Linear Parameter Research Articles

Digital Image Analysis of Vertebral Body S1 and Its Ossification Center in the Human Fetus

Objectives: The aim of the present study was to examine the growth dynamics of the first sacral vertebra and its ossification center in the human fetus, based on their linear, planar, and volumetric parameters. Methods: The examinations were carried out on 54 human fetuses of both sexes (26 males and 28 females) aged 18–30 weeks of gestation, which had been preserved in 10% neutral formalin solution. Using CT, digital image analysis software, 3D reconstruction, and statistical methods, the size of the first sacral vertebra and its ossification center was evaluated. Results: The first sacral vertebra and its ossification center grew proportionately according to fetal weeks. Conclusions: The numerical data obtained from computed tomography and the growth patterns of the body of the first sacral vertebra and its ossification center may serve as age-specific normative intervals relevant for gynecologists, obstetricians, pediatricians, and radiologists during fetal ultrasound screening. Our findings on the growth of the body of the first sacral vertebra and its ossification center may be useful in daily clinical practice, particularly in ultrasonic monitoring of normal fetal growth and in screening for congenital defects and skeletal dysplasias.

Fast adaptive unknown input observer for fault and attack estimations in nonlinear systems: an enhanced LMI approach

This paper deals with the problem of robust fault estimation for the Lipschitz nonlinear systems under the influence of sensor faults and actuator faults. In the proposed methodology, a descriptor system is formulated by augmenting sensor fault vectors with the states of the system. A novel fast adaptive unknown input observer (FAUIO) structure is proposed for the simultaneous estimation of both faults and states of a class of nonlinear systems. A new LMI condition is established by utilising the H ∞ criterion to ensure the asymptotic convergence of the estimation error of the developed observer. This derived LMI condition is deduced by incorporating the reformulated Lipschitz property, a new variant of Young inequality, and the well-known linear parameter varying (LPV) approach. It is less conservative than the existing ones in the literature, and its effectiveness is compared with the other proposed approaches. Further, the proposed observer methodology is extended for the disturbance-affected nonlinear system for the purpose of the reconstruction of states and faults/attacks with optimal noise attenuation. Later on, both designed approaches are validated through an application of a single-link robotic arm manipulator in MATLAB Simulink.

Static Output-Feedback Path-Tracking Controller Tolerant to Steering Actuator Faults for Distributed Driven Electric Vehicles

The steering system plays a critical role in the vehicle’s handling and directly influences its lateral dynamics. Faults or abnormal behavior in this system can affect performance, cause vehicle instability, and even lead to accidents. Therefore, considering these potential events is essential for designing robust controllers for autonomous vehicles. For this reason, in this work, a fault-tolerant path-tracking Static Output-Feedback controller is designed to handle steering actuator faults in autonomous vehicle steering systems. The controller adopts a Linear Parameter Varying approach to effectively handle nonlinearities associated with varying vehicle speeds and tire behavior. Furthermore, it only uses information from sensors, avoiding estimation stages. This controller can operate in two modes: a no-fault mode where only the steering is controlled to follow the reference path and a fault mode where the controller manages both the steering and torque vectoring. In fault mode, torque vectoring compensates for faults in the steering actuator. The design of the controller is completed considering gain faults in the steering system. The simulation results show that the proposed controller successfully maintains vehicle stability and significantly reduces tracking errors during high-risk maneuvers, achieving reductions of up to 50.65% in lateral error and 47.26% in heading error under worst-case fault scenarios.

