters. The nonconvex nature of the constrained optimization problem is dealt with by transforming the problem into a difference-of-convex optimization problem, which is then handled by the sequential convex programming strategy. Numerical simulation examples show that the proposed identification method is more robust than the classical prediction-error method initialized by random initial values in converging to local minima, but at the cost of heavier computational burden.

On the Cramér–Rao Bound of Power System Electromechanical Mode Meters

In this paper, an expression for the Cramer–Rao bound (CRB) on the frequency and damping of electromechanical modes is derived. This provides an invaluable tool when documenting the performance capabilities of mode meter algorithms, as the CRB is used as a benchmark to which mode meter variance may be compared. It is shown that the derived CRB expression is supported by several well-known mode estimation phenomena, and it is numerically validated using the asymptotically efficient Prediction Error Method (PEM) on Monte Carlo simulations of an autoregressive moving average (ARMA) model. Finally, a practical use case is given, in which the CRB on the frequency and damping of an inter-area mode from the miniWECC system is used to compare the performance of several well-known mode meters in a study of how sample size affects accuracy.

Dynamic Error Prediction Method of Simulation Turntable Based on ARMA-NN Model

The dynamic error correction of simulation turntable is an importance way to improve the turntable’s accuracy and reliability in the process of simulation. In this paper, an error modelling and prediction method combining ARMA (autoregressive moving average) model and NN (neural network) is proposed. In this method, an AIC criterion is used to determine the order of ARMA model, which can solve the problem to confirm the input and output variables of BP (back propagation) network. The dynamic error of simulation turntable is predicted and corrected online by this ARMA-NN model to get better performance. The validity of the method is illustrated by MATLAB simulation.

A new iterative identification method for damping control of power system in multi-interference

In this paper, we consider the closed-loop model of a power system in a multi-interference environment. For a multi-interference power system, the closed-loop identification is a difficult task. Yet, the model identification error can degrade the effect of the damping control. This could lead to instability of the power grid. Thus, for the closed-loop identification, we propose an iterative online identification algorithm based on the recursive least squares method and the v-gap distance. The convergence of the algorithm is proved by using direct method. The proposed algorithm is applied to the New England system, for which the results obtained are compared with those obtained using the prediction error method and the Runge-Kutta method. From the simulation study being carried out on the IEEE 39-bus New England system, we observe that by using the iterative identification algorithm proposed in this paper, the output response time is reduced by about half when compared with those obtained by using the prediction error method and the Runge-Kutta method. Also, the number of oscillations in the output response is less. These clearly indicate that the algorithm proposed can effectively suppress low frequency oscillation. As for the amplitudes of the output responses produced by the three methods, they are basically the same.

Adaptive feedback cancellation with prediction error method and howling suppression in train public address system

Train public address (PA) system is an important component of Passenger Information System. Acoustic feedback is a well-known problem in public address systems. It will cause howling under certain conditions, which can severely degrade sound quality and limit the maximum allowable amplification of the PA systems. The general adaptive feedback cancellation (AFC) algorithms lead to a biased estimation because of the correlation between source and feedback signals. In order to solve the problem and achieve both fast convergence and low steady-state misalignment, a novel variable step-size improved proportionate affine projection algorithm (IPAPA) based on mixed error cost function with prediction error method (PEM) and howling suppression is proposed in this paper. The experimental results demonstrate the effectiveness of the proposed algorithm.

Defect Prediction and Dimension Reduction Methods for Achieving Better Software Quality

In quality of software, a fault discovery course is anticipated; intended to recover the taking up of various methods using cluster classifiers. Initially the classifiers are qualified on software record and then utilized to forecast if a forthcoming transformation originates a defect. Shortcomings of previous classifier based error prediction methods are inadequate presentation for realistic utilization and slow-moving forecast times due to a huge number of learned machine characteristics. Feature selection is a procedure in choosing a subset of pertinent characteristics so that the eminence of forecast replica can be enhanced. So that prediction recital of grouping techniques will be enhanced or sustained, whereas learning instance is considerably abridged. This effort commences by presenting a general idea of the datasets for error prediction, and then features a novel procedure for feature assortment by means of wrapper methods namely Fuzzy Neural Network (FNN) and Kernel Based Support Vector Machine (KSVM). The features chosen from FNN and KSVM are measured as significant characters. This effort examines numerous feature selection wrapper methods that are normally appropriate to grouping based error prediction. The system castoffs not as much of significant characters until optimal grouping recital are attained. The whole number of characters utilized for guidance is considerably reduced, frequently to lower than 15% of the unique. The general performance metrics is make used to estimate grouping systems such as accurateness, Recall, Precision, and F-Measure. It demonstrates that the anticipated Hybrid Hierarchical K-Centers (HHKC) grouping executes enhanced software quality compared to conventional grouping methods.

Stable spline identification of linear systems under missing data

A different route to identification of time-invariant linear systems has been recently proposed which does not require committing to a specific parametric model structure. Impulse responses are described in a nonparametric Bayesian framework as zero-mean Gaussian processes. Their covariances are given by the so-called stable spline kernels encoding information on regularity and BIBO stability. In this paper, we demonstrate that these kernels also lead to a new family of radial basis functions kernels suitable to model system components subject to disturbances given by filtered white noise. This novel class, in cooperation with the stable spline kernels, paves the way to a new approach to solve missing data problems in both discrete and continuous-time settings. Numerical experiments show that the new technique may return models more predictive than those obtained by standard parametric Prediction Error Methods, also when these latter exploit the full data set.

Particle filtering‐based recursive identification for controlled auto‐regressive systems with quantised output

Recursive prediction error method is one of the main tools for analysis of controlled auto-regressive systems with quantised output. In this study, a recursive identification algorithm is proposed based on the auxiliary model principle by modifying the standard stochastic gradient algorithm. To improve the convergence performance of the algorithm, a particle filtering technique, which approximates the posterior probability density function with a weighted set of discrete random sampling points is utilised to correct the linear output estimates. It can exclude those invalid particles according to their corresponding weights. The performance of the particle filtering technique-based algorithm is much better than that of the auxiliary model-based one. Finally, results are verified by examples from simulation and engineering.

Model extrapolation to a real-world dataset: evaluation of tacrolimus population pharmacokinetics and drug interaction in pediatric liver transplantation patients

1. Numerous tacrolimus population pharmacokinetic (PPK) models in pediatric liver transplantation patients have been established to define an optimal dose schedule. However, the applicability of extrapolating these PPK models to our clinical center remains unknown. The goals of the present study was to evaluate model external predictiveness and establish a new model applicable to traditional therapeutic drug monitoring data.2. Published PPK models were collected from the literature and assessed using our real-world dataset including 41 pediatric liver transplantation patients via the individual prediction error method. The establishment of a new model was characterized using non-linear mixed-effects modeling.3. Nine published pediatric liver transplantation PPK models were identified, three of which could be applied to our real-world dataset. However, these models were dissatisfactory in terms of individual prediction error and hence, inadequate for extrapolation. Finally, a new model applicable to our real-world dataset was established as follows: CL/F = 22.9 × (WT/70)0.75 × (1 − WZ × 0.264) × (1 − FCZ × 0.338) × (1 + ASPI × 0.281) × (POD/41)0.0486 L/h; V/F = 906 × (WT/70) L. Where WT, WZ, FCZ, ASPI and POD were weight, Wuzhi capsule, fluconazole, aspirin and post-transplantation day, respectively. In conclusion, published models were inadequate for application to our real-world dataset. The present study produced a new model applicable to our real-world study data.