Real-time Compensation Research Articles

A Marine Magnetometer Based on TMR

TMR (tunneling magnetoresistance) has the characteristics of high sensitivity, large linear range, low power consumption, and easy miniaturization, and has received great attention in the field of miniaturized and high-performance magnetic sensors. Widely used in marine magnetic field detection, earthquake monitoring, industrial control, and other fields. In this paper, A TMR marine magnetometer with AC modulation and magnetic field feedback compensation is proposed, designed, and manufactured, which can be used for the measurement of weak marine magnetic fields. After testing, its measurement range is ±100,000nT, the noise fluctuation level is 0.27nT, and nonlinearity level reaches 0.07%. It works by means of ac modulation and real-time compensation of feedback magnetic field, which greatly reduces magnetic hysteresis and increases the linearity. Compared with the nonlinearity of TMR material (more than 20% within ±1Oe, more than 7% within ±0.3Oe), it has been significantly improved.

The Conjunctive Compensation Method Based on Inertial Navigation System and Fluxgate Magnetometer

Eliminating the magnetic interference of the carrier platform is an important technical link and plays a vital role in aeromagnetic survey. The traditional compensation method is based on the Tolles–Lawson (T-L) model and establishes the linear relationship between the aircraft interference magnetic field and the aircraft attitude. The compensation coefficients are solved by designing the calibration flight. At present, almost all aeromagnetic systems use the fluxgate magnetometer fixed to the aircraft to realize the attitude measurement of the flight platform. However, the fluxgate magnetometer has problems, such as non-orthogonal error, zero drift error, and linearity error limited by the production process, and the fluxgate magnetometer is also very susceptible to external magnetic interference as a magnetic sensor. These lead to the aircraft attitude calculated by the fluxgate magnetometer being inaccurate, thus reducing the compensation effect. In this article, we analyze the influence of the fluxgate magnetometer noise on compensation and propose a new conjunctive compensation method based on inertial navigation systems (INS) and fluxgate magnetometer information to improve the compensation effect. The flight experiment data show that the proposed method can significantly improve the quality of aeromagnetic data. Compared with the traditional compensation method only based on fluxgate magnetometer information, the improved ratio is increased by 30–60%, and it is a real-time compensation method. It shows that the proposed method has a remarkable compensation effect for aeromagnetic interference.

A Novel Dual-Differential Edge Sensor Based on the Eddy Current Effect

In this article, a kind of edge sensor based on the eddy current effect is proposed to realize accurate detection of the nano-level resolution in a large temperature span. Compared with edge sensors with different principles used in optical telescope projects, eddy current edge sensor has the advantages of being insensitive to nontarget direction and immune to nonferromagnetic medium. The proposed dual-differential edge sensor (DDES) greatly simplifies its installation and reduces the number of support components for sensors to half by replacing the complementary symmetrical installation method. By analyzing the detection principle, a kind of precise demodulation circuit and real-time temperature compensation method is also designed to guarantee the sensor’s ultrahigh stability. The prototype of the sensor is manufactured and verified that the resolution can reach within 2 nm in the range of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$300 ~\mu \text{m}$ </tex-math></inline-formula> , and the temperature drift (TD) performance is less than 6 nm/°C under the large temperature span from −25 °C to +25 °C. The installation error measurement convinced that the current structure has an excellent installation error tolerance, which has the potential to apply in the engineering application of astronomical telescope mirror splicing.

Motion tracking of a piezo-driven cell puncture mechanism using enhanced sliding mode control with neural network

This study deals with the design of a cell puncture mechanism (CPM) driven by a piezoelectric actuator to complete the cell puncture process. Then, a novel robust controller is proposed to realize precise CPM motion control. For the convenience of engineering application, the complex nonlinear hysteresis effect and unmolded term in CPM are summed up as an unknown term. Then, a simplified dynamic model is developed. Moreover, a robust controller is constructed by synthesizing the sliding mode control (SMC) with a proportional–integral–differential (PID)-type manifold and radial basis function neural network (RBFNN). The closed-loop stability and finite-time convergence of this controller are proven by the Lyapunov theory. With the self-learning ability of RBFNN, online estimation and real-time compensation of the unknown term can be realized. Moreover, the gain of the robust term in the controller can be reduced. Furthermore, the PID-type manifold improves the transient response speed of the controller and reduces the steady-state error of the system. The advantages of the PID-type manifold and RBFNN complement each another, thereby ensuring the excellent control quality of the proposed controller. Computer simulation results show the feasibility of the proposed simplified model and the robustness of the controller. These results can help improve the intelligence of CPM, particularly when this mechanism buffers from a sophisticated unstructured engineering environment.

