Recursive Least-squares Algorithm Research Articles

Fault-Tolerant Self-Tuning Control for Three-Phase Three-Level T-Type Rectifier

This paper proposes a sensorless self-tuning control algorithm for a three-phase T-type rectifier. The proposed sensorless algorithm consists of three layers including an observer, which estimates grid voltages or currents based on the Kalman filter algorithm (KFA), an online estimator, which estimates the state-space matrix parameters, and a linear quadratic tracker (LQT), which is the main controller in this study. On the other hand, the performance of the LQT depends on the gains that need to be adjusted according to the system parameters, which is a challenge. To overcome this problem, a self-tuning method based on recursive least square algorithm (RLSA) is also proposed to tune the gains of LQT online. An experimental prototype is established, and the results, including the steady-state and dynamic performances, are carried out and presented to validate the effectiveness of the proposed controller.

Robustness Enhanced Predictive Control for Dual Three Phase PMSM with Duty Ratio Modulation and Parameter-Free Solution

The classical model predictive control not only relies on the motor model but also is sensitive to the system parameters. To improve the robustness of the model predictive control system, this article proposes a parameter-free predictive control for a dual three-phase PMSM with duty ratio modulation. First, the free-model theory is employed to reconstruct the prediction model of the motor, of which no parameters are needed. So, the problem of parameter mismatch between the motor and the inverter can be handled, and enhance the robustness of the system as well. Moreover, the ultra-local model is optimized with the forgetting factor recursive least-squares algorithm to improve the identification accuracy of the estimated value. Finally, the deadbeat duty ratio modulation solution is introduced to further improve operational performance while ensuring the robustness of the system. Simulation and experiment verify the feasibility and effectiveness of the proposed algorithm.

Chatter detection for micro milling considering environment noises without the requirement of dominant frequency

Existing chatter detection methods were mainly developed for conventional milling processes, and did not consider the influences of environment noises. Thus, they are not suitable for micro milling, in which the widely used small cutting parameters easily lead to the occurrence of non-negligible noises. This article proposes a new variable forgetting factor recursive least-squares (VFF-RLS) algorithm to filter out the chatter-independent component, which is composed of environment noises and periodic components, for the signals sampled from the micro milling process. It is theoretically found that with the aid of VFF-RLS algorithm, there is almost nothing in the filtered signal for stable cuts, while chatter components will be dominant in the filtered signal for unstable cuts. This important finding confirms that some features can be easily extracted from the filtered signal to directly reflect the stable or unstable machining states without the requirement to measure the system’s dominant frequency, which is necessary for some existing methods to obtain the frequency band where chatter vibrations appear. Subsequently, a streaming feature selection considering feature interaction (SFS-FI) method is established to select optimal features and remove irrelevant and redundant features. Then, a chatter detection model is developed based on the selected features. Finally, a series of micro milling tests with various axial depths of cut and spindle speeds prove that the proposed model can accurately identify the cutting state, even for slight chatter and stable cuts with small little depths of cut, which are more easily disturbed by environment noises. Results confirm that the detection accuracy is larger than 99 %, and this fact means that the proposed method is effective and practical for detecting chatter occurring in micro milling processes.

Robust Adaptive Control of Hypersonic Flight Vehicle With Aero-Servo-Elastic Effect

This paper investigates the notch filter based robust adaptive control for the longitudinal dynamics of flexible hyper- sonic flight vehicle using finite-time design and online estimation. Considering the aero-servo-elastic effect caused by the elastic vibration at sensor position, the recursive least-square algorithm is employed to track the natural frequencies of the flexible modes, which then be used as the center frequencies for the cascade-type notch filter. Based on the filtered signal, the robust adaptive control is studied where the neural network is used to handle aerodynamics uncertainty and the disturbance observer is employed to compensate flexible coupling. The prediction error is constructed for the update laws while the nonlinear function is further developed to achieve the finite-time tracking. The uniformly ultimately bounded stability is guaranteed under the proposed approach. The effectiveness of the design is illustrated through the simulation study.

