Hybrid Machine Learning Method Research Articles

Hybrid Machine Learning and Geostatistical Methods for Gap Filling and Predicting Solar-Induced Fluorescence Values

Sun-induced chlorophyll fluorescence (SIF) has proven to be advantageous in estimating gross primary production, despite the lack of a stable relationship. Satellite-based SIF measurements at Level 2 offer comprehensive global coverage and are available in near real time. However, these measurements are often limited by spatial and temporal sparsity, as well as discontinuities. These limitations primarily arise from incomplete satellite trajectories. Additionally, variability in cloud cover and periodic issues specific to the instruments can compromise data quality. Two families of methods have been developed to address data discontinuity: (1) machine learning-based gap-filling techniques and (2) geostatistical techniques (various forms of kriging). The former techniques utilize the relationships between ancillary data and SIF, while the latter usually rely on the available SIF data recordings and their covariance structure to provide estimates at unsampled locations. In this study, we create a synthetic approach for SIF gap filling by hybridizing the two approaches under the umbrella of kriging with external drift. We performed leave-one-out cross-validation of the OCO-2 SIF retrieval aggregates for the entire year of 2019, comparing three methods: ordinary kriging, ML-based estimation using ancillary data, and kriging with external drift. The Mean Absolute Error (MAE) for ML, ordinary kriging, and the hybrid approach was found to be 0.1399, 0.1318, and 0.1183 mW m2 sr−1 nm−1, respectively. We demonstrate that the performance of the hybrid approach exceeds both parent techniques due to the incorporation of information from multiple resources. This use of multiple datasets enriches the hybrid model, making it more robust and accurate in handling the spatio-temporal variability and discontinuity of SIF data. The developed framework is portable and can be applied to SIF retrievals at various resolutions and from various sources (satellites), as well as extended to other satellite-measured variables.

Predicting corrosion behaviour of steel reinforcement in eco-friendly coral aggregate concrete based on hybrid machine learning methods

ABSTRACT This study proposes a machine learning-assisted method for assessing steel reinforcement corrosion, utilising data on chloride ion concentration (CIC) and chloride ion concentration threshold (CCT) from eco-friendly coral aggregate concrete (EFCAC). A total of 2185 data points were collected to establish the EFCAC-CIC database. A multi-objective slime mould optimised support vector regression (MOSMA-SVR) model for EFCAC-CIC was developed. The significance of each feature to EFCAC-CIC was analysed. Subsequently, a graphical user interface (GUI) was developed based on the MOSMA-SVR model. Finally, the GUI and EFCAC-CCT were used to assess the corrosion behaviour of reinforcement. Results indicate that the MOSMA-SVR model provides predictions that are closer to the actual values, with smaller mean errors and standard deviations. The performance indicators, including coefficient of determination, mean absolute error, mean absolute percentage error, mean square error, root mean square error, and a20-index, of the MOSMA-SVR model are 0.987, 0.0124, 0.0332, 2.91e − 4, 0.0171 and 0.9991, respectively, and they are superior to those of the other tested models. The water type and the water–binder ratio are identified as the two most critical factors. Furthermore, by integrating the GUI and feature importance analysis results, chloride salt-resistant EFCAC can be designed. When this is combined with the GUI and EFCAC-CCT, the corrosion of rebar in EFCAC can be assessed in real time.

Forecasting Particle Froude Number in Non-Deposition Scenarios within Sewer Pipes through Hybrid Machine Learning Approaches

Sediment deposition has a substantial effect on the hydraulic capacity of channels in urban drainage and sewer systems. In this sense, the self-cleaning concept has been extensively used in the construction of urban drainage and sewer systems. In this regard, the design of the sewer system heavily depends on the accurate forecasting of the particle Froude number (Fr). This study is conducted on experimental data sets collected from existing studies, including a wide range of dimensionless grain size of particles (Dgr), sediment median size (d), hydraulic radius (R), volumetric sediment concentration (Cv), and pipe friction factor (λ) for the condition of clear bed. We forecasted the particle Froude number using four different input combinations. We employed the Random Tree (RT) and Reduced Error Pruning Tree (REPT) methods as standalone methods, as well as Random Committee (RC) and Bagging (BA) methods as hybrid machine learning (ML) methods in particle Froude number forecasting. Hybrid machine learning methods demonstrate enhanced performance compared to both standalone machine learning methods and empirical equations. In the context of sewer system design under non-deposited bed conditions, there is a need to accurately forecast the particle Froude number, RC-RT (IA = 0.96, R = 0.928, MSE = 0.718, RRMSE = 0.197, NSE = 0.86, and PBias = -0.284) performed the best, followed by BA-RT, RC-REPT, BA-REPT, RT, and REPT. In our research, it was found that, in forecasting the particle Froude number under non-deposited bed conditions, Cv emerges as the most responsive input parameter among others.

