Multiple Time Windows Research Articles

An efficient two-phase heuristic for the home care routing and scheduling problem

This paper focuses on modeling and solving the home health care routing and scheduling problem (HHCRSP) with the consideration of skill requirements, multiple time windows, multiple services and caregivers’ duty length. A new mixed integer linear programming (MILP) model is proposed to build a daily schedule in order to minimize caregivers’ waiting times and to balance their workloads. The complexity of this problem, which is an extended version of the NP-hard VRPTW problem, emerges during the numerical resolution of random instances. To overcome these difficulties, we proposed a two-phase approach to solve the problem under study in a reasonable amount of computational time. The first phase consists of applying a simulated annealing (SA) based heuristic to generate caregivers’ routes and their assignment while the second one aims to select, for each patient, a time window, ensure the synchronization of simultaneous services and define the timetable of visits. Computational results show that the proposed two-phase approach is very efficient, fast and outperforms state-of-art heuristics and exacts methods in terms of CPU running time and solution quality.

Multisegmented Intelligent Solution for MT-HVDC Grid Protection

Fault detection continues to be a relevant and ongoing topic in multiterminal High Voltage Direct Current (MT-HVDC) grid protection. In MT-HVDC grids, however, high DC-fault currents result from a failure of a complex protective threshold in traditional protection schemes, making Voltage Source Converter (VSC) vulnerable to such potent transient currents. In this innovative single-ended DC protection scheme, multiple time window segments are used to consider the effects of the transient period across limiting inductors at each end of the link. Multiple segments of 0–0.8, 0.8–1.5, and 1.5–3.0 ms reduce relay failure and improve the sensitivity to high fault impedance while requiring minimal computational effort. It employs feature extraction tools such as Stationary Wavelet Transform and Random Search (RS)-based Artificial Neural Networks (ANNs) for detecting transmission line faults within DC networks. Its goal is to improve the accuracy and reliability of protective relays as a result of various fault events. Simulations showed that the proposed algorithms could effectively identify any input data segment and detect DC transmission faults up to 500 ohms. Accuracy for the first segment is 100% for fault impedance up to 200 ohms, whereas the second and third segments show 100% accuracy for high impedance faults up to 400 ohms. In addition, they maintain 100% stability even under external disturbances.

Energy-efficient predictive control for trams incorporating disjunctive time constraints from traffic lights

Tram operations are often blocked by traffic lights, leading to frequent decelerations and re-accelerations that increase operational energy consumption. This paper focuses on tram energy-efficient control problem incorporating time constraints from traffic lights that have multiple feasible green time windows (GTWs). We formulate the problem as a mixed-integer nonlinear program (MINLP), where binary variables are assigned to model disjunctive time constraints of the GTWs. To address computational challenge of solving the MINLP, we reformulate it as a tractable nonlinear program (NLP). Specifically, an equivalent NLP is first presented by replacing the integrality constraint with nonlinear constraints, and then the nonlinear constraints are relaxed and penalized into cost functions. To recover a solution of the MINLP, we propose a computationally efficient sequential quadratic programming algorithm in a shrinking horizon model predictive control framework, which updates the penalty parameter and quadratic programming subproblems in parallel. The solution obtained from the subproblem is feasible in each iteration, and convergence of the feasibility iterations can be enforced by the updated penalty. The performance of the proposed approach is investigated on different scenarios using real-life tram data. Results show that the method is able to generate energy-efficient driving trajectories in a dynamic environment, while crossing traffic lights in effective GTWs without unnecessary decelerations and re-accelerations.

