Applied Machine Learning on Phase of Gait Classification and Joint-Moment Regression

Abstract

Traditionally, monitoring biomechanics parameters requires a significant amount of sensors to track exercises such as gait. Both research and clinical studies have relied on intricate motion capture studios to yield precise measurements of movement. We propose a method that captures motion independently of optical hardware with the specific goal of identifying the phases of gait using joint angle measurement approaches like IMU (inertial measurement units) sensors. We are proposing a machine learning approach to progressively reduce the feature number (joint angles) required to classify the phases of gait without a significant drop in accuracy. We found that reducing the feature number from six (every joint used) to three reduces the mean classification accuracy by only 4.04%, while reducing the feature number from three to two drops mean classification accuracy by 7.46%. We extended gait phase classification by using the biomechanics simulation package, OpenSim, to generalize a set of required maximum joint moments to transition between phases. We believe this method could be used for applications other than monitoring the phases of gait with direct application to medical and assistive technology fields.

1. Introduction

Biomechanics is the study of human movement that combines the laws of physics with concepts of engineering to address physical health and performance [1]. Human gait produces a locomotion using the combination of the brain, nerves, and muscles in the lower extremities [2]. Balance and gait work uniformly as a complex sensory and motor coordination. Within this context, the assessment of gait indicates levels of physical mobility and effects of therapy or assistive technologies. A gait cycle starts at the point of initial contact of one lower extremity to the point where the same extremity touches the ground again [2]. Skeletal-based arrangements like the human body rely on muscles and tendons to manipulate joints [3]. For gait, the human leg depends on three primary joints: hip, knee, and ankle [4].

Complex biomechanic simulation environments (e.g., OpenSim [5], bioMechZoo [6]) focus on musculoskeletal models performing kinematic estimations. The inverse kinematics (IK) and inverse dynamic (ID) tools provided by OpenSim are used as a viable solution for enhancing gait phase classification by outputting a set of required joint-torques to transition between phases. To make sense of the large databases produced from motion capture systems or simulation environments, machine learning is key for gait assessment [7,8,9]. The development of classification models to determine phases of gait for a diverse group of subjects has not been popular due to the difficult task of generalizing the wide variety of human locomotion [10]. Instead, most complex models focus on pathological gait recognition (e.g., detecting disabilities that affect gait) [11], or the stance–swing phase of gait for classification [10]. Often machine learning approaches are viewed as “black boxes” that can solve any problem. However, the unwise choice of parameters can lead to ambiguous decisions or erroneous predictions [1]. As a reliable approach, literature has focused on gait recognition or detection [8,11] as the primary machine learning classification to facilitate automated discrepancies for fall detection, or changes in activities (i.e., transitioning from walking to running) [2].

Tracking the motion of human subjects performing gait can be done in a variety of ways, but the most common include: optically monitoring marker trajectory [12,13,14] or wearable IMU sensors using sensor-fusion algorithms to record angular displacements [15,16]. The majority of the subject data in this work was provided two public databases developed by Moissenet et al. (Public database provided by Moissenet et al. [13]: https://figshare.com/articles/A_multimodal_dataset_of_human_gait_at_different_walking_speeds/7734767 (accessed on 13 December 2021)) [13], and Horst et al. (Public database provided by Horst et al.: https://data.mendeley.com/datasets/svx74xcrjr/3 (accessed on 13 December 2021)) [1] that relied on optical marker-tracking systems. The additional data set for training purposes was from our own custom IMU sensors [17] collected under IRB Exemption at UC Santa Cruz.

The primary goal of this work extends the typical application of gait detection or stance–swing transitions to create a model that can accurately predict the phase of gait using joint angles. The authors believe understanding a complex breakdown of individual phases of gait, compared to just toe off, foot flat, and heel off, has deeper insights for applications such as prostheses, exoskeletons, virtual reality, etc. Machine learning has been applied to detect a variety of motions with a single sensor which we believe has an different and more general application than ours [15,18]. Since we know it is a challenge to generalize the required moments from phase to phase for all subjects, we confined our study on the sagittal plane. The paper begins by explaining the process for preparing each data set using OpenSim, a multi-body biomechanic simulation package [5], and bioMechZoo, an open-source toolbox for analyzing and visualizing movement [6] to accurately label the joint angle coordinates and phase of gait in Section 2.1. To make sense of the aggregated data set, we implemented machine learning classification algorithms such as random forest [19,20] to correlate all of the joint angle recordings with a phase of gait [2] in Section 2.2. The analysis in Section 3 demonstrated that even with a large set of joints being tracked for a cyclical movement such as gait along the sagittal plane, there is no real requirement for wearing additional sensors. Rather, there exists options to reduce the number of joints monitored and thereby yield which phase of gait we enter with a range of confidence (See

Table A6. Using feature reduction, we can demonstrate the correlation between number of joints (features) and mean accuracy (%) using Random Forest classifier. It is worth noting that 6 has only 1 combination of features, but the rest follow the format: max accuracy % (mean %).

