Methods for Fitting the Limit State Function of the Residual Strength of Damaged Ships

The limit state function is important for the assessment of the longitudinal strength of damaged ships under combined bending moments in severe waves. As the limit state function cannot be obtained directly, the common approach is to calculate the results for the residual strength and approximate the limit state function by fitting, for which various methods have been proposed. In this study, four commonly used fitting methods are investigated: namely, the least-squares method, the moving least-squares method, the radial basis function neural network method, and the weighted piecewise fitting method. These fitting methods are adopted to fit the limit state functions of four typically sample distribution models as well as a damaged tanker and damaged bulk carrier. The residual strength of a damaged ship is obtained by an improved Smith method that accounts for the rotation of the neutral axis. Analysis of the results shows the accuracy of the linear least-squares method and nonlinear least-squares method, which are most commonly used by researchers, is relatively poor, while the weighted piecewise fitting method is the better choice for all investigated combined-bending conditions.

The Fitting Optimization Path Analysis on Scale Missing Data: Based on the 507 Patients of Poststroke Depression Measured by SDS

Objective. To explore the optimal fitting path of missing data of the Scale to make the fitting data close to the real situation of patients’ data. Methods. Based on the complete data set of the SDS of 507 patients with stroke, the data simulation sets of Missing Completely at Random (MCAR), Missing at Random (MAR), and Missing Not at Random (MNAR) were constructed by R software, respectively, with missing rates of 5%, 10%, 15%, 20%, 25%, 30%, 35%, and 40% under three missing mechanisms. Mean substitution (MS), random forest regression (RFR), and predictive mean matching (PMM) were used to fit the data. Root mean square error (RMSE), the width of 95% confidence intervals (95% CI), and Spearman correlation coefficient (SCC) were used to evaluate the fitting effect and determine the optimal fitting path. Results. when dealing with the problem of missing data in scales, the optimal fitting path is ① under the MCAR deletion mechanism, when the deletion proportion is less than 20%, the MS method is the most convenient; when the missing ratio is greater than 20%, RFR algorithm is the best fitting method. ② Under the Mar mechanism, when the deletion ratio is less than 35%, the MS method is the most convenient. When the deletion ratio is greater than 35%, RFR has a better correlation. ③ Under the mechanism of MNAR, RFR is the best data fitting method, especially when the missing proportion is greater than 30%. In reality, when the deletion ratio is small, the complete case deletion method is the most commonly used, but the RFR algorithm can greatly expand the application scope of samples and save the cost of clinical research when the deletion ratio is less than 30%. The best way to deal with data missing should be based on the missing mechanism and proportion of actual data, and choose the best method between the statistical analysis ability of the research team, the effectiveness of the method, and the understanding of readers.

Shape Approximation and Size Difference of the Upper Part of the Talus: Implication for Implant Design of the Talar Component for Total Ankle Replacement

The implant design of the talar component for total ankle replacement (TAR) should match the surface morphology of the talus so that the replaced ankle can restore the natural motion of the tibiotalar joint and may reduce postoperative complications. The purpose of this study was to introduce a new 3D fitting method (the two-sphere fitting method of the talar trochlea with three fitting resection planes) to approximate the shape of the upper part of the talus for the Chinese population. 90 models of the tali from CT images of healthy volunteers were used in this study. Geometrical fitting and morphological measurements were performed for the surface morphology of the upper part of the talus. The accuracy of the two-sphere fitting method of the talar trochlea was assessed by a comparison of previously reported data. Parameters of the fitting geometries with different sizes were recorded and compared. Results showed that compared with previously reported one-sphere, cylinder, and bitruncated cone fitting methods, the two-sphere fitting method presented the smallest maximum distance difference, indicating that talar trochlea can be approximated well as two spheres. The radius of the medial fitting sphere R M was 20.69 ± 2.19 mm which was significantly smaller than the radius of the lateral fitting sphere R L of 21.32 ± 1.88 mm. After grouping all data by the average radius of fitting spheres, the result showed that different sizes of the upper part of the talus presented significantly different parameters except the orientation of the lateral cutting plane, indicating that the orientation of the lateral cutting plane may keep consistent for all upper part of the talus and have no relationship with the size. The linear regression analyses demonstrated a weak correlation ( R 2 < 0.5 ) between the majority of parameters and the average radius of the fitting spheres. Therefore, different sizes of the upper part of the talus presented unique morphological features, and the design of different sizes of talar components for TAR should consider the size-specific characteristics of the talus. The parameters measured in this study provided a further understanding of the talus and can guide the design of different sizes of the talar components of the TAR implant.

