Estimation Error Research Articles

A mean flow velocity estimation scheme based on flow field characteristics and distribution point optimization for carbon monitoring in coal-fired power plants: A numerical study

CO2 online monitoring provides a method to obtain carbon emissions by directly quantifying the flue gas flow rate and CO2 concentration. However, significant flow rate measurement errors arise due to the complexity of turbulence in large-diameter stacks. To address the issue, this study utilizes turbulence numerical simulation combined with mean velocity estimation error analysis to investigate the flow field of typical stacks in coal-fired power plants. The simulation results demonstrated that the evolution of turbulence exaggerates velocities. The flow field exhibits stable turbulence characteristics in a single-introduced stack, while in the double-introduced stack, the flow field dynamically evolves due to asymmetric collisions and abrupt expansions. Furthermore, the effects of load and temperature on the estimation error of flow velocity are established. The optimum monitoring height, the ideal chord angle and the stepped number of deployment points based on the log-linear method are determined. Within the single-introduced stack, a correction factor is introduced and a corresponding formula is established that links estimation errors with monitoring heights. This resulted in a dramatic reduction of the maximum estimation error from 14% to 0.3%. Finally, the systematic and simplified optimization scheme for estimating mean flow velocity is summarised, which provides a powerful reference for flow rate measurement for online CO2 monitoring in coal-fired power plants.

Exploring the Big Data Paradox for various estimands using vaccination data from the global COVID-19 Trends and Impact Survey (CTIS).

Selection bias poses a substantial challenge to valid statistical inference in nonprobability samples. This study compared estimates of the first-dose COVID-19 vaccination rates among Indian adults in 2021 from a large nonprobability sample, the COVID-19 Trends and Impact Survey (CTIS), and a small probability survey, the Center for Voting Options and Trends in Election Research (CVoter), against national benchmark data from the COVID Vaccine Intelligence Network. Notably, CTIS exhibits a larger estimation error on average (0.37) compared to CVoter (0.14). Additionally, we explored the accuracy (regarding mean squared error) of CTIS in estimating successive differences (over time) and subgroup differences (for females versus males) in mean vaccine uptakes. Compared to the overall vaccination rates, targeting these alternative estimands comparing differences or relative differences in two means increased the effective sample size. These results suggest that the Big Data Paradox can manifest in countries beyond the United States and may not apply equally to every estimand of interest.

Advancing state estimation for lithium-ion batteries with hysteresis through systematic extended Kalman filter tuning

Knowledge of remaining battery charge is fundamental to electric vehicle deployment. Accurate measurements of state-of-charge (SOC) cannot be obtained directly and estimation methods must be used instead. This requires both a good model of a battery and a well-designed state estimator. Here, hysteretic reduced-order battery models and adaptive extended Kalman filter estimators are shown to be highly effective, accurate predictors of SOC. A battery model parameterisation framework is proposed, which enhances standardised methods to capture hysteresis effects. The hysteretic model is parameterised for three independent NMC811 lithium-ion cells and is shown to reduce voltage RMS error by 50% across 18 h automotive drive-cycles. Parameterised models are used alongside an extended Kalman filter, which demonstrates the value of adaptive filter parameterisation schemes. When used alongside an extended Kalman filter, adaptive covariance matrices yield highly accurate SOC estimates, reducing SOC estimation error by 85%, compared to the industry standard battery model.

Image moment-based visual positioning and robust tracking control of ultra-redundant manipulator

Image moment features can describe more general target patterns and have good decoupling properties. However, the image moment features that control the camera’s rotation motion around the x-axis and y-axis mainly depend on the target image itself. In this paper, the ultra-redundant manipulator visual positioning and robust tracking control method based on the image moments are advocated.First, six image moment features used to control camera motion around the x-axis and around the y-axis are proposed. And then, a novel method is proposed to use to select image features. For tracking a moving target, a kalman filter combined with adaptive fuzzy sliding mode control method is proposed to achieve tracking control of moving targets, which can estimate changes in image features caused by the target’s motion on-line and compensate for estimation errors. Finally, the experimental system based on Labview-RealTime system and ultra-redundant manipulator is used to verify the real-time performance and practicability of the algorithm. Experimental results are presented to illustrate the validity of the image features and tracking method.

