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Digital predistortion and nonlinear behavioral modeling of power amplifiers (PA) have been the subject of intensive research in the time domain (TD), in contrast with the limited number of works conducted in the frequency domain (FD). However, the adoption of orthogonal frequency division multiplexing (OFDM) as a prevalent modulation scheme in current wireless communication standards provides a promising avenue for employing an FD approach. In this work, a procedure to model nonlinear distortion in wireless OFDM systems in the frequency domain is demonstrated for general model structures based on a sparse Bayesian learning (SBL) algorithm to identify a reduced set of regressors capable of an efficient and accurate prediction. The FD-SBL algorithm is proposed to first identify the active FD regressors and estimate the coefficients of the PA model using a given symbol, and then, the coefficients are employed to predict the distortion of successive OFDM symbols. The performance of this proposed FD-SBL with a validation NMSE of −47 dB for a signal of 30 MHz bandwidth is comparable to −46.6 dB of the previously proposed implementation of the TD-SBL. In terms of execution time, the TD-SBL fails due to excessive processing time and numerical problems for a 100 MHz bandwidth signal, whereas the FD-SBL yields an adequate validation NMSE of −38.6 dB.

The identification of nonlinear terms existing in the dynamic model of real-world mechanical systems such as robotic manipulators is a challenging modeling problem. The main aim of this research is not only to identify the unknown parameters of the nonlinear terms but also to verify their existence in the model. Generally, if the structure of the model is provided, the parameters of the nonlinear terms can be identified using different numerical approaches or evolutionary algorithms. However, finding a non-zero coefficient does not guarantee the existence of the nonlinear term or vice versa. Therefore, in this study, a meticulous investigation and statistical verification are carried out to ensure the reliability of the identification process. First, the simulation data are generated using the white-box model of a direct current motor that includes some of the nonlinear terms. Second, the particle swarm optimization (PSO) algorithm is applied to identify the unknown parameters of the model among many possible configurations. Then, to evaluate the results of the algorithm, statistical hypothesis and confidence interval tests are implemented. Finally, the reliability of the PSO algorithm is investigated using experimental data acquired from the UR5 manipulator. To compare the results of the PSO algorithm, the nonlinear least squares errors (NLSE) estimation algorithm is applied to identify the unknown parameters of the nonlinear models. The result shows that the PSO algorithm has higher identification accuracy than the NLSE estimation algorithm, and the model with identified parameters using the PSO algorithm accurately calculates the output torques of the joints of the manipulator.

This paper presents an example of solving the parameter identification problem in the case of a robot with two degrees of freedom. In this study, a weighted recursive least squares algorithm was generalised to a case of nonlinear parameterisation in which the identified parameters did not satisfy the linear model. The generalisation involved linearising the model in the neighbourhood of current values of the parameter estimates. It was assumed that the estimates were updated every N steps of signal sampling. This method of identification can be applied whenever the parameters concerning a model need to be determined at the time of measurement. This is particularly useful in adaptive control when the plant parameters vary over time.

The operation of the power amplifier (PA) in wireless transmitters presents a trade-off between linearity and power efficiency, being more efficient when the device exhibits the highest nonlinearity. Its modeling and linearization performance depend on the quality of the underlying Volterra models that are characterized by the presence of relevant terms amongst the enormous amount of regressors that these models generate. The presence of PA mechanisms that generate an internal state variable motivates the adoption of a bivariate Volterra series perspective with the aim of enhancing modeling capabilities through the inclussion of beneficial terms. In this paper, the conventional Volterra-based models are enhanced by the addition of terms, including cross products of the input signal and the new internal variable. The bivariate versions of the general full Volterra (FV) model and one of its pruned versions, referred to as the circuit-knowledge based Volterra (CKV) model, are derived by considering the signal envelope as the internal variable and applying the proposed methodology to the univariate models. A comparative assessment of the bivariate models versus their conventional counterparts is experimentally performed for the modeling of two PAs driven by a 30 MHz 5G New Radio signal: a class AB PA and a class J PA. The results for the digital predistortion of the class AB PA under a direct learning architecture reveal the benefits in linearization performance produced by the bivariate CKV model structure compared to that of the univariate CKV model.

This work presents a strategy to upgrade models for power amplifier (PA) behavioral modeling and digital predistortion (DPD). These incomplete structures are the consequence of nonlinear order and memory depth model truncation with the purpose of reducing the demand of the limited computational resources available in standard processors. On the other hand, the alternative use of model structures pruned a priori does not guarantee that every significant term is included. To improve the limited performance of an incomplete model, a general procedure to augment its structure by incorporating significant terms is demonstrated. The sparse nature of the problem allows a successive search incorporating additional terms with higher nonlinear order and memory depth. This approach is investigated in the modeling and linearization of a commercial class AB PA operating at a compression point of about 6 dB, and a class J PA operating near saturation. Results highlight the capabilities of this upgrading procedure in the improvement of linearization capabilities of DPDs.