Nonlinear dynamic analysis of aircraft CFRP sandwich wings under explosive blast loading: Introducing SVM-DNN algorithm to predict dynamical information

The aircraft wings are a crucial component, particularly during mechanical shock excitation. Thus, for the first time, an inventive adaptable model to simulate the nonlinear dynamics of the wings under explosive blast loading at the moment of the collision is described in this article. It is crucial to increase the structure's stability because of explosive blast loading. The mentioned structure is made of two composite face sheets and a carbon fiber-reinforced polymer (CFRP). Functionally graded (FG) graphene origami (GOri)-enabled auxetic metallic metamaterial (GOEAM) is introduced to improve the stability of this kind of applicable structure, especially in air maneuvers. The analysis is conducted utilizing Reddy's third-order shear deformation of Reddy theory (TSDRT), incorporating Hamilton's principle and Von Kármán nonlinear geometric assumptions. The governing and boundary equations are accurately computed at the domain and boundary edges of the doubly curved structure. The coupled mesh-free radial point interpolation method (MRPIM) and Newton-Raphson method are applied for numerically simulating the current doubly curved structure by employing Newmark's temporal integration method with a constant-average acceleration approach. The present findings are cross-checked against the machine learning method and open-source results from the literature. Based on physical data, machine learning integrates supervised machine learning to predict the nonlinear vibration of the system. In this case, nonlinear transient bending properties are found using hybrid machine learning methods and solutions. The findings demonstrate the significance of GOEAM for nonlinear vibrations of the composite system. The current study's conclusions could be used as a benchmark and useful recommendations for future structural design techniques with enhanced features.

Classifying flexible pavement defects using hybrid machine learning approach

The transportation infrastructure sector significantly impacts a country’s gross domestic product (GDP), particularly in developing nations striving to manage and maintain road networks as valuable assets. While asset generation is integral, the more intricate challenge lies in effective maintenance. Pavement monitoring, a crucial component of pavement maintenance and management systems (PMMS), evaluates defect severity, road maintenance prioritization, and maintenance types. To enhance road health monitoring, the present study introduces a hybrid machine learning (ML) method, integrating support vector machine (SVM) and convolutional neural network (CNN). The proposed semi-automated detection system aims to reduce human supervision in traditional surveys, thereby cutting down the cost of pavement distress maintenance The research utilizes data collected by the authors from Ahmedabad city, Gujarat, following Indian road congress (IRC) guidelines for defect selection. Training involves 1,000 images for each crack type, with testing on 100 images. Results indicate that the SVM-CNN model achieves 87% accuracy in training and 91% accuracy in testing for road defect classification, showcasing its efficiency in pavement maintenance and management. The system presents the potential to significantly enhance the efficiency of road maintenance processes, making it a valuable asset for developing nations striving for a more streamlined approach to road network preservation.

Predicting real-time roadway pluvial flood risk: A hybrid machine learning approach coupling a graph-based flood spreading model, historical vulnerabilities, and Waze data

Urban pluvial flash flooding (PFF), driven by extreme weather and urban expansion, introduces complex challenges that arise from the dynamic interaction of rainfall hazard, road vulnerability, and traffic exposure. These three critical components must be interconnected to provide a comprehensive prediction of roadway PFF risk. Our integrated approach combines historical data and real-time Waze flood alerts using a simplified physics-based PFF model and hybrid machine learning methods to predict flash flooding risk at the road segment scale. In a Dallas case study with four intersections, we trained multiple models with data from 15 storms and tested on 5 storms. The XGBoost method excels in test precision, while a Random Forest model offers better recall, and both methods outperform Support Vector Machines (SVM). The choice between models depends on factors such as negative class (prediction of unflooded areas) uncertainty and false positive cost (i.e., predicting no flooding incorrectly). For the case study, our approach could boost flood awareness, enhance safety, and improve urban flood management by correctly predicting 73% of risk observations during the test storm events.

