Construction of radiomics models for the individualized estimation of multiple survival stratification in glioblastoma (GBM) patients using the multiregional information extracted from multiparametric MRI that could facilitate clinical decision-making for GBM patients.A total of 134 eligible GBM patients were selected from The Cancer Genome Atlas. These patients were separated into the long-term and short-term survival groups according to the median of individual survival indicators: overall survival (OS), progression-free survival (PFS), and disease-specific survival (DSS). Then, the patients were divided into a training set and a validation set in a ratio of 2:1. Radiomics features  were extracted from multiple regions of the GBM using multiparametric MRI. Then, radiomics signatures that are related to the three survival indicators were respectively constructed using the analysis of variance (ANOVA) and the least absolute shrinkage and selection operator (LASSO) regression for each patient in the training set. Based on a Cox proportional hazards model, the radiomics model was further constructed by combining the signature and clinical risk factors.The constructed radiomics model showed a promising discrimination ability to differentiate in the training set and validation set of GBM patients with survival indicators of OS, PFS, and DSS. Both the four MRI modalities and five tumor subregions have different effects on the three survival indicators of GBM. The favorable calibration and decision curve analysis indicated the clinical decision value of the radiomics model. The performance of models of the three survival indicators was different but excellent; the best model achieved C indexes of 0.725, 0.677, and 0.724, respectively, in the validation set.Our results show that the proposed radiomics models have favorable predictive accuracy on three survival indicators and can provide individualized probabilities of survival stratification for GBM patients by using multiparametric and multiregional MRI features. Glioblastoma (GBM) is the most common primary malignant neoplasm in adults and is nearly uniformly fatal , with a As a noninvasive and preoperative routine examination for GBM , the magThe aim of the present study was to develop and validate radiomics models based on multiparameter and multiregion MRI for the individualized estimation of the multiple survival indicator stratification in GBM patients.A total of 134 patients (i) with clinical information (such as OS of patients) from The Cancer Genome Atlas TCGA1 GBM PrIn this paper, OS was defined as the time between the date of pathological diagnosis and the date of death or the date of last clinical follow-up. PFS was calculated from the date of initial diagnosis to the new tumor event whether it was (a) a progression of disease, (b) local recurrence, (c) distant metastasis, or (d) new primary tumors at all sites or the time the patient was last known to be alive. Similarly, DSS was measured from the date of initial diagnosis until death from the GBM or last follow-up examination. Then, these patients were divided into long-term and short-term survival groups respectively according to the median of OS, PFS, and DSS. Next, all patients were randomly separated into a training cohort  and a validation cohort  at a ratio of 2:1. In this retrospective study, the requirement for informed consent was waived because all the patient data in TCGA were deidentified.The main design idea of this paper is as follows: firstly, the multimodal MRI (multiparameter) data of GBM patients are preprocessed; next, the radiomics features are extracted from different regions of interest (ROIs) (multiregions), and then the analysis of variance (ANOVA) and least absolute shrinkage and selection operator (LASSO) methods are used to analyze and screen the extracted imaging features  related to the three kinds of survival endpoints. Finally, combined with clinical risk factors such as age, gender, and KPS, the radiomics nomogram, which is based on a Cox proportional hazards model, was analyzed. The overall workflow of the proposed method is shown in 3, and intensities within each volume were normalized to the [0.1] range.All 134 patients underwent four MRI modalities, i.e., T1C, T1, T2, and FLAIR sequence. The range of image acquisition parameters of the four MRI sequences is provided in In order to obtain information about the survival of patients with GBM from multiple tissue types rather than a single tissue type , five diIn order to extract high-throughput features, we obtained the original image, eight corresponding Wavelet-filtered images and five corresponding Laplacian of Gaussian (LoG) filtered in each MRI sequence. A total of 5,152 radiomics features were extracted for each patient. A detailed description of the feature extraction is provided in We use a one-way ANOVA to screen out the characteristics that are separately related to the three survival indicators and have significant differences. Then, LASSO logistic regression method was used to select the characteristics most related to the three survival indicators. LASSO is an effective regression analysis method to constrain the number of independent variables. It can perform feature selection and regularization in high-dimensional data to improve the prediction accuracy through penalty estimation function. The L1 penalty term is added to the ordinary linear model; for ordinary linear model, LASSO estimate is as follows:Where t corresponds to λ one-to-one, which is the adjustment coefficient. If λ is large, it has no effect on the estimated regression parameters, but as λ decreases, the coefficients of most covariates shrink to zero. It makes the model easier to explain: when there are a large number of independent variables, several important independent variables can be found, and the information provided by these variables is the most important in the model.With the adjustment of λ, the LASSO method can shrink all the coefficients toward zero and set the coefficients of uncorrelated features to zero. Then, 10-fold cross-validation with a maximum area under the curve (AUC) criterion was employed to find an optimal λ, where the final value of λ produces the maximum AUC. The non-zero coefficient is used to construct the regression model, and the corresponding non-zero coefficient is defined as the Rad-score. The fitting formula is generated using a linear combination of selected eigenvalues weighted by their Rad-score. The formula was then used to calculate the radiomics signature of each GBM patient to reflect his or her long-term or short-term survival.i  is the coefficient of the i-th characteristic, and vi is the i-th characteristic value of patients.Where pThe radiomics signature and each clinical factor were first inserted into a Cox proportional hazards model to test whether they were significantly independent prognostic factors for survival stratification in the training cohort. The radiomics signature and significant clinical factors were then utilized to build the Cox proportional hazards model to discriminate the short- and long-term survival outcome of the GBM patients. For comparison, Cox proportional hazards models that used only the significant clinical factors were also established. Finally, based on Cox proportional hazards model, radiomics nomograms of the three survival indicators are respectively constructed, which can directly and individually indicate the probability of survival stratification in the training queue.The discriminative ability of the radiomics nomogram was quantitatively measured using the C-index, which ranges from 0 to 1. The calibration curves were plotted using observed probabilities and the nomogram-estimated probabilities.The fitting formula that was constructed with the training cohort was applied to all GBM patients in the validation cohort, and the radiomics signature of each patient was calculated. The radiomics nomogram was then validated in this cohort using the radiomics signatures and clinical factors. Finally, the C-index was implemented to evaluate the model results for survival group stratification. Moreover, the calibration curve and the Kaplan–Meier survival curve were also constructed.To estimate the clinical utility of the radiomics nomogram, decision curve analysis (DCA) was performed by calculating the net benefits at different threshold probabilities in the combined training and validation cohorts.t tests or Mann–Whitney U tests were applied to confirm whether intergroup differences in continuous variables (such as age) existed between the short- and long-term survival groups. Either chi-square tests or Fisher’s exact tests were performed on the remaining categorical characteristics to determine whether the constituent ratios differed significantly between the groups. All statistical analyses were performed with R software version 3.6.1  using basic statistical functions or additional packages. The following R packages were used: the glmnet package was used for the LASSO logistic regression, the rms package was used for the nomograms and calibration curves, the Hmisc package was used for the comparisons between the C-indices, and the rmda package was used to implement the DCA.In this study, either Student’s Ethical review and approval were not required for the study on human participants in accordance with the local legislation and institutional requirements. Written informed consent for participation was not required for this study in accordance with the national legislation and the institutional requirements.The cohort of 40 patients ranged in age from 17 to 84 years with a median OS of 359.5 days, PFS of 195 days, and DSS of 376 days. The clinical characteristics and corresponding results of the statistical analyses comparing the long- and short-term survival groups of OS, PFS, and DSS are summarized in To determine the optimal regulation weight λ for the LASSO algorithm, features with non-zero coefficients for survival stratification were selected by 10-fold cross-validation from the 5,152 radiomics features. The illustration of feature selection using the LASSO algorithm is provided in The radiomics signatures for each GBM patient in the training and validation cohorts are presented in As mentioned above, according to different ROIs and survival endpoints, the radiomics features with non-zero coefficients corresponding to multiregion MRI and three survival periods are selected by LASSO algorithm. The number of different features extracted from each survival indicator and each region is also distinct. According to In addition, selected features from different MRI sequences have different coefficients, which can be seen as the importance of one for survival stratification. The results show that T1 sequence and FLAIR sequence account for more than the other sequences. A detailed description of the selected non-zero-coefficient features is provided in The radiomics signature, age, gender, and KPS were identified as independent predictors of survival stratification in GBM patients. The Cox proportional hazards model was applied based on three clinical predictors and/or the radiomics signature. According to In addition, it can be seen from Based on the multivariate Cox regression, the radiomics nomogram that incorporated the radiomics signature and the three clinical factors was constructed Figure 5The decision curve for the radiomics nomogram indicates that the use of the radiomics nomogram Figure 8This study investigated the prediction of multiple survival of GBM patients based on multiparametric MRI. The radiomics signature involving multiscale texture features, combined with clinical risk factors, could precisely predict the individualized probability of survival stratification for each GBM patient. The performance differs from GBM patients in OS, PFS, and DSS. Furthermore, different tumor subregions and different modalities of MRI play a significant role in the prognosis of GBM patients.In our study, the incremental value when adding the radiomics signature to the clinical factor-based nomogram was assessed. According to the C-index and Decision curves, the combination of the radiomics signature and clinical predictors demonstrated an enhanced stratification efficacy in both the training and