Studies of colonization dynamics have been based on assessment of whether serial samples represent a single population or distinct colonization events. With the use of whole genome sequencing to determine genetic distance between isolates, a common solution to estimate acquisition and clearance rates has been to assume a fixed genetic distance threshold below which isolates are considered to represent the same strain. However, this approach is often inadequate to account for the diversity of the underlying within-host evolving population, the time intervals between consecutive measurements, and the uncertainty in the estimated acquisition and clearance rates. Here, we present a fully Bayesian model that provides probabilities of whether two strains should be considered the same, allowing us to determine bacterial clearance and acquisition from genomes sampled over time. Our method explicitly models the within-host variation using population genetic simulation, and the inference is done using a combination of Approximate Bayesian Computation (ABC) and Markov Chain Monte Carlo (MCMC). We validate the method with multiple carefully conducted simulations and demonstrate its use in practice by analyzing a collection of methicillin resistant Staphylococcus aureus (MRSA) isolates from a large recently completed longitudinal clinical study. An R-code implementation of the method is freely available at:  As colonizing bacterial populations are the source for much transmission and a reservoir for infection, they are a major focus of interest clinically and epidemiologically. Understanding the dynamics of colonization depends on being able to confidently identify acquisition and clearance events given intermittent sampling of hosts. To do so, we need a model of within-host bacterial population evolution from acquisition through the time of sampling that enables estimation of whether two samples are derived from the same population. Past efforts have frequently relied on empirical genetic distance thresholds that forgo an underlying model or employ a simple molecular clock model. Here, we present an inferential method that accounts for the timing of sample collection and population diversification, to provide a probabilistic estimate for whether two isolates represent the same colonizing strain. This method has implications for understanding the dynamics of acquisition and clearance of colonizing bacteria, and the impact on these rates by factors such as sensitivity of the sampling method, pathogen genotype, competition with other carriage bacteria, host immune response, and antibiotic exposure. Colonizing bacterial populations are often the source of infecting strains and transmission to new hosts –5, makinAn example of a typical individual-level longitudinally sampled data set from a study population is shown in Previously, transitions between different colonizing bacteria have been modeled using hidden Markov models  with staStaphylococcus aureus (MRSA) genomes, obtained through a clinical trial (Project CLEAR) to evaluate the effectiveness of an MRSA decolonization protocol , gets updated to  when the extra prior information is included.The parameter vector  similar . In othed* and time difference t*. Blue colour in the figure denotes high probability of the same strain. The corresponding 50% classification curve is  a straight line with a steep positive slope. This is as expected since the same strain model can explain a greater number of mutations when more time has passed. Approximately 20 mutations draws the line between the same strain and different strains cases within the time difference up to 6000 generations. The uncertainty in the classification occurs because there is overlap in the two explanations (around d* ≈ 20) and because of the posterior uncertainty in the model parameters θ.We also analysed explicitly all observed patterns where: 1) two genomes of the same ST from the same patient are interleaved with a missing observation, i.e. the colonization appears to disappear and then re-emerge, and 2) two genomes of the same ST from the same patient are interleaved with an observation of a different ST. The numbers for the two genomes being from the same or different strain in these patterns are shown in racq and clearance rates rclear informally asA, B, C, D and E denote the numbers of possible events in consecutive samples  defined in detail in G is the total number of possible events over the whole data. The quantities A, B, D and E are random variables that depend on the same/different strain posterior probabilities and, consequently, we also compute the uncertainty estimates for these quantities in Finally, we compute acquisition and clearance rates using our model, and compare those to the ones obtained with the common strategy of using a fixed distance threshold. For the purposes of this exposition, we define the acquisition The estimated acquisition and clearance rates with 95% credible intervals are shown on the last two lines of Dj)rep,( from the posterior (by using the existing MCMC chain) and simulating a new set of distance-time difference pairs Dj)rep,( from the model using θj) occur only rarely, in keeping with the observed data. A minor discrepancy is that the fitted model tends to underestimate the frequency of distance zero while small positive distances tend to occur more frequently than observed. This could happen because we estimated the empirical densities psim using a constant time of 6, 000 (i.e. 1 year) since the acquisition (as discussed in Section Bayesian inference for the mixture model), which may lead to a slight overestimation of the distances. To explore the impact of this assumption further, we repeated the analysis so that we computed the densities psim at a constant time of 1, 000 generations. However, the mismatch did not disappear completely and the estimated mutation rate increased as a result to compensate for the occurrence of greater distances, in disagreement with the prior density from the ABC analysis and data D0. We thus believe that the current model is adequate.Example replicate data sets are shown in We presented a new model for the analysis of clearance and acquisition of bacterial colonization, which, unlike previous approaches, does not rely on a heuristic fixed distance threshold to determine whether genomes observed at different times points are from the same or different acquisition. Fully probabilistic, the model automatically provides uncertainty estimates for all relevant quantities. Furthermore, it takes into account the variation in the time intervals between pairs of consecutive samples. Another benefit is that the model can easily incorporate additional external data to inform about the values of the parameters. To fit the model, we developed an innovative combination of ABC and MCMC, based on an underlying mixture model where one of the component distributions was formulated empirically by simulation.S. aureus genomes sampled longitudinally from multiple patients. Our analysis provided evidence for occasional co-colonization and identified likely false negative samples. The output of the model consists of the same vs. different strain probability for any pair of genomes, and, by using this information to decide  when and where the colonizing strain had changed, the acquisition and clearance rates were easy to calculate. Estimates of these parameters were found to be in agreement with previous estimates derived using a fixed threshold, but now we were able to provide confidence intervals, essential for drawing rigorously supported conclusions. We believe such analyses are common enough that our method should be useful for many, and, consequently, we provide it as an easy-to-use R-code. The code includes tools for both the ABC-inference to incorporate external data of distance distributions between multiple samples at a given time point (or two time points), and the MCMC-algorithm. We note that our method does not assume recombination. Therefore, we recommend removing recombinations by preprocessing the genomes with one of the standard methods [We demonstrated the model using data on  methods –37, as wD0), assuming the population size first increases and then decreases [A central component of our approach is a model for within-host variation, required to determine how much variation can be expected if the genomes at different time points have evolved from the same strain obtained in a single acquisition. We selected for this purpose the basic Wright-Fisher model assuming constant population size and mutation rate with the understanding that these assumptions are expected to be violated to some extent in any realistic data set, but the benefits of simplicity include robustness of the conclusions to prior distributions and identifiability of the parameters from the available data. More complex models have been fitted to the distance distributions Click here for additional data file.