Daily Streamflow Forecasting Using Networks of Real-Time Monitoring Stations and Hybrid Machine Learning Methods

Considering the increased risk of urban flooding and drought due to global climate change and rapid urbanization, the imperative for more accurate methods for streamflow forecasting has intensified. This study introduces a pioneering approach leveraging the available network of real-time monitoring stations and advanced machine learning algorithms that can accurately simulate spatial–temporal problems. The Spatio-Temporal Attention Gated Recurrent Unit (STA-GRU) model is renowned for its computational efficacy in forecasting streamflow events with a forecast horizon of 7 days. The novel integration of the groundwater level, precipitation, and river discharge as predictive variables offers a holistic view of the hydrological cycle, enhancing the model’s accuracy. Our findings reveal that for a 7-day forecasting period, the STA-GRU model demonstrates superior performance, with a notable improvement in mean absolute percentage error (MAPE) values and R-square (R2) alongside reductions in the root mean squared error (RMSE) and mean absolute error (MAE) metrics, underscoring the model’s generalizability and reliability. Comparative analysis with seven conventional deep learning models, including the Long Short-Term Memory (LSTM), the Convolutional Neural Network LSTM (CNNLSTM), the Convolutional LSTM (ConvLSTM), the Spatio-Temporal Attention LSTM (STA-LSTM), the Gated Recurrent Unit (GRU), the Convolutional Neural Network GRU (CNNGRU), and the STA-GRU, confirms the superior predictive power of the STA-LSTM and STA-GRU models when faced with long-term prediction. This research marks a significant shift towards an integrated network of real-time monitoring stations with advanced deep-learning algorithms for streamflow forecasting, emphasizing the importance of spatially and temporally encompassing streamflow variability within an urban watershed’s stream network.

Hybrid Machine Learning Approach for predicting E-wallet Adoption among Higher Education Students in Malaysia

In today’s digitised world, e-wallets have been sprouting thick and fast in Malaysia as they contribute significantly to expediting onlinetransactions. The E-wallet system is not only a mechanism for businesses to acquire profit but is also one of the most secure paymentoptions for customers, particularly during the COVID-19 pandemic. However, the adoption of e-wallets among higher education students remains unfavourable, eliciting only minimal response. This study aims to analyse higher education students’ adoption of e-wallets using a hybrid machine learning method, combining clustering and decision trees. This approach provides deep insights into user behaviour, improving prediction accuracy and enabling personalised strategies for enhanced user experiences. It profiles and classifies students based on demographics and traits such as age, year of study, gender, frequency of use, future use intention, lifestyle compatibility, perceived trust, risk perception, convenience, and security factors. The analysis reveals the segmentation of the dataset into four distinct clusters, each characterised by shared attributes. These clusters are subsequently labelled descriptively and incorporated into the dataset. The dataset, now enriched with cluster information, serves as the foundation for constructing a decision tree model. The outcome of the decision tree indicates that Cluster 2 and Cluster 3 are hesitant towards e-payment. In contrast, Cluster 1 and Cluster 4 are more receptive despite security concerns, as e-wallets offer convenience despite lacking full trust, with security being a prominent concern amidst rising cyber threats. This study helps the Malaysian government and service providers promote cashless transactions and shape students’ financial independence based on their traits.

Agriculture crop yield prediction using inertia based cat swarm optimization

Crop yield prediction is among the most important and main sources of income in the Indian economy. In this paper, the improved cat swarm optimization (ICSO) based recurrent neural network (RNN) model is proposed for crop yield prediction using time series data. The inertia weight parameter is added to position equation that is selected randomly, and a new velocity equation is produced which enhances the searching ability in the best cat area. By using inertia weight, the ICSO enhances performance of feature selection and obtains better convergence in minimum iteration. The RNN is applied to produce direct graph using sequence of data and decides current layer output by involving all other existing calculations. The performance of the model is estimated using coefficient of determination (R2), root mean square error (RMSE), mean squared error (MSE), and mean absolute error (MAE) on the yield from the years 2011 to 2021 with an annual prediction for 120 records of approximately 8 million nuts. The evaluated result shows that the proposed ICSO-RNN model delivers metrics such as R2, MAE, MSE, and RMSE values of 0.99, 0.77, 0.68, and 0.82 correspondingly, which ensures accurate yield prediction when compared with the existing methods which are hybrid reinforcement learning-random forest (RL-RF) and machine learning (ML) methods.

