The non-linear characteristic of a non-contacting Inductive Proximity Sensor (IPS) with the temperature affects the computation accuracy when measuring the target distance in real time. The linear model based method for distance estimation shows a large deviation at a low temperature. Accordingly, this paper presents a non-linear measurement model, which computes the target distance accurately in real time within a wide temperature range from  An Inductive Proximity Sensor (IPS) is a kind of tiny device deployed to measure the physical parameters of the surrounding area. The improvements of IPS began in the 1990s with the large-scale integration of the electronic components , playingmization ,25. The mization  proposed crystal . The mea crystal ,28 were Focusing on the changing temperature, this paper takes a number of factors into consideration: (i) robustness to the temperature changes; (ii) high accuracy; (iii) easy ASIC implementation; (iv) flexible application. With these considerations, this paper presents a non-linear measurement model, which predicts the target distance quickly and accurately within a wide temperature range from The proposed model can perform an accurate estimation in real time within a wide temperature range.We adopt a non-linear polynomial algorithm to improve the robustness for a wide temperature range, which provides more accurate distance estimation compared to the previous work.We propose a serial dual-stage scheme to reduce the amount of online calculation and enable easy ASIC implementation.The ASIC chips were taped out using 0.18 The contributions of this work are summarized as follows:In order to analyze the classical IPS measurement circuit  accurateIn However, when the resistances  shows the solution of the classical system in Sampling ttime=t1 , we can The comparison between the computed ethod in  when Lx=In the red area of e method  works coThe analysis shown in In addition to the above IPS internal parameters, the inductance When measuring the voltage The output voltage The ADC is redesigned with the optimized temperature coefficients for gain and offset.The test results show that the deviations of The complexity of the The resistances The inductance The temperature plays a significant role in computing ethod in  largely The conclusions drawn from the above analysis and simulation can be summarized as follows:Due to the limitation of hardware resources, it is almost impossible to compute the ethod in  could laThe overall goal of this study is to successfully realize a real-time and high-accuracy measurement method within a wide temperature range. The proposed method contains an offline and an online stage to achieve computation reduction, easy portability, robustness to the temperature changes, and easy ASIC implementation.The dual-stage scheme includes an offline stage and an online stage, as shown in The online stage predicts the target distance based on a non-linear piecewise fitting scheme with the temperature feature parameters from the offline stage. Based on the voltages In The temperature feature parameters represent the complex relationship between To evaluate the algorithm comprehensively and objectively, two kinds of voltages are used in this paper: theoretical Simulation results are introduced in When When According to According to the above conclusions, we propose a temperature based piecewise fitting scheme to compute the temperature feature parameters at the different temperature ranges according to their corresponding voltage deviation. With this fitting scheme, the proposed model can better represent the IPS measurement system when the temperature is changing, which could improve the estimation accuracy.In the low temperature range of Moreover, in the temperature range of The matrix calculus module includes two parts: Vandermonde matrix construction and least squares problem calculation. The dimension of the Vandermonde matrix is The least squares problem calculation conducts the orthogonal-triangular decomposition, and it decomposes matrix Because the temperature feature parameters are calculated offline, the complexity of the computation does not increase the hardware resource consumption for the ASIC implementation. After moving all locations of the specified distance points The introduced online stage aims to predict the target distance with high accuracy and minimal hardware consumption. By means of the non-linear piecewise computation, the online stage first generates the voltage pool of Based on the temperature feature parameters, the online stage generates the voltage pool by means of the non-linear piecewise computation. The piecewise computation scheme performs both linear and non-linear polynomial calculations according to the temperature range, which could improve computation accuracy and reduce the unnecessary calculations simultaneously.To better illustrate the piecewise computation scheme, we use the input of voltage group As illustrated in Equation (3), the voltage The distance estimation module chooses the voltage value from the voltage pool of Specifically, the distance estimation module computes the deviation of The dual-stage scheme: This scheme includes an offline stage and an online stage, which enables computation reduction, flexible application, strong temperature adaptability, and easy ASIC realization.The offline calculation of the temperature feature parameters: These parameters can be calculated in an offline manner to reduce the amount of calculation and complexity significantly when computing The piecewise fitting scheme: This scheme performs the piecewise fitting at the different temperature ranges according to their corresponding voltage deviation, which makes the proposed model close to the IPS measurement system when the temperature is changing.The voltage pool generated by the online piecewise computation: The online stage generates the voltage pool by means of the non-linear piecewise computation. The temperature based piecewise computation performs both linear and non-linear polynomial online calculation according to the temperature range, which could improve the computation accuracy and reduce the unnecessary calculation simultaneously.The distance estimation: By choosing the optimal voltage value, the proposed model can predict the target distance in real time.To achieve high accuracy and easy ASIC implementation, the proposed method adopts the following:Considering the non-linear characteristic of the IPS measurement system with the change of temperature, the proposed method could successfully achieve real-time and high-accuracy target estimation under the changing temperature with low hardware resource consumption. The simulation and ASIC results are shown in Based on the stage technology of the proposed algorithm, this product was already released in 2019 for industrial fields such as landing gears.This product is implemented in an Analog Digital (AD) mixed CMOS integrated circuit, which includes the digital stage of the proposed algorithm, the Electrically Erasable Programmable Read Only Memory (EEPROM), the Low Dropout Regulator (LDO), the ADC interface logic, and the Power On Reset (POR) circuit, as shown in The die layout in The ASIC chip is fabricated in the 0.18 m×1.2 mm a. This cm×1.2 mm a, which CB board b.Both the theoretical simulation and ASIC results are conducted to evaluate the accuracy of the proposed model in this section. It is noted that the inductance cal mode  and is iAs shown in , the valFirst, the intermediate variable T method  and ΔU^1When the target moves in the IPS system, the inductance Therefore, we can conclude that all the computed Based on the calculation of the voltage In When using the IPS measurement system, the distance is the final output, so we evaluate CB board b.First, the intermediate variable T method  is definThe proposed method generates more accurate estimated values, as clearly seen at a low temperature in The estimated distance The difference between the target distance T method  is definIn our ASIC application, the most commonly used sensing distance is 4 mm. In We present the performance summary and comparison with some publicly released references, which have the same application background in the field of aviation, shown in IPS suffers from temperature changes, which significantly decrease the measurement accuracy at low temperatures. Many proposed methods such as ,28 achieThe innovations for high-accuracy measurement always increase the complexity of the ASIC implementation in the industrial fields, due to the limitation of hardware resources. We propose a serial dual-stage scheme to reduce the amount of online calculation and enable easy ASIC implementation, in which the offline stage performs a large amount of the computation and the online stage predicts the target distance with little hardware resource. Since the large amount of the parameter computation can be performed in the offline stage, the proposed system can guarantee both high accuracy and easy ASIC implementation.This model is fabricated in a 0.18