validation cohorts of the three survival indicators. The results suggested that the radiomics signature was more robust than the traditional clinical risk factors, in accordance with many previous studies focusing on radiomics nomogram –19.To develop the radiomics signature, more features are added from original and derived images. More features result from the features based on Wavelet transform and LoG transform and have coefficients of higher importance that influenced the radiomics signature model in terms of survival. Previous studies have shown that multiscale texture analyses of MRI based on feature extraction can automatically predict the survival time (OS and PFS) with a precision and speed beyond the scope of human visual analysis , 19, 20.In order to evaluate and predict the survival status of GBM patients comprehensively and systematically, we examined three different survival indicators: OS, PFS, and DSS, which are the appropriate clinical endpoints for GBM . Among tOur results showed that the OS and DSS results of GBM patients were relatively consistent, which may be due to the definition of DSS as death caused by a specific disease. And this study focused on glioblastoma multiforme and illustrated that GBM has fewer complications and high mortality. However, in the process of evaluating PFS, it is found that the result of PFS was biased. It is probably due to the large differences between individual patients and the greater changes in imaging characteristics for the progression of tumors. This finding is consistent with another previous study of GBM showing that the stratification of the PFS resulted in worse performance than OS .Our approach is based on comprehensive quantitative information from four different MRI sequences and six heterogeneous regions that enable a multiparametric three-dimensional characterization of the entire tumor. The selected radiomics features were from different heterogeneous regions and sequences of MRI. According to our research, the absolute values of coefficients obtained by the LASSO algorithm indicate the contribution of specific features for survival stratification.Concerning different heterogeneous regions, the features from the enhancing tumor core (ROI B) contributed more to the OS stratification than did the features from other subregions. Most GBM prognosis-related studies indicated the association between poor prognosis and radiomics features from contrast-enhanced regions , 31. ForIn addition, our results show that the selected features based on T1 sequence and FLAIR sequence account for more proportion see . A comprIn order to more concretely analyze the performance of single-modality and multiparameter MRI, we supplemented the comparison of their C-index of model obtained by each modality on the training set and validation set, respectively see .Some limitations of this study need to be further investigated. First, the number of enrolled subjects is relatively small in our study, and 134 subjects in TCGA-GBM dataset were used, resulting in low robustness results. This is because we have adopted relatively strict exclusion criteria such as patients with incomplete OS, PFS, and DSS data will be excluded. However, to solve this problem, we use cross-validation in the training process of building the model, which makes our result generalizable to the population. Second, the 2D manual segmentation used in this study may induce bias about tumor slice selection and manual ROI delineation. Furthermore, Hainc et al.  have invImaging-related limitations may result from the limited through-plane resolution of the T2 and FLAIR data compared to the higher-resolution T1 data. As a result, the assessment of fine structural details in one of the three spatial dimensions on the FLAIR data was hampered by some degree of blurring.In conclusion, this study provides reasonable evidence of radiomics based on multiparametric MRI in assessing OS, PFS, and DSS of GBM patients. The features based on diverse regions correlate significantly with GBM survival. Disparate MRI modalities and subregions can provide distinctive but supplemental information. Compared to several survival analysis studies of GBM patients , 30, 32,The original contributions presented in the study are included in the article/Ethical review and approval were not required for the study on human participants in accordance with the local legislation and institutional requirements. Written informed consent from the participants’ legal guardian/next of kin was not required to participate in this study in accordance with the national legislation and the institutional requirements.BW and SZ conceptualized and designed the study, developed the methodology, and analyzed and interpreted the data. SZ, YY and XW performed the data collection or acquisition, statistical analysis. LC participated in discussion and language editing.YL, DL and TY reviewed the manuscript. All authors contributed to the interpretation of the results, drafting the manuscript work or revising it critically for important intellectual content and approval of final version to be published and agreement to be accountable for the integrity and accuracy of all aspects of the work.This study was supported by the National Natural Science Foundation of China  and the National Key R & D Program of China (2018AAA0102604).The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


Mobility has been one of the most impacted aspects of human life due to the spread of the COVID-19 pandemic. Home confinement, the lack of access to physical rehabilitation, and prolonged immobilization of COVID-19-positive patients within hospitals are three major factors that affected the mobility of the general population world-wide. Balance is one key indicator to monitor the possible movement disorders that may arise both during the COVID-19 pandemic and in the coming future post-COVID-19. A systematic quantification of the balance performance in the general population is essential for preventing the appearance and progression of certain diseases , as well as for assessing the therapeutic outcomes of prescribed physical exercises for elderly and pathological patients. Current research on clinical exercises and associated outcome measures of balance is still far from reaching a consensus on a “golden standard” practice. Moreover, patients are often reluctant or unable to follow prescribed exercises, because of overcrowded facilities, lack of reliable and safe transportation, or stay-at-home orders due to the current pandemic. A novel balance assessment methodology, in combination with a home-care technology, can overcome these limitations. This paper presents a computational framework for the in-home quantitative assessment of balance control skills. Novel outcome measures of balance performance are implemented in the design of rehabilitation exercises with customized and quantifiable training goals. Using this framework in conjunction with a portable technology, physicians can treat and diagnose patients remotely, with reduced time and costs and a highly customized approach. The methodology proposed in this research can support the development of innovative technologies for smart and connected home-care solutions for physical therapy rehabilitation. The COVID-19 pandemic and subsequent stay-at-home orders put in place have caused a general reduction in physical mobility among countries across the globe . The funThe use of telehealth and telerehabilitation can help counteract the above-mentioned challenges. Many benefits exist within switching to remote care: increased access to healthcare, reduction in overall cost, increased interaction with providers and patient engagement, the ability to provide both synchronous and asynchronous treatment, and the eventual generation of large datasets for broader scientific investigation and impact. Though many approaches to telemedicine currently exist , proper Within the circumstances caused by the pandemic, there is a focus on restoring motor function in the following areas: deconditioning, strength, balance, and the ability to perform daily activities . In partAlthough the existing CDP devices are considered to be the best currently available technologies, these machines are too costly and substantial in size for in-home use, and they require a trained clinician to supervise the machine setup and operation. Technologies for home care rehabilitation must be portable, compact, and must have a user-friendly interface so that the general patient can operate the device with minimal training. Commercial balance training technologies aimed for the home environment are typically presented as “exergames” (exercise games), which utilize the body’s motion as a method of controlling gameplay and were developed to encourage activity through fun activities. For example, Wii Fit uses the body’s weight distribution on the balance board as a proxy indicator of balance ; the KinThe limitations on the CDP and exergames technologies prevent simultaneous balance assessment and training from being properly performed at home. Specifically, existing assessment metrics and testing protocols need to be improved to better understand the mechanisms that affect postural control . The theRecent studies have addressed the limited scope of quantification of existing balance assessment methods by addressing the stability of biped systems from a dynamic system perspective. In this context, balance is defined as the ability to maintain the state of a dynamic system inside a defined desired region of the state space . The quaIn this study, a state-space balance criterion  is used A computational framework is proposed in which novel balance performance measures are formulated and implemented in exercises for simultaneous balance assessment and training. The use of the balance performance measures is twofold: 1) they are used as quantitative outcomes for general balance assessment and 2) they define customized and quantifiable balance training goals across multiple exercises. This novel rehabilitation paradigm requires the integration of the following components: 1) the theoretical formulation of the novel balance performance measures, 2) the design of exercises for which the balance performance is quantified, 3) a computationally tractable model of the user (human subject).A stability criterion based on the concept of balanced regions in the COM state space  is adoptbalanced region is the set of all possible COM balanced states from which a given subject can reach an upright rest state, while avoiding a change in foot stance , represents the maximum limits of balance recovery of a subject while maintaining a given foot stance and is quantified in terms of maximum feasible range of COM velocity perturbations. The BoB is formed by the COM velocity extrema (minimum and maximum) calculated iteratively at various COM sampled positions, Pi, i = 1, …, N, and along any specified direction; hence the balanced region is a partition of the six-dimensional state space of COM Cartesian position and velocity. For practical analysis and visualization, the BoB can be evaluated for a specified plane  and projected onto a single direction of interest   .Pi, optimization finds the limiting balance recovery trajectories in the joint space that drive the biped system from its extreme initial conditions  to a rest state, without a change in foot stance. The extremized COM initial state of each trajectory solution represents a point of the BoB. From any point of the BoB, there exists at least one controlled trajectory from which the subject can reach upright quiet stance without changing contacts. Alternatively, if the optimization finds no solution at a given Pi, the feasible range of COM initial velocity that guarantees the COM will return to a stationary upright position without altering foot stance is null; in this case, any COM state at that specified Pi is unbalanced, i.e., outside of the BoB. The balancing trajectories generated from each point of the BoB satisfy the following constraints: 1) a final rest state , 2) various system and physics constraints , and 3) the preservation of the original stance . The resulting BoB is a stance-specific threshold that is customized using subject-specific body and joint parameters