Background: Tissue temperature monitoring during cutaneous laser therapy can lead to safer and more effective treatments. In this study, we investigate the use of speckle variance optical coherence tomography (svOCT) to monitor real-time temperature changes in the excised human skin tissue sample during laser irradiation. Methods: To accomplish this, we combined the pulse laser system with a reference-based svOCT system. To calibrate the svOCT, the ex-vivo human skin samples from three individuals with tissues collected from the arm, face, and back were heated with 1-degree increments. Additionally, linear regression was used to extract and evaluate the linear relationship between the temperature and normalized speckle variance value. Experiments were conducted on excised human skin sample to monitor the temperature change during laser therapy with a svOCT system. Thermal modeling of ex-vivo human skin was used to numerically simulate the laser-tissue interaction and estimate the thermal diffusion and peak temperature of the tissue during the laser treatment. Results and Conclusion: These results showed that normalized speckle variance had a linear relationship with the tissue temperature before the onset of tissue coagulation (52°) and we were able to measure the rapid increase of the tissue temperature during laser therapy. The result of the experiment is also in good agreement with the numerical simulation result that estimated the laser-induced peak temperature and thermal relaxation time. Tissue temperature monitoring during cutaneous laser therapy can lead to safer and more effective treatments. In this study, we investigate the use of speckle variance optical coherence tomography (svOCT) to monitor real-time temperature changes in the excised human skin tissue sample during laser irradiation. To accomplish this, we combined the pulse laser system with a reference-based svOCT system. To calibrate the svOCT, the ex-vivo human skin samples from three individuals with tissues collected from the arm, face, and back were heated with 1-degree increments. Additionally, linear regression was used to extract and evaluate the linear relationship between the temperature and normalized speckle variance value. Experiments were conducted on excised human skin sample to monitor the temperature change during laser therapy with a svOCT system. Thermal modeling of ex-vivo human skin was used to numerically simulate the laser-tissue interaction and estimate the thermal diffusion and peak temperature of the tissue during the laser treatment. These results showed that normalized speckle variance had a linear relationship with the tissue temperature before the onset of tissue coagulation ($52^{\circ}$) and we were able to measure the rapid increase of the tissue temperature during laser therapy. The result of the experiment is also in good agreement with the numerical simulation result that estimated the laser-induced peak temperature and thermal relaxation time. I.Cutaneous laser therapy has been widely used to treat skin conditions such as port wine stains, acne scars, photodamage, and wrinkles over the past 40 years et al.In the past, methods for real-time tissue temperature monitoring have been proposed and investigated. A thermocouple or fiber sensor has shown to be an effective method that can monitor temperature accurately, but such an approach is invasive and only can be applied to a small area et al.et al.et al.et al.et al.Optical coherence tomography (OCT) et al.et al.OCT is based on coherent imaging and as a consequence, the images contain speckle patterns. Although speckle is often viewed as a noise source, it carries information. The change of speckle pattern in the OCT images of biological tissue is an indication of motion of the tissue molecules, and this can be detected and quantitatively analyzed by calculating speckle variance between frame or lines in OCT images In this study, we proposed to use svOCT to monitor the skin tissue temperature change during cutaneous pulsed laser therapy. This approach is based on previous work that shows the speckle variance values in OCT images directly relates to the tissue temperature change II.A.The system setup is shown in The sampled spectrum OCT data was captured by a frame grabber  and processed in parallel with a discrete graphics card  for high-speed real-time imaging processing, including fast Fourier transform (FFT), background noise subtraction and speckle variance calculation. The system was set to process 1024 pixels per A-scan and 1024 A-scans per B-scan. The center wavelength of 1060 nm was chosen to achieve higher resolution with a reasonable imaging depth inside the tissue. The measured lateral scanning resolution was To simulate the tissue during cutaneous laser therapy and to heat the tissue, we used a frequency-doubled Nd:YLF pulse laser system  as the therapeutic laser. The system can provide up to 200 micro joules of energy per pulse for the treatment with the center wavelength of 532 nm, 100 Hz repetition rate and B.To quantify the relationship between the normalized speckle variance value and tissue temperature, an excised human skin sample was put on a heating pot and heated in a water bath with a hot plate  as shown in The excised human skin sample (“dog ear”) shown in To further investigate the variability among different human tissues we performed measurements using ex-vivo skin samples from three individuals with tissues collected from the arm, face and back with similar sample size. As for verifying the repeatability of the svOCT method, we performed several measurements close proximity to each other in space with the same region of interest’s (ROI) pixels. This was done since repeating the measurements on a same sample changes the tissue characteristics.C.To obtain the normalized speckle variance values, we calculated the interframe normalized speckle variance  in the SV) and the measured value  was used to conduct spatial and temporal temperature modeling of the skin tissue sample during the cutaneous laser therapy to verify the result we acquired from the svOCT system. Conduction heat flow is governed by classical Pennes bioheat transfer equation Here, Due to the symmetry of the experiment setup, the simulation was simplified and calculated in a 2D symmetry cylindrical coordinate. The dimension of the tissue sample in the simulation was set to 25 (width)According to the previous study, the water content in the dermis is around 70% III.A.Two more calibration results of dog-ear samples from the arm and the face were plotted in To further investigate the repeatability and reliability of our proposed method, the intraclass correlation coefficient . After the coagulation, the normalized speckle variance value becomes small and decrease rapidly. These results match well with the previous study on egg white protein denaturation and coagulation temperature monitoring by svOCT


In this paper, the superelasticity effects of architected shape memory alloys (SMAs) are focused on by using a multiscale approach. Firstly, a parametric analysis at the cellular level with a series of representative volume elements (RVEs) is carried out to predict the relations between the void fraction, the total stiffness, the hysteresis effect and the mass of the SMAs. The superelasticity effects of the architected SMAs are modeled by the thermomechanical constitutive model proposed by Chemisky et al. 2011. Secondly, the structural responses of the architected SMAs are studied by the multilevel finite element method (FE Cellular materials are widely used for their high strength-to-weight ratio and high energy absorption performance  to descee Feyel ), composee Feyel ), rate-dee Feyel ) and SMAee Feyel ; Chatzigee Feyel ; Xu et aee Feyel ). In thiu et al.  proposedFollowing previous works, it is therefore necessary and feasible to investigate the behavior of architected SMAs with a multilevel finite element model. Towards a better understanding of the studied architected SMA, unit cells (RVEs) with different void fractions are introduced to study the superelasticity effect of the materials and structures. In To investigate the architected SMA structures, RVEs with different geometrical parameters are studied firstly, then the structural response is investigated further by the computational homogenization method. First of all, a short presentation of the SMA constitutive model is given in the next subsection.The SMA model, proposed by Chemisky et al. , is adopf gives the martensitic volume fraction in SMA, the transformation strain The SMA constitutive model used here is able to describe four different strain mechanisms: the elastic strain The potential energy of the SMA model is based on the following Gibbs free energy expression: Substituting Equation  to Equatf:Transformation driving force related to Orientation force related to Twin accommodation related to Here, driving forces related to this dissipation expression are introduced:By introducing a series of predefined critical thresholds related to these driving forces, the evolution of phase transformation is controlled. For more clarity of the relations between the main control equations, the constitutive equations for this model are summarized in The implementation of this model in a finite element code is realized; for more details about the implementation process, see Chemisky et al.  and DuvaAn architected SMA RVE is introduced to describe the microscopic structure; see To check the effective response of the RVE, a tensile strain up to 10% in the Y direction is applied on the RVE at a constant temperature of 30 °C.N, where N denotes the total element number. Note the averaged strain is equal to the prescribed strain due to the periodic boundary conditions, Equation , lighten the structure and consider alternative manufacturing processes such as additive manufacturing. The latter can consider more complex geometries of the unit cell, which has a direct influence on the overall behavior of the structure. Note that this numerical multiscale procedure is very time consuming. To reduce the CPU time, the authors propose to associate this method with model reduction techniques. Among these techniques, we can introduce the proper orthogonal decomposition (POD) to build up a small number of basis functions where the solution can be computed . When tIn this paper, the superelasticity behavior of the architected SMA structure is studied with a 3D multiscale finite element model. Firstly, RVEs with architected SMA are built to simulate the cellular responses of the structure. The behavior of SMA is described by the constitutive model proposed by Chemisky et al. . Both te


Learning variable impedance control is a powerful method to improve the performance of force control. However, current methods typically require too many interactions to achieve good performance. Data-inefficiency has limited these methods to learn force-sensitive tasks in real systems. In order to improve the sampling efficiency and decrease the required interactions during the learning process, this paper develops a data-efficient learning variable impedance control method that enables the industrial robots automatically learn to control the contact force in the unstructured environment. To this end, a Gaussian process model is learned as a faithful proxy of the system, which is then used to predict long-term state evolution for internal simulation, allowing for efficient strategy updates. The effects of model bias are reduced effectively by incorporating model uncertainty into long-term planning. Then the impedance profiles are regulated online according to the learned humanlike impedance strategy. In this way, the flexibility and adaptivity of the system could be enhanced. Both simulated and experimental tests have been performed on an industrial manipulator to verify the performance of the proposed method. With the development of the modern robotics, compliance control is becoming an important component for industrial robots. Control of contact force is crucial for successfully executing operational tasks that involve physical contacts, such as grinding, deburring, or assembly. In the structured environment, good performances could be achieved using classical force control methods . HoweverNeuroscience studies have demonstrated how humans perform specific tasks by adapting muscle stiffness . Kieboom(1) Optimal control. The basic idea is to dynamically adjust the gains by the feedback information using optimization techniques. They are usually robust to uncertain systems. Medina  proposed(2) Imitation of human impedance. Humans have a perfect ability to complete a variety of interaction tasks in various environments by adapting their biomechanical impedance characteristics. These excellent abilities are developed over years of experience and stored in the central nervous system . For the(3) Reinforcement learning (RL). Reinforcement learning constitutes a significant aspect of the artificial intelligence field with numerous applications ranging from medicine to robotics ,26. Rese2, which is a model-free RL algorithm. It realized simultaneous regulation of motion trajectory and impedance gains using DMPs. This algorithm has been successfully extended to high-dimensional robotic tasks such as opening door, picking up pens 24], whicThe proposed learning variable impedance control method emphasizes the data-efficiency, i.e., sample efficiency, by learning a GP model for the system. This is critical for learning to perform force-sensitive tasks. Note that only the application of the strategy requires physical interacting with the robot; internal simulations and strategy learning only use the learned GP model. Although a fast converging controller is found, the proposed method still has the computation intensive limitation. The computational time for each rollout on a workstation computer with an Intel(R) Core(TM) i7-6700 K CPU@4.00 GHz is detailed in Obviously, between the trials the method requires approximately 9 min to find the (sub)optimal strategy. With the increase of sample data set, the computational time is increasing gradually, because the kernel matrices need to be stored and inverted repeatedly. The most demanding computations are the predictive distribution and the derivatives for prediction using the GP model.In this paper, we presented a data-efficient learning variable impedance control method that enables the industrial robots automatically learn to control the contact force in the unstructured environment. The goal was to improve the sampling efficiency and reduce the required physical interactions during learning process. To do so, a GP model was learned as the faithful dynamics of the system, which is then used for internal simulations to improve the data-efficiency by predicting the long-term state evolution. This method learned an impedance regulation strategy, based on which the impedance profiles were regulated online to track the desired contact force. In this way, the flexibility and adaptivity of the system were enhanced. It is worth noting that the optimal impedance control strategy, which is equipped with the similar impedance characteristics of humans, is automatically learned through several iterations. There is no need to transfer human skills to the robot with additional sampling devices. The effectiveness and data-efficiency of the system were verified through simulations and experiments on the six-DoF Reinovo industrial robot. The learning speed of this system outperforms other learning variable impedance control methods by at least one order of magnitude.Currently, the described work only focuses on the efficient learning of force control. In the future work, we will extend this system to learn to complete more complex tasks that are sensitive to contact force, such as assembly tasks of fragile components. Furthermore, parallel and online implementation of this method to improve computational efficiency would be a meaningful and interesting research direction.