Microfluidic devices for drop and emulsion production are often built using fire-shaped (or fire-polished) glass nozzles. These are usually fabricated manually with inexpensive equipment. The shape limitations and poor reproducibility are pointed as the main drawbacks. Here, we evaluate the capabilities of a new fire-shaping approach which fabricates the nozzle by heating a vertical rotating capillary at the Bottom of a Lateral Flame (BLF). We analyze the effect of the heating conditions, and the capillary size and tolerances. The shape reproducibility is excellent for nozzles of the same size produced with the same conditions. However, the size reproducibility is limited and does not seem to be significantly affected by the heating conditions. Specifically, the minimum neck diameter standard deviation is 3%. Different shapes can be obtained by changing the heating position or the capillary dimensions, though, for a given diameter reduction, there is a minimum nozzle length due to the overturning of the surface. The use of thinner  capillaries allows producing much shorter nozzles but hinders the size reproducibility. Finally, we showed an example of how the performance of a microfluidic device is affected by the nozzle shape: a Gas Dynamic Virtual Nozzle (GDVN) built with a higher convergent rate nozzle works over a wider parametric range without whipping. Microfluidics is receiving growing attention in numerous fields, especially in biotechnology where it is becoming a key tool. Research in microfluidics involves both the understanding of the physics of flows at such small scales and the development of the devices for different applications. Two-dimensional systems, usually referred to as lab-on-a-chip, have been fabricated by micromachining or soft-lithography. Low cost-high sensitivity diagnosis devices or organ-on-a-chip systems for drug development and testing are some examples . Three-dCapillary devices in which two nozzle tips are placed in front of each other are very common for emulsion production and encapsulation in the food and pharmaceutical industries ,4,6,7. AThe Gas Dynamic Virtual Nozzle (GDVN)  is anothIn capillary-based microfluidic devices, nozzles are usually fabricated by two procedures: pulling or fire-shaping . The former has been traditionally used for pipette manufacturing. The technology is mature and several commercial pullers are available, which are supplied with a cookbook indicating the adequate process parameter for a particular pipette application or geometry. In pipette pullers, the capillary ends are held by two jaws, and its central section is heated with an electrical resistance or a laser. Then, one or both jaws are moved apart stretching the capillary in the middle and producing two long and needle-shaped pipettes at the same time. To separate them, pulling may be maintained until breakage or a secondary cutting stage may be necessary. Pulled nozzles are commonly used in emulsion devices ,10. To omm I.D.) . Additiomm I.D.) ,10.Fire-shaping produces the nozzle by heating the capillary tip typically with a flame. It is also known as fire-polishing because it is used to smooth the surface of the pipette’s tip after breaking or grazing without significant change in the diameter too. When the capillary tip is heated, the glass flows to reduce its free surface driven by surface tension forces and overcoming the viscous stresses. The material moves inwards reducing the diameter and the length of the capillary. The result is a convergent-divergent nozzle much shorter than a pulled one. The use of these nozzles have extended since Switzer  includedAlthough the use of fire-shaped nozzles is extended, most researchers fabricate them manually. Very few fire-shaping systematic studies have been carried out. First, traditional fire-shaping approaches were analyzed using the flame of a vertical Bunsen burner in a setup designed to reduce the operator intervention . When thIn this work, we analyze the reproducibility and shape capabilities of a new-fire shaping approach, in which a vertical rotating capillary is heated at the Bottom of a Lateral Flame (BLF) d. The usThough the fire-shaping idea is simple, the phenomena involved in the process are not. The glass flow that gives rise to the nozzle occurs as the surface tension forces reduce the glass free surface while the viscous forces oppose the flow. The glass viscosity depends highly upon the temperature. The glass cannot stand stress and creeps above the strain temperature . In the first run of experiments, we analyzed the effect of increasing the heating time for a fixed heating position  the particular dimensions of the original capillary, which vary within the tolerances; or (ii) the variability of the shaping process itself. It is possible to produce nozzles of the same neck diameter with different heating conditions. When the nozzle is produced deeper in the flame, a longer region of the capillary is heated up to a higher temperature. Therefore, a larger length of the capillary participates in the flow, and it moves faster. The diameter reduction is reached sooner because of the faster flow, but also because a longer region of the inner surface moves inwards. This effect produces longer nozzles and neck channels. Additionally, as the glass inwards, it also flows downwards producing a larger shortening of the capillary.t is larger. The glass takes longer to increase the temperature, and the temperature will anyway be lower. The flow will be slower, as shown by the shortening reduction  establishes a limit for the nozzle neck shape. It may be smooth, spreading over the nozzle length, or abrupt, converting the nozzle almost into two tubes in series. We defined the neck aspect ratio  allows us to move the capillary horizontally for proper alignment and to control the distance z of the capillary axis to the burner tube exit. The heating time t is controlled by an Arduino board (G) and a servomotor (H) which places a ceramic plate (I) between the burner and the capillary or moves it away.z from the burner exit. The symbols represent the mean value of the measurements, and the standard deviation is used for the error bars. The white symbols correspond to the visible limit of the flame. The presence of the blue cone, which is a cold area, can be appreciated close to the burner (z) to the burner. Therefore, we chose the closest possible position (For each heating conditions To manufacture the nozzles we used cut-end glass capillaries made of borosilicate glass 3.3 (Hilgenberg GmbH). The dimensions and tolerances, according to the supplier, are shown in D, the outer diameter L and after P mentioned above.We used image analysis to obtain the shape and several geometrical parameters of the nozzles. We take three images of each nozzle with its tip submerged in glycerine and air flowing through it. The air inside the nozzle appears black in the image, making edge detection easier . A CCD camera  and backlighting were used to obtain images of the jet.We used a pneumatic tee connector  with instant fittings to assemble the device . The gla


Image neural style transfer is a process of utilizing convolutional neural networks to render a content image based on a style image. The algorithm can compute a stylized image with original content from the given content image but a new style from the given style image. Style transfer has become a hot topic both in academic literature and industrial applications. The stylized results of current existing models are not ideal because of the color difference between two input images and the inconspicuous details of content image. To solve the problems, we propose two style transfer models based on robust nonparametric distribution transfer. The first model converts the color probability density function of the content image into that of the style image before style transfer. When the color dynamic range of the content image is smaller than that of style image, this model renders more reasonable spatial structure than the existing models. Then, an adaptive detail-enhanced exposure correction algorithm is proposed for underexposed images. Based this, the second model is proposed for the style transfer of underexposed content images. It can further improve the stylized results of underexposed images. Compared with popular methods, the proposed methods achieve the satisfactory qualitative and quantitative results. Style transfer seeks an artistic style reproduction on daily photos, enabling the photos retain the original content while presenting a prescribed artistic style ,2,3. TheFor a long time, the research on neural style transfer mainly focused on two issues. It is hoped that the stylized images have a strong artistic sense and the model has good generalization for a wide application meanwhile. However, the application of style transfer is affected by many factors. Style images with large color differences from content images often generate errors during style transfer, while the inconspicuous details in low-illumination images also lead to unsatisfactory results.This paper analyzes the influence of color dynamic range of input images on the stylized result and proposes two models to improve the spatial rationality of stylized image. Firstly, to solve the unreasonable space caused by the difference in the color dynamic ranges between content image and style image, we propose a neural style transfer model (RNDT) based on robust nonparametric distribution transfer. Then, a neural style transfer model combining exposure corrected and robust nonparametric distribution transfer (EC-RNDT) is proposed to further improve the stylized result of RNDT model for underexposed content images. Experimental results show that the style transfer methods based on robust nonparametric distribution transfer not only increased the spatial rationality, but also extended the application range.The contributions of the proposed models are listed as follows: (1) We introduce a robust nonparametric distribution transfer algorithm into the style transfer model, which could improve the spatial rationality of the stylized image when the color styles of the content image and style image are quite different; (2) We introduce the adaptive exposure correction algorithm into the robust nonparametric distribution transfer to obtain the satisfactory stylized result for underexposed images.Since mid-1990s, different strategies have been used to preserve the structure of content images in the field of non-photorealistic rendering . Song etThe first neural style transfer (NST) model was proposed by Gatys et al. , which tSince the Gram-matrix based loss has limitations, many researchers found it is not the only choice for style representation. Li et al.  proposedIn addition, some research focuses on improving the stylized result through different information and strategies. Liu et al.  introducBased on the style transfer methods, many existing works focus on a specific application. Luan et al.  and MechIn recent years, the Generative Adversarial Networks (GAN)  have beeIn this paper, we analyze the factors that affect the rationality of the neural style transfer. Then two style transfer models are proposed based on robust nonparametric distribution transfer. Both style transfer models are verified in different application scenarios. Experimental results show that the proposed models can effectively improve the spatial rationality of the stylized images and preserve the structure information.The rest of this paper will be organized as follows. We introduce our style transfer models in In this section, we analyze two inevitable factors affecting the space rationality of the style transfer. One is the unreasonable space caused by the difference of the dynamic color ranges, and another one is underexposure. Both factors limit effectiveness of the neural style transfer models. Based on the analysis, we propose two neural style transfer models to ease the limitations and improve the effectiveness of the neural style transfer models. In Compared with the traditional artistic stylization, the neural style transfer method can work on any set of content images and style images. However, this approach does not yield a good stylized result for some input images. Since the colors in style images are usually more saturated than the content images, the color dynamic range of the style image is usually larger than that of the content image. We find that when the color dynamic range of the content image is much smaller than that of the style image, the artistic style texture is prone to being misplaced.To solve this problem, a neural style transfer model based on robust nonparametric distribution transfer is proposed. Before the style transfer, the color of the style image is transferred into the content image. This method is named robust nonparametric distribution transferred neural style transfer, which is shown in For the robust nonparametric distribution transfer, it is constructed by introducing the robust nonparametric kernel regression (RNKR)  into theThe IDT algorithm makes the color probability distribution of content image become that of the style image. Therefore, the color dynamic range of the content image is enhanced. Moreover, the boundaries of each object are more obvious. As a result, the content loss has a larger value at the boundary of the objects. Nonparametric kernel regression is a familiar tool to explore the underlying relation between response variable and covariates. The RNKR model  can contAlgorithm 1 The details of the Initialization of the source data repeat(1)take one rotation matrix (2)obtain the rotated samples: (3)project the samples on all axes (4)for each axis (5)remap the samples (6)rotate back the samples: (7)until convergence on all marginals for every possible rotation The final one-to-one mapping The robust nonparametric distribution transfer procedure is presented by Equation (1),orithm 1 ,44.AlgoIn the neural style transfer model, VGG-19  was usedWhen the color dynamic range of the content image is much smaller than that of the style image, the artistic style textures tend to be placed incorrectly. The proposed RNDT model can improve the stylized effect in this case. In practical applications, the stylized result of the RNDT model is more spatially reasonable in this situation.This section focuses on the daily photo stylization for cellphone users. Sometimes, photos are more likely to be underexposed. The underexposed photos usually have the following problems: (1) in the backlit area, the edge gradient of the object is smaller than normal area. The feature at the edge of the object is weakened so that the content loss function does not work well. (2) The color saturation in the backlit region is low, resulting in a small color dynamic range.To solve these problems, an adaptive detail-enhanced multi-scale retinex (DEMSR) algorithm for exposure correction is proposed. Based on DEMSR, a neural style transfer model integrating exposure corrected and robust nonparametric distribution transfer is proposed.Our proposed exposure correction algorithm for an underexposed content image consists of the following three steps.Adaptive backlit region detection. The backlit region template detection is used to determine whether to modify the image. The adaptive detection method of backlit region is shown in Equation (2),According to , the guiMSRY is an exposure corrected image in the luminance channel which is calculated by the MSR algorithm.Light restoration module. Our exposure correction algorithm is developed based on the Multi-Scale Retinex (MSR) algorithm . In the iL; (2) Enhancing the edge and stereoscopy of the object inside the backlit area. The idea of the Laplacian filter [F4 is a Laplacian filter whose window is 0.4% of the content image. DEMSRY is the exposure corrected image in the luminance channel obtained by the DEMSR algorithm. After enhancing the details, a gain compensation on DEMSRY will be conducted for the balance of the three channels. Finally, the YCbCr space is converted to the RGB space to obtain the backlit enhanced image In order to preserve the fine details after the robust nonparametric distribution transfer of the RNDT model, our method has made two improvements compared to the MSR algorithm. (1) Removing the “Halo” phenomenon to protect the reality of the boundary of the backlit area. For this purpose, the Gaussian filter used in Equation (4) is changed into a guided filter. The guided filter can protect the edge of the backlit region, while estimating the natural light n filter  is used Fusion to obtain exposure correction image. Once the backlit enhanced image is obtained, the non-backlit region is filtered by the backlit region template. The enhanced backlit area is fused with the normal area to obtain the final exposure correction image The final exposure correction image will be input to the RNDT model for getting the stylized image.The RNDT algorithm and DEMSR algorithm are implemented by Matlab, and the style transfer models use the Lua language and Torch framework. The algorithm was implemented in Python with developed codes subject to the PyTorch framework. The algorithm ran on an Ubuntu system with an Intel Xeon E5-2620 CPU (2.1 GHz) and with a 64 GB memory. Our code used a GTX 1080 Ti GPU with 11 GB memory. The implementation was not optimized and did not use multithread and parallel programming. Computing by using the test images in this section, the average computational cost of RNDT is 1.1 s, and the average computational cost of EC-RNDT is 4 s. In the experiments, all the style transfer models run in the same environment, and all the hyper-parameters are unchanged in the comparison experiments.It is a subjective task to evaluate the quality of the style transfer ,4. ThereFor the comparison experiments, the models of Gatys et al. , Huang eWhen the color dynamic range of the content image is much smaller than that of the style image, the artistic style texture is prone to be misplaced. An experiment was performed to show that the existing neural style transfer models suffer from this problem. The results are shown in To evaluate the impact of the RNDT algorithm, an experiment was performed. The experiment results are shown in To illustrate the effectiveness of the DEMSR algorithm, the intermediate results are shown in The light restoration results of the MSR algorithm and our DEMSR algorithm are compared in To further evaluate the performance of MSR and the proposed DEMSR algorithms, two quantitative metrics are adopted, which are peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) . The bigThe adjustment of parameters