in the modeling, capturing the balance capabilities of a subject as predicted by the model. Details of the numerical optimization algorithm and its solution via sequential quadratic programming can be found in previous work  and the BoB results into the following set of limiting COM initial conditions in the sagittal plane:  . The COMvelocity  for pracBoundary Margins are numerical indicators that characterize the dimension of a balance region relative to the base of support (1)  support . These iTwo categories of balance performance metrics are formulated in the COM state space, based on the balanced region concept described above:reachable boundary marginThe  support ).viable boundary marginState Margins are numerical indicators that characterize the instantaneous state of balance for a given trajectory, by measuring its relative distance to the BoB. Depending on how this distance is measured in the state space, these indicators can include position, velocity, or mixed margins. In this study, the extended Margin of Stability (eMOS) (2) y (eMOS)  is used y (eMOS) . The eMOy (eMOS) , but it The The application of the balanced region and balance performance measures within the rehabilitation context is presented. The two categories of balance performance measures are used as design criteria for rehabilitation exercises in which balance performance is simultaneously quantified and trained. For a given subject and foot stance, the balanced region and boundary margins predicted by the optimization-based algorithm provide a reference map for defining customized target states across multiple exercises.statically balanced states: a state in this partition can be driven to a static equilibrium configuration by controlling the COP position within the given base of support and/or through the regulation of whole-body linear and angular momentum. From a statically balanced state the motion could in theory be stopped instantaneously without causing the system to lose balance.1) The portion of the balanced region characterized by a COM ground projection within the edges of the base of support  is the sreachable balanced states: each of these states has a COM position outside of the footprint, hence is dynamically balanced. Because this partition contains both positive and negative COM velocity, the COM can enter it from a statically balanced state using internal dynamics and then invert its motion to recover balance. Balance recovery from reachable balanced states is only possible through the rotation of multiple body segments about the COM that generates a stabilizing angular momentum and its derivative, similar to the effect of a flywheel. Within this partition, the COP cannot be controlled and balancing must rely on a combination of favorable  COM initial conditions and whole-body inertial effects over a finite interval of time.2) The portion of balanced region included within the reachable margins is the set of viable balanced states: similar to the reachable states, they are also dynamically balanced and must rely on favorable initial conditions and whole-body inertial effects in order to reach a static equilibrium within a finite interval of time. The difference from reachable states is that the system’s COM can enter this partition only through externally imposed perturbations, e.g., external impulse. However, once the COM state is inside this partition  the external push can cease and the system in the given stance can recover balance by means of its initial conditions and actuation capacity.3) The portion of balanced region characterized by COM positions that are outside of the reachable margins, but within the viable margins, is the set of The intersections of the BoB with the edges of the base of support and the boundary margins in both anterior and posterior directions identify three partitions of the balanced region :1) The pThe above partition-based analysis of the balanced region provides a reference map that characterizes the different stability nature and means of control for a COM state within each partition . StaticaTwo types of balance exercises (perturbation-based and motor task-based) are proposed in which the requirements of a desired user’s motion are imposed in terms of COM initial, target, and final states. For each exercise, the final state is a statically balanced state, while the initial and target states are assigned to the different partitions of the balanced region, based on the exercise desired outcome. In addition, each exercise has a prescribed foot contact (or sequence of contacts), used to evaluate the associated contact-dependent balanced region.The first type of balance exercise consists in perturbation experiments guided by target states placed progressively closed to the boundaries of the balanced region   Example training exercise to reject internal perturbations from upright stance—Starting from rest, the subject is asked to initiate a forward/backward motion, come as close as possible to reachable Target A, and then invert its motion to reach a final rest state, all while maintaining a double stance configuration. Experimental reachable margins resulting from this exercise are quantified as the maximum anterior/posterior position reached by the subject’s COM before inverting its motion. The experimental and numerical reachable margins are compared to have a relative measure of the subject’s maximal COM sway capacity along a specific direction.2) Example training exercise to reject external perturbations from upright stance—Starting from rest, the subject is asked to perform a pre-balancing task in which the COM should attain initial conditions as close as possible to viable Target B using the external impulse generated, for instance, by a hand-push on a fixed handle. The subject’s state at the end of the push-off motion is recorded as the initial viable state of the balancing motion, which will terminate at upright equilibrium with no change in foot stance. The most extreme viable initial state that can be successfully attained by the subject gives the experimental viable margin, which is compared with the numerical counterpart to have a relative measure of the subject’s limits of recovery from external perturbations.Two examples of perturbation-based balance exercises during standing posture are described:This first type of perturbation-based exercises aims at simultaneously quantifying and training the general perturbation rejection capability of a subject relative to a given stance. Using the reference map, specific portions of the balanced region can be targeted for a given patient, to enhance a particular type and direction of balance control.The second type of balance exercise is specific for a motor task and focuses on quantifying the balance performance of a specific trajectory. Multiple target states are assigned either inside or outside  . The dynIn this study, balance exercises during standing posture are considered for demonstration purposes, which are characterized by a symmetric double stance, small variation of COM height, and significant COM perturbations in the sagittal plane along the anterior/posterior direction. Three increasingly complex models of human body that satisfy the exercise requirements are implemented in the balance assessment framework: a 1-DOF linear inverted pendulum (LIP) model, with a single mass and a flat foot ; a 4-DOFThe novel paradigm for simultaneous balance assessment and training is demonstrated with the results of balanced regions and balance performance measures calculated for different models of human standing posture. Experimental balance recovery trajectories extracted from published literature  are usedfl = 0.23 m.The balanced region results are presented for three increasingly complex models of a human subject in the sagittal plane, i.e., the LIP, 4-DOF, and 5-DOF models, to illustrate the effects of body and foot modeling choices on the predicted range of allowable perturbations during standing posture . The antX) and posterior (−X) direction, by sampling the COM initial positions at a constant height Y-coordinate in the upright standing configuration. The BoB of the LIP model can be found analytically using the linear inequalities that limit the position of the extrapolated center of mass  in addition to COP control. In particular, the largest boundary margins are for the 5-DOF model, due to the presence of a two-link foot that enables the additional balancing strategy of heel-to-toe foot rocking, which increases the range of feasible COM positions and velocity perturbations.The above boundary margins values predicted by the three models of human posture can be used as both targets and outcomes in COM perturbation experiments in tele-rehabilitation settings, to simultaneously assess and train a subject’s overall balance performance ability to reject internal and external perturbations.To showcase the role of boundary margins in a balance rehabilitation exercise, empirical data relative to push recovery exercises published in the literature  is partiHere, 35 perturbed COM states for one subject of the reference study are extracted, normalized, and represented against the nondimensional balanced regions . The mosLastly, the evaluation of balance performance in the motor task- based exercise is illustrated by two example trajectories extracted from the reference study , which eThe state margin eMOS is calculated for the two example trajectories to evaluate their instantaneous level of balance or imbalance . The nonThe eMOS of the reachable trajectory indicate that all three biped models correctly predict a balanced trajectory that is closer to the lower BoB boundaries for approximately 65% of the motion, after which the COM state results closer to the upper BoB lines ; left. TThe above analysis of balanced regions, boundary and state margins demonstrates an objective method of assessing a patient’s progress throughout treatment. The nondimensional boundary margins have highlighted the differences between the different modeling approaches of human standing posture: the inclusion of a multi-segment foot can lead to a more accurate balance characterization in real human subjects. Boundary margins allow the selection of customized and quantifiable targets for training balance recovery from internal and external perturbations, while state margins provide a numerical benchmark of the subject’s balance capabilities during a particular trajectory. All proof-of-concept results demonstrate the benefits of having a balance criterion that can be extended to higher-order models that can more accurately predict dynamic stability, as compared with reduced-order models.This study proposed a novel balance training and assessment computational technique, illustrated through an example subject performing a postural stability exercises obtained from a reference study . By usin


