Least-squares Parameter Estimation Research Articles

Research on Efficiency of Permanent-Magnet Synchronous Motor Based on Adaptive Algorithm of Fuzzy Control

In today’s world, energy is undoubtedly one of the most significant problems. As the global electricity consumption continues to increase, electric motors, which are widely used as power devices, account for an increasingly prominent proportion of the energy consumed. Motors now consume about 45% of the total electricity in the world (60% in China); therefore, improving motor efficiency has become an important way to achieve carbon emission reduction and sustainable development. The aim of this research was to devise a new strategy to reduce CO2 emissions other than by building green power factories, because even the building of green power factories produces a great deal of CO2 emissions, and improving motor efficiency to reduce CO2 emissions could contribute to sustainable development worldwide. However, the improvement of motor efficiency encounters challenges, such as nonlinearity and disturbances, which affect the motor performance and energy efficiency. To address this issue, this paper proposes a control algorithm for permanent-magnet synchronous motors (PMSMs) that is highly efficient and would be most widely used based on a fuzzy control adaptive forgetting factor. It aims to enhance the efficiency and accuracy of the online parameter estimation for the PMSM flux linkage, thereby achieving more precise and energy-efficient motor control. Firstly, the recursive least-squares parameter estimation algorithm is used to identify the parameters of the PMSM. This ensures that the parameter estimation values can be dynamically updated with data changes, adapting to the time-varying parameters. Secondly, the Padé approximation method is adopted, which is a method that does not depend on the motor hardware, to improve the accuracy of the linearized model of the motor. Finally, a control algorithm based on the fuzzy control adaptive forgetting factor algorithm is constructed on a physical experimental platform. A comparison of these results proves that the control technology under this algorithm provides a new energy-saving control strategy that can estimate the motor flux linkage parameters more accurately, help to reduce energy consumption, promote the use of clean energy, and achieve sustainable performance optimization.

Monitoring of recently sea level changes on the coast of New Zealand using XTRACK coastal altimetry and tide gauge data

The rise in sea level along the coasts of New Zealand has accelerated in recent decades due to the impact of climate change. Determining the effects of these changes on the coastal regions is critical for their sustainability. In order to gain insight into these impacts, the present study aimed to analyze sea level changes using satellite altimetry and tide gauge data from 11 tide gauge stations along the New Zealand coast between 1993 and 2022, as well as XTRACK data processed with the coastal altimetry approach to minimize the effects of classical altimetry near coasts. The least-squares parameter estimation method was used to analyze the data and determine annual and semi-annual seasonal effects. The results showed that a significant increase have been observed in sea level of 3.8+0.5 mm/yr along the coast of New Zealand from 1993 to 2022 using coastal altimetry data. The results of this study demonstrate the importance of closely monitoring the impacts of sea level rise on the coastal regions of New Zealand to ensure their long-term sustainability. The results also highlight the utility of using multiple data sources and methods to provide a comprehensive understanding of these changes.

Mapping site index in coniferous forests using bi-temporal airborne laser scanning data and field data from the Swedish national forest inventory

Recent advancements in remote sensing of forests have demonstrated the capabilities of three-dimensional data acquired by airborne laser scanning (ALS) and, consequently, have become an integral part of enhanced forest inventories in Northern Europe. In Sweden, the first national laser scanning revolutionised forest management planning through low-cost production of large-scale and spatially explicit maps of forest attributes such as basal area, volume, and biomass, compared to the earlier practice based on field survey data. A second scanning at the national level was launched in 2019, and it provides conditions for the estimation of height growth and site index. Accurate and up-to-date information about site productivity is relevant for planning silvicultural treatments and for the prognosis of forest status and development over time. In this study, we explored the potential of bi-temporal ALS data and other auxiliary information to predict and map site productivity by site index according to site properties (SIS) of Norway spruce (Picea abies (L.) Karst) and Scots pine (Pinus sylvestris L.) in even-aged stands in Sweden. We linked ground survey data of SIS from more than 11,500 plots of the Swedish National Forest Inventory (NFI) to bi-temporal ALS data to predict and map site index using an area-based method and two regression modelling strategies: (1) a multiple linear regression (MLR) model with an ordinary least-squares parameter estimation method, and (2) a non-parametric random forests (RF) model optimised for hyper-parameter tuning. For model development, permanent plots were used, whereas the validation was done on the temporary plots of the Swedish NFI and an independent stand-level dataset. Species-specific models were developed, and the root mean square error (RMSE) metric was used to quantify the residual variability around model predictions. For both species, the MLR model gave precise and accurate estimates of SIS. The RMSE for SIS predictions was in the range of 1.96 – 2.11 m, and the relative RMSE was less than 10 % (7.68 – 9.49 %) of the reference mean value. Final predictors of site index include metrics of 90th percentile height and annual increment in the 95th percentile height, altitude, distance to coast, and soil moisture. Country-wide maps of SIS and the corresponding pixel-level prediction errors at a spatial resolution of 12.5 m grid cells were produced for the two species. Independent validations show the site index maps are suitable for use in operational forest management planning in Sweden.