In order to show the effect of the DEMSR algorithm, we compared the results of the RNDT model with the EC-RNDT model.In In In order to show the superiority of the proposed EC-RNDT model, we compared four baseline models ,11,21,24In the experiments, the models of Gatys et al.  and HuanThe stylized results of Gatys et al.  and EC-RThe stylized results of Liao et al. and EC-RNDT model are shown in Aforementioned sections showed the color transfer of the content image. Under certain circumstances, style transfer is hoped to preserve the color of the content image but transfer the texture style. In this case, the RNDT model can achieve this demand through a slight modification. The input image of RNDT model performs a role exchange, which can realize the color-preserved transfer. That is to say, before the style transfer model, the color of style image is changed into the color of the content image. Therefore, the style transfer will only transfer the texture style of the style image. The results of color-preserved RNDT model are shown in A user study was performed to further valid the superiority of the proposed models. In the user study, we designed a webpage including 60 groups of outputs, which were viewed by participants. Each group contains two stylized image of baseline models and one stylized image from the proposed model. Participants were asked to choose the one he or she likes better. The results of user study are shown in As a form of preprocessing, the proposed model can improve the performances of the corresponding style transfer method without depending on any specific neural style transfer model. To evaluate this, two quantitative metrics were adopted, which are deception rate  and FID In this paper, we propose two models for image neural style transfer. The first model named as RNDT transfers the color of the content image to that of the style image, which makes the spatial structure of the stylized image more reasonable. The second model introduces the DEMSR exposure correction algorithm to enhance the details in the underexposed images, which can preserve the fine details in the stylized images. Experimental results show that the models have improved the spatial rationality and the artistic sense of the stylized images. The proposed models could be applied in several situations, which include underexposed images, large color-range images, and color-preserved style transfer. Therefore, our models have a high application value.The proposed RNDT and EC-RNDT models do not depend on any specific neural style transfer model. They work for the style transfer methods that only need one style image. They can improve the performances of the corresponding style transfer methods as a method of preprocessing.The proposed models achieve encouraging performance in generating stylized images. However, we have to note that our approach still has limitation. The proposed models are not end-to-end, which is not efficient. Therefore, developing an efficient end-to-end style transfer method is our future work.


This paper suggests a new control design based on the concept of Synergetic Control theory for controlling a one-link robot arm actuated by Pneumatic artificial muscles (PAMs) in opposing bicep/tricep positions. The synergetic control design is first established based on known system parameters. However, in real PAM-actuated systems, the uncertainties are inherited features in their parameters and hence an adaptive synergetic control algorithm is proposed and synthesized for a PAM-actuated robot arm subjected to perturbation in its parameters. The adaptive synergetic laws are developed to estimate the uncertainties and to guarantee the asymptotic stability of the adaptive synergetic controlled PAM-actuated system. The work has also presented an improvement in the performance of proposed synergetic controllers  by applying a modern optimization technique based on Particle Swarm Optimization (PSO) to tune their design parameters towards optimal dynamic performance. The effectiveness of the proposed classical and adaptive synergetic controllers has been verified via computer simulation and it has been shown that the adaptive controller could cope with uncertainties and keep the controlled system stable. The proposed optimal Adaptive Synergetic Controller (ASC) has been validated with a previous adaptive controller with the same robot structure and actuation, and it has been shown that the optimal ASC outperforms its opponent in terms of tracking speed and error. Pneumatic actuators such as cylinders, pneumatic stepper motors, bellows, and pneumatic engines are commonly used to date. Pneumatic Artificial Muscles (PAMs) are one type of pneumatic actuator, which are made mainly of inflatable and flexible membrane that works like inverse bellows; i.e., they contract on inflation. The force generated by PAM actuators does not depend only on pressure, but also on the state of inflation, which adds another source of spring-like behavior. These PAMs, which mimic the animal muscle, are characterized by their light weight, since the membrane forms the core element of these actuators. However, they can transfer the same amount of power as cylinders do, when both actuators have the same volume and pressure ranges ,2.PAMs are used in many applications due to their light weight, simple construction and high force/weight ratio, direct connection, easy replacement and safe operation. The PAM actuators found their application in biomechanics, bio-robotics, robotics, artificial limb replacement Moreover, since PAMs are noise-free devices, they are applicable in hospital treatments to patients who are sensitive to noise. Compared to motor actuators, PAMs do not need a gear mechanism to increase power due to their high power/volume ratios. Due to their elasticity, PAMs are useful for the natural frequency of biped locomotion. Additionally, PAMs are useful for under-water applications due to their water immunity ,4. SincePAMs are characterized by many disadvantages. As compared to other actuators, one problem which can be addressed in PAMs is their antagonistic structure. This structure does not permit one PAM in the pair to contract and relax unless another PAM inflation causes the first PAM to deflate. However, only one motor is sufficient to perform the desired movement in traditional actuators . One othScaff et al., in , proposeChoi et al., in , proposeWang et al., in , proposeAl-Jodah and Khames, in , designeMedrano-Cerda et al., in , have deLilly and Yang, in , appliedJahanabadi, in , investiTarapong and Radom, in , have deRepperger et al., in , presentLilly, in , presentBoudoua et al., in , proposeRobinson et al.  studied Shen  developeHosovsky et al.  presenteEnzevaee et al.  have preHiroki  presenteCaldwell et al. in  presenteThe works reviewed in the above literature either used intelligent control schemes, based on fuzzy logic, neural networks, optimization-based control, nonlinear control based on sliding mode control, adaptive backstepping control, or hybrid nonlinear control. Moreover, it is worthy to mention that the structure of the PAM-actuated manipulator differs from one study to another. Different from the previous studies, in this paper, an adaptive controller is developed for tracking control of PAM-manipulator based on synergetic control strategy.Forming the extended system of differential equations, which reflects different operations such as achieving the set values, coordinating observing, optimization, suppressing the disturbances etc.Synthesizing “external” controls which ensure a reduction in the extra degrees of freedom of the extended system with respect to the final manifold. The motion of the representing point is described by the equations of the system’s “internal” dynamics.Synthesizing the “internal” controls by means of forming the links between the “internal” coordinates of the system. These links ensure the reaching of the control aim.The synergetic controller directs the trajectories of the system to move onto the manifold from any initial points to their corresponding equilibrium points.The Synergetic Control (SC) theory is based a state-space theory, which is utilized for the design and control of highly complex and connected nonlinear systems. This control strategy could enable the state variables of the system to evolve on invariant manifolds chosen by the designer and to achieve the required performance in spite of the presence of uncertainties and disturbances ,25. The It has been shown that the design parameters of different adaptive and non-adaptive controllers have a direct impact on their performances. These design parameters are often selected based on the trial-and-error procedure. This old technique could not find the optimal dynamic performance of the controlled system based on the proposed controllers. Therefore, a modern optimization technique is used to tune these design parameters to improve the dynamic performance of the controlled system ,29. In tThe main problem with systems actuated by Pneumatic Artificial Muscles is that they suffer from external disturbances, uncertainties , high nonlinearities, hysteresis and time varying characteristics, which dramatically degrade the performance of tracking control. To handle this important issue, an adaptive control method is proposed for the PAM-actuated one-link robot arm, which can deal effectively with the influence produced by parametric uncertainties in actuating muscles.