Curve Fitting Process Research Articles

Identification problem of acoustic media in the frequency domain based on the topology optimization method

In this paper, the identification problem of acoustic parameters in the frequency domain is examined by means of a topology optimization (TO) approach. Data measured by acoustic receivers are collected from synthetic models and used as a reference in the optimization problem which aims at estimating the acoustic media properties that minimize a least-squares cost functional. A two-step optimization procedure is proposed to deal with multi-phase acoustic media problems by using linear and peak function material interpolation schemes. The idea is to use features from the multi-material topology optimization to reconstruct acoustic models with an increased level of sharpness. From the first step with linear interpolation, phase candidates are defined by a curve fitting process considering the summation of Gaussian curves and, therefore, this solution is used to create the peak material model for the second step. Thus, a multi-material model that is usually applied to design problems with predefined material candidates can be also used to solve this identification problem without prior knowledge of the exact properties of the model to be reconstructed. The optimization problem is solved by using a BFGS algorithm while the Levenberg-Marquardt Algorithm (LMA) is used to solve the least-squares curve-fitting problem. The proposed approach is analyzed through 2D numerical examples.

A comprehensive study of the second law of thermodynamics for a rotary regenerative heat exchanger with two types of simple and anodized aluminum sheets: an experimental study

ABSTRACT Rotary regenerative heat exchangers are commonly used in the industry. However, the corrosion of sheets that are in contact with the operating fluid is considered as the disadvantage of these heat exchangers. This causes a reduction in the lifespan of this kind of heat exchanger. The object of the present study is to evaluate and compare the exergy loss and the second law efficiency of a rotary regenerative heat exchanger, which is made from two types of simple aluminum sheets and anodized aluminum sheets are. Anodized sheets are used to enhance the corrosion resistance of the regenerative heat exchanger. The results indicated that the lower exergy loss and the dimensionless exergy loss with anodized sheets about 14–24% and 15–20% compared to the heat exchanger with simple sheets, respectively. Besides, the effects of rotational speed of the matrix, inlet temperature of hot flow, and the flow rates of hot and cold flows on the rotary regenerative heat exchanger are evaluated. Finally, some empirical correlations have been developed based on the obtained data and curve fitting process.

Array Shape Estimation of a Horizontal Suspension Hydrophone Line Array

A horizontal suspension hydrophone line array system for deep water target detection is demonstrated. Theoretical estimation of the array shapes at different array states is fulfilled through detailed kinetic analysis. When steady ocean forces solely exert on the array system from three orthogonal directions and the array is in the neutral-buoyancy state, the array shapes are parabola linetypes. When no ocean forces exert on the array system and the array is in the non-neutral buoyancy state, the static array shapes are catenary linetypes. The simulation results can guide the curve fitting process of the array shape estimation based on depth and attitude sensors.

Modeling and Identification of Temperature-Dependent Hysteresis in Piezoelectric Materials Considering Parameter Sensitivity

Hysteresis is an important nonlinearity effect in piezoelectric materials and is sensitive to temperature. This paper extends the saturated capacitor model to capture temperature-dependent hysteresis by replacing the constant parameters with functions of temperature. To obtain these functions, several sets of constant parameters are identified at different temperatures, and then each term of the parameters is fitted as a function with respect to temperature. In the curve fitting process, the parameter sensitivity is employed as a weight factor. The effectiveness of the proposed modeling and parameter determination procedure is verified with experimental data. The overall normalized root mean square error is approximately 5%, including 3% error caused by the identified parameters.

Arabic Fonts Representation in Cubic Bézier Curve using Different Soft Computing Algorithm

This study presents the comparison between two meta-heuristic algorithms for curve reconstruction of Arabic fonts. The two algorithms namely Sine Cosine Algorithm (SCA) and Whale Optimization Algorithm (WOA) are used for comparison purposes. These algorithms have been applied to optimize the solution of curve fitting problem by using cubic Bezier curve. There are several pre-processing steps involve before curve fitting process has been done. Firstly, extract the boundary. Then, detect the corner of outline fonts and the third step is chord length parameterization. The aim of this study is to find the best curve that fit the data. Sum Square Errors (SSE) has been used to calculate the error given by original image and parametric curve. The finding of this study shows that, WOA gives better curve approximation based on the errors result than SCA. This algorithm significantly improves the shape of the corner of the outline Arabic fonts.

