Surface Error Research Articles

Optimization Design of Large-Aperture Primary Mirror for a Space Remote Camera

Lightweight, high stability, and high-temperature adaptability are the primary considerations when designing the primary mirror of a micro/nano satellite remote sensing camera. In this paper, the optimized design and experimental verification of the large-aperture primary mirror of the space camera with a diameter of Φ610 mm is carried out. First, the design performance index of the primary mirror was determined according to the coaxial tri-reflective optical imaging system. Then, SiC, with excellent comprehensive performance, was selected as the primary mirror material. The initial structural parameters of the primary mirror were obtained using the traditional empirical design method. Due to the improvement of SiC material casting complex structure reflector technology level, the initial structure of the primary mirror was improved by integrating the flange with the primary mirror body design. The support force acts directly on the flange, changing the transmission path of the traditional back plate support force, and has the advantage that the primary mirror surface shape accuracy can be maintained for a long time when subjected to shock, vibration, and temperature changes. Then, a parametric optimization algorithm based on the mathematical method of compromise programming was used to optimize the design of the initial structural parameters of the improved primary mirror and the flexible hinge, and finite element simulation was conducted on the optimally designed primary mirror assembly. Simulation results show that the root mean square (RMS) surface error is less than λ/50 (λ = 632.8 nm) under gravity, 4 °C temperature rise, and 0.01 mm assembly error. The mass of the primary mirror is 8.66 kg. The maximum displacement of the primary mirror assembly is less than 10 μm, and the maximum inclination angle is less than 5″. The fundamental frequency is 203.74 Hz. Finally, after the primary mirror assembly was precision manufactured and assembled, the surface shape accuracy of the primary mirror was tested by ZYGO interferometer, and the test value was 0.02 λ. The vibration test of the primary mirror assembly was conducted at a fundamental frequency of 208.25 Hz. This simulation and experimental results show that the optimized design of the primary mirror assembly meets the design requirements of the space camera.

Numerical Simulation of Highly Dispersive Dark Optical Solitons with Kerr Law of Nonlinear Refractive Index by Laplace–Adomian Decomposition Method

This work is a numerical perspective to highly dispersive dark optical solitons by using Laplace-Adomian decomposition method. The results are reported using this scheme with highly precise accuracy and the error measure is stunningly low. The surface plots, density plots and error plots are exhibited for different parameter choices. The simulations are almost an exact replica of such solitons that analytically arise from the governing system. The suggested iterative scheme finds the solution without any discretization, linearization, or restrictive assumptions.

DSC‐based finite‐time adaptive resilient control for a class of nonstrict‐feedback switched nonlinear systems with deception attacks

AbstractIn this paper, the finite‐time adaptive resilient control problem for a class of switched nonlinear systems with deception attacks by using the dynamic surface control (DSC) strategy is addressed. A more general class of uncertain nonstrict‐feedback switched nonlinear systems with the sensor and actuator deception attacks are considered. Deception attacks can damage sensor, control and switching data, which results in the switching signal and the finite‐time control gains unknown, meanwhile the conventional dynamic surface errors inacessible. To overcome the difficulty, first, the approximation technique of neural networks (NNs) is used to deal with the unknown nonlinear terms and compensate the sensor and actuator deception attacks. Secondly, a new coordinate transformation and a novel switched adaptive finite‐time filter are designed to mitigate the effects caused by the sensor attacks and avoid the problem of “explosion of complexity”. Thirdly, Nussbaum technology is exploited to handle the unknown finite‐time control gains problem caused by deception attacks. Then, by the proposed control strategy, the practical finite‐time stability analysis is presented. Finally, a simulation example is provided to validate the feasibility of the proposed control method.

Two types of developmental surface dysgraphia: to bee but not to bea

ABSTRACTWe report on two types of developmental surface dysgraphia. One type, exhibited by 8 participants, is orthographic lexicon surface dysgraphia, which involves an impairment in the orthographic output lexicon, leading to nonword phonologically-plausible misspellings. The other type, shown by 3 participants, is disconnection surface dysgraphia. In this type, the orthographic output lexicon is disconnected from the semantic system and from the phonological input lexicon, but still contributes to spelling via support to the orthographic output buffer, resulting in mainly lexical phonologically-plausible misspellings (writing be as “bee” but not “bea”).The specific localization of the impairment in spelling, in the lexicon or in its connections, allowed us to examine the question of one or two orthographic lexicons; four participants who had a deficit in the orthographic output lexicon itself in writing had intact orthographic-input-lexicon in reading. They made surface errors in writing but not in reading the same words, supporting separate input and output orthographic lexicons.