❑To design a new classical synergetic control (CSC) algorithm for the PAM-actuated robot arm based on Lypunove-based stability analysis.❑To design a new adaptive synergetic control algorithm to cope with the problem of uncertainties inherited in parameters of the PAM-actuated robot arm.❑To prove the asymptotic stability of the PAM-based robot arm controlled by CSC and ASC, such that all errors finally converge to their corresponding zero equilibrium points based on Lypunove stability analysis.❑To better improve the dynamic performance of the PAM-actuated robot arm controlled by proposed controllers by replacing the trial-and-error procedure with the PSO technique for optimal tuning of controllers’ design parameters towards better performance of controllers.The contribution of this paper is to develop an adaptive control algorithm based on synergetic control theory for tracking control of a single-link robot arm actuated by pneumatic artificial muscles under uncertainties in muscle parameters. The proposed controller is continuous and able to prevent chattering and it can simultaneously compensate the parametric uncertainties, and it yields bounded adaptive gains. The improvement in performance of the proposed adaptive controller by PSO-tuning of its design parameters is the second contribution, which can be added as well since it has never been addressed in the literature for such PAM systems. The first controller is based on known parameters of PAM-actuated one-link robot arms named as classical synergetic controller (CSC), while the other adaptive synergetic controller (ASC) solves the problem of unknown uncertainties in system parameters. The stability of the controlled PAM robotic system is analyzed and proved based on Lypunov stability analysis. In addition, the PSO technique is introduced for tuning the designed parameters of proposed controllers to better enhance the performances of the proposed controllers. Thus, the contribution of the present work can be embodied by pursuing the following steps of objectives:Before proceeding in the control design of the PAM system, it is important to first develop the mathematical model for the system, which mimicks the actual behavior of real system. Then, the system can be analyzed and its associated controller can be designed to meet the required performance. The single link robotic arm is shown in r is the pulley radius.where, The amount of pneumatic muscle extension ively by ,16,(1)xThe forearm forms an angle The counterclockwise torque applied by the tricep muscle is described by:AM model :(5)Fb(.)In addition, It is worthy to note that the coefficient The dynamic equation of motion can be found by summing the torques, described by Equations (3) and (4), about the elbowThe time derivative of PM extension Using Equations The pressure of tricep and bicep PAM is givenEquation (16) can be rewritten in the following compact form:The variation in the pressure In this section, two control schemes have been developed for tracking control design of angular position for PAM robot arm. The first control design is established based on the classical synergetic control method. The second control design presents the development of an adaptive synergetic control algorithm for tracking control of the PAM robot arm subjected to uncertainties in system parameters.Let Using dynamic equation of the PAM robot arm, the first and second derivatives of error equations are given by, respectively,Taking the first-time derivative of Equation In order to ensure the stability and to guarantee the convergence of the state trajectories to their corresponding desired manifolds and remain on it for future time, the dynamic evolution of the macro-variable towards the manifolds is defined as follows:Using Equations (23) and (24) becomesUsing the dynamic equation of the PAM robot arm, Equation (25) becomesUsing Equation (21), one can haveIn order to ensure the dynamic Proof. The candidate Lypunov function is chosen in terms of micro-variables vector as follows:Taking The time derivative of Equation (29) givesUsing Equations (24) and (30) becomesThis indicates that the control law of Equation (28) guarantees the system stability of the PAM robotic System. □Theorem 1.For the dynamic equation of the PAM-actuated robot arm, the control signal In order to address the problem of uncertainty, which is a characteristic feature in the physical parameters of the PAMs system, and for suppressing the effects of undesired disturbances that may have an effect on the tracking performance, the ASC has been introduced to develop the necessary adaptive laws that can estimate these uncertain parameters such that the asymptotic stability of the adaptive controlled system is guaranteed. In this case, the adaptive syngeneic controller could direct all trajectories of micro-variables to the equilibrium or manifold asymptotically. When the trajectory reaches the manifold, the synergetic controller will maintain it there thereafter.Assumption 1.Two coefficients are permitted to be uncertain in their values; namely, the viscous friction coefficient and spring coefficient.Assumption 2.The variation in coefficients of bicep muscle has only been taken into account, that is, the uncertainty in viscosity coefficientand the uncertainty in spring coefficient. However, since the spring coefficient in the bicep and tricep muscles are the same, thenis assigned to the coefficient.Assumption 3.The inflation case will be only considered in developing the control law of the ASC algorithm.,Referring to Equations (8) and (10), there are three possible parameters of the system, which permit variations in their values; namely, In order to derive the adaptation law, the candidate L.F. has been chosen in terms of estimation errors as follows:Based on Equation (23), one can getThe ideal control law, given in Equation (28), is no longer applicable in the presence of uncertainty and the actual control law is defined in terms of estimated functionSubstituting Equation (38) in Equation (37) to becomeSince,By subtracting Since Equation (42) can be arranged in the formIn order to ensure Accordingly, the following adaptation laws can be deducedUsing Equations Since the time derivative of L.F (Theorem 2.If the dynamic system of the PAM-actuated manipulator is subjected to uncertainty in viscosity coefficient In order to improve the performances of the proposed controllers (CMC and ASC), the design parameters of these controllers have to be tuned to towards better performance of the controlled system. Trial-and-error procedure for finding or setting these design parameters is cumbersome and it does not lead to an optimal solution in terms of better dynamic performance of controlled systems. As such, the PSO technique has been suggested to find the optimal values of design parameters. It is well-known that the PSO algorithm has the capability to guide the performance of controllers towards optimality. In the case of CSC, the PSO technique is responsible for tuning the design parameter In PSO, each particle navigates around the search (solution) space by updating their velocity according to its own and according to searching experience of other particles. Each particle must update its velocity and position according to the number of iterations, which will be performed according to some cost function to minimize or maximize in each case. In our design, the cost function has to be minimized.The velocity of each particle is updated according to the following equation ,43:(47)Vequation :(48)Xik+The cost function used to evaluate each particle during the search of the minimum is chosen to be the Root Mean Square Error f (RMSE) function.The performance of the PSO algorithm is sensitive to PSO parameters. The adjusting of inertia value w strikes a better balance between global exploration and local exploitation. The population size is set to compromise between convergence rate and computation time. Acceleration constants The numerical values of the pair of PAM-actuated robot arms in the bicep/tricep positions are listed in The simulink model of the adaptive synegetic controlled robotic system tries to mimick the block diagram of eference  for a deThe design parameters for the CSC are The Root Mean Square Error (RMSE) is the fitness function that has been used to evaluate the iterative particles within the PSO algorithm for all controllers. Three scenarios are presented in the present work. In the first scenario, the uncertainty is not taken into account, the second scenario considered the uncertainty condition, while the third scenario has been devoted to the validation purpose. The desired angular positions for the first and second scenarios are defined byScenario I: PAM-actuated Robot Arm based on CSCThe corresponding control effects based on optimal and non-optimal CSC are depicted in Scenario II: PAM-actuated Robot Arm Based on ASCIn order to design an adaptive controller (ASC), the bicep coefficient of viscosity Scenario III: Validation of Proposed ControllerBefore