A Hybrid ToF Image Sensor for Long-Range 3D Depth Measurement Under High Ambient Light Conditions

A new indirect time of flight (iToF) sensor realizing long-range measurement of 30 m has been demonstrated by a hybrid ToF (hToF) operation, which uses multiple time windows (TWs) prepared by multi-tap pixels and range-shifted subframes. The VGA-resolution hToF image sensor with 4-tap and 1-drain pixels, fabricated by the BSI process, can measure a depth of up to 30 m for indoor operation and 20 m for outdoor operation under high ambient light of 100 klux. The new hToF operation with overlapped TWs between subframes for mitigating an issue on the motion artifact is implemented. The sensor works at 120 frames/s for a single subframe operation. Interference between multiple ToF cameras in IoT systems is suppressed by a technique of emission cycle-time changing.

Impact of sensor data pre-processing strategies and selection of machine learning algorithm on the prediction of metritis events in dairy cattle

With all the sensor data currently generated at high frequency in dairy farms, there is potential for earlier diagnosis of postpartum diseases compared with traditional monitoring methodologies. Our objectives were 1) to compare the impact of sensor data pre-processing on classifier performance by using multiple time windows before a given metritis event, while considering other cow-level factors and farm-scheduled activities; 2) to compare the performance of random forest (RF), k-nearest neighbors (k-NN), and support vector machine (SVM) classifiers at different decision thresholds using different number of past observations (time-lags) for the detection of behavioral patterns associated with changes in metritis scores; and 3) to compare classifier performance between each one of the five behaviors registered every hour by an ear-tag 3-axis accelerometer (CowManager, Agis Autimatisering, Harmelen, Netherlands). A total of 239 metritis events were created by comparing metritis scores between two consecutive clinical evaluations from cows that were retrospectively selected from a dataset containing sensor data and health information during the first 21 days postpartum from June 2014 to May 2017. Hourly sensor data classified by the accelerometer as either ruminating, eating, not active (including both standing or lying), and two different levels of activity (active and high activity) behaviors corresponding to the 3 days before each metritis event were aggregated every 24-, 12-, 6-, and 3-hour time windows. Multiple time-lags were also used to determine the optimal number of past observations needed for optimal classification. Similarly, different decision thresholds were compared in terms of model performance. Depending on the classifier, algorithm hyperparameters were optimized using grid search (RF, k-NN, SVM) and random search (RF). All behaviors changed throughout the study period and showed distinct daily patterns. From the three algorithms, RF had the highest F1 score followed by k-NN and SVM. Furthermore, sensor data aggregated every 6- or 12-h time windows had the best model performance at multiple time-lags. We concluded that the data from the first 3 days post-partum should be discarded when studying metritis, and either one of the five behaviors measured with CowManager could be used when predicting metritis when sensor data were aggregated every 6- or 12-hour time windows, and using time-lags corresponding to 2–3 days before a given event, depending on the time window used. This study shows how to maximize sensor data in their potential for disease prediction, enhancing the performance of algorithms used in machine learning.

Anomalous Attenuation of High‐Frequency Seismic Waves in Taiwan: Observation, Model and Interpretation

AbstractHigh resolution maps of seismic attenuation parameters in Taiwan have been obtained from a modified “Multiple Lapse Time Window Analysis” (MLTWA). At most of the stations in porous sedimentary and highly faulted areas in Taiwan, the conventional modeling of MLTWA based on the scalar theory of radiative transfer in a half‐space with isotropic scattering fails to explain the spatio‐temporal distribution of the whole S‐wave train. Using Monte Carlo simulations of wave transport, we demonstrate that this anomalous energy distribution in the coda may be modeled by multiple anisotropic scattering of seismic waves. In addition to the scattering quality factor , we introduce a parameter (independent of ) which determines the angular redistribution of energy upon scattering (scattering anisotropy). We inverted the attenuation parameters , and g in three frequency bands (1–2, 2–4, and 4–8 Hz). Overall, Taiwan is more attenuating than most orogens with a mean effective scattering loss and a mean intrinsic absorption of 2.5 × 10−3 and 9 × 10−3 at 1.5 Hz, respectively. Scattering loss varies over more than one order of magnitude across Taiwan while absorption variations reach approximately 30%. The more attenuating zones are the Coastal Range and the Coastal Plain where scattering dominates over absorption at low frequency, and inversely at high frequency. These regions are also characterized by strong backscattering ( < −0.85) at 1.5 Hz and rather high ratio. We propose that the observed strong back‐scattering at low frequency, related to large impedance fluctuations in the crust, is induced by the presence of fluids.