Conventional pattern-recognition algorithms for surface electromyography (sEMG)-based hand-gesture classification have difficulties in capturing the complexity and variability of sEMG. The deep structures of deep learning enable the method to learn high-level features of data to improve both accuracy and robustness of a classification. However, the features learned through deep learning are incomprehensible, and this issue has precluded the use of deep learning in clinical applications where model comprehension is required. In this paper, a generative flow model (GFM), which is a recent flourishing branch of deep learning, is used with a SoftMax classifier for hand-gesture classification. The proposed approach achieves  Surface electromyography (sEMG)-based hand-gesture classification is widely used in clinical applications, such as controlling powered upper-limb prostheses  and elecProminent deep learning has improved the performance of solutions for many practical problems. The performance of deep learning lies in the ability to learn high-level abstraction of data and discover important information hidden in the data that is otherwise hard to discover using conventional algorithms . ConvoluThe deep generative model, which is a type of deep learning model other than the deep discriminative model, models the actual distribution of the data. A deep generative model can generate input examples from the feature learned by the model, which provides a way to understand the behavior of the model. However, deep generative model is usually used for applications such as fake image generation  or speecIn this paper, a generative flow model (GFM) is used with a simple SoftMax classifier for hand-gesture classification. GFM is an unsupervised model commonly used for generating images  and synttabase 5 . Since tHuman hands are controlled by a hierarchical structure, as shown in sEMG is the bio-electrical signal generated by the muscle when activated by the spine. Conventional classification methods map the sEMG to hand gestures directly, which tries to approximate the low-level end effector system. The proposed GFM transforms sEMG into factorized features, which are, ideally, an approximation of the movement command to the spine activating the mechanism of muscle synergy. Transforming sEMG into high-level abstractions can, to some extent, increase the generalizability and robustness of the following hand-gesture classification because high-level abstractions are believed to be more easily shared among different subjects than low-level information.GFM is a recent flourishing branch of the deep generative model for transforming input data into meaningful features while requiring little or no human supervision or labeling. This model provides a practical way for employing deep learning for EMG-based hand-gesture classification and for comprehending the model. The transformed data by the GFM conform to a factorized distribution, which results in independent latent variables. Since such features are learned from unlabeled datasets and are not necessarily task-specific, downstream solutions based on the independent latent variables could potentially be more robust and more data efficient . GFM reqThe raw sEMG recorded by the two Myo armbands consists of 16 channels of sEMG sampled at a sampling rate of 200 Hz. Each channel of the raw sEMG is processed to obtain its linear envelope before being input to the GFM. The commonly used pipeline for calculating the sEMG linear envelope  is adoptx into the known prior z [x according to the change in the variable formula mentioned in [The starting point of GFM involves estimating an unknown distribution  prior z . Normallioned in  is calcuf that is differentiable almost anywhere to maximize the log-likelihood of the whole given dataset x [f to be tractable. We use a combination of the four modules actnorm, invertible 1 × 1 convolution, affine coupling layer, and multi-scale architecture as suggested in [f. The determinants of the Jacobian matrices of the first three modules mentioned are simply multiplications of their diagonal elements. The multi-scale architecture pushes half of its input to conform to a Gaussian distribution, which can reduce the variability of the latent variables caused by noise. Details on the transformation, its reverse flow, and the log-determinants of each module are shown in the The training of the ataset x . For easested in ,30 to cox and the cross-entropy loss between the output of the classifier y. The compound objective function modified from the original objective function of GFM [L is the compound objective function, c stands for the SoftMax classifier, and z will be regulated by the classifier. Accordingly, the label information is used to train the transformation f.GFM is an unsupervised learning approach. To use the factorized feature in supervised tasks, such as hand-gesture classification, GFM is combined with a SoftMax classifier. Since the input to the classifier is the factorized feature, a simple linear SoftMax classifier is adopted. To train the classifier in conjunction with GFM, the parameters n of GFM  is:(2)L=The overall structure of the proposed approach is shown in To test the performance of the proposed approach in hand-gesture classification, the proposed model is trained with the NinaPro database 5, which contains sEMG recorded with two Myo armbands. sEMG from the Myo armbands are sampled at a rate of 200 Hz. The two Myo armbands, each including 8 active single differential wireless electrodes, are placed next to each other, as shown in Two methods are used to divide the NinaPro database 5 into a train set and test set. In the first approach, the database is divided in a machine-learning way: 70% of the sEMG examples are randomly selected from the database and used to train the model, while the remaining 30% of the sEMG examples are used to test the accuracy of the proposed approach in classifying hand gestures. In the second approach, the database is divided according to subjects: sEMG examples of 7 randomly selected subjects are used to train the model, while sEMG examples of the remaining 3 subjects are used as a test set. The main difference between these two methods of division is whether the model can see sEMG examples from a subject in both the training and test sets. Obviously, the second division approach better matches the real-world applications for sEMG. In both cases, the proposed model was trained for 15 epochs at a batch size of 24. The average accuracy of the proposed approach was achieved by repeating the training and testing procedures 5 times.The raw sEMG data were transformed into factorized features, as shown in As shown in GFM, as a generative model, models the actual distribution of the data based on the distribution of the factorized feature. To see the distribution of the factorized feature and its association with different hand gestures, three commonly used hand gestures for prosthetic hand control are selected, and the distribution of their factorized features is shown in The typical features of the three hand gestures are transformed by the reverse flow of the GFM to the corresponding sEMG linear envelope. Features and the transformed sEMG linear envelope corresponding to hand gesture 0 (rest), 17 , and 18 (fingers flexed together in fist) are shown in The correlation matrix is important for evaluating the ability of a generative model in distinguishing different classes. Each element of the correlation matrix is calculated as the cosine of the angle between two hand-gesture centers. A hand-gesture center can be treated as a vector connecting the origin of coordinates to the center. The cosine of the angle between two vectors evaluates their correlations. The correlation matrix of the proposed approach is shown in a and column b is generated by a factorized feature with v is constrained in v values v determines the strength of the generated sEMG linear envelope, and the strength of the sEMG linear envelope increases with increasing v. We can also determine that each row of the factorized feature corresponds to a basic pattern of the sEMG linear envelope, which may reflect the muscle synergy taking effect underneath the sEMG recording channels. Each column of the feature corresponds to the spreading of the basic pattern with time. For example, the 11th row corresponds to a pattern of the sEMG linear envelope, where channels 16, 15, 12, 11, 10, and 4 are activated simultaneously, and the columns determine the occurrence time of the pattern. At the first column, the pattern occurs on the left side of the sub-image, while at the Since the feature learned by the GFM is factorized, each dimension of the feature is analyzed individually to evaluate its relation to the sEMG linear envelope. z and the corresponding sEMG linear envelope. The GUI is available in the We made a GUI for the readers to interact with the proposed approach to see the relation between the factorized feature A deep learning approach that can extract comprehensible features from sEMG for hand-gesture classification was proposed. The approach allows employing deep learning to clinical applications of sEMG-based hand-gesture classification where model comprehension is required.As a newly coming approach, GFM has not been widely used in applications other than image generation and speech synthesis. In most cases, the Gaussian-distributed factorized features learned by GFM are uninterpretable. Since images and speeches are intuitive for human, one can manually interpret the meaning of the factorized feature by tuning the factorized feature and check its influences on the generated samples from GFM. However, for biomedical signal, it is difficult to interpret the meaning of the factorized feature without a task-related label/event to check the generated biomedical samples from GFM. In the paper, a well-designed GFM trained under regulation of a linear SoftMax classifier can learn good features for classification, and the task-related features are well-interpretable.The proposed approach has achieved competitive accuracy for classifying hand gestures of NinaPro database 5 compared with existing methods. Overall, 69.04% ± 5.24% accuracy for 41 selected hand gestures from the database was achieved by the method described in  using thIn designing the classifier, the linear SoftMax classifier used in the proposed approach finds a good balance between learning a good distribution of the factorized feature and achieving a high classification accuracy. Actually, we had tried to combine GFM with nonlinear classifiers, such as SoftMax classifier with multiple hidden layers and CNNs. Although the nonlinear classifiers can increase the classification accuracy a little bit, the factorized feature learned by the GFM under the regulation of the nonlinear classifiers is incomprehensible. The distribution of the factorized features belonging to a hand gesture is not gathered as shown in The red square at the right bottom of the correlation matrix suggests that it is hard to distinguish hand gestures 30∼52. Hand gestures 30∼52 belong to exercise C, which consists of human grasping and functional movements. The difficulty in distinguishing functional movements is caused by the fact that functional movements activate most of the forearm muscles, while the isometric movements in exercise A and B only activate a small portion of the forearm muscles. With more muscles recruited, the hand can both exert large force and reduce fatigue while performing function movements. Based on the correlation matrix, the remarkable hand gestures out of the 53 hand gestures can be selected to reduce improper classification. Most of the widely used discriminative methods lack a way to calculate their correlation matrix for hand gestures because instead of modelling the actual distribution of the hand gestures as the proposed approach, these methods only model the decision boundary of the hand gestures, which removes the correlation information.The analysis of each dimension of the factorized feature indicates that its rows correspond to different sEMG linear envelope patterns, its columns correspond to the occurrence of the patterns, and its elements determine the strength of the pattern. The regular pattern of the factorized feature is more comprehensive than we expected. Often, representations of features in deep learning models are hard for humans to understand. Since the proposed approach is trained to distinguish hand gestures of different subjects, muscle synergy, which is a common mechanism shared among subjects, is theoretically an optimal feature for the task. From the results, we can see that the proposed approach learned to represent the sEMG linear envelope as a combination of some basic patterns of the sEMG. We suppose that these basic patterns may be reflections of the muscle synergy in the sEMG. However, the dimension of the factorized feature is much larger than that of muscle synergy, which means that there are some redundancies in the factorized feature. The dimension of the factorized feature can be reduced by adding more multi-scale modules to the GFM. However, with the dimension of the feature reduced, the accuracy of the classifier may decrease.This study has developed a comprehensible deep learning model for sEMG-based hand-gesture classification. The developed model allows the use of deep learning in clinical applications for which model comprehension is required. This study serves as a basis for future studies on employing deep learning in sEMG-based applications. Although the approach analyzes each individual dimension of the factorized feature, the exact relation between the feature and the muscles is not fully understood. In the study, we assumed that the feature reflects the muscle synergy. Further research needs to be conducted to examine more closely the links between the factorized feature and the muscle synergy.