Number of Features	6	5	4	3	2	1
KNN	90.8	90.6 (90.1)	89.3 (88.7)	86.7 (85.4)	79.7 (75.0)	49.6 (47.3)
CART	87.9	87.1 (87.0)	86.2 (85.6)	84.1 (82.4)	76.4 (71.0)	45.8 (43.1)
RNDM	91.7	91.2 (91.1)	90.0 (89.8)	87.6 (86.6)	79.8 (75.3)	45.8 (43.2)

). To further the extraction of this same data, we used ID from OpenSim to produce a relationship between phase of gait, joint angles, and required moments, creating a valuable tool for future prosthetic, exoskeleton, or biomechanics applications [21].

2. Materials and Methods

2.1. Data Preparation

In this study, we considered one hundred and nine healthy adults who range in physical characteristics (e.g., height, weight, mass, age). We used two public databases that cumulatively provided 4079 full cycles of gait, and our own database, which provided 124 cycles of gait. Moissenet database [13] used 51 participants, Horst database [14] used 56 participants, and our database used 2 participants (See

Table A9. Participant Information used in Figure 1.

	Height	Age	Weight
Male	1.66	31	67
Female	1.64	48	65.4
Female	1.56	28	50
Male	1.77	23	72.5
Male	1.83	25	73.5
Male	1.76	23	73
Female	1.69	44	65
Female	1.66	30	57.1
Male	1.88	57	86
Male	1.8	59	63.4
Female	1.7	26	61.3
Male	1.8	29	92
Female	1.58	22	67
Female	1.76	26	73.8
Female	1.71	48	59.8
Male	1.92	33	87.5
Female	1.66	31	80.5
Male	1.89	38	89.9
Female	1.7	62	60.7
Male	1.77	21	67.2
Female	1.6	24	63.5
Male	1.84	21	89.6
Female	1.55	19	56.5
Female	1.65	40	61.8
Female	1.64	40	61.5
Male	1.74	32	72.2
Female	1.64	28	61.9
Male	1.91	25	88
Male	1.82	25	79.5
Female	1.72	21	62.8
Male	1.74	39	74
Male	1.77	52	87.2
Female	1.7	35	62
Male	1.9	48	89.4
Female	1.66	63	60.2
Female	1.69	58	73
Female	1.73	50	68
Female	1.69	46	76
Female	1.67	41	60.5
Male	1.79	43	95
Female	1.69	30	58
Female	1.71	64	51.5
Male	1.72	51	65.5
Male	1.87	24	86
Male	1.72	26	50.8
Male	1.77	38	81.5
Male	1.76	42	66.1
Male	1.88	31	74.8
Male	1.83	67	98
Male	1.78	21	74
Male	1.75	29	68.9
Female	1.81	21	64.9
Male	1.84	21	80.8
Male	1.82	23	82.7
Female	1.63	26	54.9
Male	1.79	21	77.3
Male	1.91	24	94.2
Male	1.88	23	69.5
Male	1.84	26	72
Female	1.58	20	52.3
Female	1.68	25	60.4
Female	1.64	23	55
Female	1.69	21	69.7
Female	1.69	26	59.3
Female	1.67	25	54.5
Female	1.75	23	57.4
Female	1.6	27	47.3
Female	1.62	22	61.4
Male	1.81	21	82.3
Female	1.69	19	65.6
Female	1.55	22	56.7
Female	1.61	26	56
Male	1.82	21	69.1
Female	1.62	22	62.1
Male	1.74	30	80.7
Male	1.99	21	91.2
Male	1.78	21	69.5
Male	1.83	24	67.5
Female	1.81	22	62.1
Male	1.81	28	81.35
Female	1.65	21	58.1
Male	1.78	23	80.9
Female	1.68	27	67.6
Male	1.78	23	82
Female	1.67	21	58.8
Female	1.69	24	59
Female	1.72	23	56.1
Female	1.61	23	52.1
Male	1.79	30	71
Female	1.58	21	53.15
Female	1.75	21	65.15
Male	1.83	25	79.95
Female	1.64	23	54.8
Male	1.82	21	76.5
Male	1.82	22	74.6
Female	1.65	20	56.45
Male	1.88	22	78.3
Male	1.92	22	90.8
Male	1.86	24	72.2
Male	1.87	22	81.8
Female	1.67	21	61.8
Female	1.61	30	55.75
Male	1.71	20	69.75
Female	1.7	22	66.15
Male	1.86	23	73.35
Male	1.79	22	71.75
Male	1.85	19	77.75
Male	1.778	24	69.85
Male	1.83	21	68.04

). In our experiments we used a set of in-house developed 9-degrees of freedom orientation IMU sensor with a 3-axis magnetometer, 3-axis gyroscope, and 3-axis accelerometer that used the Madwick sensor-fusion algorithm to calculate angular displacement and wirelessly transmit the information to a remote host using the TCP protocol [17,22]. Figure 1 shows the correlation between the age, height, and weight for all of the participants.