Using a deep learning algorithm in image-based wavefront sensing: determining the optimum number of Zernike terms

The turbulent atmosphere usually degrades the quality of images taken on Earth. Random variations of the refractive index of light cause distortion of wavefronts propagating to ground-based telescopes. Compensating these distortions is usually accomplished by adaptive optics (AO) approaches. The control unit of AO adjusts the phase corrector, such as deformable mirrors, based on the incoming turbulent wavefront. This can be done by different algorithms. Usually, these algorithms encounter real-time wavefront compensation challenges. Although many studies have been conducted to overcome these issues, we have proposed a method, based on the convolutional neural network (CNN) as a branch of deep learning (DL) for sensor-less AO. To this objective, thousands of wavefronts, their Zernike coefficients, and corresponding intensity patterns in diverse conditions of turbulence are generated and fed into the CNN to predict the wavefront of new intensity patterns. The predictions are done for considering the different number of Zernike terms, and the optimum number is achieved by comparing wavefront errors.

Encoderless Five-phase PMa-SynRM Drive System Based on Robust Torque-speed Estimator with Super-twisting Sliding Mode Control

In this paper, a robust torque speed estimator (RTSE) for linear parameter changing (LPC) system is proposed and designed for an encoderless five-phase permanent magnet assisted synchronous reluctance motor (5-phase PMa-SynRM). This estimator is utilized for estimating the rotor speed and the load torque as well as can solve the speed sensor fault problem, as the feedback speed information is obtained directly from the virtual sensor. In addition, this technique is able to enhance the 5-phase PMa-SynRM performance by estimating the load torque for the real time compensation. The stability analysis of the proposed estimator is performed via Schur complement along with Lyapunov analysis. Furthermore, for improving the 5-phase PMa-SynRM performance, five super-twisting sliding mode controllers (ST-SMCs) are employed with providing a robust response without the impacts of high chattering problem. A super-twisting sliding mode speed controller (ST-SMSC) is employed for controlling the PMa-SynRM rotor speed, and four super-twisting sliding mode current controllers (ST-SMCCs) are employed for controlling the 5-phase PMa-SynRM currents. The stability analysis and the experimental results indicate the effectiveness along with feasibility of the proposed RTSE and the ST-SMSC with ST-SMCCs approach for a 750-W 5-phase PMa-SynRM under load disturbance, parameters variations, single open-phase fault, and adjacent two-phase open circuit fault conditions.

Advanced Dispatching of a Wind Farm Based on Doubly Fed Induction Generators for the Improvement of LVRT Capability by the ADRC Approach

This paper aims to explore a viable monitoring and management of active and reactive powers for a large-scale wind farm based on Doubly-Fed Induction Generators (DFIG) considering the voltage Fault-Ride-Through capability (FRT), especially Low-Voltage-Ride-Through (LVRT) capability by using a new control strategy, known as Active Disturbance Rejection Control. This strategy uses real-time estimation and compensation of the generalized "total" disturbance before it affects the system. The wind farm supervisory unit is used to coordinate the control of the powers production by the entire wind farm, which must take into account the couplings between each wind generator while producing the individual power commands. The turbine control units (local supervisory units) send the appropriate power references depending on the situation. This can be to produce the maximum power, to manage the active and reactive power given by the Transmission System Operator (TSO) or to meet the requirements of the grid code (LVRT capacity). However, to ensure the dispatching of the references of the active and reactive powers over the all wind generators of the wind farm and to satisfy the security of the power grid, we utilized mean of the proportional distribution algorithm. The effectiveness of the proposed supervisory approach and control strategies are tested and validated through a multiples scenarios of simulations that are made under the MATLAB/Simulink Environment. The results obtained have demonstrated the efficiency and robustness of the control methods, and also the fact that they guarantee good performance and safety of the integration of wind farms into the grid while complying with the requirements of the grid code during power system faults.

