Curve Fitting Error Research Articles

Magnetohydrodynamics tangent hyperbolic nanofluid flow across a vertical stretching surface using Levengberg-Marquardt back propagation artificial neural networks

This analysis uses the Levenberg-Marquardt back propagation artificial neural networks (LM-BP-ANNs) approach to demonstrate the mathematical strategy of neural networks for the simulation of MHD Tangent hyperbolic nanofluid (THNF) flow consisting of motile microorganisms through a vertically extending surface. The fluid flow is being investigated in terms of exponential heat source/sink, thermal radiation, and magnetic field. The modeled equations are relegated to the ordinary system of differential equations by substituting similarity variables. The ND-solve approach is applied for the modeled equations to numerically handle and generate a dataset. Several activities, including testing, verification, and training, are performed by creating a scheme for various fluid problems using reference data sets. The precision of LM-BP-ANNs is evaluated using mean square error, curve fitting error histogram, and the regression analysis plot. Furthermore, graphs are used to analyze flow parameters for concentration, momentum, and energy profiles. It has been observed that the velocity field declines as the magnetic field grows stronger. The THNF model for energy, mass, and momentum equations is tested, authenticated, and trained within an average of 10−9. The LM-BP-ANNs accomplish the highest accuracy, with a target date and absolute error reference values in the 10−4 to 10−5 range.

Thermal dynamics assessment for multi-phase flow analysis with motile cilia and electric double layer effects: Application of Levenberg–Marquardt backpropagation NNs

Ciliary movement holds substantial importance in the realm of biomedical research. Disorders arising from impaired ciliary motion, such as primary ciliary dyskinesia and specific respiratory ailments, underscore the critical need to investigate both the normal functioning and dysfunction of cilia. Such research is fundamental to the development of effective treatments and therapies. This work explores the application of Levenberg–Marquardt backpropagation neural networks (LMBP-NNs) for simulating the flow of a non-Newtonian Jeffery fluid in peristaltic motion. Inspired by synchronous ciliary movement, microfluidic systems mimicking cilia functionality have been developed. These artificial cilia can generate controlled fluid flow patterns, enabling various applications such as drug delivery, mixing, and particle sorting in lab-on-a-chip devices. The present study focuses on measuring thermal and mass transfer in beating cilia during multiphase peristaltic pumping of Jeffery fluid in two- and three-dimensional channels using transverse magnetohydrodynamics in a porous medium. The governing equations for the non-Newtonian Jeffery fluid in both the fluid and dusty phases are formulated, and exact solutions are calculated for fluid phase velocity, particulate phase velocity, temperature, concentration, and pressure gradient. The physical behavior is investigated by graphing dimensionless parameters for velocity, temperature, and concentration profiles in both solid and liquid phases. The trapping phenomena is depicted by showing streamlines of various dimensionless characteristics such as porosity velocity and volume percentage. The LMBP-NNs approach is then used to train, test, and verify the neural network models using the reference datasets. The accuracy of the LMBP-NN is assessed using statistical data such as mean square error, curve fitting graphs, regression plots, and error histograms. The study also investigates flow model limits for momentum, temperature, and concentration profiles using visual representations. This study illustrates the computational capability of LMBP-NNs in modeling the peristaltic flow of Jeffery fluid and gives useful insights into fluid flow behavior in microfluidic devices containing artificial cilia. The findings help to better understand and optimize these systems for a variety of fluid manipulation and transportation applications.

Embracing uncertainty in cerebrospinal fluid dynamics: A Bayesian approach to analysing infusion studies

IntroductionCerebrospinal fluid (CSF) infusion test analysis allows recognizing and appropriately evaluating CSF dynamics in the context of normal pressure hydrocephalus (NPH), which is crucial for effective diagnosis and treatment. However, existing methodology possesses drawbacks that may compromise the precision and interpretation of CSF dynamics parameters. Research questionThis study aims to circumvent these constraints by introducing an innovative analysis method grounded in Bayesian inference. Material and methodsA single-centre retrospective cohort study was conducted on 858 patients who underwent a computerized CSF infusion test between 2004 and 2020. We developed a Bayesian framework-based method for parameter estimation and compared the results to the current, gradient descent-based approach. We evaluated the accuracy and reliability of both methods by analysing erroneous prediction rates and curve fitting errors. ResultsThe Bayesian method surpasses the gradient descent approach, reflected in reduced inaccurate prediction rates and an improved goodness of model fit. On whole cohort level both techniques produced comparable results. However, the Bayesian method holds an added advantage by providing uncertainty intervals for each parameter. Sensitivity analysis revealed significance of the CSF production rate parameter and its interplay with other variables. The resistance to CSF outflow demonstrated excellent robustness. Discussion and conclusionThe proposed Bayesian approach offers a promising solution for improving robustness of CSF dynamics assessment in NPH, based on CSF infusion tests. Additional provision of the uncertainty measure for each diagnostic metric may perhaps help to explain occasional poor diagnostic performance of the test, offering a robust framework for improved understanding and management of NPH.