Since each database had its unique recording strategy (e.g., different marker placement and different sampling rate), the experimental data were preprocessed using Algorithm 1 to include marker numbers, frames, samples, mass, gender, and height into a single matrix representing each subject’s biometrics [23]. For example, the Moissenet and our own databases were sampled at 100 Hz, while the Horst database was recorded at 250 Hz. We downsampled Horst database to match the other two sets of data and generate a training data set that consists of over 700,000 samples at 100 Hz. It is important to note that the markers and their locations for both the Moissenet and Horst databases were interpreted by BioMechZoo solvers to output a joint angle relationship that yielded similar ranges of motion. Both of these databases included foot–ground reaction forces. We simulated the ground reaction force using “the simulated force plate” component available in OpenSim.

Algorithm 1: Data Preparation Pipeline

The organization of the data structure for the recorded motion (T) shown in Equation (1), contains a Cartesian markers ($C_{m,f}^i;m\in \{x,y,z\}$), frame number (f), and individual trials or samples (i).

$$T=\left[\begin{array}{ccccccc}{C}_{x,1}^1& C_{y,1}^1& C_{z,1}^1& \dots & C_{x,2}^1& \dots & C_{m,f}^1\\ C_{x,1}^2& C_{y,1}^2& C_{z,1}^2& \dots & C_{x,2}^2& \dots & C_{m,f}^2\\ ⋮& ⋮& ⋮& & ⋮& & ⋮\\ C_{x,1}^i& C_{y,1}^i& C_{z,1}^i& \dots & C_{x,2}^i& \dots & C_{m,f}^i\end{array}\right]$$

(1)

Figure 2 illustrates the process of extracting Cartesian coordinates from raw marker data and convert them into joint angles. This means that our system is capable accepting different sources of motion capture, and the pre-processing pipeline from Algorithm 1, we convert the data sets into a consistent parent–child joint angle relationship for all subjects. To clean up the data set, we scripted Equation (2) to determine the joint angle representation along the sagittal plane (Figure 3) for the lower extremity joints [13,14]. After the joint angles were found for all participants, we verified the alignment for all calculated joint angles to ensure they are in the same range of motion.

$${\theta }_{2D}=\frac{180}{\pi }co{s}^{-1}\left(\frac{(C_{x,1}·C_{x,2})+(C_{y,1}·C_{y,2})}{\sqrt{{\left(C_{x,1}\right)}^2·{\left(C_{y,1}\right)}^2}+\sqrt{{\left(C_{x,2}\right)}^2·{\left(C_{y,2}\right)}^2}}\right)$$

(2)

$$S=\left[\begin{array}{cccc}{g}^1& m^1& h^1& a^1\\ ⋮& ⋮& ⋮& ⋮\\ g^i& m^i& h^i& a^i\end{array}\right]\mathrm{and}L=\left[\begin{array}{ccc}P& S& {\theta }_{2D}\end{array}\right]$$

(3)

In some cases there exists multiple trials of the same subject, but in the event the participant changed, all of the subjects attributes (S): gender (g), mass (m), height (h), and age (a) were assigned as a new person. After the data sets have been labeled for phase of gait (P), subject attributes (S), and joint angle kinematics (${\theta }_{2D}$), we transitioned into the process for training both the Gait Prediction and Moment Transition Predictions (Figure 4).

2.2. Classification Techniques and Algorithms

Machine learning automates the process of interpreting large sets of data to learn and make estimations [24] as well as construct a model to perform data-driven classifications. One of the primary goals of this work was to create a model that can accurately predict the phase of gait using joint angles. The model is trained to find a correlation between the input features (i.e., the observed and recorded input data) and the output targets (i.e., different phases of gait). This correlation is used to calculate targets for stand-alone or unlabeled features. The accuracy of each model is evaluated by interpreting how well the correlation can be found by the algorithm to predict the target using the features with cross validation.

In this work we used cross-validation to quantify the performance of each model. We split a certain percentage of the labeled data to use as test data, while the remaining data was used to train a model [25]. The training data is used as an input into the model, and the output was compared to its observed target to evaluate the accuracy against the other portion of the data set. Cross-validation iterates through the set of data multiple times, where each interval selects a different set of data samples to test, providing a more consistent performance metric of the entire model [25]. The calculations from cross validation were used as a metric for accuracy to compare with the outputs of each model we train.

We used the k-Nearest Neighbors (KNN) algorithm to classify the test features based on the most frequent phase of gait of their k surrounding neighbors, or closest data samples [26]. The parameter, k, defines how many neighbors were used in each classification. A relatively larger k results in a more accurate classification due to a larger scope of data. This reduces the effect of outliers and erroneous data for each prediction. The KNN algorithm has been used in other instances of training models for gait recognition based on different bio-mechanic features, including accelerometer data [27], ground reaction forces [28], and human gait shape analysis [29].