Remaining Useful Life Prediction of PV Systems Under Dynamic Environmental Conditions

Solar power is one of the least carbon-intensive approaches for electricity generation, and so photovoltaic (PV) systems have great potential as a low-carbon technology during their long lifecycle. Consequently, remaining useful life (RUL) prediction is critical for the prognostics and health management of PV systems, potentially preventing unexpected failure and maintenance due to PV degradation. One of the major root causes of PV degradation is the dynamic environmental conditions associated with PV outdoor operation. However, RUL prediction under such dynamic environmental conditions remains challenging. This article presents a semiparametric prognostic framework for PV systems under dynamic environmental conditions. The quantitative relationship between PV degradation and environmental conditions is established to integrate environmental condition information into RUL prediction, combining the cumulative damage model with multivariate Bernstein bases. The block bootstrap method is used to estimate future environmental conditions as inputs for RUL prediction. The least-squares estimators of the model parameters can be obtained through the block coordinate descent method. Finally, applications to field data of Australian PV systems are presented to demonstrate the effectiveness of the proposed method. The proposed framework is applicable to most PV technologies.

Adaptive Two-Degrees-of-Freedom Current Control for Solenoids: Theoretical Investigation and Practical Application

In this article, an adaptive two-degrees-of-freedom current control algorithm for solenoids is presented comprising an adaptive pole placement controller in combination with a regularized least-squares parameter estimation law. An additional adaptive feedforward controller takes advantage of the estimated plant parameters to further enhance the tracking performance. The stability of the overall closed-loop system is rigorously proven. The proposed solution differs from existing approaches by the adaptive feedforward controller and the way the parameter estimation is performed. The control concept is applied with the same controller parametrization to three solenoids from different applications, with substantially differing parameters. The experimental results show high tracking performance and fast parameter convergence even with poor initial estimates and despite the nonlinear dependence of the inductance on the current and position. The experimental results are also compared to two benchmark control design paradigms known from the literature, i.e. a second-order sliding mode controller and a nonlinear model reference adaptive control solution, which are both outperformed by the proposed controller.

Composite model-reference adaptive control with least-squares estimator

This work presents a new design of a composite model-reference adaptive control (MRAC) with a least-squares parameter estimator. The objective of the design is to preserve the remarkable transient adaptation characteristic obtained by a modified MRAC algorithm recently introduced and, at the same time, enjoy the superior parameter convergence performance of a least-squares estimator. The algorithm employs two different estimators for the same controller parameter, one updated by a gradient law driven by the tracking error and the other updated by a least-squares algorithm driven by a prediction error. In this way, the performance of each one is kept unchanged. The existence of a Lyapunov function assures the global uniform stability of the proposed composite adaptive scheme and simulation results confirm and illustrate its properties.

Adaptive boundary observer for ARZ traffic flow model with domain and boundary uncertainties

This paper studies the problem of the adaptive boundary observer design for the Aw-Rascle-Zhang (ARZ) traffic flow model, which is subject to both relaxation time uncertainty in the domain and boundary input disturbance. The boundary input disturbance comes from merging vehicles’ velocities at the downstream on-ramp, and we scale the disturbance by a low-pass filter based on the ordinary differential equation (ODE). Then, the ARZ model with the domain uncertainty and boundary input disturbance can be linearized to a coupled ODE-PDE system. Based on the swapping transformation, an adaptive boundary observer with least-squares type parameter estimation is designed to estimate the traffic states, the domain uncertainty, and the boundary input disturbance, simultaneously. The exponential convergence conditions w.r.t. the observer feedback gains are given by employing the Lyapunov technique. Finally, the simulation results are presented to illustrate the effectiveness of the designed adaptive boundary observer.