Fast gas sensing scheme with multi-component gas measurement capacity based on non-dispersive frequency comb spectroscopy (ND-FCS).

A fast gas sensing scheme based on a non-dispersive frequency comb spectroscopy (ND-FCS) is proposed and experimentally demonstrated. Its capacity for multi-component gas measurement is experimentally investigated as well, by using the time-division-multiplexing (TDM) method to realize specific wavelength selection of the fiber laser optical frequency comb (OFC). A dual-channel optical fiber sensing scheme is established with a sensing path consisting of a multi-pass gas cell (MPGC), and a reference path with a calibrated signal to track the repetition frequency drift of the OFC for a real-time lock-in compensation and system stabilization. The long-term stability evaluation and the simultaneous dynamic monitoring are carried out, with the target gases of ammonia (NH3), carbon monoxide (CO) and carbon dioxide (CO2). The fast CO2 detection in human breath is also conducted. The experimental results show that at an integration time of 10 ms, the detection limits of the three species are evaluated to be 0.0048%, 0.1869% and 0.0467%, respectively. A low minimum detectable absorbance (MDA) down to 2.8 × 10-4 can be achieved and a dynamic response with millisecond time can be realized. Our proposed ND-FCS exhibits excellent gas sensing performance with merits of high sensitivity, fast response and long-term stability. It also shows great potential for multi-component gas monitoring in atmospheric monitoring applications.

Novel Real-Time Compensation Method for Machine Tool’s Ball Screw Thermal Error

The real-time compensation of thermal error in ball screws is an effective means to improve the accuracy of machining tools. However, the trade-off between robustness and computational efficiency of existing ball screw thermal error models is complicated and not conducive to practical, high-precision, real-time error compensation. Focusing on this problem, we propose an iterative prediction model of screw thermal error based on a finite difference equation. By assuming an approximately linear relationship between heat generation and the ball screw’s convection power and feed speed, a simplified and more efficient identification of physical parameters needed for the iterative model is achieved. The proposed method is integrated with a three-axis drilling and tapping machine powered by an HNC–848D controller. A test piece machine using the proposed real-time thermal error compensation method exhibited a maximum machining error of 13 µm, compared to the 71 µm of an uncompensated specimen. The proposed method is demonstrated to improve machining accuracy, especially in the X- and Y- axes, and overcome the limitations of traditional thermal error prediction models.

Prediction of Thermal Deformation and Real-Time Error Compensation of a CNC Milling Machine in Cutting Processes

This study constructs a prediction model of thermal deformation with an artificial neural network and implements the real-time error compensation for a three-axis vertical CNC milling machine in cutting processes to improve the thermal error of the workpiece. There are 32 PT-100 thermal sensors installed in key parts of the machine in order to measure the temperature of key machine parts in actual cutting conditions. Pearson’s correlation coefficients are used to select crucial temperature sensors for building the prediction model of thermal deformation. The reduced number of crucial temperature sensors in model construction can simplify the model complexity and speed up the response time of prediction. This study constructs a long short-term memory (LSTM) neural network model to predict the thermal error of the machine in cutting processes. This prediction model of thermal deformation can be further used in real-time error compensation of the workpiece in cutting processes. In an 8 h cutting experiment, the dimensions of the workpiece show that, with real-time error compensation, the thermal error in X-axis decreases from 7 µm to 3 µm, the thermal error in Y-axis decreases from 74 µm to 21 µm, and the thermal error in Z-axis decreases from −64 µm to −20 µm. The results indicate that the prediction model of thermal deformation and the real-time error compensation can significantly reduce the thermal error and improve the dimensional accuracy of the workpiece.

Temperature Drift Compensation of a MEMS Accelerometer Based on DLSTM and ISSA.