Sorption and Transport of Antibiotics in Manured Upland Agricultural Soils

Sorption and transport are important environmental behaviors of antibiotics in soils and can determine the fate of antibiotics in environments； however, limited relevant studies have been conducted on long-term manured soils. In this study, batch and repacked soil column experiments were conducted to examine the sorption and transport behavior of four veterinary antibiotics, including sulfamethazine （SMT）, florfenicol （FFC）, doxycycline （DOX）, and enrofloxacin （ENR）, in red soils, yellow soils, and calcareous soils with long-term amendment of chicken or pig manure collected in Zhejiang Province. The results showed that the sorption isothermal data of the four target antibiotics all conformed well to the linear and Freundlich models. The performance of the linear model was better for the weakly-sorbing antibiotics （SMT and FFC）, whereas the performance of the Freundlich model was better for the strongly-sorbing antibiotics （DOX and ENR）. The sorption of target antibiotics was governed by both soil and manure types. The linear sorption parameter （Kd） of SMT and FFC were positively related to the organic carbon content and pH of soils, and their sorption was mainly controlled by soil organic matter, indicating that non-electrostatic interactions （e.g., hydrogen bonding, hydrophobic interactions） played dominant roles in their sorption to the soils. Contrastingly, DOX and ENR did not show significant relationships with soil pH, organic carbon content, and cation exchange capacity, indicating that multiple mechanisms （e.g., hydrophobic interactions, hydrogen bonding, and electrostatic interactions） worked jointly in their sorption into the soils. SMT and FFC exhibited high recoveries of breakthrough curves （in ranges of 37.5%-92.3% and 45.8%-112.6%, respectively） in column transport experiments, reflecting their high leaching potentials. Contrastingly, no soil column breakthrough of DOX and ENR was observed, reflecting that the injected antibiotics were completely retained inside the soil columns. The maximum relative concentrations and breakthrough recoveries of SMT and FFC showed significant negative linear relationships with Kd. This indicates that the leaching potential of antibiotics can be predicted from sorption parameters using the regression equations established by batch and column experiments.

SOME FEATURES OF LINEAR AND ANGULAR PARAMETERS OF THE EYE’S ANTERIOR SEGMENT IN PATIENTS WITH OCULAR HYPERTENSION AND GLAUCOMA

Purpose – detection of some features of the relationship between anterior segment structures in eyes with ocular hypertension and primary glaucoma using ultrasound biomicroscopy (UBM). Material and methods A total of 60 patients (60 eyes) aged 27-60 years (46.6±11.4) with ophthalmic hypertension (n=7) and primary glaucoma (n=53) (0-2 stages in accordance with Mills glaucoma classification) were examined. They were divided into 3 groups in accordance with the axial length (AL): 16 short (<23.0mm), 23 medium (23.0-24.5mm) and 11 long eyes (>24.5mm). Main linear (mm) and angular (°) parameters of the eye’s anterior segment were measured using UBM (Ellex Eye Cubed, 40 MHz, Ellex Inc., Australia). Results The anterior chamber depth in short eyes was measured as 2.11±0.05, in medium – 2.47±0.04, in long – 3.02±0.06, posterior chamber depth: 0.58 ± 0.04, 0.65 ± 0.03, 0.69 ± 0.05. Iris thickness in root zone was 0.34±0.02, 0.34±0.01, 0.33±0.03. Ciliary body thickness at 1 mm from scleral spur: 0.47±0.03, 0.55±0.04, 0.62±0.05, at 2 mm: 0.28±0.03, 0.33±0.02, 0.38±0.03 respectively. “Trabecula-iris” distances at 250 µm from the scleral spur was: 0.09±0.03, 0.12±0.03, 0.21±0.04, at 500 µm: 0.14±0.02, 0.18±0.03, 0.27±0.03. “Trabecula-ciliary processes” was 0.65±0.05, 0.87±0.04, 1.07±0.06, length of Zinn zonules – 0.33±0.05, 0.52±0.04, 0.71±0.06 respectively. Anterior chamber angle (at 12´) was 16.34±5.65, 22.49±3.85, 27.04±3.23, “sclera-iris” angle: 15.80±2.34, 19.56±1.12, 24.97±1.59, “sclera-ciliary processes” angle – 38.21±2.44, 48.69±2.97, 51.22±3.66. Almost all patients had a predominantly flat iris profile, in short eyes it was more convex and anterior positioned, in long eyes – a straight iris profile combined with predominant posterior position, but in several cases – a concave profile. Conclusion Anterior chamber depth in combination with different AL is the most important factor in spatial arrangement of the eye's anterior segment structure. In eyes with a short AL a shallow posterior chamber depth, adjoining the iris to trabecula and partial coverage of posterior chamber by ciliary processes were observed. There were some difficulties in visualizing Zinn zonules due to coverage by ciliary processes and their adjoining to the root zone of iris in medium and long eyes. A flat iris profile was found in all 3 groups of glaucoma patients, but in eyes with medium and high AL it was more convex. Key words: ultrasound biomicroscopy, glaucoma, ocular hypertension, biometry