An Improvement of DV-Hop Localization Algorithm Based on Cyclotomic Method in Wireless Sensor Networks

Location information is one of the crucial and essential elements for monitoring data in wireless sensor networks. The distance vector-hop (DV-Hop) localization algorithm is of practical importance in improving its localization performance. To achieve global optimization, a DV-Hop algorithm based on the cyclotomic method and weighted normalization, also known as CMWN-DV-Hop, is nominated in this paper. Therefore, the segmentation and weighting factors are introduced and normalized. The weighted recursive least-squares (WRLS) algorithm is chosen to compute the coordinates of the unknown nodes. The effects of various factors on this algorithm are tested, including the number of nodes, the anchor node ratio, and the communication radius. The simulation results show that the proposed algorithm has a super performance in reducing the localization error.

Cooperative Filtering and Parameter Identification for Advection–Diffusion Processes Using a Mobile Sensor Network

This article presents an online parameter identification scheme for advection–diffusion processes using data collected by a mobile sensor network. The advection–diffusion equation is incorporated into the information dynamics associated with the trajectories of the mobile sensors. A constrained cooperative Kalman filter is developed to provide estimates of the field values and gradients along the trajectories of the mobile sensors so that the temporal variations in the field values can be estimated. This leads to a co-design scheme for state estimation and parameter identification for advection–diffusion processes that is different from comparable schemes using sensors installed at fixed spatial locations. Using state estimates from the constrained cooperative Kalman filter, a recursive least-square (RLS) algorithm is designed to estimate unknown model parameters of the advection–diffusion processes. Theoretical justifications are provided for the convergence of the proposed cooperative Kalman filter by deriving a set of sufficient conditions regarding the formation shape and the motion of the mobile sensor network. Simulation and experimental results show satisfactory performance and demonstrate the robustness of the algorithm under realistic uncertainties and disturbances.

Path Tracking Control of Intelligent Vehicles Considering Multi-Nonlinear Characteristics for Dual-Motor Autonomous Steering System

In the path tracking control of intelligent vehicles, the traditional linear control method is prone to high tracking errors for uncertain parameters of the steering transmission system and road conditions. Therefore, considering the mechanical friction in the dual-motor autonomous steering system and the nonlinearity of tires, this paper proposes a path tracking control strategy of intelligent vehicles for the dual-motor autonomous steering system that considers nonlinear characteristics. First, a dual-motor autonomous steering system considering mechanical friction and the variation of tire cornering stiffness under different tire–road friction coefficients was established based on the structure of an autonomous steering system. Second, a tire–road friction coefficient estimator was designed based on a PSO-LSTM neural network. The tire cornering stiffness under different tire–road friction coefficients was estimated through the recursive least-square algorithm. Then, the control strategy of the dual-motor autonomous steering system was designed by combining the LQR path tracking controller with the adaptive sliding mode control strategy based on field-oriented control. Here, mechanical friction and the variation of tire cornering stiffness were considered. Finally, simulation and HiL tests validated the method proposed in this paper. The results show that the proposed control strategy significantly improves the tracking accuracy and performance of the dual-motor autonomous steering system for intelligent vehicles.

Developing a New Filtered-X Recursive Least Squares Adaptive Algorithm Based on a Robust Objective Function for Impulsive Active Noise Control Systems