In order to improve the performance of a micro-electro-mechanical system (MEMS) accelerometer, three algorithms for compensating its temperature drift are proposed in this paper, including deep long short-term memory recurrent neural network (DLSTM-RNN, short DLSTM), DLSTM based on sparrow search algorithm (SSA), and DLSTM based on improved SSA (ISSA). Moreover, the piecewise linear approximation (PLA) method is employed in this paper as a comparison to evaluate the impact of the proposed algorithm. First, a temperature experiment is performed to obtain the MEMS accelerometer's temperature drift output (TDO). Then, we propose a real-time compensation model and a linear approximation model for neural network methods compensation and PLA method compensation, respectively. The real-time compensation model is a recursive method based on the TDO at the last moment. The linear approximation model considers the MEMS accelerometer's temperature and TDO as input and output, respectively. Next, the TDO is analyzed and optimized by the real-time compensation model and the three algorithms mentioned before. Moreover, the TDO is also compensated by the linear approximation model and PLA method as a comparison. The compensation results show that the three neural network methods and the PLA method effectively compensate for the temperature drift of the MEMS accelerometer, and the DLSTM + ISSA method achieves the best compensation effect. After compensation by DLSTM + ISSA, the three Allen variance coefficients of the MEMS accelerometer that bias instability, rate random walk, and rate ramp are improved from 5.43×10-4mg, 4.33×10-5mg/s12, 1.18×10-6mg/s to 2.77×10-5mg, 1.14×10-6mg/s12, 2.63×10-8mg/s, respectively, with an increase of 96.68% on average.

Deep learning driven adaptive optics for single molecule localization microscopy.

Single molecule localization microscopy (SMLM) forms super-resolution images with a resolution of several to tens of nanometers, by detecting isolated single molecule emission patterns and localizing the centers of individual probes. However, the inhomogeneous refractive indices distort and blur single molecule emission patterns, reduce the information content carried by each detected photon, increase localization uncertainty, and thus cause significant resolution loss, which is irreversible by post-processing. To compensate tissue induced aberrations, conventional sensorless adaptive optics methods rely on iterative mirror-changes and image-quality metrics to compensate aberrations. However, these metrics result in inconsistent, and sometimes opposite, metric responses which fundamentally limited the efficacy of these approaches for aberration correction in tissues. Bypassing the previous iterative trial-then-evaluate processes, we developed deep learning driven adaptive optics (DL-AO) for SMLM to allow direct inference of wavefront distortion and near real-time compensation. Our trained deep neural network (DNN) monitors the individual emission patterns from single molecule experiments, infers their shared wavefront distortion, feeds the estimates through a dynamic filter (Kalman), and drives a deformable mirror to compensate sample induced aberrations. The method simultaneously estimates and compensates 28 types of wavefront deformation shapes, restores single molecule emission patterns approaching the conditions untouched by specimen, and improves the resolution and fidelity of 3D SMLM through brain tissues over 130 µm, with as few as 3-20 mirror changes.

Nonlinearity Compensation and High-Frequency Flexibility Suppression Based RIC Method for Precision Motion Control Systems

For precision motion systems widely applied in industrial manufacturing equipments, it is critical to achieve both high trajectory tracking accuracy and superior disturbance rejection ability. In this article, a novel nonlinearity compensation and high-frequency flexibility suppression based real-time iterative compensation (RIC) method is proposed to achieve excellent tracking performance in practice. The unexpected nonlinearity and high-frequency flexible mode of the plant, which limits the achievable control performance, is first compensated and suppressed. Subsequently, a RIC method based on accurate linear prediction model is proposed to further reduce the tracking error by adding a compensation term to the initial reference trajectory. The trajectory compensation idea of RIC is comparative to remarkable iterative learning control (ILC), but the proposed RIC can online generate and adjust the compensation term during real-time motion without abundant offline iteration trials in ILC. This mechanism significantly enhances the robustness to trajectory variations and external disturbances. Comparative experiments carried out on a ball-screw-driven precision motion stage with full-closed loop position feedback validate the effectiveness and superiority of the proposed method for various trajectory tracking tasks. The proposed method outperforms ILC on tracking performance, and possesses the robustness to various disturbances and reference variations, which leads to industrial application significance.