A model for describing and predicting the creep strain of rocks from the primary to the tertiary stage

Rocks under applied stresses can exhibit more or less degree of creep. Over the years, a large number of creep models have been proposed for rocks. However, few models account for friction angle and time to failure. In most cases, curve fitting technique is applied to all of the available experimental results to obtain the required model parameters. The ability of the calibrated model (i.e. the model with the obtained model parameters) to predict the rheological behavior under untested stress conditions remains unknown. In this paper, a new model, called ubiquitous-corrosion-Coulomb (UCC) creep model, is proposed. Distinction is made between reversible and irreversible creep strains. Subcritical crack growth is related to the irreversible creep strain and delayed failure of rocks. The effect of friction angle and confining stresses on the rate of irreversible creep strain and time to failure has been considered. With the UCC model, the failure plane in creep tests making an angle of 45°−ϕ/2 with the major principal stress σ1 is explained by the fact that among the numerous micro cracks, the cracks along this orientation are the first ones becoming unstable. To test the capability of the UCC creep model against experimental results available in the literature, the required model parameters are first obtained by applying the curve-fitting technique on a part of the available experimental results. The predictability of the calibrated model is then tested against another part of the available experimental results, which are not used in the previous curve-fitting process. The results showed that the proposed UCC creep model can be used to describe and predict the creep strain and time to failure of rocks.

Models for kinetic energy and momentum correction coefficients for non-prismatic compound channels using regression and gene expression programming

This paper studies the effect of different independent variables related to the characteristics of the compound channels on the kinetic energy and momentum correction coefficients (termed as α and β, respectively) of non-prismatic compound channels. A series of experiments were carried out in a converging compound channel with three converging angles, six width ratios, six relative depths and three relative distances. Meanwhile, flow data sets from three different authors were used for diverging compound channels, which include simple rectangular and trapezoidal cross sections. In the present study, conventional multivariable regression technique and gene expression programming were used for developing different models for calculating kinetic energy and momentum correction coefficients for converging and diverging compound channels, respectively. The independent variables used in the curve fitting process were also tested for their accountability and influence on the proposed models. The developed models were finally established with the validation data set and a natural river system.

Design of Multilayer Frequency-Selective Surfaces by Equivalent Circuit Method and Basic Building Blocks

An equivalent circuit method (ECM) is proposed for the design of multilayer frequency-selective surfaces (FSSs). In contrast to the existing ECMs that were developed mainly for the analysis of the properties of a given FSS, the presented ECM aims at providing the initial design parameters of an FSS from the desired frequency response. In this method, four types of basic FSS structures are used as the building blocks to construct the multilayer FSSs, and their surface impedances in both the normal- and the oblique-incidence situations are studied in detail in order to achieve more accurate equivalent circuit (EC) representation of the entire FSS. For a general FSS design with expected frequency response, the EC parameters and the geometrical sizes of the required basic building blocks can be synthesized from a few typical S-parameter (S11/S12) samplings of the response curves via a simple least-square curve-fitting process. The effectiveness and accuracy of the method are shown by the designs of a band-pass FSS with steep falling edge and a miniaturized band-pass FSS with out-of-band absorption. The prototype of one design is fabricated, and the measured frequency response agrees well with the numerical results of the ECM and the full-wave simulations.

Estimation of the Country Ranking Scores on the Global Innovation Index 2016 Using the Artificial Neural Network Method

The Global Innovation Index (GII) aims to rank countries using different innovation factors. This ranking list enables countries to observe their potential status according to the rankings of other countries. The countries are classified under four groups according to the World Bank Income Group Classification on the GII list. The groups are named as; low income (LI), lower-middle income (LM), upper-middle income (UM) and high income (HI). Also, every country has a score in this ranking list. In this study, the ranking scores of 128 countries are estimated using the artificial neural network (ANN). We chose the relevant 27 features on GII 2016 Report, as input data. The significance of this paper is that; it is the first curve fitting and estimation of the score processes on GII 2016 dataset. The low root mean square error (RMSE) value which is obtained in an experimental study shows that the fitting structure is good enough to determine the approximate score of the countries in GII list. The results also show that the selected 27 features are sufficient for obtaining the income score of the countries. Increasing the number of features would lower the RMSE value and enable better approximation in the curve fitting process. The final results can assist the countries in achieving long-term output growth and improving their innovation capabilities.