Programming for exposure chart modelling in conventional X-ray radiography

In radiography, an exposure chart is needed to determine the correct exposure. The creation of exposure chart so far requires a lot of film. To reduce the use of film, a program was created that utilizes the principles of radiographic exposure in the form of the relationship between tube current, tube voltage, exposure time, and geometry principles. The program was validated through curve fitting and Mean Absolute Percentage Error (MAPE) by comparing the density of the specimen radiograph image with the exposure chart generated by the program. The generated exposure chart is the exposure chart for steel with voltages of 120 kV, 130 kV, 140 kV, 150 kV, and 160 kV. The resulting exposure chart has a coefficient of determination of 0.97 and has high accuracy.

Auxiliary Diagnostic Signal for Deep-Level Detection.

We propose and demonstrate that temperature-dependent curve-fitting error values of the Schottky diode I-V curve in the forward regime can be an auxiliary diagnostic signal as the temperature-scan Capacitance DLTS (CDLTS) signals and helps to work time-efficiently with high accuracy when using the Laplace Transform (LT)-DLTS or Isothermal Capacitance transient spectroscopy (ICTS) method. Using Be-doped GaAs showing overlapping DLTS signals, we verify that the LT-DLTS or ICTS analysis within a specific temperature range around the characteristic temperature Tpeak coincides well with the results of the CDLTS and Fourier Transform DLTS performed within the whole temperature range. In particular, we found that the LT-DLTS signals appeared intensively around Tpeak, and we confirmed it with the ICTS result. The occurrence of the curve fitting error signal is attributed to the relatively increased misfit error by the increased thermal emission from the deep-level trap in the case near the Tpeak, because the applied transport model excludes defect characteristics.

Research and Design of High-precision Voltage Sampling Circuit for Tumor Radiofrequency Ablation Medical Instrument

Radiofrequency ablation is a minimally invasive procedure in which tiny radiofrequency electrodes are implanted into the diseased tissue under the guidance of medical imaging (X-ray imager, CT or ultrasound), and neutral electrodes are attached to the skin of the body to carry out radiofrequency ablation, which is carried out by forming a circuit through the human body to the diseased tissue. At present, RF ablation can be applied to lung tumors, liver tumors, kidney tumors and certain heart diseases. The core component of tumor RF ablation surgery equipment is RF power source, which is a fixed frequency sinusoidal AC output signal with a frequency of 400-500Khz. The detection technology of RF voltage is extremely important, which determines the accuracy of RF ablation energy output and energy control. In this paper, we use STM32 microcontroller as the core of acquisition and control, and propose a simple and practical sampling method with high accuracy. Moreover, we have realized to control the voltage measurement error below 1% by using the error curve fitting method for software calibration.

Improving the Accuracy of Multipole Magnetic Encoder by Three-Phase Hall

Magnetic encoders have widespread applications in various fields such as aerospace, automotive, robot joint control and machine tool turntables. For instance, obtaining accurate rotation angles of motors is crucial for servo motor control. Herein, we propose an angle-solving algorithm based on a dual-multipair pole magnetic encoder. First, we analyze the nonlinearity issue caused by installation error of the Hall signal and devise a self-adjustment algorithm for the analog signal. Second, we improve the high speed and robustness of the encoder in identifying eigenvalue intervals while solving for angles. Finally, through the big data analysis, the calibration compensation of curve fitting error was performed, and experiments were conducted to verify the effectiveness of the real-time angle-solving algorithm in a high-precision encoder.