To find the nearest neighbors of each test sample, we calculated the Euclidean distance, D, between the feature sets of the test and already classified samples [30]. Each feature can be represented as:

$$f=(f_1,f_2,\dots f_n)$$

with n representing the number of features in each sample, and every $f_n$ representing one feature. A feature vector for one sample combines all relevant features for training:

$$f_v=[P,f_1,f_2,\dots ,f_n]$$

$$f_s=\left[\begin{array}{ccc}{P}^i& {\theta }_1^i& S_1^i\\ P^1& {\theta }_1^1& S_1^1\\ P^2& {\theta }_2^2& S_2^2\\ ⋮& ⋮& ⋮\\ P^n& {\theta }_1^n& S_1^n\end{array}\right]$$

The distance D between the test feature set x and the already classified feature set y can be represented with the following formula:

$$D(x,y)=\sqrt{\sum _{i=1}^n{(x_i-y_i)}^2}$$

(4)

where the iterator, i, increments for every feature used to train the model [30]. Equation (4) was evaluated for all training data samples, y. The number of samples (k) used in the training data set with the smallest distance (D) was selected as the test sample’s k nearest neighbors. The mode target value, or most frequent phase of gait within the selected neighbors, was used as the classification of the test sample x (Figure 5) [26]. This process was repeated to predict a phase of gait for each test feature set. Cross-validation repeats until all 10 folds and splits are iterated and completed. Generally, as k increases, the accuracy of the prediction increases as more data points are considered for the final classification. Decreasing k heightens the effect of inaccurate data on classifications; the balance for an ideal value of k is described using GridSearch. GridSearch finds specified parameter values through an exhaustive search process [31]. It sorts through all possible combinations of each parameter and finds the optimal values (

Table A1. Using GridSearchCV with the scikit learn tools, the best parameters were found for KNN, CART, and RNDM, where each algorithm went through a 10 fold and split using cross-validation.

KNN		CART		RNDM
algorithm	auto	ccp alpha	0.0	bootstrap	True
leaf size	30	class weight	None	ccp alpha	0.0
metric	minkowski	criterion	gini	class weight	None
metric params	None	max depth	None	criterion	gini
n jobs	None	max features	None	max depth	None
n neighbors	10	max leaf nodes	None	max features	sqrt
p	2	min impurity decrease	0.0	max leaf nodes	None
weights	distance	min impurity split	1	max samples	None
		min samples split	5	min impurity decrease	0.0
		min weight fraction leaf	0.0	min impurity split	None
		presort	deprecated	min samples leaf	1
		random state	None	min samples split	5
		splitter	best	min weight fraction leaf	0.0
				n estimators	250
				n jobs	None
				oob score	False
				random state	None
				verbose	0
				warm start	False

). Both GridSearch and feature extraction optimize the parameters of our model and the features considered to heighten the efficiency of our model for training.

We used GridSearch to programmatically iterate through different combinations of parameter values (Table A1) to find the ideal values to run the model with [32]. When applied to the KNN algorithm, it varies the number of neighbors in each classification, k, to find a balance between the model over-fitting and under-fitting our data. If the number of neighbors was small, the effect of noise on the classification become larger since the model only learned from a small subset of neighbor samples. When outliers heavily influence the model, we notice a bias towards the minor details of the data (over-fitting) rather than finding a general trend [33]. However if k is large, we notice the opposite since every test sample will be classified to the target (under-fitting). This happens to be more frequent than a smaller k in the overall training set, ignoring underlying trends in the data [33]. Finding a balance of the value of k is crucial to achieve an accurate and precise model.

We used the Classification And Regression Trees (CART) algorithm to focus on creating a decision tree that classifies the test samples [34]. Decision trees are commonly used in many situations where supervised learning is practical: forming gait pattern models using other features such as inhibitory factors of an injury [35], contact forces and angular velocity [36], as well as step length, walking speed, and stride time [37].

Each tree consists of nodes, branches, and leaves. Nodes are known as a “decision”, or a comparison or split made on a specific feature in the data set. Branches are the outcome of the decision made by the node. A leaf is a node at the end of the tree that does not have branches extending from it. It is important to note that leaf nodes do not make decisions. Each leaf represents a target or a specific phase of gait. When making a classification, the data presented in our test feature set compares each node by traversing along the corresponding branches until it reaches a leaf node [34].

When training quantitative data, each node splits at a specific feature value. In our case, a node concerning right hip angles could split at $\theta =20$. This creates the left branch at $\theta <20$ for the right hip node, and $\theta >20$ for the right branch. The ideal split yields both branches as a completely homogeneous pool of data points with the same target. Each branch splits into more nodes until every leaf node is either a product of a perfect split or until the tree reaches the maximum depth or width as specified by the parameters. The Gini impurity (I) is a quantitative measure of how accurate a split is. Ideal splits have a Gini impurity value of 0 [38], and is calculated as follows:

$$I=1-\sum _{i=1}^t{\left(p_i\right)}^2$$

(5)

where t = 7 is the number of targets, and $p_i$ is the probability of selecting a data point with target i within the entire data set.