The article presents an identification method of the model of the ball-and-race coal mill motor power signal with the use of machine learning techniques. The stages of preparing training data for model parameters identification purposes are described, as well as these aimed at verifying the quality of the evaluated model. In order to meet the tasks of machine learning, additive regression model was applied. Identification of the additive model parameters was performed on the basis of iterative backfitting algorithm combined with nonparametric estimation techniques. The proposed models have predictive nature and are aimed at simulation of the motor power signal of a coal mill during its regular operation, startup and shutdown. A comparative analysis has been performed of the models structured differently in terms of identification quality and sensitivity to the existence of an exemplary disturbance in the form of overhangs in the coal bunker. Tests carried out on the basis of real measuring data registered in the Polish power unit with a capacity of 200 MW confirm the effectiveness of the method.

The spline adaptive filter (SAF) is recently proposed to identify wiener-type nonlinear systems, which consists of an infinite impulse response filter followed by an adaptable look-up table and interpolated by a local low-order polynomial spline curve. To improve the performance of magnetostrictive actuator (MA), SAF is introduced to identify the hysteresis model of MA in this paper. In addition, a direct approach that is convenient to implement to derive the inverse model directly from experimental data is proposed to decrease the difficulty of obtaining the accurate inverse model. In order to improve the identification accuracy, a variable order fractional-order least mean square (VO-FLMS) algorithm is formulated for SAF by exploiting the fractional calculus concepts in parameters adaptation mechanism. VO-FLMS dynamically adapts the order of the fractional derivative based on the error power to achieve faster convergence rate with smaller steady-state error than least mean square algorithm and modified fractional-order least mean square algorithm. Simulation results confirm the effectiveness of SAF with VO-FLMS for nonlinear system identification. In particular, VO-FLMS can adapt nonlinearity better than other compared algorithms. Moreover, the hysteresis model and direct inverse model of MA can be precisely identified online by the proposed method in the experiments.

Aiming at the mismatch between heat supply and demand of heating system, a nonlinear model identification control algorithm based on improved neural network for short-term heat load prediction of heat supply network is proposed by using the characteristics that heat load and temperature of heating system will not change dramatically in a short period of time By using MATLAB simulation, short-term heat load rolling prediction is realized. From the experimental results, this algorithm is better than the traditional RBF neural network in the prediction accuracy, and can accurately predict the trend of heat load.

The triple inverted pendulum is a nonlinear, dynamic and unsteady system. The traditional control methods of triple inverted pendulum have problems of limited control accuracy, slow responding. This kind of pendulum system is difficult to control due to the inherent instability, nonlinear behavior and difficultly in establishing a precise mathematical model. In addition, the back-propagation (BP) algorithm has the shortage of easy trapped in local minimum. The triple inverted pendulum control based on GA–PIDNN is proposed. The PID neural network (PIDNN) is a new kind of feedforward multi-layer network. Besides multi-layer forward networks traditional merit, such as approach the ability proceed together the calculation nonlinear transformation, its middle layer has the proportional (P) integral, (I) derivative, (D) dynamic characteristic. Genetic algorithm (GA) has good parallel design structure and characteristics of global optimization. The nonlinear identification model is established, and controller is designed via GA–PIDNN based on the combination of the merits GA and PIDNN in the research of triple inverted pendulum. In simulation, through the comparative study of GA–PIDNN and PIDNN optimized by BP (BP–PIDNN), simulations results show that GA is more accurate and effective.

The wheel–rail adhesion is one of the key factors limiting the traction performance of railway vehicles. To meet the adhesion optimization needs and rapidly obtain wheel–rail creep characteristics under specific operating conditions, an engineering identification method for wheel–rail adhesion characteristics based on a nonlinear model is proposed. The proposed method, built upon the traditional Teaching-Learning-Based Optimization (TLBO) algorithm, has been adapted to the specific nature of nonlinear wheel–rail adhesion model parameters identification, enhancing both the search speed in the early stages and the search accuracy in the later stages of the algorithm. The proposed identification algorithm is validated using experimental data from the South African 22E dual-flow locomotive. The validation results demonstrate that the proposed identification algorithm can obtain a nonlinear wheel–rail adhesion characteristics model with an average adhesion coefficient error of around 0.01 within 50 iteration steps. These validation results indicate promising prospects for the engineering practice of the proposed algorithm.