proceeding in validation, it is worthwhile to note that the structure of the PAM-actuated single-link robot arm differs from its counterparts with the same link and actuation. In the present work, the cable attached to the pair of muscles that works to rotate the pulley is connected at the end of the robot arm, as shown in This paper presents a new classical and adaptive control design based on a synergetic theory for tracking control of a single-link robot arm actuated by a pair of artificial muscles. The adaptive synergetic controller has been designed to cope with inherited uncertainties in muscle parameters. The design of the proposed controllers has been developed to guarantee the stability of the controlled robotic system.According to the simulated results, one can conclude that the optimal CSC gives better tracking performance in terms of transient and steady-state characteristics than that obtained by non-optimal CSC. However, the energy drawn by the controlled system based on optimal CSC is higher than that based on the non-optimal controller. In the presence of uncertainty in muscle parameters, the tracking control performance of the adaptive controlled system based on optimal ASC is better than that based on non-optimal ASC. This will be at the expense of higher required input pressure to actuate the muscles in the case of optimal ASC. Moreover, the optimal ASC controller gives better tracking control performance than optimal CSC. Again, this superiority in performance obtained by optimal ASC was on account of higher absorbed energy needed to supply the actuating muscles. Moreover, the optimal ASC could successfully confine the estimation errors of uncertain parameters within certain bounds, which, in turn, will avoid the instability problem due to drifting in estimation errors. Another conclusion that can be drawn is that the proposed adaptive controller generates continuous and monotonic control signals. The proposed controller has been validated with previous work and it has been shown that the proposed controller gives better tracking performance in terms of tracking speed and error than the previous controller.The future work of the work will focus on real-time implementation and verification of the proposed controller on an actual PAM-actuated robot arm. In addition, a comparison study can be conducted with another adaptive control scheme for the same robot structure, or the PSO technique can be used as a comparison format with other recent optimization techniques.


In recent years, coal-fired power plants contribute the biggest part of power generation in China. Challenges of energy conservation and emission reduction of the coal-fired power plant encountering with a rapid growth due to the rising proportion of renewable energy generation in total power generation. Energy saving power generation dispatch (ESPGD) based on power units sorting technology is a promising approach to meet the challenge. Therefore, it is crucial to establish a reasonable and feasible multi-index comprehensive evaluation (MICE) framework for assessing the performance of coal-fired power units accessed by the power grid. In this paper, a hierarchical multiple criteria evaluation system was established. Except for the typical economic and environmental indices, the evaluation system considering operational flexibility and power quality indices either. A hybrid comprehensive evaluation model was proposed to assess the unit operational performance. The model is an integration of grey relational analysis (GRA) with analytic hierarchy process (AHP) and a novel entropy-based method (abbreviate as BECC) which integrates bootstrap method and correlation coefficient (CC) into entropy principle to get the objective weight of indices. Then a case study on seven typical 600 megawatts coal-fired power units was carried out to illustrate the proposed evaluation model, and a weight sensitivity analysis was developed in addition. The results of the case study shows that unit 4 has the power generating priority over the rest ones, and unit 2 ranks last, with the lowest grey relational degree. The weight sensitivity analysis shows that the environmental factor has the biggest sensitivity coefficient. And the validation analysis of the developed BECC weight method shows that it is feasible for the MICE model, and it is stable with an ignorable uncertainty caused by the stochastic factor in the bootstrapping process. The elaborate analysis of the result reveals that it is feasible to rank power units with the proposed evaluation model. Furthermore, it is beneficial to synthesize the updated multiple criteria in optimizing the power generating priority of coal-fired power units. In recent years, increased electricity consumption demand in China has been restricted by the “new normal” economic situation. At the generation side of the power grid, the share of installed renewable energy capacity has achieved to 38.1 percent of total power generating . As coalFor the power grid, ESPGD is one of the promising ways to achieve the optimal allocation of various energy generation sources based on coal-fired power units ,6,7,8. ITo determining the priority of candidate power unit with multiple performance indices, some prevalent multi-criteria decision making (MCDM) methods are available for the typical complex system, such as PROMETHEE , ELECTREIn the process of comprehensive evaluation, the importance of the index is usually different for the decision maker. To obtain the weights of the indices, some methods have been introduced in literatures such as the subjective, objective and combination methods. The subjective preference of experts can be determined by the method such as Delphi , AHP 4,,26,29,30In this paper, for assessing the comprehensive performance of coal-fired power units, we propose a multiple index evaluation system considering economic, environmental, flexibility and power quality criteria. A novel integrating objective weighting method (BECC) was developed by combining bootstrap method, entropy and correlation coefficient weighting method. The rest of the paper is organized as follows: in Integrity. Indices should be able to reflect the power grid requirements to the electricity generating facilities in an accurate and objective way according to professional theory or prior knowledge.Independence. Because of the complex relationships between indicators, the indices selected should be the one with less redundancy at the precondition of integrity.Availability. The index should be reliable and can be accessed easily in the current technical conditions.The choice of the index is very important for any successful comprehensive evaluation work. The selected indices must serve the purpose of the evaluation. Usually, the following principles should be followed:We take four categories into consideration for the comprehensive evaluation task. The index Hierarchy, shown in The economic index contains net coal consumption rate (C11), auxiliary power ratio (C12), oil consumption rate (C13) and water consumption rate (C14). Coal consumption rate is one of the most important indices representing power plant performance; the rate represents the amount of standard coal consumed per kWh. The auxiliary consumption rate reflects the electric power consumption of the power unit itself. The oil consumption is caused by the processes of unit startup-shutdown and the low-load combustion (for the flame stability of boiler). The water consumption rate reflects the water saving benefits. For these four indices, the smaller the better.2 emission concentration (C21), NOX emission concentration (C22) and dust emission concentration (C23). The emission of Hg pollutant and greenhouse gases such as CO2 are not considered mainly because such pollutant removal equipment has not been widely used in China. Pollutant emissions from coal burning are a major contributor to environmental pollution, these three indices reflect the ability of environment protection of the power unit. For these three indices, the smaller the better. All these indicators are available in the online monitoring platforms at current plants.We primarily consider the gaseous pollutant in the coal-fired boiler flue gas exhaust. That is, SOFlexibility includes fuel flexibility and operational flexibility. In this work, the indices we used only refers to operational flexibility. The flexibility requirements of the power grid system for power units mainly contain the aspects of peak adjustment depth, peak regulation speed and the ability of quick startup-shutdown, etc. Referring to standard codes of the Detailed Rules for The Implementation of Auxiliary Service Management of Power Plant Connected in North China Grid  and the Detailed Rules for The Implementation of Grid Operation Management in North China Regional Power Plant  , five indicators of Automatic Generation Control (AGC) performance are selected in our proposed multi-level index evaluation system for characterizing the flexibility features. The AGC indices can be obtained from the Supervisory Control and Data Acquisition (SCADA) platform, which is a subsystem of the Energy Management System (EMS) used in the power grid. The data are averaged on an annual level. The