Learning-based Property Estimation with Polynomials

The problem of estimating data properties using sampling frequency histograms has attracted extensive interest in the area of databases. The properties include the number of distinct values (NDV), entropy, and so on. In the field of databases, property estimation is fundamental to complex applications. For example, NDV estimation is the foundation of query optimization, and entropy estimation is the foundation of data compression. Among them, methods originating from statistics exhibit desirable theoretical guarantees but rely on specific assumptions about the distribution of data, resulting in poor performance in real-world applications. Learning-based methods, which use information from training data, are adaptable in the real world but often lack theoretical guarantees or explainability. In addition, a unified framework for estimating these frequency-based estimators with machine learning is lacking. Given the aforementioned challenges, it is natural to wonder if a unified framework with theoretical guarantees can be established for property estimation. The recent literature has presented theoretical studies that propose estimation frameworks based on polynomials. These studies also prove estimation errors with respect to the sample size. Motivated by the above polynomial estimation framework, we propose a learning-based estimation framework with polynomial approximation, which aims to learn the coefficients of the polynomial, providing theoretical guarantees to the learning framework. Through comprehensive experiments on both synthetic and real-world datasets for estimating various data properties like NDV, entropy, and power sum, our results show the superiority of our algorithms over previous estimators.

Assessing Multi‐Source Precipitation Estimates in Nepal: A Benchmark for Sub‐Seasonal Model Assessment

AbstractSub‐seasonal to seasonal (S2S) prediction provides an extended range of lead time for decision‐makers across multiple sectors. S2S forecast is crucial for a country that are susceptible to hydro‐meteorological disasters like Nepal. However, S2S forecast requires assessment with reliable datasets before its application. Since, Nepal lacks a dense station network, multi‐source precipitation estimates (MPEs) are the obvious alternatives. Therefore, using classical evaluation metrics and extreme precipitation indices, this study assessed eleven high‐resolution datasets against 159‐gauge stations over Nepal for the 2001–2020 period. These datasets are classified as gauge‐interpolated (APHRODITE), merged (TPMFD, MSWEP, CLDAS, and CHIRPS), satellite‐based (IMERGV7, IMERGV6, CMORPH, and PERSIANN), and reanalysis (ERA5‐L and HAR). Satellite datasets (except IMERGV7) failed to capture the spatial pattern of mean annual precipitation, while others broadly captured it. Most MPEs struggled to accurately estimate wet season precipitation compared to dry season. Furthermore, increasing estimation error from light to extreme precipitation and decreasing skill metrics from flat to complex terrain, demonstrate the intensity and terrain‐specific limitations of MPEs. In terms of precipitation extremes, APHRODITE exhibits the highest skill, followed by MSWEP, TPMFD, HAR, ERA5‐L, IMERGV7, CLDAS, IMERGV6, CHIRPS, CMORPH, and PERSIANN. IMERGV7 exhibits increased skill in detecting extreme precipitation and precipitation over orography against IMERGV6. APHRODITE and TPMFD datasets performed consistently well in all scales, including weekly anomaly, with an average anomaly correlation of 0.84 and 0.66 respectively. However, since APHRODITE is not widely available, TPMFD can serve as a benchmark dataset for evaluating high‐resolution S2S forecasts within the study region.

Optimisation of the Transmitter Layout in a VLP System Using an Aperture-Based Receiver

In this paper, we consider a visible light positioning (VLP) system, where an array of photo diodes combined with apertures is used as a directional receiver and a set of inexpensive and energy-efficient light-emitting diodes (LEDs) is used as transmitters. The paper focuses on the optimisation of the layout of the transmitter, i.e., the number and placement of the LEDs, to meet the wanted position estimation accuracy levels. To this end, we evaluate the Cramer–Rao bound (CRB), which is a lower bound on the mean-squared error (MSE) of the position estimate, to analyse the influence of the LEDs’ placement. In contrast to other works, where only the location of the LEDs was considered and/or the optimisation was carried out through simulations, in this work, the optimisation is carried out analytically and considers all the parameters involved in the VLP system as well as the illumination. Based on our results, we formulate simple rules of thumb with which we can determine the spacing between LEDs and the minimum number of LEDs, as well as their position on the ceiling, while also taking into account the requirements for the illumination.