Reduction and reconstruction strategy of active thermal control system based on unsupervised learning and thermo-optics for spaceborne high-resolution remote sensor

The development of small Earth observation satellites with high performance optical remote sensors has received much attention in recent years due to its responsiveness and immediacy. As one of the most resource-intensive subsystems of spacecrafts, the active thermal control system (ATCS) should be optimized; however, manual thermal design does not guarantee an optimal solution and requires months. For this purpose, we presented a ATCS’s reduction and reconstruction strategy based on an unsupervised learning framework, in which factor loadings are applied to combine kernel-based principal component analysis and Gaussian mixture model clustering. This strategy was implemented on a spaceborne high-resolution remote sensor (HRS) with 0.5 m ground sample distance. As a result, with the cumulative variance contribution rate > 90 % and 10 Gaussian distributions, the reconstructed ATCS of HRS had a 78.6 % reduction rate and took only 3 h, which suggests the high efficiency and low computational cost of the proposed strategy. Finally, the performed orbital thermal and thermo-optical integrated analyses indicated that temperature fluctuations were within ± 0.02–0.6 °C and optical surface errors were within the tolerance. The average modulation transfer function in the tangential and sagittal directions decreased by only 2 % and 2.5 %, respectively, and the radius of the spot root mean square was considerably smaller than the size of one pixel (8.75 μm). These results prove the feasibility and validity of the proposed strategy. This study solved the problem of identifying the optimal ATCS for optical remote sensors and significantly reducing the ATCS’s resource occupancy, which provided a reliable research basis for the development of high-performance small Earth observation satellites. Additionally, the proposed strategy is versatile and can be used in thermal engineering applications of various complex spacecrafts and payloads.

Pupil-difference moments for estimating relative modulation from general mid-spatial frequency surface errors

Standard surface specifications for mid-spatial frequency (MSF) errors do not capture complex surface topography and often lose critical information by making simplifying assumptions about surface distribution and statistics. As a result, it is challenging to link surface specifications with optical performance. In this work, we present use of the pupil-difference probability distribution (PDPD) moments to assess general MSF surface errors and show how the PDPD moments relate to the relative modulation.

Efficiency of the Machining Process of Circular Shapes by Electrical Discharge Technology

Due to its high machining precision, EDM technology is nowadays very important in the production of high-precision parts for various industries. The high precision of the machined surface in combination with the ability to machine circular surfaces brings, in addition to several advantages, some negatives. The most significant negative of this machining technology is the relatively low productivity as well as the overall production efficiency. The latter is affected by many accompanying phenomena. The main accompanying phenomenon that contributes to the decline in the overall economic efficiency of EDM is the microgeometry errors that occur due to the non-homogeneity of the EDM process. Another accompanying negative phenomenon is the geometric accuracy errors of the machined surface, as a consequence of systematic destruction of the wire tool electrode, faulty interpolation in its guidance, and, last but not least, its vibration. These aspects consequently lead to the requirement for multiple applications of additional finishing cuts, which significantly reduces the overall economic efficiency of the machining process. Therefore, the experimental research aimed to search for options that can effectively help to achieve higher productivity but especially the overall economic efficiency of the machining process.

Spare Parts Forecasting and Lumpiness Classification Using Neural Network Model and Its Impact on Aviation Safety

Safety critical spare parts hold special importance for aviation organizations. However, accurate forecasting of such parts becomes challenging when the data are lumpy or intermittent. This research paper proposes an artificial neural network (ANN) model that is able to observe the recent trends of error surface and responds efficiently to the local gradient for precise spare prediction results marked by lumpiness. Introduction of the momentum term allows the proposed ANN model to ignore small variations in the error surface and to behave like a low-pass filter and thus to avoid local minima. Using the whole collection of aviation spare parts having the highest demand activity, an ANN model is built to predict the failure of aircraft installed parts. The proposed model is first optimized for its topology and is later trained and validated with known historical demand datasets. The testing phase includes introducing input vector comprising influential factors that dictate sporadic demand. The proposed approach is found to provide superior results due to its simple architecture and fast converging training algorithm once evaluated against some other state-of-the-art models from the literature using related benchmark performance criteria. The experimental results demonstrate the effectiveness of the proposed approach. The accurate prediction of the cost-heavy and critical spare parts is expected to result in huge cost savings, reduce downtime, and improve the operational readiness of drones, fixed wing aircraft and helicopters. This also resolves the dead inventory issue as a result of wrong demands of fast moving spares due to human error.