In implementing carbon emission trading schemes (ETSs), the cost of carbon embedded in raw materials further complicates supplier selection and order allocation. Firms have to make decisions by comprehensively considering the cost and the important intangible performance of suppliers. This paper uses an analytic network process–integer programming (ANP–IP) model based on a multiple-criteria decision-making (MCDM) approach to solve the above issues by first evaluating and then optimizing them. The carbon embedded in components, which can be used to reflect the carbon competitiveness of a supplier, is integrated into the ANP–IP model. In addition, an international large-scale electronic equipment manufacturer in China is used to validate the model. Different scenarios involving different carbon prices are designed to analyze whether China’s current ETS drives firms to choose more low-carbon suppliers. The results show that current carbon constraints are not stringent enough to drive firms to select low-carbon suppliers. A more stringent ETS with a higher carbon price could facilitate the creation of a low-carbon supply chain. The analysis of the firm’s total cost and of the total cost composition indicates that the impact of a more stringent ETS on the firm results mainly from indirect costs instead of direct costs. The indirect cost is caused by the suppliers’ transfer of part of the low-carbon investment in the product, and arises from buying carbon permits with high carbon prices. Implications revealed by the model analysis are discussed to provide guidance to suppliers regarding the balance between soft competitiveness and low-carbon production capability and to provide guidance to the firm on how to cooperate with suppliers to achieve a mutually beneficial situation. Many co provide . China hSupplier selection is an important strategic decision in developing a competitive supply chain because firms often outsource raw materials, components, or services to suppliers to enhance the core competitiveness of the firm . MoreoveHowever, currently, low-carbon development has put higher demands on supplier selection, especially for firms under an ETS. After the implementation of an ETS, selecting the best supplier becomes a more complex multiple-criteria decision-making (MCDM) issue. In terms of economic criteria, the low-carbon capability of the supplier affects the cost structure of a firm with carbon quota constraints in two ways. On the one hand, from the perspective of the whole product life cycle, the carbon emissions generated by suppliers during raw material or component production—these emissions are called embedded carbon—are an important part of the GHGs emitted by firms. Raw materials embedded with a higher carbon content may generate a cost for extra carbon emissions. On the other hand, low-carbon raw material often has a higher price, which increases the procurement costs of the firm. Therefore, considering carbon price fluctuations, operational decisions regarding supplier selection and order allocation should be adjusted to correspondingly achieve the optimal performance of economic indicators . More im(1)How can manufacturing firms with carbon constraints choose suppliers and allocate orders among them while considering the costs of embedded carbon?(2)Have the current ETSs in China driven Chinese manufacturing firms to choose low-carbon suppliers?(3)How will a more stringent ETS impact supplier selection strategies?Therefore, low-carbon supplier selection under an ETS presents two challenges. The first challenge is to determine how to combine both tangible economic criteria and intangible traditional criteria. The second challenge is to determine how to minimize total cost by balancing the carbon cost of the embedded carbon in raw materials and the procurement cost caused by the high price of low-carbon materials. Concerning the establishment of China’s national carbon market, three issues need to be addressed:To cope with the abovementioned challenges and to answer the above three questions, this paper uses an analytic network process–integer programming (ANP–IP) model to solve the issues of low-carbon supplier selection and order allocation for a firm constrained by an ETS with multiple manufacturing plants and suppliers. The cost of the carbon embedded in the components provided by suppliers is also considered in the model; the direct and indirect costs generated by the ETS can be analyzed based on the cost of the embedded carbon. An international large-scale electronic equipment manufacturer in China is used to validate the model. In addition, different scenarios are used to analyze the impact of different carbon constraints on the supplier selection strategies of firms.The rest of the paper is organized as follows. In Concerning sustainable development with low-carbon requirements, the aspects considered become more complex when selecting suppliers, and the evaluation methods are required to be more scientific and accurate.Many approaches have been proposed to solve the issue of low-carbon supplier selection including data envelopment analysis (DEA), mathematical programming, analytic hierarchy process (AHP), analytic network process (ANP), fuzzy set theory, and hybrids of these approaches. The studies of Ho et al. (2010) and Chai et al. 2013) provided comprehensive overviews of the evaluation methods for supplier selection  provided. Each meSome early studies used mathematical programming models, including linear programming (LP), nonlinear programming, and mixed-integer programming (MIP), to solve the supplier selection issue. For example, Hong et al. (2005) proposed a mixed-integer linear programming model to select the best supplier by considering both changes in suppliers’ supply capabilities and customer needs over a specific period. Using a multi-objective programming model, Wadhwa and Ravindran (2007) selected suppliers based on the minimum price, lead time, and rejects ,16. ConcThe mathematical programming approach accurately measures the relationship between economic benefits and carbon costs. However, supplier selection cannot be measured from only an economic perspective. In particular, concerning sustainable development, many intangible factors that cannot be quantitatively measured, such as long-term partnership, service levels, brands, and the welfare of employees, must be considered. Thus, in order to consider qualitative factors besides quantitative ones, supplier selection should be treated as a multiple-criteria decision-making (MCDM) problem to obtain a comprehensive solution. The corresponding MCDM methods need to be employed to choose a preferred option, categorize the alternatives, and rank them with a preference-based approach .To select the best supplier by using a much more comprehensive perspective, the AHP and ANP have been widely used by scholars. Scholars combine the AHP or the ANP with other theories or models to improve decision-making accuracy. Hashemi et al. (2015)  used theAHP- and ANP-based methods are highly capable of dealing with both quantitative and qualitative factors. However, these methods select the best supplier only by ranking the suppliers and cannot determine the order allocation quantity, which is important for firms, especially those under an ETS. Knowing the order quantity of each supplier can help the firm analyze changes in the carbon cost and the procurement cost caused by the implementation of an ETS.Some scholars attempted to combine the AHP/ANP and mathematical programming models to select suppliers. Xia and Wu (2007)  proposedWhether an AHP/ANP-based or a mathematical programming method is used, economic criteria must be considered in supplier selection. Hashemi et al. (2015)  summarizThe AHP/ANP-based approach makes decision-making more flexible and the economic criteria more diverse, because this approach is used to measure and evaluate qualitative criteria, which constitute most of the criteria. In the current literature, quality criteria often include lot rejection rates concerning product, quality certification, and corrective and preventive capacity ,33,34. DWith the increase in requirements surrounding sustainable and low-carbon development and the improvement in consumers’ environmental awareness, environmental criteria can no longer be neglected in supplier selection. Since some environmental policies use economic measures, such as environmental taxes and ETSs, to regulate firms’ environmental behaviors, environmental indicators  can be quantified to some extent and used in the mathematical programming model. However, some qualitative indicators, such as a supplier’s low-carbon reputation, a supplier’s environmental management system, and environmental training for staff , are alsAs one of the three most important dimensions of sustainable development, the social dimension has become increasingly more of a concern for governments and consumers. Many firms, especially large firms, value their social achievements and impact. Therefore, when making decisions, these firms consider the social impact of the performance of their suppliers. In current studies, social criteria often include the public disclosure of social performance, education and training program support, and employee health and safety ,25,38,39According to the above literature review, although there have been many studies regarding supplier selection and order allocation, these studies did not sufficiently consider the carbon embedded in raw materials, which constitutes most of the carbon footprint of the product life cycle. In addition, far too little attention has been paid to the balance between procurement costs and carbon costs in ETSs. This paper uses an ANP–IP model to solve the MCDM issue of supplier selection under an ETS, and seeks to fill these gaps in the literature and contribute to the current research by considering the following three aspects. First, the cost of carbon embedded in components can be used to reflect the carbon competitiveness of a supplier; therefore, the cost of the embedded carbon is integrated into the ANP–IP model. The cost of embedded carbon could help firms deal with the gradually increasing environmental awareness of consumers and tightened ETS constraints. Second, a real-world case is used to validate the model and to analyze whether China’s current ETS affects, as expected, how firms select low-carbon suppliers; this effect has been less frequently discussed. Third, the results could be used to analyze the cost structure of the firm under an ETS by considering the direct and indirect costs caused by the ETS. This case provides inspiration for policy-makers seeking to design policies or regulations to help firms select more low-carbon suppliers and improve the ability of the overall supply chain to achieve low-carbon targets.An ANP–IP model considering evaluation and optimization is proposed. The framework of this research is provided in Step 1:Selection of the criteria and construction of the model;Step 2:Conduction of a pairwise comparison and development of a priority vector with consistency;Step 3:Construction and limitation of the supermatrix;Step 4:Evaluation of the alternatives.The ANP involves the use of relative measurements with absolute scales for both quantitative and qualitative criteria ,41,42. IThe ANP consists of criteria, alternatives, and the relationships between them. In our study, the evaluation criteria framework used to evaluate the supplier’s soft competitiveness includes 21 