Evaluation of dissipation kinetic models to describe trifluralin degradation in soil and assessing the uncertainty of the half-life estimate

In Australia, trifluralin is one of the commonly used herbicides to manage annual grasses and some broadleaf weeds. However, it may have some ecosystem impacts such as high toxicity to terrestrial and aquatic life, so it is vital to monitor the degradation of trifluralin for a considerable period for environmental safety. For risk assessment purposes, it is necessary to estimate the half-life of trifluralin, which is often evaluated using derived mathematical dissipation models. In the literature, bi-exponential (BEXP) and gamma models were suggested for modelling the dissipation of trifluralin in soil. Both models provide the half-life estimate without discussing the uncertainty of the estimate, which is a shortcoming in the literature. In this paper, we used simulation to illustrate the importance of estimate's uncertainty (standard error) and demonstrated a method to compute the standard error for the half-life estimate mathematically for kinetic dissipation models. Later, we evaluated the performance of the two suggested models using statistical indices. The computation of the half-life and the standard error of the half-life estimate were discussed. This allows us to describe the inference of the half-life parameter and determine whether the half-life estimates are significantly different against the co-variate (moisture) levels. We demonstrated the method to calculate the standard error of the half-life of trifluralin, which allows us to determine the statistical difference between the estimates. In this study, we found that the half-life of trifluralin in soil tends to increase with increasing moisture levels, and the half-life of trifluralin in soil with 100% moisture level is significantly greater than 40% and 70% moisture levels. Our findings suggest that soil moisture levels should be carefully considered before trifluralin application to minimize the non-target environmental damage.

Machine learning-based comparison of factors influencing estimated glomerular filtration rate in Chinese women with or without non-alcoholic fatty liver.

The prevalence of non-alcoholic fatty liver (NAFLD) has increased recently. Subjects with NAFLD are known to have higher chance for renal function impairment. Many past studies used traditional multiple linear regression (MLR) to identify risk factors for decreased estimated glomerular filtration rate (eGFR). However, medical research is increasingly relying on emerging machine learning (Mach-L) methods. The present study enrolled healthy women to identify factors affecting eGFR in subjects with and without NAFLD (NAFLD+, NAFLD-) and to rank their importance. To uses three different Mach-L methods to identify key impact factors for eGFR in healthy women with and without NAFLD. A total of 65535 healthy female study participants were enrolled from the Taiwan MJ cohort, accounting for 32 independent variables including demographic, biochemistry and lifestyle parameters (independent variables), while eGFR was used as the dependent variable. Aside from MLR, three Mach-L methods were applied, including stochastic gradient boosting, eXtreme gradient boosting and elastic net. Errors of estimation were used to define method accuracy, where smaller degree of error indicated better model performance. Income, albumin, eGFR, High density lipoprotein-Cholesterol, phosphorus, forced expiratory volume in one second (FEV1), and sleep time were all lower in the NAFLD+ group, while other factors were all significantly higher except for smoking area. Mach-L had lower estimation errors, thus outperforming MLR. In Model 1, age, uric acid (UA), FEV1, plasma calcium level (Ca), plasma albumin level (Alb) and T-bilirubin were the most important factors in the NAFLD+ group, as opposed to age, UA, FEV1, Alb, lactic dehydrogenase (LDH) and Ca for the NAFLD- group. Given the importance percentage was much higher than the 2nd important factor, we built Model 2 by removing age. The eGFR were lower in the NAFLD+ group compared to the NAFLD- group, with age being was the most important impact factor in both groups of healthy Chinese women, followed by LDH, UA, FEV1 and Alb. However, for the NAFLD- group, TSH and SBP were the 5th and 6th most important factors, as opposed to Ca and BF in the NAFLD+ group.

Performance of different modeling techniques in testing the impact of environmental variables on eel landing in Ichkeul Lake, a RAMSAR Wetland and UNESCO biosphere reserve