Cascaded Feedforward Neural Network Based Simultaneously Fast and Precise Multi-Characteristics Extraction and BFS Error Estimation

We present and investigate a scheme to realize fast and precise multi-characteristics extraction and error estimation of Brillouin frequency shift (BFS) simultaneously based on a cascaded feedforward neural network for a Brillouin optical time-domain analyzer (BOTDA) system. The cascaded feedforward neural network is composed of two neural networks in series, where the pre-network is used to extract linewidth (FWHM), signal-to-noise ratio (SNR) and BFS from noised gain spectrum and the post-network utilizes these characteristics and known frequency step to estimate the statistical error of the extracted BFS. The extracted BFS can be used to obtain the environment information along the fiber, while the extracted SNR, FWHM and the estimated BFS error can be utilized to verify the validity of data and monitor the performance of the BOTDA system. The creation process and the performance of the pre-network, post-network and cascaded network are described and analyzed in detail. Both simulation and experimental results show that the cascaded feedforward neural network has higher accuracies on extractions of characteristics (BFS, SNR, FWHM) and error estimation than conventional Lorentzian curve fitting method and error estimation formula when the scanning frequency step of system is large or SNR is low. More importantly, the network is more than 300 times faster than the LCF for simultaneously multi-characteristics extraction and error estimation, which make it possible to real-time monitor the performance of BOTDA system.

Forecasting Monthly Wind Energy Using an Alternative Machine Training Method with Curve Fitting and Temporal Error Extraction Algorithm

The aim of this research was to forecast monthly wind energy based on wind speed measurements that have been logged over a one-year period. The curve type fitting of five similar probability distribution functions (PDF, pdf), namely Weibull, Exponential, Rayleigh, Gamma, and Lognormal, were investigated for selecting the best machine learning (ML) trained ones since it is not always possible to choose one unique distribution function for describing all wind speed regimes. An ML procedural algorithm was proposed using a monthly forecast-error extraction method, in which the annual model is tested for each month, with the temporal errors between target and measured values being extracted. The error pattern of wind speed was analyzed with different error estimation methods, such as average, moving average, trend, and trained prediction, for adjusting the intended following month’s forecast. Consequently, an energy analysis was performed with effects due to probable variations in the selected Lognormal distribution parameters, according to their joint Gaussian probability function. Error estimation of the implemented method was carried out to predict its accuracy. A comparison procedure was performed and was found to be in line with the conducted Markov series analysis.

An Autonomous Storage Optimization LRM Generation Strategy Based on Cascaded NURBS

Automatic control of intelligent vehicles depends heavily on accurate lane-level location information. The traditional digital map cannot meet the automatic driving requirements, and it is very difficult for lane-level road maps (LRMs) to achieve a good balance between the representation accuracy and data storage volume. To tackle this problem, we obtain the recursive definition of a lane line by analyzing road lanes using the fractal geometry theory. Subsequently, we construct a recursive feedback system and model it. On this basis, an autonomous storage optimization LRM generation strategy based on cascaded NURBS is devised. According to the input data density, this framework generates an LRM with the minimum data storage volume within the error constraint. It is mainly composed of two modules: (1) a random fractal and (2) an adaptive iteration memory optimizer, based on cascaded NURBS error feedback. First, the whole lane is divided into several meta lane line modules. Second, data sampling/interpolation is carried out iteratively according to the NURBS fitting error and symmetry of road geometry. In this way, the storage space used to store lane lines and other information is automatically optimized. Last, a simulation experiment is carried out by using a dataset obtained from a park. The simulation results show that the proposed method can achieve high accuracy and high storage efficiency. Under the constraint of a 0.1 m curve fitting error, the average memory demand of the lane line elements is less than 2.4 bytes/m.

Systemic Illiquidity Noise-Based Measure—A Solution for Systemic Liquidity Monitoring in Frontier and Emerging Markets

The paper presents an alternative approach to measuring systemic illiquidity applicable to countries with frontier and emerging financial markets, where other existing methods are not applicable. We develop a novel Systemic Illiquidity Noise (SIN)-based measure, using the Nelson–Siegel–Svensson methodology in which we utilize the curve-fitting error as an indicator of financial system illiquidity. We empirically apply our method to a set of 10 divergent Central and Eastern Europe countries—Bulgaria, Croatia, Czechia, Estonia, Hungary, Latvia, Lithuania, Poland, Romania, and Slovakia—in the period of 2006–2020. The results show three periods of increased risk in the sample period: the global financial crisis, the European public debt crisis, and the COVID-19 pandemic. They also allow us to identify three divergent sets of countries with different systemic liquidity risk characteristics. The analysis also illustrates the impact of the introduction of the euro on systemic illiquidity risk. The proposed methodology may be of consequence for financial system regulators and macroprudential bodies: it allows for contemporaneous monitoring of discussed risk at a minimal cost using well-known models and easily accessible data.