The feature with the smallest Gini impurity is chosen as the root of the tree. In other words, if we randomly classified according to the target distribution of the data set, the feature with the smallest possibility of incorrect classification is the root (see Figure 5) [39]. Once we select a feature as the root node and splits according to the smallest Gini impurity value, choosing the next node and split is repeated with the data subset of each branch until a complete tree has formed. As seen in Figure 5, our classification in a decision tree followed the splits made by the nodes for a test feature set until a leaf node, or target, is reached.

The parameters of maximum depth and width of a decision tree prevent the common problem of overfitting in decision trees [34]. Suppose we let the tree grow until every split reaches an impurity of 0. In that case, every feature set likely traces a unique path to an individual leaf node due to noise in the data, making the classification overfitted and heavily affected by every outlier. To prevent this, we restrict the number of splits and nodes through a tree’s maximum depth and width. GridSearch iterates through different threshold values, so the parameter values shown in Table A1 avoid underfitting and overfitting.

The random forest (RNDM) algorithm uses many different decision trees, as constructed in the CART algorithm, to create a forest [40]. The most frequent classification made among all the decision trees in the forest is the classification of test data points [40]. The logic behind using a forest of trees formed by randomly selected data samples and features is that the entire forest will have a low correlation between each tree. The product of uncorrelated models is far more accurate than any individual prediction. Similar to the wisdom of crowds, trees with erroneous data are protected by a more significant amount of trees with more accurate models.

We began the random forest algorithm developing each decision tree by creating a bootstrapped data set as portrayed in Figure 5 [40]. With repetition, a set of data samples randomly selected from the entire data set is the bootstrapped data set that will form our tree. Every bootstrapped data set has the same number of samples as the entire data set, so that most bootstrapped sets include the repetition of random samples.

For each bootstrapped data set, decision trees were formed with a random selection of m features. Typically $m=\sqrt{n}$, with n being the total number of features in the data set (Figure 4). The process of creating a decision tree (Algorithm 2) uses each tree formed from calculating Gini impurity to determine the order of features as nodes and the optimal split per node. The process of building different bootstrapped data sets and creating decision trees with random subsets of features for each bootstrapped group repeats until the maximum number of trees t is reached. When classifying a test sample with the random forest algorithm, a test feature set serves an an input into all the decision trees in the forest. The most frequent target output of the trees is the classification derived from the test data.

The random forest algorithm is optimized using the parameters m, the number of features used in each tree, and t, the number of trees in a forest (Table A1). A GridSearch through both these parameters usually reveals an increase in accuracy with the typically selected value of m = $\sqrt{n}$, and a larger t to account for more significant variation in datasets. GridSearch is essential to prevent underfitting and overfitting in the RNDM algorithm due to the randomness of sample and feature selection.

Algorithm 2: Classification of phase of gait in relation to joint angles using Random Forest.

2.3. Extra Trees Regressors

Regression is another approach of supervised machine learning that outputs numerical values as a target, rather than as a category [41]. The previous KNN and decision tree algorithms are applied as regression techniques by changing the target from categories into continuous values. For example, a KNN classification can be turned into regression by averaging the numerical targets of the k nearest neighbors rather than taking the most categorical frequent target. Similarly, the leaves become prediction values rather than categories in a regression algorithm in algorithms with decision trees.

The extra trees algorithm is very similar to the random forest algorithm, creating many decision trees to form a forest. However, there are two critical differences between random forest and extra trees. Extra trees do not use a bootstrapped dataset like random forest. Each decision tree was formed by every sample in the entire training set [42]. Additionally, the extra trees algorithm uses a random split while creating decision trees, rather than calculating the optimal split with weighted Gini impurities like a typical decision tree [42]. Although, it is essential to note that extra trees still use Gini to calculate feature importance. Predictions in extra trees are made by averaging the output of all the trees in the forest for every test sample set [42]. When employing GridSearch in extra trees regression, the same parameters iterated through during the random forest algorithm are optimized (Table A1) so that the decision trees that make up the forest do not underfit or overfit the dataset.

2.4. Algorithm Applications

The classification algorithms (KNN, CART, Random forest) use the feature set that included joint angles (right and left hip, knee, and ankle) and participant information (e.g., height, mass, gender, age). Our feature set comprises 10 individual features, 6 joint angles, and 4 participant attributes. The target is the individual phase of gait for each data sample. We employ a 10-fold cross-validation and a 20/80 train–test split across all models when evaluating accuracy. The data is iterated 10 separate times during cross-validation to evaluate the accuracy. Each iteration selects a different 20% portion of the data set to reserve as sample test data points while the other 80% is selected as training data for the model.