criteria. The criteria were first determined by conducting a detailed analysis of the current literature. We also conducted in-depth interviews with managers in the procurement sector where the case firm operated to make the multiple-criteria indicator framework more practical. The criteria and their influencing relationships to evaluate the supplier’s soft competitiveness are shown in These 21 indicators are divided into 4 clusters: quality, delivery and service, business continuity, and social impact. The quality cluster, which includes indicators Q1–6, reflected the supplier’s performance in terms of product quality. Q1 is the percentage of processed parts that are rejected for a certain number of pieces, which is a direct manifestation of product quality. Q2 indirectly reflects the quality performance of the supplier. Q3 has the potential to improve the quality level. Q5 can affect the rejection rate of a product and influence quality performance. Q6 has the potential to affect the delivery schedule and the performance of the supplier’s after-sales service. The delivery and service cluster reflects the level of the supplier’s on-time delivery and after-sales service, including indicators DS1–5. In this cluster, DS3 affects the capability of handling abnormal quality, the other criteria in the same cluster, and the long-term relationship between the supplier and the manufacturer. DS4 reflects the ability of suppliers to deal with temporary increases and decreases in orders. The business continuity cluster includes indicators BC1–6. BC3 indicates whether the firm is willing to contract with the supplier to cooperate for a long time. Many other indicators affect the long-term relationship between the firm and the supplier. Moreover, once the long-term relationship is formed, it will further affect other aspects of the performance of the supplier. In terms of BC4, suppliers who are flexible in terms of responding to policy changes and are consistent with policy guidance have better business continuity. The social impact cluster, which includes indicators SI1–4, reflects the social requirements of the firm for its suppliers’ performance in terms of sustainable development. The relationships among the clusters are shown in Once the ANP model was constructed, the criteria were pairwise compared both with and between clusters to form a comparison matrix. In this study, the pairwise comparison includes three types of comparisons, namely, pairwise comparisons of clusters, pairwise comparisons of criteria with regard to their cluster, and pairwise comparisons of the dependencies of the criteria. For the ANP, a 9-point scale indicating how many times an element dominated another is used for comparison. The comparison judgment is translated into numerical values, namely, equally important = 1, moderately more important = 3, much more important = 5, very much more important = 7, and extremely more important = 9.CR = CI/RI was proposed by Saaty to measure the inconsistency of the pairwise comparison, where RI was the so-called average consistency index and CR value is more than 10%, the problem and judgements have to be investigated and revised [After the pairwise comparisons have been conducted, each normalized comparison matrix is used to calculate the local priority of every criterion, which will then be used to form a supermatrix. The consistency ratio  revised ,43.m decision makers is derived by the geometric mean of preference of all of the experts as A reciprocal judgement matrix aijk)1/m .A supermatrix consisting of all local priority matrices is formed for overall criteria prioritization and alternative ranking. However, this supermatrix is unweighted. The unweighted supermatrix is weighted by multiplying the blocks by the corresponding cluster priority. This weighted supermatrix is eventually used to capture the final influence ranking of the criteria.To evaluate the soft competitiveness of the suppliers, alternatives are also pairwise compared with respect to each criterion. Similar to the process used for criteria ranking, each set of comparison matrices is used to calculate the local rankings of the alternatives; these local rankings are then used to form the supermatrix for the final rankings.With the establishment of ETSs, suppliers have started to adopt more energy-efficient equipment and use low-carbon methods of production to reduce the carbon emissions of their production process. Component suppliers have developed different low-carbon capacities; therefore, these suppliers provide components with different embedded carbon emissions and prices. The ANP model in our study has provided us with the performance and ranking of the three suppliers’ soft competitiveness. The relative score of each supplier is seen as a soft competitiveness index, which is included as one of the constraint conditions of the IP model. This model requires that the soft competitiveness of all of the procured components has to be above average.The problem lies in deciding which supplier should provide which manufacturing plant components and the quantities of the components that should be provided. The objective is to minimize the total cost. Given that only the relationship between suppliers and manufacturers is considered in this paper, the total cost to be minimized includes the procurement cost for the components, the cost of transporting the components, the cost of producing the final products, and the carbon cost. Under an ETS, the firm is allocated a carbon cap by regulatory agencies. This cap is the total carbon quota constraint for the two manufacturing plants of the firm. If the total carbon emissions of the two plants are higher than the cap, the firm has to buy more carbon permits from the carbon market at the current carbon price to cover the additional emissions. If the total carbon emissions of the two plants are lower than the cap, the firm can sell its additional permits in the carbon market and gain a profit. The total demand for the final products of the two manufacturing plants is assumed to be determined. The variables and parameters used in the IP model are defined in The IP model used for the supplier selection and order allocation under the ETS is calculated as follows:Equation (1) is the objection function to be minimized. The first part of Equation (1) is the procurement cost for the components and the cost of transporting the components from the suppliers to the manufacturers. The second part is the cost of producing the final products, and the third part of Equation (1) is the carbon cost. We define the carbon emissions of the entire process, from purchasing components to production, as Equation (8).m can meet the production requirements. Equation (3) ensures that the number of final products from all of the manufacturing plants can meet the demand. Equation (4) limits the production of the manufacturing plant m so that production cannot exceed the plant’s maximum capacity. Equation (5) ensures that the average soft competitiveness of all of the purchased components is not below the average soft competitiveness of the three suppliers. To achieve cost minimization, the soft competitiveness performance of the suppliers may have been sacrificed to some extent. However, the soft competitiveness of the components cannot be below average. Equations (6)–(7) enforce integrality and nonnegativity on the decision variables.Therefore, the total cost includes the procurement cost for the components, the cost of transporting the components, the cost of producing the final products, and the carbon costs. When The case firm in this study is an international large-scale electronic equipment manufacturer, and the main products of the company include mobile phones, computers, and electronic watches. In this study, the computer product of the case firm is considered for a specific application of low-carbon supplier selection. Due to the diversity of the raw material and component accessories, to simplify the problem this paper addresses, only suppliers providing the Liquid Crystal Display (LCD) computer screens are considered. The case firm has two manufacturing plants (which are located in Chengdu city and Changsha city) and three LCD suppliers  .In order to evaluate the suppliers’ soft competitiveness, we conducted in-depth interviews with three managers in the procurement department. In addition to helping us improve the criteria framework, each procurement manager was required to compare all of the criteria in pairs and give them a score of 1–9 to reflect the relative importance. Through the interviews, we learned that this electronic equipment manufacturing company considered the low-carbon production capacity of the suppliers when making decisions regarding supplier selection. However, the cost caused by the embedded carbon of the raw materials was not taken into consideration. Based on the ANP described in Due to the establishment of China’s unified carbon market in 2017, some suppliers implement low-carbon production. Supplier Shenzhen has put the most effort into low-carbon production, thus resulting in an obvious reduction in the carbon embedded in each unit of product. Supplier Beijing has also implemented a low-carbon production mode, but exhibited less effort than supplier Shenzhen. Supplier Wuxi has made no improvements in low-carbon production. The distances from the suppliers to the manufacturers, the embedded carbon intensities, that is, the embedded carbon emissions per unit of component, and the prices of each supplier are shown in 2 per unit product. All components are transported by road freight and have a carbon emission coefficient of 0.15 kg CO2 per ton per mile. The weight of each screen is approximately 2 kg. The two manufacturing plants are required to meet the order demand of 175,287 computers. The product capacity of each plant does not exceed 100 thousand units. The product capacities of the suppliers are considered to be sufficient to meet the needs of the manufacturers, as they also provide the LCD screen products to computer manufacturers of other brands.To reduce the impacts of costs and carbon emissions generated in the assembly process on total cost, we assume that the unit cost of assembling a computer is 1000 Yuan and that the production carbon intensity is 50 kg COBefore the implementation of the ETS, the components offered by the three suppliers had the same embedded carbon intensities and prices. Changes in the decision regarding supplier selection and order allocation are affected by the decision to consider both cost and soft competitiveness. To highlight these changes, Scenario 1 and Scenario 2 are designed to solve these two respective problems for the model.Scenario 1: Only cost is considered before ETS implementation;Scenario 2: Both cost and soft competitiveness are considered before ETS implementation.As illustrated in No carbon cost is generated in either Scenario. The LCD screens offered by the three suppliers have the same price, thus, when considering supplier selection only from the perspective of cost, the only difference between the suppliers is the transportation cost. In Scenario 1, the optimal decision is to choose the Shenzhen supplier, which is closest to the two plants. However, when considering soft competitiveness, the Wuxi supplier is selected instead because the Shenzhen supplier performs worse than the other two suppliers in terms of soft competitiveness and cannot meet the requirements of the firm. Supplier Wuxi has a relatively higher