Advanced modeling techniques, including Random Forest (RF) and Cubist model (CB), were used to assess the relationship between environmental factors and European eels (Anguilla anguilla) abundance and to provide insights into the lake's ecological status while considering climate change and anthropogenic influences. A comprehensive dataset, attained through extensive environmental and biological monitoring for the period 2010–2020, was employed. The performance of the models is carried out using key metrics including the root mean square error (RMSE), coefficient of determination (R²), and mean estimation error (MAE). In addition, a sensitivity analysis was conducted to ascertain the relative significance of the thirteen input variables in shaping the predictions of the models. The precision of the CB and RF models in predicting eel landings surpassed that of Multiple Regression. In the training dataset, the CB model achieved R2=0.55, RMSE=7.68 tons, and MSE=6.20 tons, and the RF model achieved R2=0.56, RMSE=7.20 tons, and MSE=5.56 tons. High accuracy was maintained on the testing dataset, with CB achieving R2=0.73, RMSE=5.13 tons, and MSE=5.89 tons, and RF achieving R2=0.73, RMSE=5.81 tons, and MSE=4.67 tons. The scatter plot between predicted and measured eel landings indicated that the RF model tends to overestimate lower values and underestimate higher values of eel landings, while the CB model gave better performance in this context. Further, the carried sensitivity analysis using the CB model unequivocally identified three pivotal factors – water level, salinity, and turbidity level – as the most influential determinants governing the landing of eels in this ecosystem. Thus, the CB model is considered to be more promising for interpreting the relationship between environmental parameters and eel landings, which could be used by managers for an effective lake management strategy.

Adaptive cyber-tolerant finite-time frequency control framework for renewable-integrated power system under deception and periodic denial-of-service attacks

This work concentrates on designing and applying an adaptive cyber-tolerant finite-time frequency control framework for smart power systems under state-dependent sensor deception and periodic denial-of-service (DoS) attacks. An adaptive radial-basis function neural network (RBFNN)-based disturbance observer (DO) is designed to estimate undeniable plant disturbances, which includes structural uncertainties and unmodelled dynamics. Then, the DO-based resilient secondary control law based on the adaptive nonlinear sliding mode strategy for the cyber-physical power system (CPPS) is derived to guarantee global uniform asymptotic stability of the parametric error and the selected nonlinear sliding manifold. Furthermore, an in-depth analysis of uniformly ultimately boundedness (UUB) of the estimation error of RBFNN has been demonstrated. Numerical simulation and qualitative assessment have revealed the proficiency of the applied feedback control framework for the undertaken CPPS and a high-degree of cyber-tolerance against malicious attacks.

Estimating hydraulic diffusivity in coastal confined aquifer under tidal fluctuation using a frequency domain model

Oceanic tidal propagation into the coastal aquifers is a cost-effective method for estimating hydraulic parameters in coastal aquifers, and identifying the most suitable parameter estimation method for coastal aquifers based on the observations has become an intensively studied subject. In this study, the frequency domain model, LPMLE3 (combination of a local polynomial (LP) signal processing technique with a maximum likelihood estimator (MLE)), was applied to estimate the hydraulic diffusivity (λ) of the coastal aquifer by adjusting the mathematical model in LPMLE3. The mathematical model in LPMLE3 has been adjusted by removing the convective term from the convective diffusion equation within LPMLE3, and a newly developed frequency-domain analytical solution that describes the head changes due to tidal fluctuations in coastal confined aquifers was used to replace the diffusion term. For comparison, an analytical solution in the time domain was also derived by Green’s functions method. After that, the particle swarm optimization algorithm and Markov Chain Monte Carlo method were used to estimate λ. Results show that LPMLE3 performed well in estimating homogeneous or heterogeneous aquifers with complicated boundary conditions. The estimated error of λ is within 10 % in a heterogeneous aquifer when the variance of the natural logarithm of the aquifer hydraulic conductivity is less than 0.05 (σlnK2≤0.05). If the coastal aquifer has a sloping beach, the estimated λ by LPMLE3 method accurately when the sloping beach angle is greater than 65°. As for an inclined coastal aquifer, the dip angle has a greater influence on the offshore areas than the nearshore areas and the estimation errors are relatively small (less than 15 %) when the dip angle is within a range of 0- 15°.

Quantifying instantaneous nitrogen oxides emissions from power plants based on space observations

Thermal power plants are significant contributors to nitrogen oxides (NOx), impacting global atmospheric conditions and human health. Satellite observations, known for their continuity and global coverage, have become an effective means of quantifying power plant emissions. Previous studies, often accumulating long temporal data into integrated plumes, resulted in substantial errors in annual emissions at the individual power plant level due to neglecting variations in emissions and diffusion conditions. This study presents, for the first time, the quantification of instantaneous NOx emissions based on single overpass observations from the Tropospheric Monitoring Instrument (TROPOMI) aboard the Sentinel-5 Precursor satellite. By addressing the temporal variability of power plant emissions, it effectively reduces annual estimation errors. Comparative analysis between the Exponentially-Modified Gaussian (EMG) and Gaussian Plume Model (GPM) simulations demonstrates the capability of EMG to provide instantaneous emission estimates based on actual plumes, exhibiting closer proximity to actual monitoring values than GPM. Applying the EMG method, we quantify the instantaneous emission rates of six power plants in the United States. Comparing annual emission estimations at individual power plants with traditional integrated plume results, our method demonstrates a 63.7 % improvement in annual emission estimations. This study offers more detailed data on power plant emissions, providing a new avenue for better understanding the emission behavior of thermal power plants.