Before selecting specific algorithms to use, we bench-marked the mean accuracy (with the standard deviation) in

Table A5. Accuracy of prediction (%) of Cross-Validation (CV) on 10-fold experiments using Linear, CART, KNN, and RNDM using all available features.

Classifier	KNN	CART	NB	SVM	RNDM
Mean (± SD)	0.902 (± 0.012)	0.857 (± 0.018)	0.796 (± 0.017)	0.665 (± 0.023)	0.905 (± 0.011)

using cross-validation on 10-fold experiments for a sample set employing all available features to help us narrow our chosen algorithms to KNN, CART, and RNDM. It is important to note that the parameters found from cross-validation and GridSearch mentioned in the previous sections were consistent for all feature combinations. The Naive Bayes (NB) and Support Vector Machine (SVM) algorithm produced models with relatively low accuracy compared to the other algorithms. As a linear classifier, the NB algorithm was unfit for our human gait classification with natural variances. The inefficiency of the SVM classifier with the Radial Basis Function (RBF) kernel and its proneness to over-fitting given larger data sets makes it unsuitable for training our model, and its shortcomings are prevalent in a 22% average decrease in accuracy compared to the algorithms we employed (Table A5). In addition, this SVM algorithm is particularly sensitive to noise, which makes it unsuitable for classifying our data with human variation. Therefore, we chose a final selection of the KNN, CART, and Random forest algorithms for our phase of gait prediction.

Since joint moments are only calculated for the subset of .mot data processed through OpenSim, we use regression techniques to roughly predict the moments corresponding to the joint angles from the .c3d files. In this scenario, the joint angles and participant information are the features, while we have a multi-class target: the moments for each of the six joints. By calculating moments for every test sample, we observed the trends of joint moments over each phase to approximate the maximum moment needed to move from one phase to the next, an addition to our overall gait pattern model.

To predict joint moments from the joint angles extracted from .c3d files, we created a model with the extra trees regressor using joint angles and moments from OpenSim. Our features were joint angles and participant information, and our targets were joint moments. A separate model was created for each phase, as seen in Figure 6. The regression accuracy calculated by cross-validation for each model is recorded in

Table A7. A table of the regression accuracy per phase when generating the Extra Trees model to predict joint moments from joint angles. The accuracy is the coefficient of determination, $R^2$, of the prediction. The best possible score is 1.0.

Phase of Gait	Regression Accuracy (${\mathit{R}}^2$ Error)
1	0.567
2	0.592
3	0.713
4	0.840
5	0.568
6	0.727
7	0.505

, where each model’s coefficient of determination exceeds 0.5, meaning each model accounts for a majority of the variance of the outputted moments. For this application, where joint angle trends varied greatly with each participant and even between each gait cycle, the extra trees outperformed all other regression algorithms due to the randomness in splitting nodes to smooth noise in the data set. It is important to note that due to the variance of subjects’ physical characteristics (i.e., subjects can be very small to large), the regression accuracy per phase may seem lower than normal. This does not affect the system’s ability to take physical characteristics and derive a estimation on required moments to transition between phases of gait.

3. Results and Discussion

The typical application for monitoring human gait focuses on the stance–swing transitions for cycle tracking (95% accuracy) [43], or rely heavily on the measurements on the foot (98% accuracy) [44]. This work aims to be less biased and dependent on a specific body part (in the event there is limb loss), and instead demonstrates the numerical trade-offs between tracking different joints on the human body. To increase the efficiency of our model, we reduced the number of features used while training to reduce the training run-time and ease the process of data collection [19]. Our models used a maximum of n = 10 features to train: joint angles (${\theta }_{2D}$ = 6), and four participant attributes. Each test included the four participant attributes while training a model,

$$\sum _{i=1}^{{\theta }_{2D}}\left(\genfrac{}{}{0pt}{}{6}{i}\right)=\sum _{i=1}^6\frac{6!}{(6-i)!·i!}=63$$

where the joint angle feature combinations are iterated through to find the ideal combination of the least number of features n and highest accuracy. This method trained the models ranging from just one joint angle, or all six, meaning the model trains on a minimum of five features and a maximum of ten. Some joints reveal themselves to affect the correlation between features and target more than others after analyzing the accuracy of the model of each joint combination.

As previously mentioned, the feature set, or input into the model, compromises of six joint angles and four participant attributes. The target, and eventual output of the models, is the individual phase of gait for each data sample. We used a 10-fold cross-validation and a 20/80 train–test split across all models when evaluating accuracy in recognizing the collection of joint angles. The data is iterated during cross-validation to evaluate the accuracy between the labelled data set as well as for parametric configurations. To find the performance of our models against the labeled data versus predicted data, we used confusion matrices to find mean accuracy (

Table A2. K-Nearest Neighbors Classification report with a confusion matrix for all the phases of gait (left) and scores (right).