Bi-level optimization for customized bus routing serving passengers with multiple-trips based on state–space–time network

The emerging customized bus (CB) can serve personalized trip requests in a more flexible and convenient way, especially for passengers who have multiple-trip requests in a short time period. Considering the CB service for passengers with multiple trips (CSPMT), a loading-state-oriented state–space–time network-based bi-level programming model is proposed to optimize the routing of CBs, with the objectives of maximizing the operational profit and minimizing the travel cost, while considering the characteristics of multiple trips, time windows, capacity and mixed loads. Besides, a nested algorithm combining the genetic algorithm (GA) and the augmented Lagrangian relaxation-based dynamic programming algorithm is proposed. Then, the proposed model and algorithm are verified and analyzed through a Sioux Falls network and a Beijing sketch network. It can be found from the results that the method can optimize a CB routing plan for passengers with multiple-trip requests and for different network scales. The proposed bi-level model and corresponding algorithm can better adapt to passengers’ personalized trip requests, and promote a higher level of public transport service which will attract more residents from private cars to public transportation, ultimately reducing energy consumption and exhaust emissions, and promoting the sustainable development of modern metropolises.

An adaptive large neighborhood search algorithm for Vehicle Routing Problem with Multiple Time Windows constraints

<p style='text-indent:20px;'>The Vehicle Routing Problem with Multiple Time Windows (VRPMTW) is a generalization of problems in real life logistics distribution, which has a wide range of applications and research values. Several neighborhood search based methods have been used to solve this kind of problem, but it still has drawbacks of generating numbers of infeasible solutions and falling into local optimum easily. In order to solve the problem of arbitrary selection for neighborhoods, a series of neighborhoods are designed and an adaptive strategy is used to select the neighborhood, which constitute the Adaptive Large Neighborhood Search(ALNS) algorithm framework. For escaping from the local optimum effectively in the search process, a local search based on destroy and repair operators is applied to shake the solution by adjusting the number of customers. The proposed method allows infeasible solutions to participate in the iterative process to expand the search space. At the same time, an archive is set to save the high-quality feasible solutions during the search process, and the infeasible solutions are periodically replaced. Computational experimental results on VRPMTW benchmark instances show that the proposed algorithm is effective and has obtained better solutions.</p>

Study of MI-BCI classification method based on the Riemannian transform of personalized EEG spatiotemporal features.

Motor imagery (MI) is a traditional paradigm of brain-computer interface (BCI) and can assist users in creating direct connections between their brains and external equipment. The common spatial patterns algorithm is the most popular spatial filtering technique for collecting EEG signal features in MI-based BCI systems. Due to the defect that it only considers the spatial information of EEG signals and is susceptible to noise interference and other issues, its performance is diminished. In this study, we developed a Riemannian transform feature extraction method based on filter bank fusion with a combination of multiple time windows. First, we proposed the multi-time window data segmentation and recombination method by combining it with a filter group to create new data samples. This approach could capture individual differences due to the variation in time-frequency patterns across different participants, thereby improving the model's generalization performance. Second, Riemannian geometry was used for feature extraction from non-Euclidean structured EEG data. Then, considering the non-Gaussian distribution of EEG signals, the neighborhood component analysis (NCA) algorithm was chosen for feature selection. Finally, to meet real-time requirements and a low complexity, we employed a Support Vector Machine (SVM) as the classification algorithm. The proposed model achieved improved accuracy and robustness. In this study, we proposed an algorithm with superior performance on the BCI Competition IV dataset 2a, achieving an accuracy of 89%, a kappa value of 0.73 and an AUC of 0.9, demonstrating advanced capabilities. Furthermore, we analyzed data collected in our laboratory, and the proposed method achieved an accuracy of 77.4%, surpassing other comparative models. This method not only significantly improved the classification accuracy of motor imagery EEG signals but also bore significant implications for applications in the fields of brain-computer interfaces and neural engineering.