A Magnetic Compensation System Composed of Biplanar Coils Avoiding Coupling Effect of Magnetic Shielding

Magnetic compensation coils are often used to improve the effectiveness of a magnetically shielded room (MSR), but a distortion of the field is caused by the shielding layer consisting of high-permeability material, which leads to a reduction in compensation capacity. To solve this problem, a new method is presented in this article based on a target-field method, an image method, and particle swarm optimization. By this way, a magnetic compensation system composed of biplanar coils is designed and fabricated to compensate the background field for a wearable magnetoencephalography device inside the MSR, and the coupling effect between the magnetic shielding material and the compensation field is effectively avoided. Experimental data show that these compensation coils produce uniform fields and field gradients with the inhomogeneity of less than 3.8%, consistent with the simulation results. In addition, this system realizes a real-time compensation to the residual field and field gradient in the MSR.

An efficient thermal error prediction model using neural networks and key temperature points for gantry machining centers

Abstract The gantry machining center is popular for various fabrications, such as milling and tapping. However, thermal errors introduced by the rotation of spindle, workpiece processing, and cooling significantly degrade fabrication precision. The objective of this study is to establish an appropriate and efficient thermal error prediction model for the spindle of gantry machining center. The model will then aid real-time compensation for the error. Firstly, this study presents a systematic strategy for selecting key temperature points on the gantry machining center, reducing the number of required sensors. Subsequently, a thermal error model is developed based on the selected key temperature points. The model will be capable of predicting thermal errors in the x- and z-direction. Finally, this work both validates the thermal error model and exhibits real-time compensation capabilities using a real machine.

Real-time trajectory position error compensation technology of industrial robot

In order to meet the requirements of high positioning accuracy and trajectory accuracy of industrial robots in the field of high-precision operation, this paper studied the real-time compensation method of the robot trajectory error used laser tracker to measure the end position of robot in real time. This real-time error calculation method of robot trajectory based on continuous dynamic time warping (CDTW), which was studied to determine the position error of robot trajectory at each moment. Moreover, this paper researched the PID parameter tuning technology of response surface model method based on gray analysis and got a real-time compensation method. The compensation value was fed back to the robot for motion compensation in real time through KUKA RSI. The last, the influence of compensation parameters and period was analyzed and the error compensation experiment of positioning, linear trajectory and arc trajectory were carried out. After compensation, the absolute positioning error of the robot was less than 0.06 mm and the trajectory position error was less than 0.15 mm, which greatly improved the position accuracy of the robot.

Input-Output-Improved Reservoir Computing Based on Duffing Resonator Processing Dynamic Temperature Compensation for MEMS Resonant Accelerometer.

An MEMS resonant accelerometer is a temperature-sensitive device because temperature change affects the intrinsic resonant frequency of the inner silicon beam. Most classic temperature compensation methods, such as algorithm modeling and structure design, have large errors under rapid temperature changing due to the hysteresis of the temperature response of the accelerometer. To address this issue, we propose a novel reservoir computing (RC) structure based on a nonlinear silicon resonator, which is specifically improved for predicting dynamic information that is referred to as the input-output-improved reservoir computing (IOI-RC) algorithm. It combines the polynomial fitting with the RC on the input data mapping ensuring that the system always resides in the rich nonlinear state. Meanwhile, the output layer is also optimized by vector concatenation operation for higher memory capacity. Therefore, the new system has better performance in dynamic temperature compensation. In addition, the method is real-time, with easy hardware implementation that can be integrated with MEMS sensors. The experiment's result showed a 93% improvement in IOI-RC compared to raw data in a temperature range of -20-60 °C. The study confirmed the feasibility of RC in realizing dynamic temperature compensation precisely, which provides a potential real-time online temperature compensation method and a sensor system with edge computing.