Prediction of futile recanalisation after endovascular treatment in acute ischaemic stroke: development and validation of a hybrid machine learning model

BackgroundIdentification of futile recanalisation following endovascular therapy (EVT) in patients with acute ischaemic stroke is both crucial and challenging. Here, we present a novel risk stratification system based on hybrid...

Detection of sarcasm in tweets using hybrid machine learning method

<p>When one wants to express the contrary of what they mean, especially when insulting someone, sarcasm is used. One of the challenges associated with the control and management of content on social networking sites such as Twitter and other social media sites, is the recognition of sarcasm. Because sarcasm is purposefully conveyed through ambiguous word choice, even for humans it can be challenging to identify. Existing methods for automatically detecting sarcasm rely heavily on lexical as well as linguistic clues the majority of the time. On the other hand, these methods have not yielded a large or even a minor enhancement in terms of the correctness of the mood. The purpose of this study is to increase the accuracy of sentiment analysis by proposing a system that is both reliable and effective at identifying sarcasm. In this investigation, three different types of features are focussed: lexical, sarcastic, and context features. These feature sets are utilised in the process of categorising tweets as either sarcastic or not sarcastic. This research presents a sarcastic feature set coupled with an efficient hybrid machine learning approach, which ultimately results in improved accuracy. The results of the experiments reveal that the recommended hybrid machine learning method achieves 97.3% accuracy for sarcastic feature sets which is better when compared to existing machine learning techniques namely k-nearest neighbor, random forest, support vector machine and decision tree for the selection of the appropriate features.<strong></strong></p>

RipViz: Finding Rip Currents by Learning Pathline Behavior.

We present a hybrid machine learning and flow analysis feature detection method, RipViz, to extract rip currents from stationary videos. Rip currents are dangerous strong currents that can drag beachgoers out to sea. Most people are either unaware of them or do not know what they look like. In some instances, even trained personnel such as lifeguards have difficulty identifying them. RipViz produces a simple, easy to understand visualization of rip location overlaid on the source video. With RipViz, we first obtain an unsteady 2D vector field from the stationary video using optical flow. Movement at each pixel is analyzed over time. At each seed point, sequences of short pathlines, rather a single long pathline, are traced across the frames of the video to better capture the quasi-periodic flow behavior of wave activity. Because of the motion on the beach, the surf zone, and the surrounding areas, these pathlines may still appear very cluttered and incomprehensible. Furthermore, lay audiences are not familiar with pathlines and may not know how to interpret them. To address this, we treat rip currents as a flow anomaly in an otherwise normal flow. To learn about the normal flow behavior, we train an LSTM autoencoder with pathline sequences from normal ocean, foreground, and background movements. During test time, we use the trained LSTM autoencoder to detect anomalous pathlines (i.e., those in the rip zone). The origination points of such anomalous pathlines, over the course of the video, are then presented as points within the rip zone. RipViz is fully automated and does not require user input. Feedback from domain expert suggests that RipViz has the potential for wider use.

An integrated GIS-based multivariate adaptive regression splines-cat swarm optimization for improving the accuracy of wildfire susceptibility mapping

A hybrid machine learning method is proposed for wildfire susceptibility mapping. For modeling a geographical information system (GIS) database including 11 influencing factors and 262 fire locations from 2013 to 2018 is used for developing an integrated multivariate adaptive regression splines (MARS). The cat swarm optimization (CSO) algorithm tunes the parameters of the MARS in order to generate accurate susceptibility maps. From the Pearson correlation results, it is observed that land use, temperature, and slope angle have strong correlation with the fire severity. The results demonstrate that the prediction capability of the MARS-CSO model outperforms model tree, reduced error pruning tree and MARS. The resulting wildfire risk map using MARS-CSO reveals that 20% of the study areas is categorized in the very low wildfire risk class, whereas 40% is under the very high class of fire hazard.