soft competitiveness level and is closer to the two plants.2. Scenarios 3 and 4 are designed to analyze the impact of soft competitiveness.The carbon emissions before the implementation of the ETS is an important benchmark for the allocation of free carbon quotas. Therefore, we calculate the carbon emissions of the firm in Scenario 1 and Scenario 2 to be 48.61 and 48.77 thousand tons of carbon emissions, respectively. The difference in carbon emissions between the two scenarios is mainly due to the change in transportation distance after changing the supplier selection and order allocation plan. Under the current ETS in China, the free quota allocated to a firm generally accounts for 75–90% of its historical annual carbon emissions. Therefore, to further analyze the impact of ETS implementation on supplier selection and order allocation, it is assumed that the total amount of the free quota allocated to the firm is 40 thousand tons. In China’s actual carbon market, the average carbon price is set to the equivalent of 30 Yuan/ton COScenario 3: Only cost is considered under the current ETS;Scenario 4: Both cost and soft competitiveness are considered under the current ETS. The solutions to Scenarios 3 and 4 are illustrated in However, comparing Scenario 3 with Scenario 1 shows that after ETS implementation, the firm chooses the Wuxi supplier, which has the worst low-carbon performance. This indicates that the current carbon quota constraints have not driven the firm to select the low-carbon suppliers, Beijing and Shenzhen. In contrast, because these two suppliers have higher-priced products, the firm prefers the Wuxi supplier due to the lower product price. That is, in Scenario 3, the increase in the procurement cost is higher than the carbon cost. After balancing the carbon cost and procurement cost, the Wuxi supplier, whose product has the lowest price and the highest embedded carbon intensity, becomes the optimal selection.To achieve the carbon emission reduction target, carbon quota constraints will be gradually strengthened in the future, thereby leading to an increase in the carbon price. The National Development and Reform Commission of China stated that 200–300 Yuan per ton is the ideal carbon price. Thus, Scenarios 5 and 6 are designed to analyze whether more stringent carbon quota constraints will drive firms to select low-carbon suppliers. The carbon price is set to 300 Yuan per ton.Scenario 5: Only cost is considered under a more stringent ETS;Scenario 6: Both cost and soft competitiveness are considered under a more stringent ETS.The solutions for Scenarios 5 and 6 are illustrated in Under more stringent carbon constraints, some components are purchased from the most low-carbon supplier, which is the Shenzhen supplier, thus indicating that after balancing the carbon cost with other costs, the firm starts to consider the low-carbon production capacity of the supplier. In Scenario 6, the Shenzhen supplier is no longer considered because of its poor performance in terms of soft competitiveness. Meanwhile, although the distance from the Beijing supplier to the two plants is the longest, the relatively stronger low-carbon capacity and the highest level of soft competitiveness of the Beijing supplier help the supplier gain an order of 75,287 units for the Chengdu plant.By applying the above ANP-IP model to the case firm under China’s ETS, it can be seen that whether a decision regarding supplier selection and order allocation is optimal is directly affected by comprehensive consideration of the indicators and the stringency of the carbon quota constraints. The cost structures of the firm in different scenarios are further analyzed in this paper . Only thThe difference between Scenario 3 and Scenario 5 is caused by the substantial increase in carbon prices. In Scenario 3, all orders are allocated to the least low-carbon supplier (Wuxi), while in Scenario 5, some of the orders are allocated to the most low-carbon supplier (Shenzhen). The different order allocations in these scenarios indicate that the more stringent ETSs with higher carbon prices will affect the optimal decision concerning supplier selection and order allocation. Comparing the cost structures in the two scenarios shows that no carbon cost is generated in Scenario 5, therefore, the increase in the carbon price does not cause a large increase in the carbon cost. Meanwhile, the transportation distance in Scenario 5 is shorter, resulting in a much smaller transportation cost. The only increased cost in Scenario 5 results from the improved procurement price of the LCD screen, that is, the impact of the more stringent ETS on the firm does not result from the direct cost pressure caused by the high carbon price, but from the indirect cost pressure caused by the suppliers’ transfer of a part of the low-carbon investment to the product. Meanwhile, if the low-carbon technologies and investment of supplier Shenzhen achieve scale, the production and management costs will be reduced, thus leading to a lower price of the supplier’s LCD screen. In terms of cost, the Shenzhen supplier will have a greater competitive advantage in the industry.In both Scenario 4 and Scenario 6, both the cost and the soft competitiveness of the alternatives are comprehensively considered in the selection of suppliers and the allocation of orders. In Scenario 4, the firm chooses the least low-carbon supplier (Wuxi) for all of the LCD screens. However, in Scenario 6, which is affected by the more stringent ETS with a higher carbon price, the firm allocates some of the orders to the relatively more low-carbon supplier (Beijing). The transportation distances in the two scenarios are almost the same, thus leading to almost identical transportation costs. Compared with the carbon cost in Scenario 4, the carbon cost in Scenario 6 is significantly higher, that is, when considering the suppliers’ soft competitiveness, the strict ETS will greatly increase the direct cost pressure on the firm. An indirect cost pressure of the ETS is also generated, but the extent is relatively small. The Wuxi supplier has stronger soft competitiveness, but the supplier has to be abandoned by the firm under the stricter ETS because its embedded carbon intensity of the components supplied by the supplier is too high. Therefore, the supplier with strong soft competitiveness should engage in low-carbon production as soon as possible to gain an even greater competitive advantage after the implementation of the ETS.The difference between Scenario 5 and Scenario 6 is the consideration of the supplier’s soft competitiveness for supplier selection. In Scenario 5, some of the LCD screens are purchased from the most low-carbon supplier, i.e., Shenzhen. Thus, even if the carbon price is very high at this time, no carbon cost is generated, that is, the stringent ETS does not exert a direct cost pressure on the enterprises. However, in Scenario 6, the most low-carbon supplier (Shenzhen) is replaced by the other two suppliers because of its poor performance in terms of soft competitiveness. Although the procurement cost decreases to some extent, the carbon cost and transportation cost increase significantly, thus resulting in an increase in the total cost. Therefore, the suppliers that have already paid attention to low-carbon production should consider the coordinated development of soft competitiveness and low-carbon production capacity to obtain a strategic competitive position among industrial competitors. In addition, if the firm can build long-term relationships with low-carbon suppliers and cooperates to improve the suppliers’ capabilities and performances in all aspects, the firm can achieve a mutually beneficial result.The ETS has become one of the most popular ways to reduce GHGs. Under the ETS, the selection of the best supplier becomes a more complex MCDM issue and presents two key challenges. The first challenge regards the combination of both tangible and intangible indicators involved in this issue. The second challenge revolves around the balance the cost of carbon embedded in raw materials and other costs, such as procurement cost.To solve the problems of supplier selection and order allocation under an ETS, an analytic network process–integer programming (ANP–IP) model, which first evaluates and then optimizes the problem, is proposed. The carbon embedded in the components offered by the suppliers is also considered. We first construct an evaluation framework for each supplier’s soft competitiveness, which includes multiple important criteria that needs to be considered in terms of quality, delivery and service, business continuity, and social impact. The ANP is applied to evaluate each firm’s performance and to calculate a soft competitiveness index for each supplier. This soft competitiveness index is integrated into the constraint conditions of the IP model to determine the optimal supplier combination and the order allocation plan in order to minimize the total cost. By using this model, multiple intangible criteria for the selection of suppliers is comprehensively considered, and order allocation among suppliers is determined to minimize the total cost.A real-world-based case of an international large-scale electronic equipment manufacturer with two plants that manufacture computer products and three LCD screen suppliers located in China is used to validate the model. This paper provides an approach for the decision-maker of the case firm to select suppliers under an ETS, whereby the case firm can consider the carbon embedded in the components to minimize the total cost without losing traditional soft competitiveness performance when allocating the order. The results also clearly demonstrate the impact of changes in the supplier selection strategy on the firm’s total cost and total cost composition under ETS scenarios with different constraint strengths. Correspondingly, we show how suppliers can balance soft competitiveness and low-carbon production capability to maintain their competitive position. We also show how the case firm can cooperate with its suppliers to achieve a mutually beneficial situation.The current carbon quota constraints are not stringent enough to drive the case firm to select a low-carbon supplier. When the price of the products increases, the firm prefers the least low-carbon supplier because the supplier has the lowest price. However, a more stringent ETS with a higher carbon price will affect the optimal decision concerning supplier selection and order allocation. The impact of the more stringent ETS on the firm does not result from the direct cost pressure caused by the high carbon price but from the indirect cost pressure caused by the suppliers’ transfer of part of the low-carbon investment in the product.Suppliers with strong soft competitiveness should engage in low-carbon production as soon as possible to maintain their competitive position after the implementation of an ETS. As soon as suppliers can achieve a relatively strong low-carbon capability, they should try to make investments to achieve scale and to reduce the price of their low-carbon products, which can help suppliers achieve an even greater competitive advantage. Moreover, soft competitiveness and low-carbon production capacities have to be developed in a coordinated fashion. Finally, if firms build long-term relationships with low-carbon suppliers and cooperate to improve the suppliers’ capabilities and performance, firms can achieve results that are beneficial for both parties.