A Method of Reducing Invalid Steering for AUVs Based on a Wave Peak Frequency Tracker

The motion control of autonomous underwater vehicles (AUVs) is affected by waves near the ocean surface or in shallow-water areas. Therefore, to counteract the influence of waves, we need to remove them by designing a filter. The wave peak frequency is important in wave filter design. This paper focuses on the identification of the wave peak frequency using the least-squares parameter estimation algorithm. The input–output expression of the wave disturbance model is derived by eliminating the intermediate variable. Based on the obtained identification model, an auxiliary model-based recursive extended least-squares identification algorithm is developed to estimate the model parameters. The effectiveness of the proposed method is verified with simulated tests of the heading control system of an AUV. The simulation results demonstrate that the proposed method is effective for the identification of the wave peak frequency, and an observer with a wave peak frequency tracker can significantly reduce invalid steering.

Verifying the Effect of Wingtip Propellers on Drag Through In-Flight Measurements

This work presents the effect of wingtip-mounted propellers on the aircraft drag polar, identified from in-flight measurements. In previous wind-tunnel experiments, significant reductions in drag and an increase in propulsive efficiency through interaction between induced flow by the wingtip-mounted propellers and the flowfield of the wing itself have been claimed. So far, however, these effects have never been verified in actual flight. That gap is closed here by presenting the results of in-flight measurements. A 33.3% scaled version of the manned, electric e-Genius aircraft has been fitted with a wingtip propulsion system and an elaborate measurement system, which allows quantifying the aforementioned effects. The drag polar is deduced through weighted least-squares parameter estimation for different settings and configurations of the wingtip propellers. The findings are compared to results from previous wind-tunnel experiments. The paper further discusses secondary effects that were observed during the flight tests and their influence on the general potential of wingtip propulsion.

Ordinary least squares estimation of parameters of linear model

This research article primarily focuses on the method of ordinary least squares estimation of parameters of linear model. Here an innovative proof of Gauss-Markoff theorem for linear estimation has been presented. An extensive discussion in evaluating Best Linear Unbiased Estimator (BLUE) of a linear parametric function of the classical linear model is made by using the Gauss-Markoff theorem. Furthermore the importance of mean vector and covariance matrix of BLUE is discussed. Moreover generalized Gauss-Markoff theorem for linear estimation, properties of OLS estimators and problems of linear model by violating the assumptions are extensively discussed.

Robust multi-stage model-based design of optimal experiments for nonlinear estimation

We study approaches to the robust model-based design of experiments in the context of maximum-likelihood estimation. These approaches provide robustification of model-based methodologies for the design of optimal experiments by accounting for the effect of the parametric uncertainty. We study the problem of robust optimal design of experiments in the framework of nonlinear least-squares parameter estimation using linearized confidence regions. We investigate several well-known robustification frameworks in this respect and propose a novel methodology based on multi-stage robust optimization. The proposed methodology aims at problems, where the experiments are designed sequentially with a possibility of re-estimation in-between the experiments. The multi-stage formalism aids in identifying experiments that are better conducted in the early phase of experimentation, where parameter knowledge is poor. We demonstrate the findings and effectiveness of the proposed methodology using four case studies of varying complexity.

Efficiency analysis for quantitative MRI of T1 and T2 relaxometry methods

This study presents a comparison of quantitative MRI methods based on an efficiency metric that quantifies their intrinsic ability to extract information about tissue parameters. Under a regime of unbiased parameter estimates, an intrinsic efficiency metric was derived for fully-sampled experiments which can be used to both optimize and compare sequences. Here we optimize and compare several steady-state and transient gradient-echo based qMRI methods, such as magnetic resonance fingerprinting (MRF), for joint and mapping. The impact of undersampling was also evaluated, assuming incoherent aliasing that is treated as noise by parameter estimation. In vivo validation of the efficiency metric was also performed. Transient methods such as MRF can be up to 3.5 times more efficient than steady-state methods, when spatial undersampling is ignored. If incoherent aliasing is treated as noise during least-squares parameter estimation, the efficiency is reduced in proportion to the SNR of the data, with reduction factors of 5 often seen for practical SNR levels. In vivo validation showed a very good agreement between the theoretical and experimentally predicted efficiency. This work presents and validates an efficiency metric to optimize and compare the performance of qMRI methods. Transient methods were found to be intrinsically more efficient than steady-state methods, however the effect of spatial undersampling can significantly erode this advantage.