FACIAL IMAGE CAPTIONING USING DNN

Facial analysis, encompassing emotion, age, and gender detection, shows potential in various applications such as human-computer interaction, business, security, and health. This study delves into the development and evaluation of a deep neural network (DNN) model for facial emotion, age, and gender detection. Utilizing a convolutional neural network (CNN) architecture trained on diverse datasets for each task, our model proves effective in predicting facial features. The accuracy of needs assessment is X%, the marginal error (MAE) of age estimation is Y years, and the accuracy of gender classification is Z%.

Tracking SARS-CoV-2 variants of concern in wastewater: an assessment of nine computational tools using simulated genomic data.

Wastewater-based surveillance (WBS) is an important epidemiological and public health tool for tracking pathogens across the scale of a building, neighbourhood, city, or region. WBS gained widespread adoption globally during the SARS-CoV-2 pandemic for estimating community infection levels by qPCR. Sequencing pathogen genes or genomes from wastewater adds information about pathogen genetic diversity, which can be used to identify viral lineages (including variants of concern) that are circulating in a local population. Capturing the genetic diversity by WBS sequencing is not trivial, as wastewater samples often contain a diverse mixture of viral lineages with real mutations and sequencing errors, which must be deconvoluted computationally from short sequencing reads. In this study we assess nine different computational tools that have recently been developed to address this challenge. We simulated 100 wastewater sequence samples consisting of SARS-CoV-2 BA.1, BA.2, and Delta lineages, in various mixtures, as well as a Delta-Omicron recombinant and a synthetic 'novel' lineage. Most tools performed well in identifying the true lineages present and estimating their relative abundances and were generally robust to variation in sequencing depth and read length. While many tools identified lineages present down to 1 % frequency, results were more reliable above a 5 % threshold. The presence of an unknown synthetic lineage, which represents an unclassified SARS-CoV-2 lineage, increases the error in relative abundance estimates of other lineages, but the magnitude of this effect was small for most tools. The tools also varied in how they labelled novel synthetic lineages and recombinants. While our simulated dataset represents just one of many possible use cases for these methods, we hope it helps users understand potential sources of error or bias in wastewater sequencing analysis and to appreciate the commonalities and differences across methods.

Model misspecification, measurement error, and apparent supralinearity in the concentration-response relationship between PM2.5 and mortality.

A growing number of studies have produced results that suggest the shape of the concentration-response (C-R) relationship between PM2.5 exposure and mortality is "supralinear" such that incremental risk is higher at the lowest exposure levels than at the highest exposure levels. If the C-R function is in fact supralinear, then there may be significant health benefits associated with reductions in PM2.5 below the current US National Ambient Air Quality Standards (NAAQS), as each incremental tightening of the PM2.5 NAAQS would be expected to produce ever-greater reductions in mortality risk. In this paper we undertake a series of tests with simulated cohort data to examine whether there are alternative explanations for apparent supralinearity in PM2.5 C-R functions. Our results show that a linear C-R function for PM2.5 can falsely appear to be supralinear in a statistical estimation process for a variety of reasons, such as spatial variation in the composition of total PM2.5 mass, the presence of confounders that are correlated with PM2.5 exposure, and some types of measurement error in estimates of PM2.5 exposure. To the best of our knowledge, this is the first simulation-based study to examine alternative explanations for apparent supralinearity in C-R functions.