Design of electronic cam for lower hook mechanism of fishing net-weaving machine based on polynomial fitting

The working efficiency and stability of the double hook-based fishing net-weaving machine is mainly determined by the lower hook mechanism. In this work, a new kind of lower hook mechanism, which is driven by four servo motors, is presented, and the electronic cam curve of the lower hook mechanism is introduced. First, cubic B-spline interpolation is used to get the basic motion path of the lower hook plate, and then the piecewise quintic polynomial fitting method is used to fit the motion path. Finally, self-adaptive mutation-based particle swarm optimization is put forward and used to obtain the optimal parameters of the quintic polynomial, which performs better compared with the other two particle swarm optimization algorithms in this study. Experiments suggest that the electronic cam curve generated by the piecewise quintic polynomial fitting has got 55.91% (horizontal motors) and 60.96% (vertical motors) optimization in maximum motor torque compared with curves generated by cubic B-spline interpolations. In addition, the new lower hook mechanism and its moving curve described in this paper improved the theoretical weaving speed of the fishing net-weaving machine, providing a basis for digital improvement of the knotted net-weaving industry.

Polynomial fitting method of background correction for electron backscatter diffraction patterns

A raw electron backscatter diffraction (EBSD) signal can be empirically decomposed into a Kikuchi diffraction pattern and a smooth background. For pattern indexing, the latter is generally undesirable but can reveal topographical, compositional, or diffraction contrast. In this study, we proposed a new background correction method using polynomial fitting (PF) algorithm to obtain clear Kikuchi diffraction patterns for some applications in nonconductive materials due to coating problems, at low accelerated voltage and at rough sample surfaces and for the requirement of high pattern quality in HR-EBSD. To evaluate the quality metrics of the Kikuchi patterns, we initially used three indices, namely, pattern quality, Tenengrad variance, and spatial–spectral entropy-based quality to detect the clarity, contrast, and noise of Kikuchi patterns obtained at 5 and 15 kV. Then, we examined the performance of PF method by comparing it with pattern averaging and Fourier transform-based methods. Finally, this PF background correction is demonstrated to extract the background images from the blurred diffraction patterns of EBSD measurements at low kV accelerating voltage and with coating layer, and to provide clear Kikuchi patterns successfully.

Research on Conducted Disturbance to Secondary Cable Caused by Disconnector Switching Operation

The disconnector switching operation in GIS not only generates very fast transient overvoltage (VFTO) in primary equipment, but also couples to the secondary system, which affects normal operation of the secondary equipment. In this study, aiming at the conducted disturbance caused by the disconnector switching operation of the 1,000-kV UHV GIS test circuit on the secondary cable, a broadband equivalent circuit model of the potential transformer and the grounding grid is proposed based on the vector fitting method and the impedance synthesis method, and the accuracy of the model is tested. On the basis of this model, the conducted disturbance voltage of the secondary cable core is obtained by combining the measured typical disturbance source waveform. The research results of the influencing factors of conducted disturbance show that the amplitude of the disturbance voltage generated by the capacitive conduction is higher than that generated by the resistive conduction, but the main frequency of the resistive conducted disturbance voltage is higher. The amplitude of the conducted disturbance voltage will decrease with the increase of the length of the cable and the length of the grounding wire. The single-ended grounding of the secondary cable shield at the GIS side will cause serious disturbance voltage. The research results of this study will be beneficial to the protection of secondary cable electromagnetic disturbance in the intelligent substation and have reference significance for the implementation of secondary equipment protection measures in the intelligent substation.