Hybrid machine learning method for classification and recommendation of vector-borne disease

<p>Vector-borne diseases (VBD) are a class of infectious illnesses that are transmitted to humans and animals through the bites of arthropod vectors, such as mosquitoes, ticks, and fleas. These diseases are caused by a variety of pathogens, including bacteria, viruses, and parasites, and are a significant global public health concern. Vector-borne diseases are prevalent in many parts of the world, particularly in tropical and subtropical regions, where the vectors thrive. This research has contributed by constructing a hybrid machine learning based prediction model, which helps to discover patients who are infected by vector-borne disease at an earlier stage and also helps with the categorization and diagnosis of severe vector-borne disease. The model that has been proposed is made up of units: data conversion, data preprocessing, normalization, extraction of feature, splitting of dataset, and classification and prediction unit. The fact that the suggested prediction model is capable of identifying vector-borne disease in its early phases as well as categorizing the kind of disease using the medical report of a sufferer is one of the innovative aspects of the model. The 7 distinct conventional machine learning and single hybrid machine learning (HML) are applied for classification and Recurrent Neural Network (RNN) based reinforcement learning are utilized for recommendation. In order to evaluate the effectiveness of the system that’s been proposed, a number of tests were carried out. A dataset consisting of 1539 different cases of a disease transmitted by vectors has been collected. The 11 common vector-borne diseases namely malaria, dengue, Japanese encephalitis, kala-azar and chikungunya were taken for experimental evaluation. The performance accuracy of the proposed prediction model has been measured at 98.76%, which assists the healthcare team in making decisions on a timely basis and ultimately helps to save the patient’s lives. The final phase system provides the recommendation for those classifiers resulting in four different classes such as normal, mild, moderate and severe respectively. The recommendation is also demonstrating future direction for cure of vector borne disease.</p>

BOO-ST and CBCEC: two novel hybrid machine learning methods aim to reduce the mortality of heart failure patients

Heart failure (HF) is a leading cause of mortality worldwide. Machine learning (ML) approaches have shown potential as an early detection tool for improving patient outcomes. Enhancing the effectiveness and clinical applicability of the ML model necessitates training an efficient classifier with a diverse set of high-quality datasets. Hence, we proposed two novel hybrid ML methods ((a) consisting of Boosting, SMOTE, and Tomek links (BOO-ST); (b) combining the best-performing conventional classifier with ensemble classifiers (CBCEC)) to serve as an efficient early warning system for HF mortality. The BOO-ST was introduced to tackle the challenge of class imbalance, while CBCEC was responsible for training the processed and selected features derived from the Feature Importance (FI) and Information Gain (IG) feature selection techniques. We also conducted an explicit and intuitive comprehension to explore the impact of potential characteristics correlating with the fatality cases of HF. The experimental results demonstrated the proposed classifier CBCEC showcases a significant accuracy of 93.67% in terms of providing the early forecasting of HF mortality. Therefore, we can reveal that our proposed aspects (BOO-ST and CBCEC) can be able to play a crucial role in preventing the death rate of HF and reducing stress in the healthcare sector.

Time series forecasting of oil production in Enhanced Oil Recovery system based on a novel CNN-GRU neural network

An accurate prediction of oil production is critical for the oilfield development, and many deep learning models have been widely employed for this purpose. However, those methods show insufficiencies in extracting complex features from multivariable time series datasets, which leaves the prediction of oil production still challenging. In this study, a novel CNN-GRU model combining Convolutional Neural Networks (CNN) and Gate Recurrent Unit (GRU) neural network was proposed to accurately predict oil production for Enhanced Oil Recovery (EOR) performance. The CNN layer can extract the features from variables affecting oil production, and the GRU layer models temporal information using the transmitted features for prediction. The Bayesian Optimization algorithm (BO) was employed to design the optimal hyper-parameters of CNN-GRU. For evaluation purpose, two case studies were carried out with the production data from a CO2-EOR project and a waterflooding project. The prediction performance of the proposed approach was compared with typical deep learning methods and a hybrid (statistical and machine learning) method. The results of experiments and comparisons indicate that the proposed CNN-GRU model outperforms other prediction approaches. The CNN-GRU model provides future oil production of wells, enabling engineers to make informed decisions in development plan of reservoirs.