Factors Affecting Weigh Tape Reading in the Measurement of Equine Body Weight.

Accurate measurement of equine body weight is important for evaluating medication dosages and feed quantities. Different methods exist for measuring body weight, including weigh tapes (WT), though accuracy varies. Measurements could be affected by external variables, such as time of day, human error, or uneven surfaces, and also horse-based variables, such as height and body condition score (BCS). The aim of this study was to investigate how different horse-based variables affect WT reading. A retrospective analysis was performed using anonymised data from feed company nutrition consultations (Baileys Horse Feeds). Data included a range of horse-based variables, a WT reading, and true body weight measured on a weighbridge. All horses were over two years of age. Likelihood ratio tests were used to assess whether adding different horse-based variables significantly improved the fit of the quadratic regression model. The variables included were height, BCS, breed, muscle top-line score, and bone type. Exploratory analysis showed that the WT generally underestimated body weight, particularly for horses with higher body weight. Adding height and muscle top-line scores did not significantly improve the fit of the model, suggesting no influence on WT reading over and above actual body weight. Adding breed groupings, BCS, and bone density did improve the fit. Each 0.5 unit increase in BCS increased the WT estimate by 1.24 kg (p < 0.001). These results confirm that a WT does not provide accurate body weight measurements, and generally underestimates body weight, though more so for heavier horses, being more accurate in pony breeds.

Five-degrees-of-freedom error motion measurement method of precision rotary table based on BMPES

It is essential to obtain the five-degrees-of-freedom (5-DOF) error motion of a rotary table to reconstructthe real trajectory of the rotating shaft, but there are many error coupling problems when measuring the error motion of a rotary table. In order to improve the measurement accuracy of the 5-DOF error motion of the rotary table, a method of measuring the error motions based on bidirectional multi-point error separation (BMPES) is proposed. First, by analyzing the motion characteristics of the rotary table with multiple degrees of freedom error during the rotation, a detection system with a double-layer structure probe arrangement is designed. Then, the three-point method is used in the radial direction to separate the roundness error of the measuring disk, which improves the measurement accuracy of radial error. Finally, the coupling relationship between the mixing errors collected by the axial probes is researched, and a face-four-point error separation method is proposed, which can separate the flatness error of the lower surface of the measuring disk and complete the decoupling of the tilt error and the axial runout error. Simulation results show that for the measurement of radial, tilt and axial errors, the measurement errors of the BMPES method proposed in this paper are reduced by 97.89%, 68.40% and 99.99%, respectively, compared with the five-point method, and when eccentricity errors exist, the measurement errors of the radial and tilt errors are reduced by 99.06% and 85.67%, which verifies that the method can accurately obtain the 5-DOF motion of the rotary table errors.

Automatic Kidney Segmentation Method Based on an Enhanced Generative Adversarial Network

When deciding on a kidney tumor's diagnosis and treatment, it is critical to take its morphometry into account. It is challenging to undertake a quantitative analysis of the association between kidney tumor morphology and clinical outcomes due to a paucity of data and the need for the time-consuming manual measurement of imaging variables. To address this issue, an autonomous kidney segmentation technique, namely SegTGAN, is proposed in this paper, which is based on a conventional generative adversarial network model. Its core framework includes a discriminator network with multi-scale feature extraction and a fully convolutional generator network made up of densely linked blocks. For qualitative and quantitative comparisons with the SegTGAN technique, the widely used and related medical image segmentation networks U-Net, FCN, and SegAN are used. The experimental results show that the Dice similarity coefficient (DSC), volumetric overlap error (VOE), accuracy (ACC), and average surface distance (ASD) of SegTGAN on the Kits19 dataset reach 92.28%, 16.17%, 97.28%, and 0.61 mm, respectively. SegTGAN outscores all the other neural networks, which indicates that our proposed model has the potential to improve the accuracy of CT-based kidney segmentation.