It is well-known that performance of the classical algorithms for active noise control (ANC) systems severely degrades when implemented for controlling the impulsive sources. The objective of this paper is to propose a new recursive least squares (RLS) algorithm (and its variant) for being implemented in the framework of ANC systems. The proposed RLS-based adaptive algorithm employs an objective function designed to achieve robustness against the impulse type sources. The derivation of the algorithm is quite straightforward; however, a few modifications have been incorporated to address the application at hand. In order to improve upon the numerical stability issue of RLS-based adaptation, it is suggested to employ smoothing while updating the inverse correlation matrix. Furthermore, it is proposed to introduce a step size in the update equation of the adaptive algorithm. This results in the fixed step-size modified filtered-x (MFx) robust RLS (FSS-MFxRRLS) algorithm. As expected, a fixed value step size results in a trade-off situation for convergence speed and steady-state misalignment. In order to address this issue of a trade-off situation, the idea of a convex combined step size (CCSS) is introduced into the adaptive procedure to develop the CCSS-MFxRRLS algorithm. When the ANC is started, the CCSS strategy (automatically) selects a large-valued step size to achieve a fast initial convergence. As the ANC system converges at the steady-state, the CCSS is automatically tuned to a small value which improves the steady-state performance of the proposed CCSS-MFxRRLS algorithm. Extensive simulations have been designed to mimic many scenarios for practical applications of ANC for impulsive sources. The simulation results demonstrate that the proposed CCSS-MFxRRLS algorithm is very effective in many practical scenarios involving ANC of impulsive sources.

Channel temporal correlation-based optimization method for imperfect underwater acoustic channel state information

The rapid time variations and large channel estimation errors in underwater acoustic (UWA) channels mean that transmitters for adaptive resource allocation quickly become outdated and provide inaccurate channel state information (CSI). This results in poor resource allocation efficiency. To address this issue, this paper proposes an optimization approach for imperfect CSI based on a Gauss–Markov model and the per-subcarrier channel temporal correlation (PSCTC) factor. The proposed scheme is applicable to downlink UWA orthogonal frequency division multiple access systems. The proposed PSCTC factors are measured, and their long-term stability is verified using data recorded in real-world sea tests. Simulation and experimental results show that the optimized CSI effectively mitigates the effects of the temporal variability of UWA channels. It demonstrates that the resource allocation scheme using optimized CSI achieves a higher effective throughput and a lower bit error rate than both imperfect CSI and the CSI predicted by the recursive least-squares (RLS) algorithm.

Low-Complexity Data-Reuse RLS Algorithm for Stereophonic Acoustic Echo Cancellation

Stereophonic audio devices employ two loudspeakers and two microphones in order to create a bidirectional sound effect. In this context, the stereophonic acoustic echo cancellation (SAEC) setup requires the estimation of four echo paths, each one corresponding to a loudspeaker-to-microphone pair. The widely linear (WL) model was proposed in recent literature in order to simplify the handling of the SAEC mathematical model. Moreover, low complexity recursive least- squares (RLS) adaptive algorithms were developed within the WL framework and successfully tested for SAEC scenarios. This paper proposes to apply a data-reuse (DR) approach for the combination between the RLS algorithm and the dichotomous coordinate descent (DCD) iterative method. The resulting WL-DR-RLS-DCD algorithm inherits the convergence properties of the RLS family and requires an amount of mathematical operations attractive for practical implementations. Simulation results show that the DR approach improves the tracking capabilities of the RLS-DCD algorithm, with an acceptable surplus in terms of computational workload.

Data-Driven Adaptive Steady-State-Integral-Derivative Controller Using Recursive Least Squares With Performance Conditions

This paper presents a data-driven adaptive steady state-integral-derivative (SS-ID) control algorithm that uses gradient descent and recursive least squares (RLS) with a forgetting factor. A simplified first-order differential equation of the control system was designed and its parameters were estimated in real-time using the RLS algorithm. The steady-state control input for target-state tracking was derived based on the estimated parameters and steady-state performance conditions. The gradient of the integrated control error to the gain was estimated based on the least-squares method, using the saved past error and gain data in a finite sliding window to determine the control input. The integral gain was adapted based on the gradient descent method, using the estimated gradient, integrated error, and adaptation rate. Simplified control error dynamics were designed, and their parameter was estimated using the RLS algorithm. The derivative control gain can be adapted in real time using the estimated parameters from the simplified control error dynamics and time constant-based performance conditions. The proposed controller was designed in the MATLAB/Simulink environment. A performance evaluation was conducted under various scenarios using a DC motor simulation model and an actual test platform equipped with an optical encoder.