Sequential linear programming-based parameter optimization of dynamic reactive power compensation devices for security enhancement and new energy power transmission increasing

Sequential linear programming-based parameter optimization of dynamic reactive power compensation devices for security enhancement and new energy power transmission increasing

Calibration of Linear Muskingum Model Coefficients and Coefficient Parameters Using Grey Wolf and Particle Swarm Optimization

Calibration of Linear Muskingum Model Coefficients and Coefficient Parameters Using Grey Wolf and Particle Swarm Optimization

Morphometric Analysis of Kajali River Basin Using Geospatial Techniques

Soil and water are the important natural resources and important input for agricultural production. The present study has been attempted to delineate and determine morphometric characteristics of Sakharpa watershed in Ratnagiri district by using Remote Sensing and GIS. The delineation of watershed was performed in QGIS 3.18.3 software. The study area was obtained from SRTM DEM with 30meter resolution after delineation. Sakharpa watershed shows a dendritic drainage pattern. The results found for morphometric parameters were Bifurcation Ratio (Rb)2-5.5, Form factor (Ff) 0.32, Elongation ratio (Re) 0.63, Circulatory ratio (Rc) 0.32, Shape index (Sw) 3.18,Drainage density (Dd)1.18km/km2, Stream frequency (Fs)1.48 km-2, Texture ratio (Rt)1.08, Drainage texture (Dt)2.24,Constant of channel maintenance (C)0.84km2/km, Length of overland flow (Lg) 0.42, Basin relief (R) 763.92 m, Relief Ratio (Rr) 0.045,Relative Relief (Rhp) 1.27,Ruggedness Number (Rn) 0.904. The study concluded that the watershed is elongated in shape, have dense vegetation and homogeneous with less structural disturbance. This morphometric analysis of drainage basin helps to planning and development of watershed also helps to understand relation between linear, areal and relief parameters of drainage basin.

Застосування методів машинного навчання для визначення параметрів лінійної оптики пучка в накопичувальному кільці ThomX

The linear optics parameters are one of the most significant properties of the beam, which are controlled at the particle accelerators. Classical methods of analysis, such as component-independent analysis, employ turn-by-turn readings of the beam position monitors. As an alternative to the component-independent analysis, machine learning and neural networks are proposed for determining the beam parameters. This approach relies on the same input data as classical algorithms. This work shows training and usage of the neural network for analysis of the data from the collector ring of the ThomX accelerator facility.

Dynamical complexity of postural control system in autism spectrum disorder: a feasibility study of linear and non-linear measures in posturographic analysis of upright posture

BackgroundAutism Spectrum Disorder (ASD) is a neurodevelopmental disorder, characterized by impairments in social interaction and communication with restricted and repetitive behavior. Postural and motor disturbances occur more often in ASD, in comparison to typically developing subjects, affecting the quality of life. Linear and non-linear indexes derived from the trajectory of the center of pressure (COP) while subjects stand on force platforms are commonly used to assess postural stability. The aim of the present feasibility study was to investigate whether combining linear and non-linear parameters of the COP during stance in subjects with ASD, could provide insight on specific features of motor dysfunction possibly linked to ASD cognition and clinical characteristics.MethodsTwenty-two males, aged 10–15 years, including subjects with ASD and healthy controls (N = 11, respectively), were studied. They all had normal cognitive level and independent walking ability. A piezoelectric force platform was used to evaluate posture over three feet positions, with eyes open, closed and during visually-guided saccades. Linear (sway path, total area and root mean square) and non-linear parameters (fractal dimension and sample entropy) of the COP were measured to determine postural stability and the complexity and regularity of the COP signals. GLMM analyses were performed to assess COP parameter changes across experimental conditions and subject groups. Finally, Spearman correlations evaluated the significance of potential relationships between linear and non-linear measures as well as between non-linear parameters and clinical data in patients with ASD.ResultsCompared to controls, subjects with ASD showed reduced postural stability and complexity, with higher regularity of COP trajectories, particularly in the most unstable feet positions, during visually-guided saccades and in the medial-lateral direction. Spearman correlations indicated that, in the patients’ group, postural instability was associated with a decrease in the geometric complexity and an increase in the regularity of the COP trajectory. Moreover, the increase in regularity of the COP trajectory was associated to the severity of restricted and repetitive behavior.ConclusionsThe results of this study highlight the importance of combining linear and non-linear measures in evaluating postural control in patients with ASD, also with respect to the outcome of interventions on these patients targeting postural balance.