A mathematical model of the dynamics of lymphatic filariasis in Caraga Region, the Philippines.

Despite being one of the first countries to implement mass drug administration (MDA) for elimination of lymphatic filariasis (LF) in 2001 after a pilot study in 2000, the Philippines is yet to eliminate the disease as a public health problem with 6 out of the 46 endemic provinces still implementing MDA for LF as of 2018. In this work, we propose a mathematical model of the transmission dynamics of LF in the Philippines and a control strategy for its elimination using MDA. Sensitivity analysis using the Latin hypercube sampling and partial rank correlation coefficient methods suggests that the infected human population is most sensitive to the treatment parameters. Using the available LF data in Caraga Region from the Philippine Department of Health, we estimate the treatment rates r1 and r2 using the least-squares parameter estimation technique. Parameter bootstrapping showed small variability in the parameter estimates. Finally, we apply optimal control theory with the objective of minimizing the infected human population and the corresponding implementation cost of MDA, using the treatment coverage γ as the control parameter. Simulation results highlight the importance of maintaining a high MDA coverage per year to effectively minimize the infected population by the year 2030.

A STUDY ON MATHEMATICAL AND STATISTICAL ASPECTS OF LINEAR MODELS

The primary objective of this research article is to present the mathematical and statistical aspects of linear models and their characteristic properties. Linear model is the most common modeling used in science. Actually linear models have many different meanings depend on the context. Linear model is often preferred than other model such as quadratic model because of its ability to interpret easily. In the other hand most of the real life cases have linear relationship .Modeling the cases using linear model will able us to determine the relative influence of one or more independent variables to the dependent variable. In the present talk an attempt has been made to propose the specific forms of simple and multiple linear regression models. In this conversation mathematical aspects of linear models have been extensively depicted. Different types of mathematical models are discussed here and the methods of fitting transformed models are proposed.Furthermore specific form of linear statistical model is presented and the crucial assumptions of general linear model are extensively discussed.At the last stage of this article the method of ordinary least squares estimation of parameters of a linear model has been proposed

Research on the Modeling Method of Microwave Power Module Cascade Converter

It is difficult to obtain the accurate small signal modeling by traditional modeling method especially for the complex converter. System identification is a new method to construct the high voltage cascade converter small signal modeling. The first-stage and the second-stage can be analyzed on the whole. The improved least-square parameter estimation is used to analyze the sampling data of input and output. Furthermore, the system parameter and accurate system modeling can be acquired. Comparing the step response of system model with the Pspice stimulating result, the validity of the method is verified.

Ordinary least squares estimation of parameters of linear model

This research article primarily focuses on the method of ordinary least squares estimation of parameters of linear model. Here an innovative proof of Gauss-Markoff theorem for linear estimation has been presented. An extensive discussion in evaluating Best Linear Unbiased Estimator (BLUE) of a linear parametric function of the classical linear model is made by using the Gauss-Markoff theorem. Furthermore the importance of mean vector and covariance matrix of BLUE is discussed. Moreover generalized Gauss-Markoff theorem for linear estimation, properties of OLS estimators and problems of linear model by violating the assumptions are extensively discussed.