Solving a pickup and delivery routing problem for fourth‐party logistics providers

AbstractThis paper studies a pickup and delivery routing problem for fourth‐party logistics providers. The problem aims to schedule routes of vehicles to pick up orders from suppliers and deliver them to factory locations considering multiple time windows at suppliers and factory locations, a non‐conventional cost structure, and certain factory dock constraints. We formulate the problem as a mathematical model and develop an efficient algorithm based on the adaptive large neighborhood search to solve the problem. The algorithm incorporates several heuristics to efficiently explore the search space for optimal solutions. The algorithm is refined through extensive statistical experiments to optimize the performances of the heuristics and to tune the parameters of the algorithm. The mathematical model and algorithm are evaluated on several problem instances based on a real case study in Europe. The numerical results demonstrate that the solution algorithm consistently obtains near‐optimal solutions to real‐sized problem instances.

Showcasing model performance across space and time using single diagrams

Model states are often validated against observations to establish the veracity of the model. However, when a model state is compared with multiple in-situ observations scattered in space, no single diagram exists that can showcase the statistical measure of correlation, root mean square error and the standard deviations of the concerned variables across all the locations. We present a simple but efficient representation of correlation, root mean square error and standard deviation of the model and the observation across multiple in-situ locations in a single diagram and name it as the “Performance Across Space (PAS)” diagram. We also present a diagram that showcases the comparison of model state and observation at a single location across multiple time windows in a single diagram and call it “Performance Across Time (PAT)” diagram. We highlight the effectiveness of these diagrams through realistic ocean models and realistic in-situ observations. We show using a PAT diagram that the ocean model NEMO fares better in simulating ocean sea surface temperature during boreal winters compared to boreal summers. We also illustrate how the PAS diagrams can be used in assessing the efficacy of data assimilation. Though the examples shown here are from the field of oceanography, the display mechanism can be extended to any field.

The Vehicle Routing Problem with Availability Profiles

In business-to-consumer (B2C) parcel delivery, the presence of the customer at the time of delivery is implicitly required in many cases. If the customer is not at home, the delivery fails—causing additional costs and efforts for the parcel service provider as well as inconvenience for the customer. Parcel service providers typically report high failed-delivery rates, as they have limited possibilities to arrange a delivery time with the recipient. We address the failed-delivery problem in B2C parcel delivery by considering customer-individual availability profiles (APs) that consist of a set of time windows, each associated with a probability that the delivery is successful if conducted in the respective time window. To assess the benefit of APs for delivery tour planning, we formulate the vehicle routing problem with availability profiles (VRPAP) as a mixed integer program, including the trade-off between transportation and failed-delivery costs. We provide analytical insights concerning the model’s cost-savings potential by determining lower and upper bounds. In order to solve larger instances, we develop a novel hybrid adaptive large neighborhood search (HALNS). The HALNS is highly adaptable and also able to solve related time-constrained vehicle routing problems (i.e., vehicle routing problems with hard, multiple, and soft time windows). We show its performance on these related benchmark instances and find a total of 20 new best-known solutions. We additionally conduct various experiments on self-generated VRPAP instances to generate managerial insights. In a case study using real-world data, despite little information on the APs, we were able to reduce failed deliveries by approximately 12% and overall costs by 5%. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.1182 .