Crop mapping through a hybrid machine learning and deep learning method

A major function of satellite imagery is crop identification and separation, which is of key importance in acreage estimation, yield estimation, and agricultural management. This study aimed to examine the capability of the object-based method and machine learning and deep learning algorithms in combining optical and radar images to generate crop-type maps. For this purpose, Sentinel-1 and Sentinel-2 satellite images were used for the 2019 crop year in the northwest of Ardabil, Iran. Image segmentation was performed through the multiscale method and various spectral, textural, and radar backscattering characteristics. The main features were identified using Random Forest feature selection and fed to support vector machine, random forest, and convolutional neural network algorithms. The results of these algorithms were combined via the majority voting method. The results showed that the convolutional neural network algorithm performed better than other methods with an overall accuracy of 88.03% and a kappa coefficient of 85.99%. Meanwhile, the support vector machine method showed poor performance compared to the other two methods. According to the findings, combining the results of these algorithms through the majority voting method yielded the best crop identification result with an overall accuracy of 90.34% and a Kappa coefficient of 88.72%.

Damage detection of offshore jacket structures using structural vibration measurements: Application of a new hybrid machine learning method

The artificial intelligence (AI) technologies, such as meta-heuristic computing and deep learning, have provides solid technical support for structural health monitoring (SHM) of offshore jackets. In this paper, a physics-enhanced AI method based on the parametric damage identification is developed for SHM of the offshore jacket structures. In this new method, a hybrid kernel function-based kernel extreme learning machine (HKELM) is proposed to construct an AI structure to enhance the SHM detection capacity on the structural modal parameters extracted by the parametric damage identification technique. Simulation analysis is carried out to verify the feasibility of the HKELM-based method using the response signals of a jacket structure under impact force, and the result demonstrates good damage location capability of the proposed method. Furthermore, to select proper parameters for the HKELM, the whale optimization algorithm (WOA) is applied to optimize the values of the regularization coefficient and kernel parameter array. Then, the wavelet denoising (WD) is introduced to preprocess the vibration signals to improve the damage detection ability of the WOA-HKELM. Lastly, experimental tests are performed to validate the effectiveness of the proposed method in utilizing the structural modal parameters for identifying the structural damage. The analysis results illustrate that the proposed method produces satisfactory damage location ability under the influence of actual noise in the vibration signals. Meanwhile, this method has broad application prospects in the SHM of other offshore structures.

Hybrid approaches to machine learning in software development: Applying artificial intelligence to automate and improve processes

The study on hybrid machine learning approaches is relevant because these approaches have great potential to improve predictive accuracy and software automation, and their use is becoming more widespread. The purpose of this study was to provide recommendations for the use of hybrid machine learning methods and analyse the areas of application of artificial intelligence, which is used to automate and improve processes. Problems related to hybrid approaches to machine learning were identified using the analytical method. The use of the statistical method allowed assessing the development of stability and performance of hybrid machine learning approaches. Features and differences of machine learning in the field of software development are noted. Errors and reasons that are made when improving development processes are analysed. It is established that a comprehensive analysis of the functioning of artificial intelligence is important to assess its effectiveness, development, and complexity of work in automation and improvement of development. The issues of evaluating the work of this type of approach, the expediency of their use, limitations in the process, and the impact of restrictions on the result are considered. It is determined that the use of artificial intelligence in the process of automation and improvement of development processes will improve the quality of resource optimisation. The study offers recommendations that will contribute to the effective regulation of this issue. The practical value of the study lies in the possibility of applying the results obtained to eliminate errors in the development and improvement of hybrid approaches, investigating the reliability of using artificial intelligence, considering various factors that serve as the basis for recommendations on appropriate use

A smart walker based on a hybrid motion model and machine learning method

Due to the degeneration of musculoskeletal structure and strength, the elderly population is facing significant mobility challenges. Walkers are widely used for mobility-impaired people. In this research, a smart walker has been developed by using a hybrid motion model (HMM) and a machine learning model based on the vertical interaction force to match the velocity between the walker and its user, which can reduce the horizontal interaction force thus to help lower the operational effort. It is equipped with only force sensors on the handlebars as a human-robot interface. The human motion is modeled by using the HMM in which an inverted pendulum model is used in the single support phase and a constant velocity model is used in the double support phase. A novel gait phase detector is built based on a machine learning method to correlate the force information and the walking gait phases. Experiments with three subjects are carried out to verify the effectiveness of the gait phase detection method and the hybrid motion model. The results demonstrate that the walker can accurately identify gait phases with more than 90 % accuracy and the horizontal interaction force is reduced to around 50 % of that under the constant velocity model and power-off condition when using the HMM during walking.