Statistical Inference Using Partially Accelerated Life Test Model for the Weibull Population Mean Unified Hybrid Censored Data

In this paper, estimates of the parameters and the acceleration factor of a new distribution known as the Weibull Population Mean Distribution (WPMD) are explored. We propose the use of the model suggested by Abd-Elrahman [A better alternative to the generalized Bilal distribution: A new model and applications, Int. J. Reliab. Qual. Saf. Eng. 30(6) (2023) 2350027, doi: 10.1142/S0218539323500274] for estimating these parameters. To accomplish this, we employ the maximum likelihood estimation method via a Constant-Stress Partially Accelerated Life Test (CSPALT) model. In this study, we have utilized Unified Hybrid (UH) censored data obtained from the WPMD. Confidence intervals for the model parameters and the acceleration factor are constructed based on the approximate Fisher information matrix. The average and Mean Squared Error (MSE) of estimates are computed to evaluate the performance of the proposed method under the CSPALT model. Additionally, a real data set is provided for illustrative purposes, and a numerical analysis of the UH Censoring Scheme (UHCS) is carried out. Finally, concluding remarks are presented.

Data-driven traffic sensor location and path flow estimation using Wasserstein metric

This paper introduces link information value obtained by the traffic sensors and presents a traffic sensor location and flow estimation joint optimization model in an urban road network. In contrast to most previous studies, this paper adds new traffic sensors into the existing sensor network and proposes a data-driven path flow measurement method based on Wasserstein metric, which is utilized to measure the distance between the estimated traffic flow distribution and the actual distribution. Furthermore, this paper develops a customized greedy algorithm by combining a search strategy for the link information value to obtain the optimal sensor location scheme and perform traffic flow estimation under different budget conditions. Numerical experiments are conducted on Sioux-Falls test network and Eastern Massachusetts interstate highway subnetwork to verify the accuracy and effectiveness of the proposed model based on Wasserstein metric and the developed solution method. Computational results show that the sensor location scheme generated by the model based on Wasserstein metric can reduce the estimation error of the traffic flow compared with KL divergence model under the same deployment cost. Additionally, the customized greedy algorithm can achieve the better performance than the Brute force algorithm in terms of computing time and solution quality.

Outlier‐resistant state estimation for complex networks with random false data injection attacks under encoding–decoding mechanism

SummaryThis article focuses on the outlier‐resistant state estimation problem for discrete time‐varying complex networks (TVCNs) affected by random false data injection attacks (FDIAs) under an encoding–decoding mechanism (EDM). From the perspective of information security, a uniform‐quantization‐based EDM is employed to encrypt the transmitted data. During the data transmission process, a set of independent random variables governed by Bernoulli distribution is introduced to characterize the occurrence of random FDIAs. For the purpose of alleviating the passive impact of potential measurement outliers, a saturation structure is adopted during the estimator design. The gain matrix is given by minimizing the upper bound of estimation error covariance. According to the stochastic analysis method, it is shown that the state estimation error is bounded exponentially in mean‐square sense by providing new sufficient condition. It should be noted that we make the first attempt to develop new outlier‐resistant state estimation method with performance evolution criterion in the time‐varying perspective for TVCNs with random FDIAs under EDM. Finally, a simulation example with comparative experiment is presented to illustrate the effectiveness of the newly presented outlier‐resistant estimation algorithm.

Inductance Estimation Based on Wavelet-GMDH for Sensorless Control of PMSM

In permanent magnet synchronous motor (PMSM) sensorless drive systems, the motor inductance is a crucial parameter for rotor position estimation. Variations in the motor current induce changes in the inductance, leading to core magnetic saturation and degradation in the accuracy of rotor position estimation. In systems with constant load torque, the saturated inductance remains constant. This inductance error causes a consistent error in rotor position estimation and some performance degradation, but it does not result in speed estimation errors. However, in systems with periodic load torque, the error in the saturated inductance varies, consequently causing fluctuations in both the estimated position and speed errors. Periodic speed errors complicate speed control and degrade the torque compensation performance. In this paper, we propose a wavelet denoising-group method of data handling (GMDH) based method for accurate inductance estimation in PMSM sensorless control systems with periodic load torque compensation. We present a method to analyze and filter the collected three-phase current signals of the PMSM using wavelet transformation and utilize the filtered results as inputs to GMDH for training. Additionally, a method for magnetic saturation compensation using the inductance parameter estimator is proposed to minimize periodic speed fluctuations and improve control accuracy. To replicate the load conditions and parameter variations equivalent to the actual system, experiments were conducted to measure the speed ripples, inductance variations, and torque component of the current. Finally, software simulation was performed to confirm the inductance estimation results and verify the proposed method by simulating load conditions equivalent to the experimental results.