Observation of ionic conductivity on PUA-TBAI-I2 gel polymer electrolyte

Jatropha oil-based polyurethane acylate gel polymer electrolyte was mixed with different concentrations of tetrabutylammonium iodide salt (TBAI). The temperature dependences of ionic conductivity, dielectric modulus and relaxation time were studied in the range of 298 to 393 K. The highest ionic conductivity of (1.88 ± 0.020) × 10–4 Scm−1 at 298 K was achieved when the gel contained 30 wt% of TBAI and 2.06 wt% of I2. Furthermore, the study found that conductivity-temperature dependence followed the Vogel-Tammann Fulcher equation. From that, it could be clearly observed that 30 wt% TBAI indicated the lowest activation energy of 6.947 kJ mol−1. By using the fitting method on the Nyquist plot, the number density, mobility and diffusion coefficient of the charge carrier were determined. The charge properties were analysed using the dielectric permittivity, modulus and dissipation factor. Apart from this, the stoke drag and capacitance were determined.

Comparative Study of AC Signal Analysis Methods for Impedance Spectroscopy Implementation in Embedded Systems

For embedded impedance spectroscopy, a suitable method for analyzing AC signals needs to be carefully chosen to overcome limited processing capability and memory availability. This paper compares various methods, including the fast Fourier transform (FFT), the FFT with barycenter correction, the FFT with windowing, the Goertzel filter, the discrete-time Fourier transform (DTFT), and sine fitting using linear or nonlinear least squares, and cross-correlation, for analyzing AC signals in terms of speed, memory requirements, amplitude measurement accuracy, and phase measurement accuracy. These methods are implemented in reference systems with and without hardware acceleration for validation. The investigation results show that the Goertzel algorithm has the best overall performance when hardware acceleration is excluded or in the case of memory constraints. In implementations with hardware acceleration, the FFT with barycentre correction stands out. The linear sine fitting method provides the most accurate amplitude and phase determinations at the expense of speed and memory requirements.

Temperature Analysis of Flaring (AR11283) and non-Flaring (AR12194) Coronal Loops

Here, we study the temperature structure of flaring and non-flaring coronal loops, using extracted loops from images taken in six extreme ultraviolet (EUV) channels recorded by Atmospheric Imaging Assembly (AIA)/ Solar Dynamic Observatory (SDO). We use data for loops of X2.1-class-flaring active region (AR11283) during 22:10UT till 23:00UT, on 2011, September 6; and non-flaring active region (AR12194) during 08:00:00UT till 09:00:00UT on 2014, October 26. By using spatially-synthesized Gaussian DEM forward-fitting method, we calculate the peak temperatures for each strip of the loops. We apply the Lomb-Scargle method to compute the oscillations periods for the temperature series of each strip. The periods of the temperature oscillations for the flaring loops are ranged from 7 min to 28.4 min. These temperature oscillations show very close behavior to the slow-mode oscillation. We observe that the temperature oscillations in the flaring loops are started at least around 10 minutes before the transverse oscillations and continue for a long time duration even after the transverse oscillations are ended. The temperature amplitudes are increased at the flaring time (during 20 min) in the flaring loops. The periods of the temperatures obtained for the non-flaring loops are ranged from 8.5 min to 30 min,but their significances are less (below 0.5) in comparison with the flaring ones (near to one). Hence the detected temperature periods for the non-flaring loops' strips are less probable in comparison with the flaring ones, and maybe they are just fluctuations. Based on our confined observations, it seems that the flaring loops' periods show more diversity and their temperatures have wider ranges of variation than the non-flaring ones. More accurate commentary in this respect requires more extensive statistical research and broader observations.