18F-FDG PET and DCE kinetic modeling and their correlations in primary NSCLC: first voxel-wise correlative analysis of human simultaneous [18F]FDG PET-MRI data

ObjectivesTo decipher the correlations between PET and DCE kinetic parameters in non-small-cell lung cancer (NSCLC), by using voxel-wise analysis of dynamic simultaneous [18F]FDG PET-MRI.Material and methodsFourteen treatment-naïve patients with biopsy-proven NSCLC prospectively underwent a 1-h dynamic [18F]FDG thoracic PET-MRI scan including DCE. The PET and DCE data were normalized to their corresponding T1-weighted MR morphological space, and tumors were masked semi-automatically. Voxel-wise parametric maps of PET and DCE kinetic parameters were computed by fitting the dynamic PET and DCE tumor data to the Sokoloff and Extended Tofts models respectively, by using in-house developed procedures. Curve-fitting errors were assessed by computing the relative root mean square error (rRMSE) of the estimated PET and DCE signals at the voxel level. For each tumor, Spearman correlation coefficients (rs) between all the pairs of PET and DCE kinetic parameters were estimated on a voxel-wise basis, along with their respective bootstrapped 95% confidence intervals (n = 1000 iterations).ResultsCurve-fitting metrics provided fit errors under 20% for almost 90% of the PET voxels (median rRMSE = 10.3, interquartile ranges IQR = 8.1; 14.3), whereas 73.3% of the DCE voxels showed fit errors under 45% (median rRMSE = 31.8%, IQR = 22.4; 46.6). The PET-PET, DCE-DCE, and PET-DCE voxel-wise correlations varied according to individual tumor behaviors. Beyond this wide variability, the PET-PET and DCE-DCE correlations were mainly high (absolute rs values > 0.7), whereas the PET-DCE correlations were mainly low to moderate (absolute rs values < 0.7). Half the tumors showed a hypometabolism with low perfused/vascularized profile, a hallmark of hypoxia, and tumor aggressiveness.ConclusionA dynamic “one-stop shop” procedure applied to NSCLC is technically feasible in clinical practice. PET and DCE kinetic parameters assessed simultaneously are not highly correlated in NSCLC, and these correlations showed a wide variability among tumors and patients. These results tend to suggest that PET and DCE kinetic parameters might provide complementary information. In the future, this might make PET-MRI a unique tool to characterize the individual tumor biological behavior in NSCLC.

Real-Time Data Logging and Online Curve Fitting Using Raspberry Pi in Physics Laboratories

The results of PISA 2015 indicate that Taiwanese students have excellent mathematical and scientific knowledge but are weak in applying such knowledge and in conducting practical experiments in the laboratory. To support students conducting practical experiments in physics laboratories, a real-time data logging system and an online tool for fitting experimental data were developed. During data logging in an experiment, the data was immediately plotted, which enabled students to observe the characteristics of the plot. The online curve fitting system, which employed Internet of Things technologies, allowed students to fit experimental data to various mathematical functions and plot a function curve superimposed on the data. Two empirical studies were conducted involving first-year university students and secondary school teachers. The results indicated that these developed tools improved students' understanding of an experiment's mathematical characteristics. The average curve fitting error rates of students and teachers were 4.62% and 1.4%, respectively.

A generalized differential method to calculate lumped kinetic triplet of the nth order model for the global one-step heterogeneous reaction using TG data

Computing kinetic triplet is of importance for the process safety of combustion/gasification industries to establish the chemical reaction scheme and to assess the hazardous risk. Few approaches have been capable of calculating lumped kinetic triplet at one time efficiently, which might be attributed to the fact that the analytical solution for the nonlinear ordinary differential equation (NNODE) for the nth order reaction model has not been found yet. This paper presents an analytical solution of NNODE to compute kinetic triplet. Results showed that the proposed method (mass fraction curve-fitting error ϕ = 1.49%–2.07%) is more efficient to compute kinetic triplet of the nth order reaction model, comparing to genetic algorithm (GA) optimization (ϕ = 1.43%–1.81%), Coats-Redfern (ϕ = 2.36%–3.16%), peak-shape, and isoconversional methods. A compensation effect between lnA and Ea is observed due to heating rates. Effects of exported data quality and smooth processing on computation of kinetic triplet are discussed. It is the first time that an analytical solution of NNODE (nth order model) for global one-step heterogeneous reaction is derived for computing kinetic triplet. This work may help to search for analytical solutions of power-law and Avrami-Erofeev models in the future to efficiently calculate kinetic triplet for accelerating and sigmoidal reaction systems.