Modeling and Parameter Identification of a Cooling Fan for Online Monitoring

In many industrial fields, cooling fan systems have been widely implemented in electronic equipment such as network hosts, product line junction boxes, manufacturing facilities, computer numerical control (CNC) machine systems, cooling units of array servers, and many other power systems. These systems usually require high computation power and release high heat. Once the cooling fan systems malfunction or the cooling efficiency degrades, it could result in lower system performances or even cause serious damage to the core systems. Thus, there is a growing interest in monitoring and detecting the cooling fan operation status. As a result, the status of the cooling fan systems needs to be monitored in real-time. In this article, dynamics modeling, parameter identification, and online fan speed monitoring of a cooling fan system are presented. First, the nonlinear model of the cooling fan system is derived from blade aerodynamics with a driving motor. Next, a discrete model is applied based on the bilinear transformation of the description of the dynamic behavior and is further used for the least-square (LS) parameter estimation. To suppress the measurement noise, a regulation filter (RF) is further presented to improve the parameter identification precision. In addition, a Levenberg–Marquardt (LM) optimization is further applied for parameter refinement. Simulation comparison studies are considered to validate the proposed method. Moreover, many experiments are conducted to verify the feasibility and reliability for different types of fans. Unlike common conventional monitoring methods, the proposed framework does not apply constant threshold or need any training stages. The alarm threshold is adjusted automatically according to the current operation status. Finally, an embedded measurement and monitoring instrument is developed for demonstrating the effectiveness of the proposed method. Experiments firmly verify the novelty of the model-reference-based online cooling fan monitoring techniques.

A novel fractional grey Riccati model for carbon emission prediction

Greenhouse gas emissions bring severe challenges to the global climate, and CO2 emission prediction can provide decision support for atmospheric environmental governance and regional sustainable development. However, previous studies only focused on forecasting accuracy and neglected modeling mechanisms. To solve this problem, this paper proposes a novel fractional grey Riccati model (FGRM(1,1) model), which combines the Environmental Kuznets Curve hypothesis and differential information principle. The least-squares parameter estimation and mathematics analytical methods are utilized to obtain model parameters and the discrete response function, and the bare bone fireworks algorithm is introduced and designed to obtain the optimal fractional order. 20 data sets from M-competition are studied for confirming the effectiveness of the proposed model, and the performance test shows that it has higher stability and accuracy. Finally, the proposed model is employed to estimate and forecast the CO2 emissions of the United States, China, and Japan. Compared with three types of classical models without considering modeling mechanisms, the results show that the FGRM(1,1) model demonstrates better estimation in all cases and efficiency in short-term carbon emission forecasting. Results also indicated that these three countries all will reduce their carbon emissions gradually in future and the carbon emissions under current policies are estimated to be 0.31% (Japan), 4.52% (U.S.) and 4.49% (China) below 2020 levels by 2025, respectively.

COMPARISONS OF SOME BIASED ESTIMATORS FOR LINEAR MEASUREMENT ERROR MODELS

Measurement errors are very often come upon in data analysis. Classical statistical methods become disadvantageous and ordinary least squares estimator of parameters turns into inconsistent and biased, in the existence of measurement errors in the data. Although some methods are used, the performances of them are not good enough in the presence of multicollinearity and measurement errors in the data, simultaneously. That’s why researchers have been inquiring about the estimation of the parameters if the measurement error models have multicollinearity, lately. Especially, biased estimation techniques have been researched in the existence of multicollinearity for measurement error models recently. In this paper, the ridge and Liu estimation approaches to the measurement error models in the existence of multicollinearity are investigated. The comparisons of the biased estimators’ performances are analyzed theoretically and numerically.

Control for Leader–Follower Consensus of Multi-agent Systems with Actuator Faults Using Decentralized Robust Fault-tolerant Control

The leader–follower consensus tracking is one of the important problems in multi-agent systems (MASs) which can be influenced by actuator faults. The main issue of the paper is fault occurrence, and the challenge is to design an appropriate decentralized fault-tolerant control (FTC) based on fault estimations to minimize the effects of actuator fault and maintain the tracking problem. In this paper, the Luenberger detection filter is adopted for the fault detection process and fault estimations are obtained by recursive least-square (RLS) parameter estimation method. The procedure utilized for FTC is fault hiding technique so that using virtual actuator methodology, the effects of faults are partially improved and a robust controller is combined with a virtual actuator to reduce the tracking error. The main contribution of this paper is designing a robust FTC which not only can compensate for the performance degradation, but also can make the system robust against fault estimation error uncertainties. It is also proved that the tracking error of faulty agents converges to zero asymptotically and the consensus tracking is preserved by using the proposed method. The effectiveness of the proposed method is verified through simulations.