Fluorescence lifetime estimation by 1-bit photon autocorrelation procedure from time-series data recorded using a high-speed digitizer

We propose a photon-counting fluorescence lifetime measurement scheme that uses a 1-bit autocorrelation procedure. The proposed scheme is an extension of the previously reported lifetime measurements using the autocorrelation analysis (Nishimura et al. in: Phys Med Biol 48:N283–N290, 2003; Nishimura et al. in: J Biomed Opt 12:020503, 2007). The fluorescence photons obtained from a high-repetition-rate, pulsed excitation light source are fed into a photodetector, and its output photoelectron pulse train is stored in a transient memory composed of a high-speed digitizer that retains time information over a large number of excitation cycles. After the stored data have been binarized, a 1-bit autocorrelation procedure is performed to estimate the fluorescence lifetimes through a repetitive curve-fitting process. We could successfully demonstrate this scheme in nanosecond fluorescence lifetime measurements with a progressed high-speed digitizer, which requires no synchronization with the excitation timing. To date, the minimum sampling interval and the maximum number of sample points of the digitizer are 400 ps and ~ 1 × 109, respectively. We present the results of some fluorescence lifetime measurements of standard samples that were performed as a proof of principle experiment.

Ductile fracture behavior of ECAP deformed AZ61 magnesium alloy based on response surface methodology and finite element simulation

The response surface methodology in the design of experiments (DOE) wizard and Gurson-Tvergaard-Needleman (GTN) model were employed to estimate the optimum GTN damage parameters and to validate their significant effects respectively on the ductile fracture behavior of ECAP deformed AZ61 magnesium alloy. Hollomon's flow stress was applied to identify uniform deformation and non-uniform deformation regions to investigate the void nucleation and coalescence processes separately. The significance of statistical results was evaluated with the analysis of variance (ANOVA) based on P-values and coefficients of determination (R2). Correspondingly, the contributions of ECAP plastic deformation and the corresponding local plasticity (damage progresses) on the progress of GTN ductile fracture damage parameters were studied. Desirability function was used to show the significance of individual and interaction effects of optimum initial damage parameters on the respective response variables. By using response surface methodology, the optimum GTN damage parameters were determined at the corresponding positions of each critical response variables. Results also showed that varying both stress triaxiality and damage variables simultaneously can greatly affect the curve fitting process of experimental, simulation and GTN model curves. However, at constant stress triaxiality condition, the GTN model curve was observed perfectly fitting with the tensile test curve.

Research on Trajectory Reconstruction Method Using Automatic Identification System Data for Unmanned Surface Vessel

The unmanned surface vessel (USV) trajectory with spatial and temporal information plays an important role in its positioning and navigation. Unlike traditional trajectory reconstruction methods, this paper proposes a novel method based on the automatic identification system (AIS) for USV. Aside from the AIS data applied for restoring the USV’s trajectory, the proposed method considers the constraints of the vessel’s navigation state, maneuvering factors and time stamps. This method consists of three steps: AIS data restoration, Empirical Mode Decomposition (EMD) denoising and Fermat’s spiral fitting. Firstly, AIS data restoration is applied to eliminate abnormal data. Next, the EMD noise reduction algorithm is used to reduce the jitters and interference of Speed over Ground (SOG) and Course over Ground (COG) components, and the denoised latitude and longitude positions are calculated using the kinematics model of the vessel. Finally, a curve fitting process based on Fermat’s spiral is employed to reconstruct a smoother trajectory. Several experiments illustrate that the low-cost AIS equipment is compatible with the navigation system of the USV. The reference trajectory is determined by Global Position System (GPS) and Inertial Measurement Unit (IMU) modules in USV. Compared to conventional methods, the residual errors of the proposed method is smaller. The results show that the novel trajectory reconstruction method is effective and can be applied to USV’s positioning and navigation.