A Bootstrap-Based Tooth Surface Errors Statistics Methodology for Batch Hypoid Gears after Heat Treatment

In the manufacturing and production of hypoid gears, it is a necessary key problem to improve the tooth surface heat treatment precision and production efficiency of the hypoid gears. How to use advanced statistical theory and methods to evaluate the whole batch machining quality of the tooth surface after heat treatment is particularly urgent. In this connection, for the same batch of hypoid gears with the same gear material, numerical control gear milling method, and heat treatment specifications, a bootstrap-based statistics scheme of tooth surface errors after heat treatment is proposed in this paper. The bootstrap statistics model of the tooth surface errors for the batch hypoid gears is established. The bootstrap probability eigenvalues and confidence intervals of the measurement sequence points on the tooth surface errors are solved, and the optimizing selection of the single sampling numbers and the repeated sampling times is completed. On this basis, by applying the cubic NURBS surface fitting method, the mean value difference surface of the batch tooth surface errors data is constructed, the statistics laws of the whole batch tooth surface errors after heat treatment is determined, and the effective evaluation of the whole batch tooth surface accuracy is realized. Finally, the feasibility and correctness of the bootstrap-based statistics scheme are verified by the tooth surface errors bootstrap statistics application experiment of one kind of hypoid gear. The results show that with the help of the bootstrap statistics method proposed in this paper, it is not necessary to accurately measure the tooth surface errors of the whole batch of hypoid gears one by one. Only by randomly selecting 10 tooth surface samples and repeatedly sampling 2000 times, the original sample characteristic values of the whole batch tooth surface errors can be accurately estimated, and the heat treatment deformation statistics laws of the whole patch tooth surfaces can be also counted.

A novel machining approach of freeform multi-mirror mold via normal swing cutting

Freeform optical elements have found wide applications in the fields of virtual /augmented reality (VR/AR), aerospace and biomedical engineering. Machining complex freeform surfaces on Nip mold with traditional Slow/Fast tool servo (STS/FTS) is difficult due to its large slope angles and multi-mirror structure. We developed a novel normal swing cutting method to solve these issues. The three translational motions were synchronized with the rotation of B axis to generate a normal swing cutting path for fabrication of freeform multi-mirror mold. The mathematical model of tool path for the normal swing cutting was established. A trial cutting process flow of spherical copper columns was carried out where the main error sources were identified and compensated before machining the freeform surface mold and the profile error of spherical copper columns after compensation machining was predicted accurately. To validate the effectiveness of the presented novel cutting method and trial cutting compensation, cutting experiments of a multi-mirror mold with freeform surface were conducted. As a result, the PV-values of the S1 and S2 freeform surface with error compensation machining were improved to 1.1 μm and 1.0 μm based on the on-machine measurement. The results were basically consistent with the surface errors obtained from off-machine measurements, which were 1.2 μm and 1.03 μm respectively. The surface roughness of three local areas was less than Sa 9 nm. This confirms the effectiveness of the developed novel machining methods for the complex freeform surface. Prospects of the new machining method were discussed to provide guidance to the future research.

Glioblastoma multiforme growth prediction using a Proliferation-Invasion model based on nonlinear time-fractional 2D diffusion equation

The glioblastoma multiforme (GBM) is the fast-growing and aggressive type of tumor of the brain or spinal cord that is associated with high morbidity and mortality. Therefore, accurate knowledge of the tumor growth process in different time intervals seems necessary to adopt optimal treatment methods. In this study, with a combination of available early stages imaging data and using image processing methods, a time fractional reaction–diffusion equation based on the moving least squares method was implemented for predicting the growth of the GBM tumor model implemented in the mouse brain. The obtained results demonstrate that the Proliferation-Invasion model implemented by a time fractional form shows more agreement with the experimental results. As a result, using a fractional derivative of order α=0.9 results in the lowest prediction error of the tumor surface (less than 1%). In addition, to reducing the cost and side effects of theranostic methods, the presented model will have the possibility to consider the effects of therapeutic factors, such as hyperthermia, radiography, and surgery, on tumor growth. The ability to use the patient’s characteristics in diagnostic and treatment considerations and the development of personalized medicine can also be considered one of the capabilities of the presented model.