Research on Influence of CMM Sampling Points on Detection of Feature Parameters for Turbine Blade

Sampling plan is an essential part for measuring profile of turbine blade with coordinates measuring machine(CMM), and the detection of feature parameters is a key component of turbine blade inspection. However, the influence of the sampling strategy on the blade feature parameters evaluation has been rarely studied. In order to understand the correlation between the sampling strategy and the accuracy of blade profile feature parameters, firstly, the extraction methods of turbine blade feature parameters were proposed, and these methods were compiled into an executable program TBGeoInspect. Secondly, based on the level principle, the unified mathematical representations of uniform sampling, curvature-based sampling, chord deviation sampling, weighted curvature-based sampling, and curvature-arc length sampling were given. The effect of these five sampling algorithms on the accuracy of turbine blade profile feature parameters was gained through simulation and experiment results of blade sampling. The results validate that the uncertainty of turbine blade feature parameters and sectional curve fitting error are lowest with curvature-arc length sampling method under the same number of sampling points.

An experimental and theoretical stress-strain-damage correlation procedure for constitutive modelling of granite

In this study, new theoretical and experimental stress-strain-damage correlation procedures for hard rock constitutive models are proposed. The damage-plasticity modelling framework is first supplied with the unified yield-failure criterion to describe the failure behaviour of granite under triaxial compression. This unified criterion allows the initial yield surface to evolve to a final failure surface through the utilisation of an appropriate damage evolution law. This evolution automatically captures the quasi-brittle behaviour of rocks under shearing at low confining pressure and ductile response under high confining pressure, as well as the transition from quasi-brittle to ductile reactions. In this theoretical sense, damage and plasticity are tightly coupled to govern the behaviour of rocks under different confining pressures without requiring any separate formulations for softening or hardening. Next, an innovative experimental correlation procedure is proposed to better link the experimental damage measure to stress states throughout triaxial loading. By obtaining full stress, strain and acoustic emission damage results from testing it was possible to construct a series of evolving yield surfaces from experiment. These surfaces, coupled with experimental damage evolution with respect to accumulated plastic strain, provide a comprehensive data set to a constitutive model for calibration. The results of numerical simulation show that this new method to incorporate coupled stress-strain-damage evolution characteristics directly from experiment removes the need for trial and error curve fitting. Also, by maintaining a closer link to detailed experimental results, the model is easier to calibrate and can be relied upon to predict the damage and stress states for compressive stress regimes. Finally, it is shown that the theoretical and experimental procedures can capture the key behaviours of granite under a range of confining pressures.

Association of respiratory integer and fractional-order models with structural abnormalities in silicosis

Background and objectiveInteger and fractional-order models have emerged as powerful methods for obtaining information regarding the anatomical or pathophysiological changes that occur during respiratory diseases. However, the precise interpretation of the model parameters in light of the lung structural changes is not known. This study analyzed the associations of the integer and fractional-order models with structural changes obtained using multidetector computed tomography densitometry (MDCT) and pulmonary function analysis. MethodsInteger and fractional-order models were adjusted to data obtained using the forced oscillation technique (FOT). The results obtained in controls (n = 20) were compared with those obtained in patients with silicosis (n = 32), who were submitted to spirometry, body plethysmograph, FOT, diffusing capacity of the lungs for carbon monoxide (DLCO), and MDCT. The diagnostic accuracy was also investigated using ROC analysis. ResultsThe observed changes in the integer and fractional-order models were consistent with the pathophysiology of silicosis. The integer-order model showed association only between inertance and the non-aerated compartment (R = −0.69). This parameter also presented the highest associations with spirometry (R = 0.81), plethysmography (−0.61) and pulmonary diffusion (R = 0.53). Considering the fractional-order model, the increase in the poorly aerated and non-aerated regions presented direct correlations with the fractional inertance (R = 0.48), respiratory damping (R = 0.37) and hysteresivity (R = 0.54) and inverse associations with its fractional exponent (R = −0.62) and elastance (−0.35). Significant associations were also observed with spirometry (R = 0.63), plethysmography (0.37) and pulmonary diffusion (R = 0.51). Receiver operator characteristic analysis showed a higher accuracy in the FrOr model (0.908) than the eRIC model (0.789). ConclusionsOur study has shown clear associations of the integer and fractional-order parameters with anatomical changes obtained via MDCT and pulmonary function measurements. These findings help to elucidate the physiological interpretation of the integer and fractional-order parameters and provide evidence that these parameters are reflective of the abnormal changes in silicosis. We also observed that the fractional-order model showed smaller curve-fitting errors, which resulted in a higher diagnostic accuracy than that of the eRIC model. Taken together, these results provide strong motivation for further studies exploring the clinical and scientific use of these models in respiratory medicine.