Radar-based breast imaging has shown promise as an imaging modality for early-stage cancer detection, and clinical investigations of two commercial imaging systems are ongoing. Many imaging algorithms have been proposed, which seek to improve the quality of the reconstructed microwave image to enhance the potential clinical decision. However, in many cases, the radar-based imaging algorithms have only been tested in limited numerical or experimental test cases or with simplifying assumptions such as using one estimate of permittivity for all patient test cases. In this work, the potential impact of patient-specific permittivity estimation on algorithm comparison is highlighted using representative experimental breast phantoms. In particular, the case studies presented help show that the permittivity estimate can impact the conclusions of the algorithm comparison. Overall, this work suggests that it is important that imaging algorithm comparisons use realistic test cases with and without breast abnormalities and with reconstruction permittivity estimation. A competing system developed by Microwave Vision Group  is being used in clinical investigations at the National University of Ireland Galway (Ireland) [Radar-based imaging is an emerging modality for breast cancer detection . In receIreland) ,9,10. ThIreland) .Several imaging reconstruction algorithms for radar-based imaging have been developed (known as beamformers) and many introductory books, comprehensive reviews and open-source implementations of these algorithms have been published ,13,14,15However, it is known that an incorrect estimate of the breast dielectric properties can impair the image quality of radar-based breast images . In partThe goal of this study is to examine the impact of patient-specific permittivity estimation algorithms on beamformer comparisons in healthy and tumor experimental models. Although patient-specific permittivity estimation and sophisticated beamformers have been shown to improve image quality independently in certain cases, the impact of patient-specific permittivity estimation on beamformer comparative studies is unknown. The remainder of this paper is structured as follows: Many reviews, books and editorials have been published about microwave imaging and microwave breast imaging in recent years ,35,36,37The Delay-and-Sum (DAS) imaging algorithm was the first proposed for radar-based breast imaging and has been used in both mono- and multistatic configurations ,39. Math to date ,5,40, anI(r)=w(r) to date .calculating a separate weighting factor to reward points where tumors are more likely based either on epidemiological studies or on characteristics of the scattered signals (Equation );prioritizing scattered signals collected at certain locations based on the relative locations of the antennas and points of interest or on the antenna radiation patterns (Equation );by improving the quality of the input signals prior to imaging through improved artefact removal algorithms or other noise reduction techniques.Many extensions to DAS have been proposed which aim to improve the image quality. The extensions can be broadly classified into three types:In most cases, these modified beamformers have been tested in limited numerical or experimental test cases, and most radar-based operational systems have used traditional DAS . In thisThe DMAS beamformer was first proposed in . DMAS aiAlthough this does not increase the amount of independent information, this pairwise multiplication artificially increases the number of channels in the summation. The DMAS beamformer assumes that signals with a high degree of coherence should be rewarded by multiplication, whereas incoherent signals should not increase in energy after multiplication.A fundamental assumption of radar-based imaging is that knowledge of propagation within the breast can be used to synthetically focus the recorded electromagnetic energy to points within the breast. This is represented by the propagation delay, Equation . The proSeveral patient-specific permittivity estimation methods have been proposed which are reviewed in detail in . PatientTo assess the performance of beamformers, it is necessary to identify a set of evaluation metrics for the radar-based images. In many cases, image quality has been defined using the signal-to-mean ratio (SMR) and the signal-to-clutter ratio (SCR). Typically, the SMR is calculated by dividing the mean energy of the tumor area (the area surrounding the maximum intensity of the image) by the mean energy of the image of the ipsilateral breast, where the tumor area is twice the full-width half-maximum (FWHM) of the response of highest energy in the image. Similarly, the SCR is calculated by dividing the maximum energy of the tumor area  by the maximum energy in the background of the image. Additionally, in images of test scenarios with abnormalities, the localization error, or the distance between the maximum response in the image and the location of the abnormality, is used as a measure of quality. Lower localization error means higher image quality.In this work, the SCR and the FWHM of the images using different beamformers is compared. Although recent studies have suggested that these metrics may not be sufficient to distinguish images of modelled healthy and cancerous cases , the SCRAdditionally, the images are analyzed quantitatively and annotated as containing a tumor or not according to the criteria described in detail in . BroadlyIn this section, the experimental methods are described. The BRIGID breast and tumor phantom set was used to assess the performance of the imaging algorithms which is fully presented in . The brea hemispherical skin which varied between 1 to 3 conical glandular structures to model breast lobes radiating from the areola with relative permittivity of an adipose layer with relative permittivity of Breast phantoms were hemispherical with diameter of 14 In each breast phantom, a hole was left in which a tumor “plug” could be inserted. Each tumor phantom was embedded in a plug of adipose tissue, and the tumor phantom had a mean relative permittivity of terature ,52,53.The BRIGID phantom set contains breast phantoms which vary according to the volume of glandular tissue present within the phantom, known as the volume glandular fraction (VGF). Recent advances in three-dimensional imaging using breast tomosynthesis have allowed the VGF to be quantified, such as in a study of 219 women in . This stIn this work, images of four breast phantoms with VGF varying from 0% to 20% are analyzed as the healthy cases, specifically 0%, 10%, 15% and 20% as shown in Signals are acquired from the breast phantoms using experimental hardware developed at NUI Galway, Ireland which is described fully in . Experim studies ,56. The inclusion of a suction system to ensure the breast contacts the radome ;undersizing the radome compared to the reported breast size to improve the fit ;use of a coupling medium to help reduce air gaps between the breast and the antennas ,56,58;automated metrics to ensure the breast is well-situated prior to the scan .A reference scan with a homogeneous breast phantom was used to account for differences between the antennas. This reference scan was used to calculate a “calibration factor” which was then applied to neighboring antennas such that the response of each antenna was the same. While effective in these experimental studies, this calibration is not optimized for use with patients without optimization to ensure the breast contacts the antennas correctly. Many approaches have been proposed in the literature to overcome these issues:® system and hundreds of women [After acquisition, all signal processing and imaging was performed in the frequency domain using MERIT, an open-source toolbox for microwave imaging . First, of women ,58, the Next, an assumed estimate of the relative permittivity of the breast was used to synthetically focus all signals to a point of interest within the breast . ConsideFor each test case, a cost function is used to estimate the “quality” of that image. Specifically, the Absolute Gradient, AG, from  is applifirst, the impact of permittivity estimation in phantoms without abnormalities is discussed in secondly, the ability of DMAS to compensate for errors in the permittivity estimation process is considered in thirdly, the permittivity estimation algorithms are applied to images of the same scene reconstructed with different beamformers to estimate if the characteristics of the images are different in The results of this paper are presented in a three stages:In this section, the impact of permittivity estimation on beamformer selection in breast phantoms without abnormalities is discussed. First, the images of the four breast phantoms without abnormalities using both the DAS and the DMAS beamformers are investigated in The images in Considering the least dense breast phantom initially a,b, it cHowever, in the denser breast phantoms, Considering the images selected by using the permittivity estimation method described in , the parFor the less dense breast phantoms, the parameter search algorithm would select images reconstructed at different permittivity values, In this section, the effect of using DMAS instead of DAS are analyzed. The reconstruction permittivities are chosen using the parameter search algorithm applied to the DAS images. Additionally, case studies are presented which show how the beamformer comparison can depend on the permittivity chosen for reconstruction.First, a case study is shown in Considering the lowest estimate of Overestimating the relative permittivity by 5% in Finally, overestimating the relative permittivity by 10% in Considering all 20 cases (five tumor phantoms different in size in four breast phantoms differing in VGF), 14 are detected using DAS and permittivity estimation. For these 14, the DAS image is compared to the DMAS image at the same estimate of the permittivity. For 3 of the 14 images , the DMAS image is “sharper” with SCR at least 1 dB higher and FWHM approximately 2 mm smaller. For a further 6 of the 14 , the images were similar where the SCR was within 1 dB and the localization was within 1 cm. However, for 5 of the 14 cases , the image deteriorated such that the tumor was not detected: for all five, the location of the maximum image response was more than 5 cm away from the location of the tumor phantom.For the 6 of 20 cases where DAS and permittivity estimation did not detect the tumor, in 2 cases, the DMAS image was very similar to the DAS image but with less clutter. In 3 more cases, the DMAS image would also not have located the tumor in the right location, but the main response in the image was in a different location when compared to the DAS image. In only 1 case, P5 in 10% phantom, did the DMAS image reconstructed at the same permittivity as the DAS image correctly identify the tumor where the DAS image would not have.Finally, in this section, images selected by DMAS and the permittivity estimation algorithm are compared to the DAS image at the same permittivity as the DMAS images, and to the DAS images selected by the permittivity estimation algorithm. Overall, the sensitivity from the DMAS images with permittivity estimation was 10 out of 20 cases compared to the 14 out of 20 for DAS with permittivity estimation.For the 20 breast and tumor phantom combinations, in 9 cases the permittivity estimation algorithm selected a DMAS image reconstructed within For the remaining 11 cases where the reconstruction permittivity selected by the parameter search algorithm from the DMAS image differed from the DAS image, 7 of the 11 DAS images correctly identified the tumor whereas only 3 of the 11 DMAS images did. Interestingly, of the four images where DAS with permittivity estimation outperformed DMAS with permittivity estimation, two (P1 and P5) were in the breast phantom with 0% VGF.In this work, the potential impact of permittivity estimation on beamformer comparative study design is highlighted. Although many comparative studies of various beamformers have been published in the literature, most use the simplifying assumption that the same estimate of the permittivity can be used for all test cases, although this is known to impair the image quality. Similarly, the majority include only test cases with tumors, and do not compare the beamformers in test cases without tumors.The original DAS beamformer is compared to the DMAS beamformer, which was identified as a promising beamformer from a recent comparative study using five clinical case studies. The results in this paper suggest that DMAS may reconstruct an image of higher quality (defined primarily in terms of SCR) than the original DAS, however, this may result in more false positives such as in the less dense breast phantoms in this paper.The importance of including realistic patient-specific estimation when comparing beamformers is also shown. A case study showing how the conclusion of a beamformer comparison study may vary depending on the permittivity estimate is presented. In this case study, as the estimate varies by 5%, it could be concluded that both beamformers perform the same, or that DMAS localizes the tumor where DAS does not, or that neither DAS nor DMAS localizes the tumor. Hence it is important to consider realistic and varied test cases when comparing beamformer performance.Future work in this area should include the development of metrics to quantify the image quality which are useful to distinguish images of healthy and abnormal breasts. Future studies should consider the effects of permittivity estimation when designing and comparing beamformer performance experimentally and clinically.