	1	2	3	4	5	6	7		Precision	Recall	F1-Score	Support
1	18,885	1140	19	7	54	18	1149	7	0.89	0.89	0.89	21,272
2	1145	17,179	864	10	33	47	8	6	0.89	0.89	0.89	19,286
3	25	928	14,827	807	28	100	37	5	0.89	0.89	0.89	16,746
4	13	7	814	10,169	778	37	51	4	0.86	0.86	0.86	11,869
5	29	28	20	765	22,132	824	32	3	0.92	0.93	0.93	23,830
6	9	27	55	18	889	28,913	1183	2	0.93	0.93	0.93	31,094
7	1194	5	20	28	26	1200	14,700	1	0.86	0.86	0.86	17,173
								accuracy			0.90	141,270
								macro avg	0.89	0.89	0.89	141,270
								weighted avg	0.90	0.90	0.90	141,270

,

Table A3. Classification and Regression Trees Classification report with a confusion matrix for all the phases of gait (left) and scores (right).

	1	2	3	4	5	6	7		Precision	Recall	F1-Score	Support
1	17,894	1404	51	22	67	27	1807	7	0.84	0.84	0.84	21,272
2	1321	16,452	1366	25	49	55	18	6	0.85	0.85	0.85	19286
3	38	1411	14,037	1041	57	118	44	5	0.84	0.84	0.84	16,746
4	26	23	1099	9334	1264	61	62	4	0.79	0.79	0.79	11,869
5	50	35	72	1229	21,234	1171	39	3	0.89	0.89	0.89	23,830
6	32	64	94	64	1267	27,874	1699	2	0.90	0.90	0.90	31,094
7	1847	13	54	70	43	1735	13,411	1	0.79	0.78	0.78	17,173
								accuracy			0.85	141,270
								macro avg	0.84	0.84	0.84	141,270
								weighted avg	0.85	0.85	0.85	141,270

and

Table A4. Random Forest Classification report with a confusion matrix for all the phases of gait (left) and scores (right).

	1	2	3	4	5	6	7		Precision	Recall	F1-Score	Support
1	19,106	855	18	8	46	10	1229	7	0.89	0.90	0.90	21,272
2	974	17,381	850	4	31	40	6	6	0.90	0.90	0.90	19,286
3	33	990	14,833	737	24	98	31	5	0.89	0.89	0.89	16,746
4	13	9	823	10,118	839	31	36	4	0.87	0.85	0.86	11,869
5	32	22	22	785	22,207	741	21	3	0.92	0.93	0.93	23,830
6	15	28	39	16	881	29,053	1062	2	0.93	0.93	0.93	31,094
7	1228	5	19	26	22	1304	14,569	1	0.86	0.85	0.85	17,173
								accuracy			0.90	141,270
								macro avg	0.89	0.89	0.89	141,270
								weighted avg	0.90	0.90	0.90	141,270

). If the model yields the correct phase of gait given the joint angle(s) compared with the labeled data set, that is considered a successful prediction. Hip joint angles are particularly effective in training the model (Figure 7), and models training with KNN using feature combinations with just three joint angles can reach over 85% accuracy with one or both hip joint features. The CART algorithm also undergoes the same feature selection process among 63 feature combinations and achieves over 84% accuracy with just three joint angle features, slightly underperforming the KNN algorithm. The RNDM algorithm involved the same overall feature selection in the data set as other algorithms with 63 feature combinations. Random forest outperforms both KNN and CART (Figure 7) and was able to reach over 87% accuracy with just three features, revealing the importance of randomness when analyzing human data. Refer to Figure 7, which shows a significant association between both the hip joint angles and higher accuracy for all algorithms and combinations of joint angles.

Due to the nature of unique gait motions across individuals, we focused on the strong connection between phase of gait, joint angles, and joints’ moments. Focusing on the lower extremity joint angles for human gait is informative enough for phase classification. This approach can bridge this form of kinematic analysis toward joint dynamics. It is a well-known challenge to generalize the required moments from phase to phase for all subjects, but by taking advantage of OpenSim’s inverse dynamics solver (ID):

$$\tau =M\left(q\right)\ddot{q}+C(q,\dot{q})+G\left(q\right)$$

We purposed our joint angles for generalizing moments:

$$\tau =2m\omega \times \alpha +m\omega \times (\omega \times {\theta }_{2D})+G\times {\theta }_{2D}$$

(6)

where $\tau$ represented the generalized forces, m is the mass, $\omega$ is angular velocity, $\alpha$ is angular acceleration, G is gravitational forces, and ${\theta }_{2D}$ is the joint angles from Equation (2). Our Moment Prediction Model (Figure 6) interpreted those joint angles (${\theta }_{2D}$) and predicted the maximum moments (Nm/kg) to transition between phases of gait. This correlation between joint angles, moments, and phase of gait aim to deliver an extremely adaptable model. The output (Figure 8) has the potential to be applied as a bookmark or characterization for assistive technologies to replicate given the physical characteristics of their users.