A real-time approach to robust identification of tyre–road friction characteristics on mixed-μ roads

ABSTRACTThe interaction between the tyre and the road is crucial for understanding the dynamic behaviour of a vehicle. The road–tyre friction characteristics play a key role in the design of braking, traction and stability control systems. Thus, in order to have a good performance of vehicle dynamic stability control, real-time estimation of the tyre–road friction coefficient is required. This paper presents a new development of an on-line tyre–road friction parameters estimation methodology and its implementation using both LuGre and Burckhardt tyre–road friction models. The proposed method provides the capability to observe the tyre–road friction coefficient directly using measurable signals in real-time. In the first step of our approach, the recursive least squares is employed to identify the linear parameterisation form of the Burckhardt model. The identified parameters provide, through a T–S fuzzy system, the initial values for the LuGre model. Then, a new LuGre model-based nonlinear least squares parameter estimation algorithm using the proposed static form of the LuGre to obtain the parameters of LuGre model based on recursive nonlinear optimisation of the curve fitting errors is presented. The effectiveness and performance of the algorithm are demonstrated through the real-time model simulations with different longitudinal speeds and different kinds of tyres on various road surface conditions in both Matlab/Carsim environments as well as collected data from real experiments on a commercial trailer.

The Inductive and Capacitive Characteristics of Carbonate-Derived Carbons

Due to the increasing modern dependence on electronic devices, the production of carbon materials for supercapacitive and battery-based applications is an area of current research and innovation. It has been known for a considerable time that carbons can be formed through the electrolytic reduction of molten carbonate salts [1], however, little research has been put into in-depth understanding of the electrochemical characteristics of these materials. Electrochemical impedance spectroscopy can tell us a lot about the suitability of these materials for supercapacitive applications. This research investigates how the characteristics of carbons derived through molten carbonate reduction change based on synthesis conditions, with a particular focus being placed on the inductive and capacitive behaviour of the materials and on how inductances arise (Figure 1 (i)). This is done through the application of equivalent circuit modelling (Figure 1 (ii)) to cells constructed from synthesised and activated carbons, and the subsequent mathematical modelling of the system using complex non-linear least squared error curve fitting (CNLS) based on the interior-point algorithm in the MATLAB program. The frequency-dependant capacitance of the materials (Figure 1 (iii)) is reported and used as a point of comparison. Optimal carbon synthesis conditions of 500°C or low deposition current densities of 0.15 A/cm2 have been found to both reduce inductive behaviour, and to produce carbons with capacitances as high as 160 F/g, close to 90% of that of the examined activated carbon. [1] Hughes, M.A., J.A. Allen, and S.W. Donne, Carbonate Reduction and the Properties and Applications of Carbon Formed Through Electrochemical Deposition in Molten Carbonates: A Review. Electrochimica Acta, 2015. 176: p. 1511-1521. Figure 1

Real-Time Curvature Detection of a Flexible Needle with a Bevel Tip.

As one of the major methods for the diagnosis and treatment of cancers in their early stages, the percutaneous puncture technique has bright prospect in biopsy, ablation, proximity radiotherapy, and drug delivery. Recent years, researchers found the flexible needle cannot realize feedback control during the puncture surgeries only by path planning. To solve this problem, the flexible needle is tried to achieve real-time detection in this paper. Compared with previous methods, the strain gauges glued on the needle surface rather than the medical imaging techniques is used to collect the information to reconstruct the needle curve, which is benefit to integrate the whole system and obtain a more simple and accurate closed-loop control. This paper presented the math model of curve fitting and analyzed the causes of curve fitting errors. To verify the feasibility of this method, an experiment setup was built. Results from the experiments validated the solution in this paper to be effective.