Validation of Parallel Distributed Adaptive Signal Processing (PDASP) Framework through Processing-Inefficient Low-Cost Platforms

The computational complexity of the multiple-input and multiple-output (MIMO) based least square algorithm is very high and it cannot be run on processing-inefficient low-cost platforms. To overcome complexity-related problems, a parallel distributed adaptive signal processing (PDASP) architecture is proposed, which is a distributed framework used to efficiently run the adaptive filtering algorithms having high computational cost. In this paper, a communication load-balancing procedure is introduced to validate the PDASP architecture using low-cost wireless sensor nodes. The PDASP architecture with the implementation of a multiple-input multiple-output (MIMO) based Recursive Least Square (RLS) algorithm is deployed on the processing-inefficient low-cost wireless sensor nodes to validate the performance of the PDASP architecture in terms of computational cost, processing time, and memory utilization. Furthermore, the processing time and memory utilization provided by the PDASP architecture are compared with sequentially operated RLS-based MIMO channel estimator on 2×2, 3×3, and 4×4 MIMO communication systems. The measurement results show that the sequentially operated MIMO RLS algorithm based on 3×3 and 4×4 MIMO communication systems is unable to work on a single unit; however, these MIMO systems can efficiently be run on the PDASP architecture with reduced memory utilization and processing time.

Rotor Temperature Estimation for Magnetically Suspended Turbo Molecular Pump Based on Flux Linkage Identification

Monitoring rotor temperature is a significant issue for safe operations in magnetically suspended turbo molecular pump (MSTMP). The increase in rotor temperature may cause the irreversible demagnetization of the permanent magnet (PM) and destroy the vacuum environment, eventually affecting the efficiency and security of the MSTMP system. Unfortunately, the direct measurement of the rotor temperature is complicated in practice due to the difficulty of accessing temperature sensors on a rotating shaft. This article proposes a novel rotor temperature estimation method based on the identification of the PM flux linkage. In order to address rank-deficiency in the identification of multiparameters, the resistance is calculated from the measured stator temperature, and two recursive least square (RLS) algorithm segments are combined to identify the inductance and flux linkage. Furthermore, the dynamic factor is introduced into the RLS algorithm to enhance the identification accuracy and convergence rate of the algorithm. The experiment results on the MSTMP test rig, equipped with the infrared temperature measuring module, demonstrate that the identified flux linkage has a good performance for the estimating rotor temperature under different working conditions.

Comparative analysis of features of online numerical methods used for parameter estimation of PMSM

As permanent magnet synchronous motors (PMSM) have high power density, efficiency, good dynamic performance, and small size they are becoming popular in electric vehicle (EV) applications. Control performance and the efficiency of the system get affected due to electrical, mechanical parameters. Parameters value gets affected by voltage source inverter (VSI) non-linearities, temperature and magnetic saturation effects. If exact parameters for particular torque speed requirement are found, the efficiency of system increases. There are various offline and online methods for finding parameters. Offline methods are easy to implement but requires extra setup and estimate parameters in steady state. Because the effects of transient conditions are taken into account during identification, online methods for obtaining real-time data under running conditions are becoming more popular. An overview about online numerical methods to estimate electrical parameters of PMSM is given. It discusses difference between various methods in terms of computational cost, convergence speed, noise and identification error. Choosing of method will be easy using this work. For inductance estimation, the extended Kalman filter (EKF) algorithm has an identification error of 0.24% under temperature effect and -0.3% under VSI non-linearities effect. The identification error for Rs and ψf using the recursive least square (RLS) method is 0.5% and 0.02%, respectively, when temperature is considered. EKF and RLS algorithms are proposed.