five indices are introduced as follows.AGC availability ratio (C31) is the ratio of AGC input time to the effective running time during the statistical period. AGC regulation rate factor (C32) is the ratio of the regulating rate to the standard regulating rate of the electric power generation unit. The regulating rate is the average of the rising rate and the decline rate in the statistical period. AGC regulation precision factor (C33) is the ratio of the regulation deviation to the allowable deviation. The regulation deviation is the value between the AGC load instruction with the actual stable output of generator responding. AGC response time factor (C34) is the ratio of actual response time to the standard response time. The AGC response time is used to break through the regulation dead zone in the same adjustment direction with the EMS signal based on the original generator output point. AGC adjustable capacity (C35) refers to the ratio of the adjustable unit capacity for the power grid to the design load rate.For a coal-fired power generator, the power quality control mainly refers to the regulation of voltage quality and frequency quality. The adjustment ability of power units can be reflected by the indices from the primary frequency control (PFC) and automatic voltage control (AVC) systems. The power quality indices contain five C-level indices.PFC operation ratio (C41) is the ratio of PFC running time to the power unit operation time available to the grid. PFC correct action rate (C42) refers to the ratio of the PFC correct action number to the total adjustment times during the statistical period. PFC speed variation rate (C43) is the ratio of the static speed increase to the rated speed. The static speed increase happens in the process of power load varying from the rated load to the empty load. For the unit, the greater the index value, the smaller the contribution to the grid peak shaving. AVC operation ratio (C44) is the ratio of AVC running time to the power unit operation time available to the grid. AVC qualification ratio (C45) is the ratio of the AVC correct action times to the total adjustment times during the statistical period.In this section, a hybrid evaluation model was developed for coal-fired power units. The model integrates the GRA theory, AHP weighting method and a proposed entropy-based objective weighting method (BECC). The subsection provides an overview of some key theories including sensitivity analysis method and finally illustrates the integrated algorithm.Grey system theory has been widely used in various fields of science because of its advantages in evaluating complex systems with various correlated indicators, and the GRA method ,17,26 isThe grey relational theory determines the correlation degree according to the similarity among the sequence curves, i.e., the more similarity between two sequences, the higher the correlation degree will be. Therefore, in each index layer, we assume an ideal or optimal index sequence as a reference and then consider the similarity of the indices between the evaluated alternatives and the reference sequence. The more similarity between the two index sequences, the better the comprehensive performance of the alternatives investigated. Therefore, when evaluating a system using the GRA method, an ideal alternative with optimal indices should be introduced first as a reference sequence, then the grey relational coefficients between the reference sequence and each alternative are calculated to establish the grey relational coefficient matrix.For The indices usually have different dimensions and magnitudes. Therefore, the normalizing procedure may be carried out with the indices. For the index which is the bigger the better (or benefit attributes), it can be normalized as:According to the GRA theory, set Based on the methodology of GRA and the indices weights It is significant to utilize the sample information sufficiently in calculating objective weight, because the algorithm is only based on the intrinsic structure of the selecting sample data. Entropy principle is a well-known tool to quantify the uncertainty of raw data. Besides, the influence of the correlation between indicators should be considered either at the same time. On the other hand, the size of the sample we faced is usually too small as the difficulty of collecting data. Thus, based on entropy principle, the CC weight method and bootstrap resample simulation approach are integrated into BECC method.Bootstrap ,39 is thStep 1.An empirical probability distribution Step 2.Generating a resampled sequence Step 3.Calculating the estimated parameter Step 4.Repeating Step 2 and Step 3 for Step 5.Constructing a new estimate distribution based on the resampled data sequence For a statistical sample sequence Entropy is initially a concept of thermodynamics, which is used to describe an irreversible phenomenon of the motion state, and later in the information field, it is used to measure the uncertainty of things. The entropy weight is calculated out by the judgment matrix ,20,31. FFor the decision matrix The first step, normalizing the matrix:The second step, calculating the entropy of each index:The third step, calculating the entropy weight value:The linear correlation coefficient (CC)  between We use the sum vector This subsection introduces the integrating algorithm of BECC in details. Setting the entropy and CC weights as the estimating parameters in the bootstrap procedure (see A), resample matrices of entropy (see B) and CC (see C) weights with the dimension of Due to the difference between the largest and the smallest CC weights element is outstanding, root squared method is employed to shorten the difference . Based oThe BECC weight calculation algorithm is shown in The AHP method ,19,26 reFirst, the pairwise comparison matrix Then we standardize the comparison matrix For the normalized matrix To validate the decision of the AHP, the following steps are developed. Consequently, normalizing the matrix composed of The maximum eigenvalue CR) is carried out to check the consistency:m is the dimension of the comparison matrix) and RI is the random index.Using the criteria in Finally, if the value It is reasonable to combine two kinds of weighs to take full performance advantage of objective weight (by BECC method) and subjective weight (by AHP method), the two type weight are combined to generate a comprehensive weight, the following production method should be used. It terms to be:A hybrid model is developed with the methods mentioned in Firstly, C-level evaluation is implemented by GRA with BECC weighting method. In this step, only objective weight is used in exploiting the C-level indices data, the AHP method is not used. The reason for this strategy is illustrated as follows. The AHP method, which needs a lot of expert knowledge to fulfill the pairwise comparison matrix , usuallySecondly, grey relational evaluation vectors of each B-level index from the C-level evolution step by Equation (6) constructs a B-level decision matrix. For this matrix, BECC method is implemented again and the AHP method is also used in this step to get a combined weight The stability of evaluation results is an important aspect that should be taken into account with the multiple index comprehensive evaluation problem. The sensitivity analysis is used to produce complementary information to the evaluation process. The weight sensitivity was theoretically analyzed under the assumption that every index of the alternatives was perturbed with the same ratio while the other indices kept unchanged. The sensitivity analysis result can draw out the supplementary conclusion with the robustness of the evaluation results. The weights with the high sensitivity should be got particular attention because the evaluation results will easier vary with a little weight change. The following approach is employed to quantify the weight sensitivity .For the evaluation matrix shown in Equation (1), if the ranking result of alternatives The varied weight Supposing the evaluation value The inequality expression can be got from Equations (22)–(24):Considering that Here we got the final absolute minimum change Due to the changed weights While the corresponding relative weight change Supposing the minimum critical value of index weights change with the formula:Then we define the sensitivity coefficient of weights as the term of:The In order to calculate the proposed model, we developed a series of programs containing the subroutines of GRA, weighting calculation and sensitivity analysis, etc. The programs were performed by Matlab (v. 8.3.0.532) on a personal computer equipped with an Intel(R) Core(TM) i5-2400 CPU @ 3.10 GHz configuration and 64-bit Windows 7 system.This section conducts a comprehensive evaluation with the data of seven 600 MW subcritical coal-fired condensing power units in North China in the year 2016, which belong to the North China power grid. The detailed data we used are shown in 2, selective catalytic reduction (SCR) system for NOX and electrostatic precipitator (ESP) for dust removal. To meet the demand of new ultra-lower emissions of China, these units had been further reformed except units 2 and 5. The reform measures include