DIFFERENTIAL MUELLER-MATRIX MAPPING OF THE POLYCRYSTALLINE COMPONENT OF BIOLOGICAL TISSUES OF HUMAN ORGANS

The article presents the materials of diagnostic application of the method of differential Mueller-matrix mapping of optically anisotropic architectonics of the layers of soft matter of the female reproductive sphere – histological sections of uterine biopsy. The efficiency and accuracy of differential diagnostics of benign and precancerous conditions of endometrial tissue are considered using statistical analysis of algorithmically reproduced maps of average values of linear and circular birefringence and dichroism parameters of optically anisotropic architectonics of representative samples of native histological sections of the uterine wall. The values of the balanced accuracy of differential diagnostics are presented by using the technique of statistical analysis of coordinate distributions of the mean values of the optical anisotropy parameters.

Vehicle active suspension control considering parameter uncertainty and velocity variation

Due to the uncertainty in vehicle model parameters, the control performance of active suspensions often deteriorates, especially under extreme conditions such as high velocities and full loads. To address this challenge, this paper proposes a novel robust finite frequency H ∞ output feedback control strategy based on linear parameter varying (LPV) systems. First, we establish a new LPV model for the half-car active suspension control system, taking into account the uncertainties associated with vehicle velocity and sprung mass. Next, a robust finite frequency H ∞ output feedback controller is designed using a gain scheduling approach, formulated through a set of linear matrix inequalities (LMIs). Finally, simulation results demonstrate that the proposed velocity-dependent robust control strategy significantly reduces the root mean square (RMS) values of vertical acceleration by approximately 21% to 31% under various conditions of sprung mass and vehicle speed compared to traditional control methods.

NUMERICAL MODELING OF EMBANKMENT ON THIN CLAY SOIL WITH GEOFOAM

Soft soils cause problems in road subgrades because they have low bearing capacity. Embankments on soft ground need to be identified and reviewed before construction starts. Various soil reinforcement techniques can be used to improve soft soil conditions. This research focuses on using geofoam material as an embankment on soft soil. The aim is to analyze the modeling of soft soil embankment with geofoam. The research method is a numerical method using the Plaxis 2D version 2023 application. There are two models in this study, namely the embankment model without geofoam, 100 cm thick subgrade, and the embankment model with 30 cm thick and 40 cm thick geofoam. The embankment geometry model is assumed to be symmetrical, hardening soil parameters are used to model soft soil for analyzing consolidation settlement, and elastic linear parameters to model geofoam. The type of FEM analysis in this research is plain strain. Numerical results at a maximum load of 100 kN showed a settlement of 0.1587 mm at 30 cm geofoam thickness and 0.1507 mm at 40 cm geofoam thickness. Deformation of 16 mm in 30 cm thick geofoam and 15.22 mm in 40 cm thick geofoam. Soil stress of 201 kN/m² in 30 cm thick geofoam and 192 kN/m² in 40 cm thick geofoamm. In conclusion, the model of embankment on soft soil with geofoam is that the thicker the geofoam used, the smaller the settlement and the stress on the soil that occurs.

On The Pros and Cons of Using Excel for Regression Analysis

Excel is a useful and powerful software for simple regression analysis without any programming skills and that is why, it is widely preferred by the undergraduate students from various areas such as chemistry, biology and agriculture as well as many engineering disciplines such as chemical engineering, food engineering and bioengineering. Parameter values and coefficient of determination (R2) can be easily obtained together with the graphical representation for those models exist in Excel such as linear and exponential models. It is also possible to visually examine the model fit and experimental data together on the same graph. For linear models (linear in parameters) Excel Add-In Data Analysis-Regression tool creates a summary output, and parameter estimates, parameter uncertainties, adjusted R2 (R2adj) and root mean square error (RMSE) values can be found even for the models that do not exist in Excel. For nonlinear models (nonlinear in parameters) Excel Add-In Solver tool can be used to obtain parameter estimates (but not uncertainties), and R2, R2adj and RMSE can be calculated manually. Despite these advantages, there are some shortcomings of Excel for regression analysis. For linear models with no-intercept Excel reports the incorrect and overoptimistic R2 and also reports incorrect and overpessimistic R2adj. Excel has also some nonlinear models such as exponential and power models in it; however, Excel computes linear parameter estimates for those nonlinear models and again optimistic R2 is calculated. This paper aims (i) to show these inaccuracies with their reasons by using published data, (ii) how to obtain the correct results, (iii) to warn the instructors who would use Excel for regression analysis in class. Excel users (instructors, students, professionals in any field) should be aware of the pitfalls when using Excel for regression.