Comparison of the material models in rubber finite element analysis

In rubber product design finite element analysis is widely used. The aim of this research is to choose the appropriate material models and to determine the related material parameters for finite element analysis of a rubber jounce. Rubber products can suffer from large deformation upon working conditions while behaving as a non-linearly elastic, isotropic and incompressible material. Hyperelastic material models accurately describe the observed material behaviour. Uniaxial compression test of rubber specimen has been performed to determine the stress-strain curve. Using test data and ANSYS for curve fitting process, the material constants for Mooney-Rivlin and Yeoh model have been established. Finite element analysis of the compression test has been made to validate the specified material constants. It can be stated that three term Yeoh model showed better agreement with the test data than the one term formula. Two term Mooney-Rivlin model showed good match with the measurement data, thereby it is also recommended for the future investigations of rubber jounce.

Adaptive inverse analysis (AIA) applied and verified on various fiber reinforced concrete composites

During the past decades several inverse approaches have been developed to identify the stress-crack opening ( $${\sigma }-w$$ ) by means of indirect test methods, such as the notched three point bending-, wedge splitting-, and round panel testing. The aim is to establish reliable constitutive models for the tensile behavior of fiber reinforced concrete materials, suitable for structural design. Within this context, the adaptive inverse analysis (AIA) was recently developed to facilitate a fully general and automatized inverse analysis scheme, which is applicable in conjunction with analytical or finite element simulation of the experimental response. This paper presents a new formulation of the adaptive refinement criterion of the AIA method. The paper demonstrates that the refinement criterion of the nonlinear least square curve fitting process, is significantly improved by coupling the model error to the crack mouth opening and the crack opening displacement relationship ( $$w_{\mathrm{cmod}}-w_{\mathrm{cod}}$$ ). This enables an adaptive refinement of the $${\sigma }-w$$ model in the line segment with maximum model error, which entails significant improvement of the numerical efficiency of the AIA method without any loss of robustness. The improved method is applied on various fiber reinforced concrete composites and the results are benchmarked with the inverse analysis method suggested by the Japanese Concrete Institute (Method of test for fracture energy of concrete by use of notched beam, Japanese Concrete Institute Standard, Tokyo, 2003) and recently adopted in ISO 19044 (Test methods for fibre-reinforced cementitious composites—load-displacement curve using notched specimen, 2015). The benchmarking demonstrates that the AIA method, in contradiction to the JCI/ISO method, facilitates direct determination of the tensile strength and operational multi-linear $${\sigma }-w$$ models.

Updating the ELISA standard curve fitting process to reduce uncertainty in estimated microcystin concentrations

This study is aimed at exploring the optimal ELISA standard curve fitting process for reducing measurement uncertainty. Using an ELISA kit for measuring cyanobacterial toxin (microcystin), we show that uncertainty associated with the estimated microcystin concentrations can be reduced by defining the standard curve as a four-parameter logistic function on the natural log concentration scale, instead of the current approach of defining the curve on the concentration scale. The model comparison method is outlined in this paper, allowing it to be transferable to test different statistical models for other ELISA test kits.

Energy efficiency and lighting design in courtyards and atriums: A predictive method for daylight factors

The proper design of courtyards and atriums is key in providing sufficient daylight inside buildings as well as major energy savings in electric lighting. Although a suitable design requires calculations using lighting simulation software or complex algorithms, architects lack a quick and precise procedure to determine proper design. The aim of this research is therefore to offer a fast accurate method for determining the daylight factor for different points on a rectangular courtyard or the central space of an atrium, based on the variable geometry and reflectance of the inner surfaces. Firstly, daylight factors are defined using measurements in scale models in an artificial sky and values obtained in real courtyards under real overcast skies. The sky component is subsequently defined based on earlier studies and Tregenza algorithms in order to quantify the reflected component. Following the curve fitting process, a predictive method of daylight factors is defined and compared with the previous measures. The comparison demonstrates that the predictive method offers an average accuracy of over 90% based on a quick and easy calculation. Finally, the energy saving in electric lighting is quantified following the predictive method established.