technologies such as low NOX combustion retrofit coupling with SCR, high-frequency power source retrofit of ESP system and the upgrading of desulfurization system, etc.All the units are equipped with a flue gas purification system, that is, a wet flue gas desulfurization (WFGD) system for SOThe comprehensive evaluation was carried out with the hybrid model introduced in The evaluation result listed in In order to decide the AHP weights of the four B-level indices, experts have been invited to developed pairwise comparison matrix until the consistency check is passed through. Then the AHP weight The objective weight of BECC The final evaluation result, i.e., grey relational degree vector of B-level indices can be calculated with the B-level evaluation matrix, and the corresponding integrated weight is shown in Finally, the ranking sequence of the evaluated power units based on the grey relational degree from large to small is as follows:The result represents the comprehensive performance of power units with multiple evaluation criteria. The sorting result shows that unit 4 is the best one according to the proposed multi-level evaluation system. That means, for example, in an ESPGD situation with the seven competitive candidate coal-fired power units, unit 4 will gains the power generating right first.The excellent performance of unit 4 is due to its economic index which is highest among the seven units, besides, the environmental index and flexibility index performance is higher than the other ones either in a large extent. Unit 2 is the worst one because of the environmental index value is too small, and at the same time, the weight of environmental factor is the most important among the B-level indices. With the similar reason of unit 2, the comprehensive performance of unit 5 is undesirable either, which is just a little better than unit 2.It is clear that the proposed evaluation framework is different from the typical evaluation method which only considers the economic factor . If the alternative units are assessed in a typical way, unit 2 is the best, and followed by unit 3, due to the outstanding performance of the net coal consumption rate (C11) index. It is obviously unreasonable in considering the environmental and other aspect evaluation indices. Thus, it is shown that the multi-index comprehensive evaluation is necessary.The evaluation results also points out the retrofit direction of the units in improving comprehensive performance to achieve a higher score. Taking unit 5 for example, which is sorted as the sixth in the ranking list, the poor score mainly caused by the low performance of economic and environmental factors. However, in considering the flexibility criteria, the performance value is the best one due to the C35 index with a value of 55% adjustable power capacity. That means, if we want to improve the comprehensive performance of unit 5, the economic and environmental performance should be improved by the means such as energy saving retrofits or ultra-low emission reform.The above discussion about the result shows that the comprehensive evaluation is reasonable and acceptable. The result can point out the weak part of the power generation operation and management of a unit, and the result may provide guidance for the promotion of operating performance.The final result of the proposed hybrid evaluation model will be varied when the weights with a possibility of uncertainty. In the process of determining combined weight in the B-level indices with AHP method, the expert preference was integrated as the subjective knowledge. However, the experience may vary with different experts, that means, the result got from the same evaluation model may be changed with different evaluation person. Thus, it is important to carry out weight sensitivity analysis in exploiting the latent evaluation information. Sensitivity results are shown in From This section validated the effectiveness of the BECC weighting by comparing it with many other objective weighting methods M2–M5 in .The evaluation values of grey relational degree and unit ranks have been listed in The evaluation result shown in  was repeThe uncertainty of each evaluation result  is primarily caused by the BECC weights (C-level and B-level). Additionally, averaged values and the corresponding standard errors of B-level weight are shown in In order to illustrate the calculation process of the BECC weight, a visualization work about the entropy and correlation coefficient weight was developed. Distributions of entropy and correlation coefficient weight were obtained by resampling the initial data about power units 5000 times. The resampled data were calculated by the steps shown in The energy conservation and emission conduction for the overall energy system is a complicated integration engineering. The ESPGD method based on multi-index comprehensive evaluation is a promising approach to cope with the question. Some suggestions were proposed here.1. Accelerating the reforming of the auxiliary services marketThe improvement of the flexibility  has no direct economic benefit on the unit itself, which just supplies peak shaving service for the power grid and mainly for the renewable energy generation power system. However, the improvement of the flexibility of coal-fired power units is a benefit for energy conservation and emission reduction of the overall power system. Thus a reasonable economic compensation for peak-shaving to the grid will facilitate the positivity increasing of the power plant flexibility performance retrofit. Therefore, the government energy sector should construct the improving measures of the auxiliary service market as soon as possible.2. Promoting the integrating of multiple indices online monitoring systemThe comprehensive evaluation is based on statistical data. In this paper, annual mean values were employed in the case study. It may be made more meaningful by employing online measurement values of the evaluated indices with a month or daily average to accomplish a dynamic evaluation process. However, what the power grid concerns is still the AGC, PFC, and AVC performance indices by EMS online monitoring. The economic indices such as standard coal consumption and environmental pollution indices are not integrated into EMS well in some regional power grid in China. Fortunately, the online environmental parameters supervision system has been completed due to the rigorous air pollution problem in recent years, and the remote standard coal consumption supervision system has been constructed in mainstream energy companies. Therefore, the power grid should make an effort in integrating the economic indicator and environmental protection indicator into the EMS to bring ESPGD into reality.The multi-index evaluation model is feasible for coal-fired power units. Comparing with the traditional ESPGD method, which is only based on economic and environmental principles, the comprehensive evaluation method introduced in this paper involves the operational flexibility and electricity quality performance indices at the same time. The evaluation results demonstrated that the method is suitable for the practical requirement.The proposed objective weighting method BECC uses bootstrap skills to utilize the population information contained in the selected samples, and BECC also considers the mutual redundancy among indicators by introducing the correlation coefficient into the classical entropy weights. It is proved to be feasible by comparing with some other methods in the literature. Through 5000 times cycles of the whole evaluation model, the statistical result also proved that it is stable with an ignorable uncertainty caused by the stochastic factor in the bootstrapping process.It is an alternative route to integrate a variety of mature methods to get a hybrid model. It is beneficial to assimilate the advantages of each method and reduce the shortcomings. Subjective empirical knowledge is necessary for the assessment process. For example, the AHP could improve the evaluation results which developed just based on the pure data analysis. Additionally, sensitivity analysis of criterion weighting is a good way of exploiting the rich information of the model robustness. The sensitivity analysis in the case study, for example, shows the environmental factor with the biggest sensitivity coefficient.In this paper, a multiple index comprehensive evaluation system is constructed for the ranking of coal-fired power units in an ESPGD system. The evaluation system considers four catalog indices covering the economy, environmental protection, flexibility and electricity quality aspects. A hybrid evaluation model integrating GRA and a combined weight method is developed and a novel weighting method BECC is proposed based on an entropy method. A case study is carried out using the hybrid evaluation model and a sensitivity analysis is given too. The following conclusions can be obtained:We believe that the comprehensive evaluation method proposed in the paper is beneficial to the energy saving power generation dispatch (ESPGD) system. The evaluation results could identify the shortage of the various performance of coal-fired power unit and provide the instruction for its improvement.