Enhancement of Molecular Structural and Linear/Nonlinear Optical Features of Chitosan/Titanium Dioxide Nanocomposite Films for Food Packaging and Optoelectronic Applications

The current study aims to synthesize and characterize nanocomposite films of chitosan and titanium dioxide in terms of molecular structure, thermal and optical properties for use in food packaging and optoelectronic applications. The Fourier-transform infrared (FTIR) spectroscopy was used to study the interaction between the TiO2-NPs and chitosan and the analysis confirmed that TiO2-NPs interacted with chitosan and demonstrated good compatibility. Differential scanning calorimetry and thermogravimetric analysis revealed that increasing the concentration of TiO2-NPs improved the thermal stability of the nanocomposites. The linear optical properties in the UV-Vis range (200–800 nm) were measured spectrophotometrically. Below 400 nm, the transmittance spectra of the nanocomposites show decreased degrees of transparency, indicating their capacity to entirely block UV-light transmission. Tauc's model was used to identify the types of electronic transitions in the samples. The single-oscillator model was utilized to investigate the dispersion energy and parameters. Nonlinear optical properties were also investigated. UV-Vis in the region (360-410 nm), the analysis revealed that increasing the concentration of TiO2-NPs from 0 to 12 wt% reduced the absorption edge from 2.716 to 2.043 eV, decreased the direct (3.282 to 2.798 eV) and indirect (2.417 to 1.581 eV) energy band gaps, increased the Urbach energy from 0.692 to 1.295 eV, decreased the dispersion energy from 11.324 to 5.621 eV, decreased the single oscillator energy from 6.308 to 5.393 eV, and improved the other linear and nonlinear parameters. The findings support the usage of CS/TiO2 nanocomposite films in the packaging industry and a variety of optical applications.

Validation of a Simple HPLC/UV Method for Assay and In Vitro Release of Glycosaminoglycan from Pharmaceutical Formulations.

This study encompasses the validation of a simple, rapid, and sensitive HPLC/UV method developed in accordance with the guidelines set by ICH Q2(R2) for obtaining the active pharmaceutical ingredient from the glycosaminoglycan family in topical formulations. Previous methods reported for analyzing glycosaminoglycans in semisolid formulations are relatively complex and time-consuming, involving extraction, purification, and derivatization. This developed analytical method allows for straightforward extraction of the active pharmaceutical ingredient from the matrix, enabling the direct injection of samples. This method was performed and validated for the assay of the pharmaceutical gel and cream formulations to investigate the parameters of linearity (r = 0.9997 for the gel formulation and r = 0.9993 for the cream formulation), precision, accuracy, specificity, and robustness by HPLC/UV. Additionally, this method was used to determine the active ingredient in in vitro release studies. In vitro similarity correlation against commercial products was performed according to the Mann-Whitney U statistical test. The similarity results were 96.5-102.7% for the gel formulation and 98.0-106.0% for the cream formulation, which remained within the limits (75-133.33%) according to USP 1724. This proved that in vitro release profiles for both formulations were like those of the commercial product. In light of the research findings, we believe that the HPLC/UV analysis presented can be further enhanced in the future for determining the levels of active ingredients in various pharmaceutical formulations or for monitoring the levels of glycosaminoglycans in biological matrixes.

Fault-tolerant observer-based leader-following consensus control for LPV multi-agent systems using virtual actuators

This paper introduces a fault-tolerant consensus control approach for a continuous multi-agent system with actuator faults. The faults in the multi-agent system are modelled as additive and multiplicative actuator faults. The objective is to design a leader-following control for consensus-based Linear Parameter Varying (LPV) multi-agent systems. The proposed control approach employs a leader-following strategy, where the dynamics of the LPV virtual leader are defined. The synchronisation error between the followers and the virtual leader is considered, and a consensus control law is introduced. The fault-tolerant mechanism involves the design of a distributed LPV observer and an LPV virtual actuator. Fault-tolerance is achieved through the redistribution of control inputs based on the effectiveness of actuators and dynamic virtual actuators. The primary focus is on establishing Linear Matrix Inequalities (LMIs) conditions ensuring the existence of LPV consensus control, LPV observers, and LPV virtual actuator gains. To demonstrate the effectiveness of the proposed fault-tolerant control, simulation results considering a team of Unmanned Aerial Vehicles (UAVs) in formation under actuator faults are presented.