Subsurface damages and surface roughness are two significant parameters which determine the performance of silicon carbide (SiC) ceramics. Subsurface damages (SSD) induced by conventional polishing could seriously affect the service life of the workpiece. To address this problem, vibration-assisted polishing (VAP) was developed to machine hard and brittle materials, because the vibration-assisted machine (VAM) can increase the critical cutting depth to improve the surface integrity of materials. In this paper, a two-dimensional (2D) VAM system is used to polish SiC ceramics. Moreover, a theoretical SSD model is constructed to predict the SSD. Furthermore, finite element simulation (FEM) is adopted to analyze the effects of different VAP parameters on SSD. Finally, a series of scratches and VAP experiments are conducted on the independent precision polishing machine to investigate the effects of polishing parameters on brittle–ductile transition and SSD. With the rapid development of space optics, the dimensional stability of optical components is widely applied in the aerospace industry. Silicon carbide (SiC) ceramics are a representative material due to its inherent features, for example, low density, low thermal coefficient, stable chemical properties, and high-temperature wear resistance. In general, the machining process of SiC mainly consists of wire sawing, grinding, lapping, and polishing. Among the various machining methods, polishing is the last step to obtain good surface integrity. However, SiC ceramics have poor machinability due to their high hardness and brittleness ,2,3,4. TIn conventional precision polishing, abrasive polishing is the most commonly adopted method. In order to obtain better surface integrity, some researchers recently developed an effective method to prevent surface and subsurface damages on SiC ceramics, which is called vibration-assisted polishing (VAP) ,7. It isAt present, the Preston equation , and experiments. Aida et al. investigated the material removal characteristics of GaN, including the relationship between the SSD depth and the abrasive grain size . The resAt present, the establishment of SSD models based on indentation fracture mechanics is considered as an effective method to predict SSD depth. However, due to the inaccuracy of the mathematical model, many other scholars attempted to achieve a more accurate SSD depth through experimental exploration. Lucca et al. presented a variety of techniques to evaluate the surface alterations of some ceramics and glasses during processing . Ding etHowever, the experimental testing occupies massive time and expends high cost; thus, FEM is an effective means to analysis and test values of fracture for multiple materials such as metal alloys and ceramic materials . CervinoMotivated by the abovementioned literature, a theoretical model of SSD was established to evaluate crack length, which was based on the removal mechanism for VAP SiC ceramics in this paper. Then, in order to explore the relationship between the SSD and processing parameters, a 3D FEM model was applied to simulate single-abrasive VAP SiC ceramics with various processing parameters . At the same time, a series of scratch tests and single-factor experiments were conducted to validate the reliability of the VAP and theoretical model of SSD.The mechanical structure of the VAP system based on flexure hinges is shown in Deformation not only occurs on the LSFHs, but also on the RCFHs. Because the tool holder can be simplified as a rigid bar, it is appropriate to make an assumption that the motion is generated by flexure hinges.As shown in In term of Z-axis.In the experiment, when two sinusoidal voltages are input to the PEAs, the moving displacement of the tool tip with respect to the PEAs can be expressed asIn order to simplify the equation, it is assumed that Based on the first derivative of the tool motion displacement versus time, the single abrasive velocity with respect to the workpiece can be obtained as follows:The polishing is actually a complex process that is not quantitatively removed. To explore this process, the polishing is usually simplified to the scratch process of a signal abrasive, as shown in The tangential force of the single abrasive can be expressed asThe equivalent mass of the abrasive is Then, in the 2D vibration, the normal force of the grain isThe tangential and normal friction force of abrasive isTherefore, the VAP force of the single abrasive can be determined asThe polishing process can be simplified as a single abrasive scratch on the workpiece, as shown in There are two forms of cracks, including lateral cracks and median cracks, during the VAP of hard and brittle materials, which cause SSD and degradation of the material strength . mc can be considered as a parameter to evaluate the functional properties of the materials [The median crack extends perpendicularly to the processing surface with an incisive abrasive, which can be classified as an SSD. The depth of the median cracks is generally considered to be the SSD depth. The depth of the median cracks aterials .(11)cm=The calculation of SSD can be expressed by Equation (12) based on the relationship between the abrasives and the SiC.The plastic deformation force of the single abrasive intruding into the workpiece at a depth of echanics .(13)hi=Combining Equations (11)–(13), the SSD can be obtained as follows: The material parameters of SiC ceramics are shown in Considering that the removal mechanism in SiC processing mainly aims at the prevention of brittle fractures, the Johnson–Holmquist (JH-2) model can be applied, because it is based on elastic–plastic damage, which can be used to simulate the mechanical behaviors of brittle materials under high strain, high strain rate, and large pressures . The JH-In order to qualitatively analyze the diversified evolutions of SSD during the SiC VAP process, a 3D single abrasive model was established using ABAQUS/Explicit. The model size was set as 18 μm × 12 μm × 7 μm, as shown in f was 10 kHz. Meanwhile, the surface quality of the workpiece was poor. When the VAP frequency increased to 30 kHz, the damages of the workpiece were reduced, as well as the SSD. Generally speaking, a relatively higher VAP frequency can decrease the SSD, thereby improving the quality of the subsurface. Thanks to the frequency increase, the abrasive particles were separated from the workpiece more often during the same processing time, causing the VAP force to decrease, which reduced the surface damages and SSD of the workpiece.Z-axis, where the indenter was clamped in the tool holder. A 3D dynamometer (Kistler 9257B Switzerland) was used to control the force of the polishing tool on the workpiece surface. The SiC ceramic workpiece was rectangular with a size of Z-direction. The machine parameters of the VAP single-factor tests are listed in To explore the critical depth of SiC ceramics in the ductile–brittle transition, scratch tests were conducted using an independent precision polishing machine. The device could be controlled flexibly to determine the experimental parameters. The experiment set-up is shown in The surface roughness of the SiC sample was detected by the non-contact white-light interferometer . In order to study the depth of SSD on different parameters, a scanning electron microscope (SEM) was used to observe subsurface cracks. The cross-section polishing method was used to observe the subsurface of SiC ceramics. As the cracks were too tiny, the cross-sections of SiC ceramic samples should be polished with an argon ion polishing machine and chemically etched using HF solution to enable the visibility of subsurface cracks. Before being observed, the SiC sample should be ultrasonically cleaned several times. Finally, the maximum depth of cracks was selected from the micrographs.The actual 2D motions of the VAP device were measured with two displacement sensors, and then data were fitted by MATLAB. The typical results at different amplitudes of voltage are shown in In order to investigate the variations of brittle–ductile transition in the scratch tests under different conditions, a white-light interferometer (ZYGO) could be used to obtain accurate depth values. Based on the scratch tests, we can clearly conclude that VAM could increase the critical depth of cut. However, it is difficult to ensure processing in the ductile region due to the machine tool accuracy and workpiece assembly error. We could use the VAP method to reduce surface and subsurface damages. According to Upon substituting the experimental parameters into Equation (22), the theoretically predicted value of SSD depth could be obtained. To reduce measurement time and cost, a 500 μm × 10μm area in the cross-section of SiC ceramics was polished on an argon ion polishing machine. Following the use of SEM to observe the SSD depth of SiC ceramics, the predicted and measured values are listed in According to the results and analysis, it is clearly shown that there is a good agreement between theoretical calculations and experiment with respect to the depth of SSD as a function of VAP parameters. However, there is a certain difference between theoretical values and experimental values. The main reasons are as follows: (1) the establishment of the mathematical model does not take into account some factors such as heat change, multi-abrasive coupling, tool wear, and so on; (2) elastic and plastic deformation of SiC ceramics is not considered in the theoretical equations; (3) the chemical reaction caused by etching is uncontrollable; (4) a smaller observation range results in the maximum SSD depth not being seen.This study was carried out to investigate the critical cut depth in the vibration-assisted processing of SiC ceramics using a single diamond abrasive grain scratch model. First of all, the SSD of the SiC workpiece was analyzed based on the effects of different polishing parameters. Furthermore, combining the kinematic characteristics of VAP and the damage characteristics of the brittle materials, surface damages and SSD of SiC ceramics were analyzed. Finally, a theoretical model of SSD was established to predict the SSD values, and a 3D FEM simulation was used for qualitative analysis of the established model. The SSD value of the SiC workpiece was measured using the section polishing method, and the obtained results indicate the following:(1) The critical cut depth of VAP is much larger than in conventional polishing in the scratch tests, indicating that VAP can increase the critical cut depth of SiC ceramics, and VAP is a superior method to improve the surface integrity of SiC ceramics in polishing.(2) In the simulation, the removal process of SiC ceramics can be understood for the generation and propagation of microcracks. The simulation results indicate that the vertical amplitude , the lateral amplitude, the frequency, and the abrasive grain size have the most significant effects on SSD. The SSD depth increases as the vertical amplitude and abrasive grain size increase. However, increasing the lateral amplitude and frequency can lead to a reduction of the SSD depth.(3) The experiments were also carried out to analyze the effects of different processing parameters on the SSD depth and surface quality. In addition, the experimental results verified the validity of the theoretical and simulation results.