The ability to select, isolate, and manipulate micron-sized particles or small clusters has made optical tweezers one of the emergent tools for modern biotechnology. In conventional setups, the classification of the trapped specimen is usually achieved through the acquired image, the scattered signal, or additional information such as Raman spectroscopy. In this work, we propose a solution that uses the temporal data signal from the scattering process of the trapping laser, acquired with a quadrant photodetector. Our methodology rests on a pre-processing strategy that combines Fourier transform and principal component analysis to reduce the dimension of the data and perform relevant feature extraction. Testing a wide range of standard machine learning algorithms, it is shown that this methodology allows achieving accuracy performances around 90%, validating the concept of using the temporal dynamics of the scattering signal for the classification task. Achieved with 500 millisecond signals and leveraging on methods of low computational footprint, the results presented pave the way for the deployment of alternative and faster classification methodologies in optical trapping technologies. First introduced in 1986 by Arthur Ashkin ,3, to enThe classification task of trapped particles has been shown over three major approaches. The first, arguably simpler, explores spatial image information, either using the image directly acquired from the microscope under external illumination ,6 or usiA second common methodology combines optical tweezers with Raman spectroscopy, collecting and analyzing the spectral signature of the trapped particles . CommonlMore recently, a third approach sought trapped particle identification using the scattered signal signature in the temporal domain. The general concept rests on the fact that the signal scattered from trapped beads is related to their physical dynamics. This fact has been used for force calculation  and predWithin this context, this work explores the classification of trapped beads from their scattering signal temporal dynamics, using a standard optical tweezers system equipped with a quadrant photodetector (QPD). It is proposed an alternative pre-processing strategy based on the Fourier transform of the acquired signal and subsequent principal component analysis, a methodology with a significantly lower computational load when compared with other previously reported feature extraction methods used in this topic of research . The resOptical tweezers exploit light-induced forces generated by a tightly focused beam to trap and manipulate particles. The combination of the gradient force  and the scattering component (associated with the radiation pressure and photon momentum transference) creates an effective three-dimensional harmonic potential well that allows 3-D manipulation, provided the target specimen fulfils certain criteria regarding its refractive index and size ,23.m is the mass of the particle, a as: Nevertheless, while the optical trap brings a trapped particle towards an equilibrium position, it still experiences a characteristic Brownian-type motion ,23. Indemr¨(t)=−γThe existence of the Brownian motion allows us to experimentally probe physical properties of the trapped particle such as the optical force acting on it. Indeed, a wide range of passive methods  exist fx axis, and T the absolute temperature. One of the drawbacks of the method is that precise information regarding the standard deviation of the position must be computed. This can be accomplished using the information of a QPD but requires prior calibration procedures [The first method explores the equipartition theorem that states that, at thermal equilibrium, each degree of freedom contributes with ing that ,27:(3)12ocedures ,29.The second method works around some of the drawbacks of the equipartition method by exploiting the evaluation of the dynamics in the frequency domain. At low Reynolds number, it can be shown that the one-sided power spectrum of the fluctuations of a trapped bead is given by the equation ,27: (4)SBy fitting the power spectrum to a Lorentzian function, the roll-off frequency can be easily extracted. This approach requires previous information regarding the particle radius as well as the drag coefficient to be known ,28. As sThe temporal scattering signal depends on the particle characteristics, such as their size and refractive index . With thX, Y, x and y position of the particle scattered laser beam, along with the integral of the optical signal  for which schematic is provided in ibration , may allFor testing the classification capabilities of the system, a set of reference particles (from Phosphorex) of different sizes and materials was used. The experimental measurements were conducted within aqueous solutions  of 0.05 to 8 μm . For eacX, Y, The classification procedure proposed in this work aims to utilize the 3-channel signal acquired from the QPD  was applied using the sklearn library [For the purpose of increasing the amount of data to train the model and approximate to a real-world scenario, each acquired signal  was divided into individual segments of 500 milliseconds forming the total dataset to be classified. Then, for each signal and for each channel, was computed the Fourier transform using the fast Fourier transform (FFT) algorithm of the standard  library , keepingsklearn library were used. In particular, random forests (RF), support vector machines (SVM), k-nearest neighbors (KNN), and neural-network (NN) classifiers. The distinct algorithms were chosen to guarantee the diversity of the classification strategy employed and understand if any particular classifier is more suitable for this type of dataset. For each method, the hyper-parameter optimization was performed using a stratified 6-fold cross-validation procedure. For each fold, a subset containing all the signals corresponding to an individual particle of each type is left outside the training dataset and used only for the test dataset. Finally, the accuracy was computed using the same procedure after the hyper-parameter tuning procedure.To assess the performance of several classification algorithms and achieve the best results, a comprehensive set of algorithms exploiting the modular framework of the The results obtained for the accuracy of each method are presented in Regarding the accuracy of the discrimination of particles itself, the confusion matrix for each algorithm was computed see , accumulFinally, it was also compared the performance of using all 3-channel information from the QPD against using only the This manuscript explored the possibility of classifying trapped particles on an optical tweezers setup by using scattered signal information from the trapping laser acquired by a quadrant photodetector. To perform dimensionality reduction and extraction of relevant features from the 3-channel time signal, a pre-processing procedure was introduced based on the transformation to the Fourier domain and subsequent principal components analysis. The processed data was then used to train and test various standard machine-learning classification models with a stratified cross-validation procedure. The results obtained suggest that this methodology can successfully discriminate a 6-class identification problem in controlled experimental conditions: polystyrene particles of 3 d signal ,19.Overall, compared with the previous literature on the topic ,19, we sTo finalize, we can also put the work in a broader perspective by discussing it at the application level. Indeed, while multiple experimental techniques are known capable of identifying micrometer size particles, the features of the OT systems offer an array of unique possibilities. For example, when compared with systems based on flow cytometry or electrodynamic balance ,35,36, O


This article proposes the integration of structural sizing, topology, and aerodynamic optimization for a morphing variable span of tapered wing (MVSTW) with the aim to minimize its weight. In order to evaluate the feasibility of the morphing wing optimization, this work creates a numerical environment by incorporating simultaneous structural sizing and topology optimization based on its aerodynamic analysis. This novel approach is proposed for an MVSTW. A problem-specific optimization approach to determine the minimum weight structure of the wing components for its fixed and moving segments is firstly presented. The optimization was performed using the OptiStruct solver inside HyperMesh. This investigation seeks to minimize total structure compliance while maximizing stiffness in order to satisfy the structural integrity requirements of the MVSTW. The aerodynamic load distribution along the wingspan at full wingspan extension and maximum speed were considered in the optimization processes. The wing components were optimized for size and topology, and all of them were built from aluminum alloy 2024-T3. The optimization results show that weight savings of up to 51.2% and 55.7% were obtained for fixed and moving wing segments, respectively. Based on these results, the optimized variable-span morphing wing can perform certain flight missions perfectly without experiencing any mechanical failures. Aeronautical engineering research has made substantial progress in the past few decades due to the aviation industry requirements . In globThe aviation industry has invested in developing novel types of aircraft with very good performance, capable of meeting diverse flight requirements. These objectives have prompted engineers to develop new design techniques for reducing aircraft weight. Our structural optimization method to reduce aircraft weight needs to utilize topology, size, and shape optimization approaches. Hence, aircraft configurations are subjected to different constraints that must be addressed during the optimization ,7. The TMultiple optimization techniques have been used in a variety of engineering design domains, and their application has spread throughout the field of aerospace engineering ,11. For Airbus has applied Topology optimization in the A380 aircraft design program to generate its new lighter aircraft components. The most well-known optimized components for the Airbus A380 are the leading-edge ribs and the fuselage door intercostals, which led to weight savings of approximately 1000 kg for each aircraft . The BoeOktay et al. ,18 conduThe Finite Element Method (FEM) and topology optimization (TO) have been linked with computer-aided engineering (CAE), and they are now considered the most advanced tools and methodologies in the aircraft design field. The combination of the FEM with TO makes it possible to obtain major weight reductions, thus resulting in material and fuel savings while maintaining the final product’s robustness properties ,20. FurtThe LARCASE laboratory at ÉTS presented a wide range of research activities in the multidisciplinary fields of aeroservoelasticity. Some of these studies were applied on unmanned aerial systems (UAS). The LARCASE team developed sophisticated methodologies for predicting the aerodynamic behavior and performance of the unmanned aerial systems UAS-S4 and UAS-S45 of Hydra Technologies ,23,24. TThe first part of this investigation deals with allocating the best locations of wing components inside the VSMTW, based on the results of our TO methodology . TO was Global aerospace and aviation centers have conducted a high number of studies which demonstrated the wing shape modification benefits. Our initial investigation