PICAFlow: a complete R workflow dedicated to flow/mass cytometry data, from pre-processing to deep and comprehensive analysis

Abstract Summary PICAFlow is a R-written integrative workflow dedicated to flow/mass cytometry data handling, from pre-processing to deep and comprehensive analysis. It is designed as a powerful all-in-one tool which contains all the necessary functions and packages presented in a user-friendly and ease-to-use fashion. PICAFlow also includes important features that are very frequently lacking in other close software, such as interactive R Shiny applications for real-time data transformation and compensation as well as normalization methods aiming to remove batch effects and unwanted inter- and intra-group heterogeneity. It also allows to perform dimensionality reduction, cell clustering (using different available approaches), as well as complementary statistical analyses and export different support for data interpretation and visualization. Availability PICAFlow is available as a R-written package hosted at the following GitHub repository: https://github.com/PaulRegnier/PICAFlow and is complemented by a fully detailed tutorial available at the following URL: https://paul-regnier.fr/tutoriel-picaflow/.

Detecting Photoactivatable Cre-mediated Gene Deletion Efficiency in Escherichia coli.

Gene deletion is one of the standard approaches in genetics to investigate the roles and functions of target genes. However, the influence of gene deletion on cellular phenotypes is usually analyzed sometime after the gene deletion was introduced. Such lags from gene deletion to phenotype evaluation could select only the fittest fraction of gene-deleted cells and hinder the detection of potentially diverse phenotypic consequences. Therefore, dynamic aspects of gene deletion, such as real-time propagation and compensation of deletion effects on cellular phenotypes, still need to be explored. To resolve this issue, we have recently introduced a new method that combines a photoactivatable Cre recombination system and microfluidic single-cell observation. This method enables us to induce gene deletion at desired timings in single bacterial cells and to monitor their dynamics for prolonged periods. Here, we detail the protocol for estimating the fractions of gene-deleted cells based on a batch-culture assay. The duration of blue light exposure significantly affects the fractions of gene-deleted cells. Therefore, gene-deleted and non-deleted cells can coexist in a cellular population by adjusting the duration of blue light exposure. Single-cell observations under such illumination conditions allow the comparison of temporal dynamics between gene-deleted and non-deleted cells and unravel phenotypic dynamics provoked by gene deletion.

Real-Time Temperature Drift Compensation Method of a MEMS Accelerometer Based on Deep GRU and Optimized Monarch Butterfly Algorithm

In recent years, inertial sensors based on Micro-Electro-Mechanical Systems (MEMS) have become increasingly popular. They have been widely used in various fields due to their low cost, small size, and low power consumption. It seems that MEMS inertial sensors may eventually fully occupy the middle to lower end inertial navigation application market that traditional inertial sensors previously occupied. To realize the full potential of MEMS inertial sensors, one of the critical issues is their temperature drift. This paper first proposed a recursive model for real-time compensation. Then three algorithms were proposed, including a two-layer deep gated recurrent unit recurrent neural network (GRU-RNN, short GRU), deep GRU based on monarch butterfly algorithm (MBA), and deep GRU based on optimized monarch butterfly algorithm (OMBA). Each of these three algorithms is combined with the real-time compensation model to compensate for the temperature drift of a MEMS accelerometer. The experimental results proved the correctness of these three methods, and the MEMS accelerometer’s temperature drift is compensated effectively. The results indicate that the deep GRU + OMBA shows the best performance for the temperature drift compensation combined with the real-time compensation model. After deep GRU + OMBA method compensation, the angle random walk, the bias instability, the rate random walk, and rate ramp of the MEMS accelerometer were improved from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4.97e^{-4} \, mg\,\,\cdot s^{\frac {1}{2}}$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4.90e^{-4} \, mg$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$5.57e^{-5} \, mg/ s^{\frac {1}{2}}$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.82e^{-6} \, mg\,\,/ s$ </tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3.90e^{-5} \, mg\,\,\cdot s^{\frac {1}{2}}$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.07e^{-5} \, mg$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.12e^{-6} \, mg/ s^{\frac {1}{2}}$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3.59e^{-8} \, mg\,\,/ s$ </tex-math></inline-formula> , respectively. Their percentage of improvement reaches 96.50% on average.