A Robust Possibilistic Programming Approach for a Road-Rail Intermodal Routing Problem with Multiple Time Windows and Truck Operations Optimization under Carbon Cap-and-Trade Policy and Uncertainty

This study investigates a road-rail intermodal routing problem in a hub-and-spoke network. Carbon cap-and-trade policy is accommodated with the routing to reduce carbon dioxide emissions. Multiple time windows are employed to enhance customer flexibility and achieve on-time pickup and delivery services. Road service flexibility and resulting truck operations optimization are explored by combining truck departure time planning under traffic restrictions and speed optimization with the routing. To enhance the feasibility and optimality of the problem optimization, the routing problem is formulated in a fuzzy environment where capacity and carbon trading price rate are trapezoidal fuzzy parameters. Based on the customer-centric objective setting, a fuzzy nonlinear optimization model and its linear reformation are given to formulate the proposed routing problem that combines distribution route design, time window selection and truck operations optimization. A robust possibilistic programming approach is developed to optimize the routing problem by obtaining its robust solutions. A case study is presented to demonstrate the feasibility of the proposed approaches. The results show that the multiple time windows and truck operations optimization can lower the total costs, enhance the optimality robustness and reduce carbon dioxide emissions of the routing optimization. The sensitivity analysis finds that increasing the lower bound of the confidence level in the robust possibilistic programming model improve the robustness and environmental sustainability; however, worsen the economy of the routing optimization.

Optimizing modeling windows to better capture the long-term variation of PM2.5 concentrations in China during 2005–2019

Including data of different time intervals during model development influences the predicting accuracy of PM2.5 but has not been widely discussed. Therefore, we included modeling data with multiple time windows to identify optimized modeling time windows for capturing the long-term variation of PM2.5 in China during 2005–2019. In general, we incorporated PM2.5 measurements, aerosol optical depth (AOD), meteorological parameters, land use data, and other predictors to train random forest models. The study period was separated into two phases (2013–2019 and 2005–2012) according to the availability of PM2.5 measurements. First, we trained models with two strategies of choosing time windows to compare model performance in predicting PM2.5 from 2013 to 2019, when measurements were available. Strategy 1a (ST1a) refers to training one model with all available data, and Strategy 1b (ST1b) refers to training multiple models each with one-year data. Second, we trained models with additional ten strategies (ST2a-ST2j) based on data from different time windows during 2013–2019 to compare the accuracy in predicting PM2.5 before 2013, when measurements were unavailable. The internal and external cross-validation (CV) indicated that the model performance of ST1b was better than ST1a. Predictions based on ST1a tended to underestimate PM2.5 levels in 2013 and 2014 when PM2.5 concentrations were high, and overestimate after 2017 when PM2.5 dropped dramatically. The external CV of predicting historical PM2.5 was the most robust in ST2i (averaged predictions from two models developed by 2013 and 2014 data, respectively). Models with data closer to historical years and PM2.5 levels performed better in predicting historical PM2.5 concentrations. Our results suggested that training models with data of current-years performed better during 2013–2019, and with data of 2013 and 2014 performed better in predicting historical PM2.5 before 2013 in China. The comparison provided evidence for choosing optimized time windows when predicting long-term PM2.5 concentrations in China.

Unrelated parallel machine scheduling with multiple time windows: An application to earth observation satellite scheduling

In this paper, we investigate a variant of the unrelated parallel machine scheduling problem with multiple time windows that is widely employed in the scheduling of earth observation satellites. Two mixed-integer linear programming formulations are proposed based on the concept of non-immediate precedence and the deep analysis of the relationship of time windows. To facilitate the problem solving, we develop a bidirectional rolling horizon preprocessing algorithm to reduce the problem size. Based on detailed overlapping analysis, more inequalities are obtained to tighten the formulations. Furthermore, the dominance among derived inequalities is analyzed, and only nondominated inequalities are appended to limit the size of the problem. The proposed formulation and algorithm can optimally solve instances of up to 800 jobs and 20 machines within 20 min. Moreover, to verify the practicality of our method, we also conducted numerous experiments on realistic instances of satellite scheduling. The experimental results prove that our algorithm is effective for obtaining optimal solutions and can be applied in practice.