dealt with calculating wing aerodynamic performance by utilizing Computational Fluid Dynamics (CFD). That work proved that the wing area’s increase using its span morphing technique led to increased aerodynamic performance, with its associated fuel consumption savings and expanded flight envelope range . FurtherAn optimized baseline wing was designed based on the TO results, and subsequently examined using Finite Element Analysis. Based on several test cases, this optimized wing demonstrated excellent mechanical behavior and reliable structural integrity for given boundary conditions .A baseline wing was designed using the telescopic mechanism and the variable-span morphing wing theory based on the aerodynamic optimization results . The winThe topology optimization method was performed in order to effectively allocate the internal structural elements inside both segments. The data and boundary conditions were computed at sea level altitude and maximum speed. Moreover, a safety factor of 1.5 and a 3 g load factor was added to the designed wing to overcome the various flight conditions. TO found that both segments must have two spars, with an optimal distance between them of 351.559 mm for the fixed segment, and 163.379 mm for the moving segment. TO also suggested seven ribs; the new configurations of spars and ribs is therefore illustrated in The ribs are situated in both segments in accordance with the topology optimization results from analyzing solid wing segments at the proposed locations, as listed in The aluminum alloy 2024-T3 was selected for the first topology optimization process. This investigation chose the same material to continue the optimization process with the aim to reduce wing component weight. The aluminum alloy 2024-T3 is an isotropic material with good durability and mechanical properties combined with high strength and resistance to fatigue. This material is commonly employed in the design of aircraft components. The aluminum alloy 2024-T3 material properties are represented in Γy)Γ. According to these regulations, aircraft structures must withstand static loads, that were determined in this paper by their corresponding aerodynamic pressures without causing any structural damage or failure. The fixed wing ribs were evaluated using the average values of lift loads calculated for the fixed segment. The same approach was chosen for the moving segment, with its load’s values listed in The combination of sizing and topology optimization (STO) is a powerful approach for reducing structural configuration weight while maintaining its overall stiffness and structural integrity . FurtherThis study’s main objective is the determination of the most efficient solution for producing lightweight components of a variable morphing wing while maintaining their optimal mechanical properties. Therefore, the STO results were obtained for ribs, spars, and support elements for each segment, and then were tested for the validation of their mechanical properties (displacements and stresses).Topology optimization is a mathematical method used to formulate, and then to determine an optimum distribution of a material within a pre-defined design space. An optimized structural material configuration within a design domain can be obtained by considering its specific boundary conditions and constraints. The structural design fundamental materials are treated as solid, whereas null materials are regarded as void. Hence, the unnecessary structural weight can be eliminated. A commercial topology optimization application, Atair’s OptiStruct, is used in this investigation to manage the given design constraints by defining the objective functions for individual load cases. This application was designed to manage the constraints with the aim to ensure that design specifications were satisfied; therefore, in this paper, essential materials of the design are established, and the process to eliminate redundant elements is defined. Minimizing the compliance while maximizing the structural stiffness under specific design constraints can indeed meet the design requirements.As mentioned above, the TO used in this study is combined with Finite Element Analysis (FEA), while the density-based approach is conducted. The design loads and parameters are applied to the wing components in order to deal with the material density distribution and its other mechanical properties .ix, of the ith element may take values between 0 and 1, or ix (0 ≤  ix  ≤  1), wherein the 0 value represents a material as void, and the 1 value represents the material as solid. The pseudo-density variable can be defined with the following equation:iρ is the density of the ith element, ρ0 is the density of the base element, and ix is the pseudo-density of the ith element.TO is based on the Solid Isotropic Material with Penalization (SIMP) method. The design domain is optimized by minimizing the objective function, which refers to the structural compliance. The objective function variable is the material density, that defines whether a finite element is solid or void. The pseudo-density, p is the exponent of the penalty parameter. Equation (5) can then be expanded the using the young modulus for solid and void regions:The formulation of the SIMP method defines the relationship between the material pseudo-density variable and its stiffness properties, as follows :(5)E(xi)p, should be selected to be large enough , so that the volume constraint is active when the intermediate densities are penalized. Since the intermediate densities are close to 0, the material is unnecessary and may be therefore considered void. Contrarily, if the intermediate densities are close to 1, the material is critical to the structure’s integrity and can be considered as solid [The penalty factor value, as solid .V denotes the total volume and iV expresses the volume of the ith element.The volume fraction is a constraint to the total volume of the design domain related to the pseudo-density, as represented in the following equation:x, in the formulation c(x) presents the volume fraction f is the load vector, V0 is the initial volume, and V is the final volume. K is the global stiffness matrix and U is the global displacement, such that KU equals F, the force vector. In addition, eu represents the displacement vector, and k0 is the elemental stiffness matrix.The objective function of the TO is to minimize the structural compliance, that is subjected to the design constraints and can be defined with the following mathematical statement:R. The filter radii around the centers of elements i and e are denoted by ir and er, respectively. The weighting function is ith element is iv [The shape of the density filter is selected as defined by Sigmund ,39. The nt is vi .V denotes the volume of the continuum, f is the distributed body force, u is the displacement area, t is the traction force, Fi represents the point load on the ith node, iu is the ith displacement degree of freedom, and S is the surface area of the continuum.In this study, the major objective is to minimize each component’s weight within the optimized span morphing wing. TO ensures the lightest possible wing weight by maximizing its static stiffness. Therefore, minimizing compliance is a means to increase the structural stiffness subjected to the set load. The compliance optimization can be expressed as follows :(10)C=∫VF is the nodal forces vector, and u is the nodal displacement. The nodal displacement can then be found with the following equation:The static stiffness can be obtained by applying static loading to wing components (for both segments). The deformation value under a static load refers to the displacement mechanical resistance . The stif(x) represents the objective function, g(x) denotes the constraints, x are the design variables, which are considered as independent variables of the f(x), and minx and maxx are the upper and lower bound constraints, respectively.As already mentioned, the main objective of the structural TO of the morphing wing design problem is to maximize the wing’s stiffness while minimizing its weight. The density-based approach is coupled with the static linear method , so thatThe TO algorithm coordinates the distribution of the material throughout the design domain by optimizing the user-defined objective function under certain constraints. In this study, each wing component’s design space for both segments was defined as a separate element in the optimization process.The gradient-based optimization method is widely utilized, as it is recognized as a very efficient method. The constraints’ screening process was applied to compute the set constraints, thereby minimizing the required gradients.The compliance of the static structural stiffness is completely transformed into potential deformation energy . The staThis investigation’s primary goal is to design a robust structure by reducing the weight of a variable-span morphing tapered wing (VSMTW). The main challenge is to combine the strength with light weight properties of the wing. The objective is to maximize the stiffness by optimizing the material distribution within the wing components’ volume space. Many factors must be considered in the optimization process, including the computational area, mesh generation, and boundary condition settings. For more accurate and reliable results, the pressure was calculated separately for each wing component. The optimization settings of the wing components were found as described in the following sub-sections .A baseline wing for both segments had a skin thickness of 2 mm for its optimization process. Size optimization (SO) was conducted in a 2D environment, and then the results were extended to a 3D environment, and they were further chosen to design the best possible wing skin . In factThe aerodynamic loads were applied, and the design variables were considered as scalar parameters. These parameters were defined for the optimization problem in this investigation because of the fact that the wing skin thickness influences the system responses. The optimization responses were defined for two variables, which were the design volume and the selected stress. The objective function concerned the minimization of the structural mass of the wing skin. The design constraints were determined in this investigation as the lower and upper bounds of the maximum stress values, which was less than 200 MPa due to the stress response based on the design variable. The design variable was defined with an initial value of 2 mm, with a lower bound of 0.5 mm and an upper bound of 2 mm ,45. The The spar is one of the most important wing components, as it can support the heaviest aerodynamic loads affecting the aircraft wing. A spar is designed as an extended beam along the wingspan, which supports the wing submitted to the bending load. Thus, it should withstand the impacts of shear, tensile, and compressive loads. In our project, the previous TO of baseline solid wings design suggested the use of two spars for each wing segment at defined locations, as shown in The structural weight was considered in the problem formulation for the wing spars, as the main aim of our design was to find the optimal wing structural parameters. This objective was used to determine the wing minimum weight while satisfying its strength, durability, and versatility constraints .The I-beam section was selected for modeling the wing spars (except at their connecting points with the ribs) because it provided high mechanical advantages compared to other beam section