Digital template-guided genioplasty for patients with jaw deformity resulting from temporomandibular joint ankylosis: A comparison between single- and double-layer genioplasty

The aim of this study was to compare single- and double-layer digital template-assisted genioplasty for the correction of jaw deformity resulting from temporomandibular joint ankylosis (TMJA). Thirteen patients with jaw deformity resulting from TMJA who underwent lateral arthroplasty, costochondral graft, or total joint replacement combined with single- or double-layer digital template-assisted genioplasty were included. Computed tomography data were obtained for the preoperative design. Digital templates were designed and manufactured using three-dimensional printing to assist with the chin osteotomy and repositioning in single- or double-layer genioplasty. Of the 13 patients included, seven underwent single-layer genioplasty and six underwent double-layer genioplasty. The digital templates precisely reflected the osteotomy planes and repositioning of the chin segments intraoperatively. The radiographic evaluation showed that the patients who underwent double-layer genioplasty exhibited more chin advancement (11.95 ± 0.92 mm vs 7.50 ± 0.89 mm; P < 0.001) with a slightly larger mean surface error (1.19 ± 0.14 mm vs 0.75 ± 0.15 mm; P < 0.001) than those who underwent single-layer genioplasty. This indicates that double-layer genioplasty better promoted chin advancement and improved the facial shape, but was accompanied by more surgical error compared with the preoperative design. Furthermore, hardly any nerve damage was observed. Digital templates are useful for assisting in surgical procedures.

3D shape reconstruction of the femur from planar X-ray images using statistical shape and appearance models

Major trauma is a condition that can result in severe bone damage. Customised orthopaedic reconstruction allows for limb salvage surgery and helps to restore joint alignment. For the best possible outcome three dimensional (3D) medical imaging is necessary, but its availability and access, especially in developing countries, can be challenging. In this study, 3D bone shapes of the femur reconstructed from planar radiographs representing bone defects were evaluated for use in orthopaedic surgery. Statistical shape and appearance models generated from 40 cadaveric X-ray computed tomography (CT) images were used to reconstruct 3D bone shapes. The reconstruction simulated bone defects of between 0% and 50% of the whole bone, and the prediction accuracy using anterior–posterior (AP) and anterior–posterior/medial–lateral (AP/ML) X-rays were compared. As error metrics for the comparison, measures evaluating the distance between contour lines of the projections as well as a measure comparing similarities in image intensities were used. The results were evaluated using the root-mean-square distance for surface error as well as differences in commonly used anatomical measures, including bow, femoral neck, diaphyseal–condylar and version angles between reconstructed surfaces from the shape model and the intact shape reconstructed from the CT image. The reconstructions had average surface errors between 1.59 and 3.59 mm with reconstructions using the contour error metric from the AP/ML directions being the most accurate. Predictions of bow and femoral neck angles were well below the clinical threshold accuracy of 3°, diaphyseal–condylar angles were around the threshold of 3° and only version angle predictions of between 5.3° and 9.3° were above the clinical threshold, but below the range reported in clinical practice using computer navigation (i.e., 17° internal to 15° external rotation). This study shows that the reconstructions from partly available planar images using statistical shape and appearance models had an accuracy which would support their potential use in orthopaedic reconstruction.

Transmission performance evaluation of non-circular spur bevel gear based on a novel isochronal measurement method

This paper aims to study the transmission performance evaluation of non-circular spur bevel gear (NCSB-gear) based on a novel isochronal measurement method. Firstly, the mathematical model of NCSB-gear is established. Then a novel isochronal measurement method is proposed, and the actual tooth surfaces are reconstructed by non-uniform rational B-spline interpolation. The advantages of the proposed method are discussed based on the geometric characteristics of tooth surface and measurement fitting error. A pair of forged NCSB-gears is measured through a coordinate measurement machine and the maximum tooth surface fitting error by the proposed method reduces 2μm compared with the traditional method. Moreover, deviation tooth contact analysis (DTCA) and load tooth contact analysis (LTCA) are conducted to evaluate the transmission performance. Finally, the transmission performance of measured NCSB-gear is obtained by a gear rolling tester. By comparing the TCA calculation of different measurement methods, it is found that the relative error of the maximum transmission error based on the isochronal measurement method reduces 4.719% compared with the traditional measurement method, thus verifying the validity of the proposed measurement method.