Assessing Performance of Estimation Techniques in Time Series Analysis when Trend-cycle Component is Linear

Abstract: Two decomposition techniques are Buys-Ballot and least square techniques are presented in this study. The two important patterns that may be discussed are trend and seasonality and two competing models are additive and multiplicative models. The trend-cycle component is linear. The emphasis is to assess the performance of Buys-Ballot estimates and least square estimates using accuracy measures (Mean Error (ME), Mean Square Error (MSE), Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE). Results show that the two estimation techniques are very good in estimating the linear trend parameters and seasonal effects when the model for decomposition is additive. It differs for multiplicative model.

Enhancing hospital protection measures reduces frontline medical workers’ stress during the pandemic

Frontline medical workers (FMWs) faced high stress levels in frontline clinics during the COVID-19 pandemic. This study aims to alleviate FMWs’ psychological stress by enhancing protection measures, which includes refining the selection process, improving protective measures for their work in frontline clinics, and determining the appropriate time for evacuation. A Chinese-language-version stress questionnaire, covering stress-related issues and sociodemographic characteristics, was administered to FMWs in Shanghai during the COVID-19 pandemic in 2022, yielding 107 valid responses. The questionnaire’s reliability and validity were subsequently confirmed. Exploratory factor analysis (EFA) was applied to the stress-related questions, with the KMO and Bartlett’s test values of 0.886, 877.8522 (df = 120, p < 0.0001), respectively. Structure equation modeling (SEM) was used to confirm the factors and measure the relationships among the stress-related questions, factors and sociodemographic characteristics. The parameters of SEM named SOFAIDC were significant with SRMSR, RMSEA, AGFI, NFI, and PNFI being 0.0422, 0.0507, 0.9946, 0.9958, and 0.7615, respectively. Paired sample t-tests revealed the significant decrease in FMWs’ stress score of the current week and the previous week, with all t-values being negative and significant (p < 0.01). A latent growth model (LGM) named LGM30 verified the overall decreasing stress trend over the weeks, with high R-squares (> 0.80), significant positive linear and negative quadratic time parameters. Based on the trajectory analysis, a stress scorecard with an AUC of 0.856 was developed. This study found that there are four factors for FMWs’ psychological stress (anxiety about infection, exhaustion, lack of cognition for infection, and hesitant feeling), and improving targeted hospital protection could alleviate FMWs’ psychological stress through SOFAIDC, as all the total effect of factors or items from the feeling of being protected by hospital were negative. Meanwhile, although overall FMWs’ stress trend has decreased, 22.43% of FMWs have maintained or experienced a high stress trend, and the stress might increase over weeks in frontline clinics. To perfect hospital protection to alleviate FMWs’ psychological stress, the scorecard could be used to select FMWs with low-stress trends, LGM30 could be used to determine the withdrawal time (such as week 8), and targeted hospital protections could be designed based on the relationships between feeling of being protected by the hospital and factors in SOFAIDC, such as providing adequate protective equipment, improving the rationality of FMWs’ work schedules, recruiting personnel with higher education levels, and paying adequate monetary compensation.

Finite‐Time Functional Interval Observer Design for Nonlinear Discrete‐Time Switched Descriptor Systems

ABSTRACTIn this article, the finite‐time functional interval estimation method for nonlinear discrete‐time switched descriptor systems with perturbations is investigated. To deal with the nonlinear terms in the switched system, the nonlinear error system is converted into a linear parameter varying form using the reformulated Lipschitz property. Firstly, a functional observer with finite‐time gain is constructed for the nonlinear switched descriptor system. Then, based on the proposed finite‐time functional observer, the reachability analysis is applied to design a finite‐time functional interval observer. Finally, the superiority and effectiveness of the interval estimation method presented in this paper are verified through a simulation of the circuit system.