shapes. The I-beam shapes bear higher loads than the other beam section shapes, supported very well the other wing components, withstood mechanical fatigue (such as torsions and deformations), reduced the load intensity on the other wing components, and led to low costs and weight ,47.TO is an iterative process needed to reach the optimized system’s best-converged solution based on the objective function, and certain design constraints. In a 3D environment, all wing spars are subjected to the same analyses procedures . As the The baseline TO proposes seven ribs for both wing segments, as shown in The optimum material distribution inside the ribs was determined by the original design space configuration and the boundary conditions. A uniform tetrahedron mesh with elements of 3 mm in size was generated for the wing ribs for the two segments in order to implement TO. Both wing ribs were discretized into various elements, and their node numbers were based on their rib’s sizes.The initial design of the wing support elements, including its leading-edge ribs, trailing edge ribs, stringers, and stiffeners for the optimized wing based on the TO method were designed. The support elements of both wing segments were designed as shear webs to be stabilized against buckling loading, bending loading, torsion loading, and vertical shear loading. Other loads besides the aerodynamic loads and inertial loads applied to the wings can be considered in the design process according to their shapes and structural masses. In addition, the payload, expressed by electronic devices or surveillance cameras, can be carried on the wings and/or on the fuselage. This extra equipment adds more weight, thus contributing to the existing bending, shear, and torsion loads of the wing.The shear web structure of wing components provides a reliable design by enabling them to carry loads on the wing in different directions. The support elements’ structure for both segments of a VSMTW is shown in The current meshing and boundary conditions of support wing elements were similar to those of the spars and ribs. The layout of the support elements’ structure of the wing, the geometry of the mesh model, and its boundary conditions were established based on parametric data obtained from the aerodynamic investigation, as listed in The number of meshing elements and nodes differs for each component, depending on its dimensions. The attached area between wing components cannot change from its initial design. Therefore, the edges of the support element components and the loci binding to other wing components were considered as non-designable areas. Since there are various places where links must be made to connect the wing components, such as spars and ribs, these components were defined with fixed areas during the TO. They represent the bonding with other wing components, and thus they can be altered throughout the optimization.As described in the previous sections, aerodynamic analysis and optimization were conducted on the VSMTW for the UAS-S4 under different flight conditions . Thus, tAll these parameters were considered as either optimization objectives or constraints. Skin thickness and other wing components are known as sizing and topology variables, respectively. Sizing optimization (SO) of the wing skin for both segments was performed by adding the design constraints to the structural stiffness. A very small number of optimization iterations were used to converge rapidly towards the optimal solution by obtaining a highly efficient skin thickness, as shown in SO was performed on both wing segments. The interpretations of its results for both wing segments are shown in An initial wing skin thickness was chosen to be 2 mm for both wing segments. The FEM evaluations of a fixed and a moving wing skin are shown in The maximum stress value of the wing two segments skin was restricted to 200 MPa for the highest efficiency in order to withstand the aerodynamic loading acting on its surface. The same boundary condition was applied to both wing segments. Hence, SO and FEAs were based on the wing design volume and shape. The maximum deformations and stresses obtained under extreme flight conditions, as well as other important parameter values obtained from the optimization results, are shown in TO was implemented to determine the spars that would achieve wing maximum stiffness and reduce the weight. A Computational Fluid Dynamics (CFD) study of the wing structure was conducted to obtain high levels of fidelity. This analysis provided the pressure loading cases for extreme flight conditions. The aerodynamic analysis of the wing structure was performed at the sea level altitude and maximum speed (68 m/s) to ensure the optimal distribution of aerodynamic loading over the wingspan, as shown in The minimization of structural compliance using constraints is defined as a volume fraction by 30%. The design variable is the structural weight for an allocated global compliance-based stress. The TO results are summarized in TO based on the FE modeling of the wing spar is an iterative process, as shown in The merit of TO within OptiStruct is that the FE properties were updated depending on the optimization results. This component simulation-based TO approach guides detailed structural design and provides an alternative way to reduce wing spars’ structural weight. Furthermore, The same procedures applied to the wing spars were chosen for the wing ribs as well. An optimization approach based on the Finite Element Model (FEM) was implemented for each rib, depending on its calculated loading. The material density of each element was defined as a design variable. Two analysis responses expressed in terms of structural compliance and volume fraction were identified, in which the volume fraction was classified as a constraint, and the compliance was defined as an objective function. The typical setup of the TO led to compliance minimization by using the volume fraction parameter as a constraint; the converged solution was obtained using an iterative process, as illustrated in The FE models based on the TO process for the selected ribs shown in The optimized wing segments modeled as solid suggest that a wing should have strut elements obtained from TO in order to meet their strengths requirements. Various aerodynamic load scenarios obtained for extreme flight conditions were evaluated to design the support parts, as indicated in The basic structure of support elements was highly minimized based on the TO results, thereby reducing the support elements weights. Moreover, it is clear that the structural compliance decreased as the number of iterations increased, as shown in The main parameters’ values were calculated in the optimization analysis. The values of the results depended on the number of iterations and the mechanical analysis and they differed between each individual component of the support elements, as the forces and the geometric shapes differed from one support element to another. Several support elements were eliminated from the optimization process due to the difficulties in their implementation in terms of their geometrical and physical obstacles such as cylindrical shape.Generally, the morphing wing configuration is used for the accomplishment of multiple missions in an individual flight. The work presented here was applied on both Hydra Technologies’ UAS-S4 and UAS-S45 Baalam . First, The optimized wing model was built from aluminum 2024-T3, with its fixed and moving segments weighing 16.3 kg and 10.3 kg, respectively. The wing components’ structure manufacturing includes the arrangement of the spars, ribs, and support elements based on the TO results, and then, the design of a skeleton model of the wing structure. In the present optimization investigation, the TO method was performed on the wing components, including its spars and ribs. Minor support elements were eliminated from the TO method, as they were ineffective from a structural perspective.The highest challenge in this phase of optimization was the implementation of the TO on the fixed segment ribs. Given the space required to house the moving segment, we assumed that there should be a cavity in the middle of each rib, as seen in After incorporating the structural layout data of the optimized wing components in the whole design, the weights of the optimized wing components were reduced from 16.3 kg for the fixed wing segment and 10.3 kg for the moving wing segment to 7.96 kg and 4.57 kg, respectively.This article addresses recent advancements in integrating aerodynamic approaches and optimization methods in order to develop the concept of the morphing variable span of tapered wing (MVSTW) design. This phase of wing component optimization is subordinated to the previous topology optimization phase, which was used to allocate the wing components inside the MVSTW. The optimization was performed using Altair’s OptiStruct solver, connected with the aerodynamic research results obtained using the XFLR5 code. Then, these results were incorporated into SO and TO, and then utilized to solve relevant optimization problems.The optimization framework for wing components was developed in order to minimize the weights of the MVSTW components while optimizing their structure stiffnesses. The study’s main objective was to identify and thus assess the feasibility of implementing this optimization process for skin and internal wing elements, such as ribs, spars, and others. This novel technique was suggested for the MVSTW based on a telescopic mechanism, which involved sliding a telescopically stretched wing into a fixed wing segment. This approach increased the difficulty of our work by requiring us to pay high attention to wing several components during the optimization process. For example, the fixed wing ribs should have a cavity for sliding the moving segment into the wing to fit a complex geometric shape when applying SO and TO (or STO).This analysis aims to minimize the weight of the MVSTW by maximizing its stiffness and minimizing its total structural compliance parameters in order to reinforce structural durability, and to satisfy the MVSTW’s structural integrity criteria. The STO findings revealed an advantage in structural weight savings for fixed and moving wing parts components. When the weights of the baseline wing segments were compared to the weights of the optimized wing segments, the optimized wing components’ weights for both segments decreased from 16.3 kg to 7.96 kg for the fixed wing segment, and from 10.3 kg to 4.57 kg for the moving wing segment. Based on the TO results of both MVSTW segments, the wing components’ configurations, including the spars, ribs, and support elements, were redesigned and further developed. In addition, the wing skin was chosen depending on the SO results. The aerodynamic loads were distributed along wingspan length and further obtained under extreme flight conditions. Following the weight savings obtained by the STO techniques on the wing components, the optimized wing shape fulfilled the structural integrity design criteria.Future research will include additional investigations to develop a reliable adaptive morphing wing. Optimizations will be conducted on composite materials with the aim to achieve greater weight reduction in the MVSTW. Following the optimization of the wing segments using composite materials, the MVSTW configuration and its actuation mechanism integration will be evaluated. The gains obtained by these optimizations will further reduce the fuel consumption.