Intelligent prediction for digging load of hydraulic excavators based on RBF neural network

Traditional modeling methods for digging load of excavators are often computationally expensive and require prior knowledge of soil parameters, which severely limits their engineering applications. According to the digging load characteristics in typical digging tasks, this paper presents an intelligent prediction method for digging load based on radial basis function (RBF) neural networks. The recursive least-squares (RLS) algorithm is used for weights updating. Back propagation neural network (BPNN), coupled discrete element method (DEM) and multi-body dynamics (MBD) simulation, and analytical model are applied for comparative studies. The simulation results illustrate that the RBF neural network model outperforms other comparative models in terms of prediction accuracy and computational cost. The hardware-in-loop (HIL) experiments are conducted to validate the proposed approach. Experimental results demonstrate that the error in the dynamic behavior of the excavator under the predicted digging load is less than 7%. This paper lays the foundation for digging load prediction in intelligent excavators.

A digital twin-based framework for multi-element seismic hybrid simulation of structures

This paper proposes a digital twin-based multi-element hybrid simulation (DMHS) framework to predict the nonlinear cyclic response of structural components (digital twin), e.g., seismic fuses, that are not physically tested due to laboratory limitations by leveraging the experimental test data collected from the physical test specimen (physical twin) during hybrid simulation. This data-based simulation approach can address biased results of hybrid simulation of structures that contain multiple critical components while improving the efficiency of the seismic hybrid simulation. The digital twin is trained in two phases: (1) passive (initial) training phase using past experimental test data before the hybrid simulation starts, and (2) recursive model updating phase using the active (real-time) data produced by the physical specimen during hybrid simulation. The passive training is achieved using the Prandtl–Ishlinskii (PI) hysteresis model combined with the sparse identification technique, while the recursive least-squares algorithm is used in the second phase as the model updating scheme. In particular, the sparse identification technique facilitates the selection of the optimal number of hysteretic model parameters in the passive training phase, which are then tuned in the model updating phase. The architecture of the proposed DMHS framework is first presented, followed by digital twin training steps. The application of the proposed DMHS is then demonstrated, and its simulation accuracy is assessed through virtual hybrid simulation of a two-storey steel buckling-restrained braced frame, which consists of a digital twin (second-storey brace) and a virtual experimental specimen (first-storey brace) integrated into the numerical model of the structure that is subjected to a set of earthquake ground motion accelerations. The results obtained from the verification study serve to validate the proposed architecture of the DMHS framework and evaluate the accuracy and efficiency of this technique in simulating the nonlinear seismic response of structural systems.

New adaptive robust [formula omitted] control of smart structures using synchrosqueezed wavelet transform and recursive least-squares algorithm

Two kinds of uncertainties, one due to the dynamic earthquake loads with a wide frequency band and the other due to structural parameters exist in large and complex real-life structures. Most existing control algorithms consider only one of them, resulting in difficulty to guarantee necessary control performance for large complex structures, such as better vibration suppression on structural peak response and robustness performance. Considering the two uncertainties simultaneously, in this paper, a new adaptive robust H∞ control methodology is presented for vibration control of structures through adroit integration of synchrosqueezed wavelet transform (SWT) and recursive least-squares (RLS) algorithm. The robust H∞ control is more effective than the traditional LQR/LQG control in terms of the stability and robustness of the control system. The external excitation signal from ground sensors is filtered by a low-pass filter based on SWT and then inputted into the filtered-x RLS adaptive controller. The effectiveness, accuracy, and computational efficiency of the new adaptive control method is demonstrated using a 76-story wind-excited benchmark super high-rise building structure and a 24-story shear-wall building with an active tuned mass damper (ATMD) system on the top floor. Compared with the existing linear quadratic Gaussian control algorithm, the wavelet-hybrid feedback-least mean square algorithm and the robust H∞ control algorithm, the simulation results show that the control effect and robust performance indexes of the structure are increased by 5%–35% and 5%–25%, respectively, using the new control methodology.