Optical modeling of a cylindrical-hemispherical receiver for parabolic dish concentrator

Among all sub-systems of a solar thermal energy system, the receiver plays a significant role when it gets heat energy from the concentrator. The reliability of such systems depends on the amount of solar energy that the receiver collects and other optical parameters like focal length, aperture diameter, surface absorptivity, and slope error. The present paper discusses the optical analysis of a cylindrical-hemispherical receiver coupled with a parabolic dish concentrator having 3-m diameter. The study has been carried out using the SolTrace software by varying the parameters like receiver aperture diameter (Da) ranging from 0.125 to 0.162m, surface error of the concentrator varying from 1.7453 to 34.907 mrad, and also surface absorptivity (α) changing from 75 to 95% for different receiver distances (H) ranging from 1.7 to 1.95m. The simulation results show that the optical efficiency is maximum when the receiver with 0.150-m aperture diameter is placed at a distance of 1.85m from the concentrator. An increase in slope errors from 1.7453 to 17.453 mrad decreases the average optical efficiency by almost 50% for all receiver diameters. It is also noticed that uniform heat flux distribution can be achieved when the receiver's position is maintained at H = 1.85m from the concentrator for 0.150-m receiver diameter and 95% absorptivity of the receiver surface. The simulated results of heat flux intensity on the receiver surface are then compared and validated by the experimental results available in the literature. The simulated optical efficiency of the present receiver is found to be 8% higher when compared with a conventional cylindrical receiver with similar dimensions.

Revisions in written composition: Introducing speech-to-text to children with reading and writing difficulties

The ability to perform revisions targeting the content of the text is important for text quality improvement, and it is hypothesized that lower-level transcription processes need to be automatized in order to free up capacity for higher-level processes such as revision. However, for people with reading and writing difficulties due to underlying difficulties with decoding and spelling, the transcription process is rarely automatized because of their troubles with spelling. One possible way to circumvent spelling difficulties, and possibly gaining capacity for higher level processes such as revision, is to write using speech-to-text (STT). This study investigates the revisions performed when children with reading and writing difficulties (n= 16), and a reference group without such difficulties (n= 12), compose text using STT and using a keyboard. More specifically, the study investigates whether, and if so how, revisions at various levels, errors left in the final text product, and text quality differ between conditions and between groups. The compositions were logged using keystroke logging (keyboard) and audio- and screen-recording (STT). The level of revisions were manually coded. The results showed that children with reading and writing difficulties gain more from composing with STT compared to keyboard than the reference group. They leave fewer errors in their final text product when composing by means of STT, even though they need to engage more in the correction of surface errors because of the large number of STT errors. Despite the numerous STT errors, neither the proportion of meaning-related revisions nor text quality decreased in composing with STT (for either of the groups). Taken together, the results suggest, albeit not emphatically, that STT may be appropriate as a facilitatory tool for children with reading and writing difficulties. However, more research is needed to investigate instruction that addresses strategies for STT transcription and highlights the shortcomings of the tool in the target language, and also focuses specifically on higher-level aspects of composition such as planning or revising, in order to gain further knowledge about the feasibility of using STT as a means of composition for children who struggle with writing, and its possible effects over time.

Effect of mass flow ratios on the conjugate heat transfer of a metal turbine vane at medium temperature

To investigate the effect of mass flow ratios on the conjugate heat transfer of an air-cooled turbine vane, the surface static pressure test experiments and heat transfer experiments at medium-temperature (407.3 K) and medium-pressure (98.49 kPa) were conducted. An infrared thermal imager was used in the experiments to measure the temperature distribution of the test vane's outside surface. The effects of MFR (mass flow ratio), and mainstream Reynolds number were investigated. The experimental results show that the vane surface temperature is affected by both internal and external cooling. When the MFR was relatively small (MFR=1.0%, 2.0%, 3.0%), the integrated cooling effectiveness on the pressure surface gradually decreased along the coolant passage. At the same MFR, due to the different flow states on the vane surface, the integrated cooling effectiveness corresponding to the maximum mainstream inlet Reynolds number (2.64 × 105) was the smallest, and the cooling effect deteriorated most noticeably at the leading edge. The cooling effect deterioration at the leading edge occurred when the MFR was lower than 4.0%. In addition, the growth rate of integrated cooling effectiveness prior to MFR=4% was significantly higher than that after 4.0%. When the MFR increased from 1.0% to 4.0%, the integrated cooling effectiveness increased by 89.8% with a faster growth rate, whereas it only increased by 14.9% when the MFR increased from 4.0% to 7.0%. An empirical correlation of the spanwise-averaged cooling effectiveness was also obtained. The mean relative error of the pressure surface was 7.64%, and that for suction surface was 3.27%.