The Prevalence of Psychotic Symptoms, Violent Ideation, and Disruptive Behavior in a Population With SARS-CoV-2 Infection: Preliminary Study.

BackgroundThe COVID-19 disease results from infection by the SARS-CoV-2 virus to produce a range of mild to severe physical, neurological, and mental health symptoms. The COVID-19 pandemic has indirectly caused significant emotional distress, triggering the emergence of mental health symptoms in individuals who were not previously affected or exacerbating symptoms in those with existing mental health conditions. Emotional distress and certain mental health conditions can lead to violent ideation and disruptive behavior, including aggression, threatening acts, deliberate harm toward other people or animals, and inattention to or noncompliance with education or workplace rules. Of the many mental health conditions that can be associated with violent ideation and disruptive behavior, psychosis can evidence greater vulnerability to unpredictable changes and being at a greater risk for them. Individuals with psychosis can also be more susceptible to contracting COVID-19 disease.ObjectiveThis study aimed to investigate whether violent ideation, disruptive behavior, or psychotic symptoms were more prevalent in a population with COVID-19 and did not precede the pandemic.MethodsIn this preliminary study, we analyzed questionnaire responses from a population sample (N=366), received between the end of February 2021 and the start of March 2021 (1 year into the COVID-19 pandemic), regarding COVID-19 illness, violent ideation, disruptive behavior, and psychotic symptoms. Using the Wilcoxon rank sum test followed by multiple comparisons correction, we compared the self-reported frequency of these variables for 3 time windows related to the past 1 month, past 1 month to 1 year, and >1 year ago among the distributions of people who answered whether they tested positive or were diagnosed with COVID-19 by a clinician. We also used multivariable logistic regression with iterative resampling to investigate the relationship between these variables occurring >1 year ago (ie, before the pandemic) and the likelihood of contracting COVID-19.ResultsWe observed a significantly higher frequency of self-reported violent ideation, disruptive behavior, and psychotic symptoms, for all 3 time windows of people who tested positive or were diagnosed with COVID-19 by a clinician. Using multivariable logistic regression, we observed 72% to 94% model accuracy for an increased incidence of COVID-19 in participants who reported violent ideation, disruptive behavior, or psychotic symptoms >1 year ago.ConclusionsThis preliminary study found that people who reported a test or clinician diagnosis of COVID-19 also reported higher frequencies of violent ideation, disruptive behavior, or psychotic symptoms across multiple time windows, indicating that they were not likely to be the result of COVID-19. In parallel, participants who reported these behaviors >1 year ago (ie, before the pandemic) were more likely to be diagnosed with COVID-19, suggesting that violent ideation, disruptive behavior, in addition to psychotic symptoms, were associated with COVID-19 with an approximately 70% to 90% likelihood.

Quantitative Analysis Using Consecutive Time Window for Unobtrusive Atrial Fibrillation Detection Based on Ballistocardiogram Signal.

Atrial fibrillation (AF) is the most common clinically significant arrhythmia; therefore, AF detection is crucial. Here, we propose a novel feature extraction method to improve AF detection performance using a ballistocardiogram (BCG), which is a weak vibration signal on the body surface transmitted by the cardiogenic force. In this paper, continuous time windows (CTWs) are added to each BCG segment and recurrence quantification analysis (RQA) features are extracted from each time window. Then, the number of CTWs is discussed and the combined features from multiple time windows are ranked, which finally constitute the CTW–RQA features. As validation, the CTW–RQA features are extracted from 4000 BCG segments of 59 subjects, which are compared with classical time and time-frequency features and up-to-date energy features. The accuracy of the proposed feature is superior, and three types of features are fused to obtain the highest accuracy of 95.63%. To evaluate the importance of the proposed feature, the fusion features are ranked using a chi-square test. CTW–RQA features account for 60% of the first 10 fusion features and 65% of the first 17 fusion features. It follows that the proposed CTW–RQA features effectively supplement the existing BCG features for AF detection.