A Heterogeneous Federated Transfer Learning Approach with Extreme Aggregation and Speed

Federated learning (FL) is a data-privacy-preserving, decentralized process that allows local edge devices of smart infrastructures to train a collaborative model independently while keeping data localized. FL algorithms, encompassing a well-structured average of the training parameters (e.g., the weights and biases resulting from training-based stochastic gradient descent variants), are subject to many challenges, namely expensive communication, systems heterogeneity, statistical heterogeneity, and privacy concerns. In this context, our paper targets the four aforementioned challenges while focusing on reducing communication and computational costs by involving recursive least squares (RLS) training rules. Accordingly, to the best of our knowledge, this is the first time that the RLS algorithm is modified to completely accommodate non-independent and identically distributed data (non-IID) for federated transfer learning (FTL). Furthermore, this paper also introduces a newly generated dataset capable of emulating such real conditions and of making data investigation available on ordinary commercial computers with quad-core microprocessors and less need for higher computing hardware. Applications of FTL-RLS on the generated data under different levels of complexity closely related to different levels of cardinality lead to a variety of conclusions supporting its performance for future uses.

Practical Model for Short-Circuit Current Calculation of Photovoltaic Power Station Based on Improved RLS Algorithm

In recent years, with the rapid economic development, the development speed of all walks of life has entered a new level, and the power industry has also developed rapidly. Driven by market demand, China’s power transmission range and power transmission capacity will enter a new level. At the same time, the problems brought about by the development of the power system are equally severe. Due to the large load density in individual areas, the detection of short-circuit current must be improved as an important issue. The purpose of this paper is to study how to improve the practical model of short-circuit current calculation of photovoltaic power plants, so that it can be well applied to the current high-density current detection in China. Therefore, this paper improves the recursive least squares (RLS) algorithm and applies it to the practical model of short-circuit current calculation of photovoltaic power plants and describes the improvement process of the algorithm in detail. At the same time, this paper designs relevant experiments and analysis to count the data of the improved RLS algorithm in the short-circuit current calculation of the actual photovoltaic power station and combines the data of this part to test and analyze the ability of the algorithm. The experimental results in this paper show that the improved RLS algorithm has a very good improvement in the calculation accuracy of the short-circuit current calculation of photovoltaic power plants in the actual model calculation. At the same time, the calculation efficiency is also improved, and the current tracking effect is also improved by 7%.

A Novel Noise Suppression and Artifact Removal Method of Mechanomyography Based on RLS, IGWO-VMD, and CEEMDAN

Mechanomyography (MMG) signals have extensive applications in muscle function assessment and human intention recognition. However, during signal acquisition, MMG signals are easily contaminated by noise and artifacts, which seriously affects the recognition of their characteristics. To address these issues, a novel noise suppression and artifact removal method based on recursive least square (RLS), improved Gray Wolf Optimizer-optimized variable mode decomposition (IGWO-VMD), and complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) is proposed. In this paper, the RLS algorithm is first applied to adaptively filter out the power line interference (PLI). Then, IGWO is designed to select the appropriate VMD parameters and use the VMD to decompose the noisy signal into band-limited intrinsic mode functions (BLIMFs). In addition, the BLIMFs are classified into the low-frequency part and high-frequency part according to the given correlation coefficient (CC) threshold value. The effective components of the low-frequency part are identified by the center frequency. Meanwhile, the high-frequency part is decomposed by CEEMDAN, and its effective components are obtained according to the proposed sample entropy threshold range. Finally, the effective components of the low and high-frequency parts are reconstructed to obtain the denoised signal to realize the extraction of useful signals. Simulation experiment results demonstrate that the proposed method outperforms the classical methods and the designed IGWO-VMD method in terms of denoising performance. The effectiveness of the proposed method is verified through the measured MMG signal experiments. The proposed method not only effectively suppresses noise and artifacts but also overcomes the limitations of VMD and CCEMDAN.