An inertially stabilized platform (ISP) is generally equipped with a position and orientation system (POS) to isolate attitude disturbances and to focus surveying sensors on interesting targets. However, rotation of the ISP will result in a time-varying lever arm between the measuring center of the inertial measurement unit (IMU) and the phase center of the Global Positioning System (GPS) antenna, making it difficult to measure and provide compensation. To avoid the complexity of manual measurement and improve surveying efficiency, we propose an automatic estimation method for the dynamic lever arm. With the aid of the ISP encoder data, we decompose the variable lever arm into two constant lever arms to be estimated on line. With a complete 21-dimensional state Kalman filter, we accurately and simultaneously accomplish navigation and dynamic lever arm calibration. Our observability analysis provides a valuable insight into the conditions under which the lever arms can be estimated, and we use the error distribution method to reveal which error sources are the most influential. The simulation results demonstrate that the dynamic lever arm can be estimated to within  m, an accuracy that is equivalent to the positioning accuracy of Carrier-phase Differential GPS (CDGPS). Airborne earth observation takes the aircraft as the platform, and it uses remote sensing load such as synthesize aperture radar (SAR) and charge coupled device (CCD) array camera to acquire a wide range, highly accurate and multilayered space-time information of global surface and deep earth . A positThe key algorithm for POS is still SINS/GPS integrated navigation ,6. For tMany efforts have been devoted to improving SINS/GPS integration accuracy by attenuating the lever arm uncertainty. One method is manual measurement by a total station ,14, whicTo maintain imaging quality, aerial surveying sensors are required to move in a straight line with a given direction, but a plane may deviate from the ideal motion trajectory, due to gusts, air turbulence, or flight control errors ,21. ConsThe rest of this paper is organized as follows: As shown in Based on the established frames, the related lever arms are defined as follows:Three lever arms—Since the attitude matrix  the ISP :(2)Cbcb=Referring to Equation (2), the angular rate of the  follows :(3)ωbcbbAccording to the lever arm effect , if the Similarly, the position and velocity parameter correlations among the point In a normal integrated navigation mechanism, the velocity and/or position differences between the SINS and GPS solutions are generally taken as the measurement values. To improve the measurement accuracy, the dynamic lever arm Combining Equations (9) and (11) yields:This means that the dynamic lever arm As shown in Equation (11), if the SINS/GPS integrated navigation model can be designed to estimate the lever arms The corresponding state equation of Kalman filter is:ailed in . The symFor loosely coupled SINS/GPS integrated navigation, there are two measurement models to be selected in practical POS, including position measurements and position/velocity measurements. The associated measurement equations are:Since Equation (11) can be rewritten as:In this paper, we depict the position measurement equation as an example, while the position/velocity measurement equations have the same results.Usually, an observability analysis for an integrated navigation system is conducted to determine whether a specific error state is observable, and under what conditions it can be estimated . AccordiThe position measurement in Equation (15) can be rewritten as an error model:Clearly, this is not a deterministic system, but a stochastic case. However, the related theoretical analysis is still useful for revealing the observable conditions and guiding the design of verification trajectories. Ignoring the driving noise and measurement noise temporarily, Equation (18) itself determines the observability of the associated errors If only the ISP rotates, If only the attitude of the vehicle changes, In summary, the estimate of constant lever arms In aerial mapping missions, the aircraft usually maneuvers intentionally before entering the sensing area to enhance the observability of the POS ,20, espeobtained ,17. As lIt should be noted that the auxiliary matrix The term SP PAV80  and GSM3SP PAV80  can provThe time delay of the GPS information relative to SINS is another major error source. Since the GPS receiver and the SINS unit are two separate subsystems, the frequency difference between the 1PPS and SINS sampling clock could cause the time delay to be a variable . Thus, the method of taking the time delay as a constant error state to be estimated will not work. The effective way is to discipline the SINS sampling clock with 1PPS , or to rAssuming that The purpose of error distribution analysis for stochastic systems is to evaluate the final estimation accuracy of the concerned states, and to distinguish which error sources primarily contribute to the concerned estimation uncertainties. Monte-Carlo simulations are appropriate to determine error distributions, but suffer from a large computational burden. Based on the law of large numbers , Monte-CThree system models are involved in the covariance analysis method: the real world model, the full-order design filter, and the reduced-order filter model . The reaIn this paper, the real world model is defined in For the reduced-order filter model, after the state equation and measurement equation are established and discretized, we update the standard linear Kalman model in two calculation loops : the staIt can be seen that the covariance calculation loop is independent of the state filtering loop. Once the filter is designed and the trajectory is selected, the associated matrices In the full-order filter model, the state equation and measurement equation are extended as follows:It can be seen that there are three types of errors that affect the estimation results: the initial state errors The filtering gain matrix Since the gain matrix Firstly, based on linear propagation characteristics of associated errors, and setting Secondly, setting Thirdly, setting Therefore, the estimation accuracy of Therefore, according to the above covariance analyzing method, the error distribution budgets of the full order filter or real-world model can be constructed from the calculation of the reduced order filter. The complexity and computational burden of simulation are greatly reduced.Initial position: latitude, longitude and altitude ;Initial Velocity: Initial Attitude: pitch, roll and heading °.Lever arms to be estimated: Considering the extremely high accuracy requirements for a lever arm in POS, it is difficult to find another more accurate benchmark to evaluate the estimation results. As an expedient, we carried out a series of simulation tests instead of real tests to verify the proposed method. Considering the effect of the time-asynchrony error, we assume that the aircraft flies at 50 m/s uniform speed, and the angular motion excitations are added into the simulation trajectory. The initial values needed for the trajectory are given as:To verify the observability analysis results in As shown in Referring to the system POS AV610 produced by Applanix ,35, we sWe use the reduced-order filter model with parameters set as in As shown in To evaluate lever arm estimation accuracy and positioning accuracy, we carried out 100 Monte-Carlo simulations, 50 times for each trajectory. The final lever arm estimation results at the end of every test are shown in .As shown in In manual measurements, the lever arms can be measured with an accuracy of 1 mm level by a laser total station instrument , if the The purpose of the lever arm compensation is to obtain a higher positioning accuracy of SINS/GPS integration. Assuming that the lever arm has been manually measured with an accuracy of 1 mm, under the same simulation conditions, we obtain the positioning results of the SINS/GPS integration as shown in The positioning accuracy of The error distribution simulation tests are devoted to determining which error sources primarily affect the estimation accuracies of specific parameters. For sake of simplicity, the associated error sources in full-order model are classified into eight categories, as shown in n times, their effects will also increase n times.As shown in The ISP equipped in a POS results in a variable lever arm, making it difficult to compensate. Instead of inefficient manual measurement strategies, our proposed method uses the encoder data from ISP gimbals to decompose the dynamic lever arm into two constant lever arms to be estimated automatically. Based on the established 21-dimensional state Kalman filter, our error analysis and simulation tests provide some meaningful conclusions. First, rotation of the ISP and an attitude change of the vehicle are necessary to determine the dynamic lever arm. Second, encoder errors of the ISP have a limited effect on estimation accuracy, so that general turntables can be accepted if the lever arm