New exact and heuristic algorithms to solve the prize-collecting job sequencing problem with one common and multiple secondary resources

We study the prize-collecting job sequencing problem with one common and multiple secondary resources. In this problem, a set of jobs is given, each with a profit, multiple time windows for its execution, and a duration during which it requires the main resource. Each job also requires a preassigned secondary resource before, during, and after its use of the main resource. The goal is to select and schedule the subset of jobs that maximize the total profit. We present a new mixed integer linear programming formulation of the problem and a branch-cut-and-price algorithm as an exact solution method. We also introduce a heuristic algorithm to tackle larger instances. Extensive numerical experiments show that our exact algorithm can solve to optimality literature instances with up to 500 jobs for a particular dataset and up to 250 jobs for another dataset with different characteristics. Our heuristic builds high-quality solutions in a small computational time. It computes new best-known solutions for most of the larger instances.

Fault Diagnosis Method and Application of ESP Well Based on SPC Rules and Real-Time Data Fusion

Aiming at the popularization and application of a real-time monitoring parameter acquisition system of the electric submersible pump (ESP) well, this paper proposes a fault diagnosis method of ESP well operation based on the SPC rule and prior knowledge fusion. Based on the study of parameter variation rules of ESP well, the SPC expansion rule model is established; by analyzing the variation of some typical characteristic parameters of ESP well, combined with SPC expansion rules and expert experience, a priori knowledge of fault diagnosis of ESP well is formed, that is, multiparameter fault analysis table and weight factor; the SPC extended rule model and prior knowledge are fused to establish the fault probability model of ESP well, form the fault diagnosis method of ESP well, develop the online fault diagnosis software of ESP well, and deploy it in 425 ESP wells in a block. Taking five types of tubing leakage, pump wear, shaft breakage, gas influence, and pump plugging as examples, the application process of fault diagnosis method is analyzed. The research and application show that compared with other fault diagnosis methods, this method needs a smaller time window and higher diagnosis accuracy. By setting multiple time windows, this diagnosis method is applied to calculate the fault probability of ESP well in real time, solve the real time and accurate identification of 14 sudden faults and gradual faults, and significantly improve the intelligent diagnosis level of production faults of ESP well.

Feature Extraction Method Based on Filter Banks and Riemannian Tangent Space in Motor-Imagery BCI.

Optimal feature extraction for multi-category motor imagery brain-computer interfaces (MI-BCIs) is a research hotspot. The common spatial pattern (CSP) algorithm is one of the most widely used methods in MI-BCIs. However, its performance is adversely affected by variance in the operational frequency band and noise interference. Furthermore, the performance of CSP is not satisfactory when addressing multi-category classification problems. In this work, we propose a fusion method combining Filter Banks and Riemannian Tangent Space (FBRTS) in multiple time windows. FBRTS uses multiple filter banks to overcome the problem of variance in the operational frequency band. It also applies the Riemannian method to the covariance matrix extracted by the spatial filter to obtain more robust features in order to overcome the problem of noise interference. In addition, we use a One-Versus-Rest support vector machine (OVR-SVM) model to classify multi-category features. We evaluate our FBRTS method using BCI competition IV dataset 2a and 2b. The experimental results show that the average classification accuracy of our FBRTS method is 77.7% and 86.9% in datasets 2a and 2b respectively. By analyzing the influence of the different numbers of filter banks and time windows on the performance of our FBRTS method, we can identify the optimal number of filter banks and time windows. Additionally, our FBRTS method can obtain more distinctive features than the filter banks common spatial pattern (FBCSP) method in two-dimensional embedding space. These results show that our proposed method can improve the performance of MI-BCIs.