Investigation on similarity laws for dynamic properties of presses

The present paper deals with the experimental investigation of dynamic similarity laws of technical structures based on modal analyses of a reference and a scaled servo-screw press. At first, a brief introduction into the theoretical background is given and similarity principles for mechanical systems and used modal global and local correlation criteria are explained. After the description of the measurement setup and its evaluation, a comparison of the reference and the scaled press is carried out. The comparison is based on modal parameters obtained by experimental modal analysis where different data acquisition methods are used. For the reference press, frequency response functions (FRF) are obtained by impact hammer and acceleration sensors and for the scaled press by electrodynamic shaker and a laser scanning vibrometer. The acquired FRF’s are basis for the following curve fitting process to determine the modal parameters of both systems. Subsequently, the derivation of scale factors from modal parameters is characterized using eigenvalue and eigenvector related correlation criteria. The impact of different slide positions as well as the influence of various contact conditions between slide and frame on the scaling factors are analyzed and discussed. The investigation of slide position and contact condition influences are carried out using the obtained experimental modal parameters in combination with linear-elastic finite element models.

Curve Fitting of NURBS Curve for CNC Motion Controller

This paper proposes a real-time coplanar Non-Uniform Rational B-Spline (NURBS) curve fitting in a CAD/CAM system to improve fitting quality and reduce calculation effort. Curve segmentation is applied to filter the line segments and reshape the different NURBS curve segments. Both position errors and the first derivative are considered to avoid over fitting of the NURBS curve. After the fitted NURBS curve is obtained, the corresponding interpolation for each interpolated time is further processed to obtain the motion command for each axis. The real-time NURBS curve fitting process consists of (1) discrete points import, (2) linear segment filter, (3) curve reshaping, (4) curve fitting considering both the position errors and the first derivative. Simulation results show the proposed approach effectively improves the fitting quality and calculation efficiency.

Optimization of first order decay gas generation model parameters for landfills located in cold semi-arid climates

Canada has one of the highest waste generation rates in the world. Because of high land availability, land disposal rates in the province of Saskatchewan are high compared to the rest of the country. In this study, landfill gas data was collected at semi-arid landfills in Regina and Saskatoon, Saskatchewan, and curve fitting was carried out to find optimal k and Lo or DOC values using LandGEM, Afvalzorg Simple, and IPCC first order decay models. Model parameters at each landfill were estimated and compared using default k and Lo or DOC values. Methane generation rates were substantially overestimated using default values (with percentage errors from 55 to 135%). The mean percentage errors for the optimized k and Lo or DOC values ranged from 11.60% to 19.93% at the Regina landfill, and 1.65% to 10.83% at the Saskatoon landfill. Finally, the effect of different iterative methods on the curve fitting process was examined. The residual sum of squares for each model and iterative approaches were similar, with the exception of iterative method 1 for the IPCC model. The default values in these models fail to represent landfills located in cold semi-arid climates. The use of site specific data, provided enough information is available regarding waste mass and composition, can greatly help to improve the accuracy of these first order decay models.

Improved Liver R2* Mapping by Averaging Decay Curves

Liver R2* mapping is often degraded by the low signal-to-noise ratio (SNR) especially in the presence of severe iron. This study aims to improve liver R2* mapping at low SNRs by averaging decay curves before the process of curve-fitting. Independently filtering echo images by nonlocal means (NLM) demonstrated improved quality of R2* mapping, but may introduce new errors due to the nonlinear nature of the NLM filter, during which the averaging weights may vary with different image contents at multiple echo times. In addition, the image denoising effect of the NLM may decline when no sufficient similar patches are available. To overcome these drawbacks, we proposed to filter decay curves instead of images. In this novel scheme, decay curves were averaged in a local window, each with a weight assigned according to the curve-similarity measured by the distance between one of the neighboring curves and the targeted one. The proposed method was tested on simulated, phantom and patient data. The results demonstrate that the proposed method can provide more accurate R2* mapping compared with the NLM algorithm, and hence has the potential to improve diagnosis and therapy in patients with liver iron.