In recent years, the research on electroencephalography (EEG) has focused on the feature extraction of EEG signals. The development of convenient and simple EEG acquisition devices has produced a variety of EEG signal sources and the diversity of the EEG data. Thus, the adaptability of EEG classification methods has become significant. This study proposed a deep network model for autonomous learning and classification of EEG signals, which could self-adaptively classify EEG signals with different sampling frequencies and lengths. The artificial design feature extraction methods could not obtain stable classification results when analyzing EEG data with different sampling frequencies. However, the proposed depth network model showed considerably better universality and classification accuracy, particularly for EEG signals with short length, which was validated by two datasets. Epilepsy is characterized by recurrent seizures caused by the abnormal discharge of brain neurons, which often bring physical and psychological harm to patients. Approximately 50 million epilepsy patients have been documented globally, and epilepsy has become one of the most common nervous system diseases endangering human health worldwide. Brain wave is a synaptic postsynaptic potential generated by numerous neurons when the brain is active. It can record brain wave changes during brain activity and reflect the electrophysiological activities of the cerebral cortex or scalp surface of brain neurons . AccordiSince the 1980s, scholars have been conducting research on epilepsy based on electroencephalography (EEG), among which the identification of epilepsy by analyzing EEG data is one of the important research contents . With thWith the development of science and technology, the accuracy of medical EEG acquisition equipment has been improved. In addition, some portable EEG acquisition equipment has been developed. For example, emotive has been widely used in brain-computer interface –13 becauAt present, in-depth learning technology is a popular research area. Given this technology's autonomous learning characteristics from data, it can directly skip the manual design features and extraction process in the traditional methods, avoid the difficulties of manual design features in traditional methods, and manually adjust numerous parameters. In-depth learning technology can accomplish numerous tasks that are difficult to complete in the traditional methods . Some reThe remainder of this paper is organized as follows. This section first describes two open datasets and classifies and compares the EEG data at different sampling frequencies using an artificial design feature method and deep network autonomous feature learning method.The first dataset comes from the dataset published by Andrzejak et al. . This daThe second dataset was collected by Boston Children's Hospital . EEG sigThe signal is a cortical signal, the signal on the left side of the black line is no epilepsy, and the signal on the right side of the black line is epilepsy, as shown in The two datasets are the most widely used in the current research on epilepsy data classification and detection. Given that the sampling frequency of signals in the two datasets is fixed, we use the signal processing library in SciPy  to obtaik-nearest neighbor (k-NN), linear classifier (LDA), support vector machine (SVM), decision tree (DT), multilayer perceptron (MLP), and Gaussian naive Bayes (GNB). These classification algorithms adopt self-contained parameters in the library. Tables Features or design new features should be selected for classification based on the artificial design feature extraction method. The current study selects the feature extraction methods –27, whicTables k-NN decreases, and those of LDA and SVM change substantially. This section presents the classification results of the self-learning feature method based on the convolutional neural network (CNN) for the preceding datasets. Tables The results of training and testing for the same sampling frequency data are listed in Tables 1This section first describes the model structure based on CNN and the training methods for different length sample data.Numerous methods of feature extraction are based on artificial design. However, when the data changes, the classification effect based on the general feature extraction method is not stable. In this study, the classification model based on CNN can independently learn and classify data features, including the two steps of feature extraction and classification see . It atteThe left side is a classification process based on artificial design features, which requires two steps. The right side is to input data into the network model and output the classification results directly, as shown in X. The convolutional layer is equivalent to the feature extractor. This layer uses multiple convolution kernels to convolute x and obtains several feature maps that can keep the main components of the input signal. The convolution calculation formula is as follows:fnk represents the feature map of layer k, fmk−1 is the feature map of the upper layer, wm,nk represents the convolution kernels of the mth feature map of layer k − 1 to the nth feature map of layer k, bnk is the neuron bias, and gk(·) is the activation function. When k = 1, that is, the first convolution operation on sample data, fmk−1 = x and M = 1, because only one feature map in the upper layer is x and N is the number of convolution kernels. Given that the input data X is one-dimensional, the feature map fnk output by convolution operation is also one-dimensional. In this model, the pooling operation divides fnk with length l into J regions of equal length without overlap, and each region has i/j elements and extracts the maximum value from each region. Hence, the size of the feature map can be reduced to a downsampling. In this way, the strongest features in each region can be selected, and the ability to distinguish the overall features of the model can be enhanced. After the pooling operation, fnk changes from the original length l to j, where the maximum pooling operation is pk, and i = l/j is the reduction ratio of the feature map. Thereafter, the pooling operation is as follows:CNN is a feedforward neural network that improves the classification ability of patterns by posterior probability. The network mainly includes convolutional, pooling, fully connected, and softmax layers. The convolution layer convolutes the input signal data through different convolution kernels to obtain the feature map . The pooling layer is the process of downsampling the feature map obtained from the convolution operation of the upper layer. The network often increases the network depth by iterating the convolutional and pooling layers. Meanwhile, the fully connected layer connects all feature maps from the upper layer to the hidden layer of a common neural network and eventually outputs the classification results through the softmax layer. This study proposes a multilayer network with cubic iterative convolutional and pooling layers, fully connected layer, and softmax layer to classify EEG data (hereinafter referred to as CNN-E). The model classifies the one-dimensional EEG data of a single channel and makes the input sample data fnk−1. The output of all neurons in the upper layer fnk−1 is mapped to a dimension array V by reshape operation, and V is input to the fully connected layer. Thereafter, the fully connected layer can be expressed as follows:wc and bc are the weights and biases, respectively, of the fully connected layer and c is the output of the fully connected layer. Lastly, the final result is output via softmax, and the operation is as follows:Each neuron in the fully connected layer connects to all neurons in the upper layer y is obtained.The classification result N training samples, xi)( represents a sample labeled li)(. Sample xi). Although there are considerable differences in the spectral characteristics of samples when the input sample signal is supplemented, the CNN-E model can extract deep features and reduce the feature dimension of the samples. Hence, the model achieves a good classification effect.In practical application, the EEG classification model faces different sampling frequency data and can also process different lengths of signal data. However, numerous artificial design features have constraints on data length when extracting features. For example, when data length is only one second or the sampling frequency is not high, meaningful time-domain, frequency-domain, or nondynamic features cannot be extracted. Previous classification studies are mostly based on time windows. All samples are divided into new sample sets according to a certain length of time windows, and training and test sets are divided thereafter for training and testing, respectively, the model. Given that the proposed model can be adapted to different lengths of the sample data, we use the experiments in the previous section as bases in utilizing different lengths of time windows to segment the sample data without overlap. The window length is 1 sec, 2 seconds to the signal length. If the sample length of dataset 1-0 is 23.6 sec, then its maximum window length is 23 sec. The sample length of dataset 2 is 16 sec, and its maximum window length is 16 sec. In real life, there are diverse types of EEG signals. The current research on EEG classification has focused on classification accuracy, but the universality of the methods has seldom been discussed. To solve the problem, this study constructed a CNN-E classification model based on CNN. The model could be applied to classify EEG signals with different sampling frequencies and could be adapted to signals of different lengths. This study also analyzed the possible problems in the classification of EEG signals with different sampling frequencies by the traditional feature extraction-based classification method. Our results showed that the traditional method has relied heavily on the design of the feature extraction method, and there were difficulties in feature design and selection. Moreover, the classification accuracy fluctuated substantially for EEG data with different sampling frequencies. These feature extraction methods had length constraints when processing samples with short data length. However, the CNN-E model could independently learn the characteristics of the sample data and could be adapted to all types of data length because of the use of effective data completion methods. Our results showed that the CNN-E model performed well in the classification of EEG data at the same sampling frequency, at different sampling frequencies, and at different lengths.Although we only used two different datasets to test the robustness of the CNN-E model, we would use additional datasets to validate the reliability of this model in the future. Moreover, the performance of the CNN-E model, particularly the visual expression of the features learned by the CNN network, needs further improvement.