Typically healthy humans follow a very similar gait pattern. However, it is important to note that there are still noticeable differences between Subject One’s and Subject Two’s phase of gait and joint moment relationship (e.g., Phase 6 in Figure 8c). The results demonstrate that each person’s gait is unique in relying on different joints to move. Subject One is a 28-year-old female that is 1.56 m in height, and weighs 50 kg. Subject Two, a 23-year-old male that is 1.76 m tall and weighs 73 kg, shows more of a minor moment requirement to transition between phases of gait than Subject One. It is essential to recognize that both subjects were chosen from different databases, yet they yielded similar trends. For example, monitoring the left knee in Figure 8d indicated that Subject Two had a larger moment to transition from Phase 3 to 4 with a 31% difference compared to Subject One (

Table A8. Required moment transitions between gait cycles as predicted by Random Forest regression for Subject One, Subject Two, and All Partipicants. See Figure 1 for physical characteristics (e.g., mass, height, weight).

Subject One	Moment (Nm/kg)
Gait Transition	Right Hip	Left Hip	Right Knee	Left Knee	Right Ankle	Left Ankle
$1⟶2$	0.080 (± 0.014)	0.040 (± 0.011)	0.110 (± 0.013)	0.048 (± 0.015)	0.777 (± 0.013)	0.244 (± 0.021)
$2⟶3$	0.072 (± 0.018)	0.245 (± 0.025)	0.112 (± 0.020)	0.090 (± 0.018)	0.075 (± 0.013)	0.391 (± 0.021)
$3⟶4$	0.167 (± 0.036)	0.333 (± 0.033)	0.180 (± 0.029)	0.285 (± 0.030)	0.297 (± 0.017)	0.427 (± 0.029)
$4⟶5$	0.065 (± 0.010)	0.078 (± 0.015)	0.134 (± 0.024)	0.042 (± 0.006)	0.299 (± 0.011)	0.022 (± 0.005)
$5⟶6$	0.263 (± 0.032)	0.109 (± 0.021)	0.216 (± 0.054)	0.030 (± 0.004)	0.341 (± 0.016)	0.049 (± 0.015)
$6⟶7$	0.506 (± 0.002)	0.105 (± 0.004)	0.089 (± 0.006)	0.030 (± 0.006)	0.313 (± 0.008)	0.100 (± 0.004)
$7⟶1$	0.424 (± 0.086)	0.294 (± 0.074)	0.236 (± 0.060)	0.478 (± 0.118)	0.261 (± 0.074)	0.307 (± 0.060)
Subject Two	Moment (Nm/kg)
Gait Transition	Right Hip	Left Hip	Right Knee	Left Knee	Right Ankle	Left Ankle
$1⟶2$	0.157 (± 0.002)	0.047 (± 0.010)	0.121 (± 0.015)	0.054 (± 0.011)	0.132 (± 0.020)	0.247 (± 0.018)
$2⟶3$	0.088 (± 0.019)	0.388 (± 0.020)	0.122 (± 0.018)	0.116 (± 0.016)	0.088 (± 0.020)	0.410 (± 0.0160)
$3⟶4$	0.162 (± 0.022)	0.470 (± 0.033)	0.169 (± 0.020)	0.393 (± 0.013)	0.294 (± 0.009)	0.424 (± 0.010)
$4⟶5$	0.051 (± 0.008)	0.088 (± 0.010)	0.132 (± 0.020)	0.062 (± 0.004)	0.359 (± 0.015)	0.013 (± 0.0027)
$5⟶6$	0.159 (± 0.009)	0.075 (± 0.015)	0.123 (± 0.011)	0.045 (± 0.007)	0.387 (± 0.017)	0.048 (± 0.004)
$6⟶7$	0.512 (± 0.004)	0.122 (± 0.006)	0.260 (± 0.002)	0.104 (± 0.005)	0.485 (± 0.009)	0.107 (± 0.007)
$7⟶1$	0.605 (± 0.038)	0.135 (± 0.017)	0.384 (± 0.017)	0.341 (± 0.033)	0.340 (± 0.025)	0.251 (± 0.022)
All Participants	Moment (Nm/kg)
Gait Transition	Right Hip	Left Hip	Right Knee	Left Knee	Right Ankle	Left Ankle
$1⟶2$	0.109 (± 0.062)	0.102 (± 0.072)	0.127 (± 0.039)	0.118 (± 0.080)	0.109 (± 0.062)	0.295 (± 0.097)
$2⟶3$	0.104 (± 0.065)	0.270 (± 0.117)	0.122 (± 0.063)	0.116 (± 0.050)	0.104 (± 0.064)	0.387 (± 0.052)
$3⟶4$	0.130 (± 0.030)	0.435 (± 0.239)	0.189 (± 0.056)	0.331 (± 0.130)	0.131 (± 0.031)	0.354 (± 0.152)
$4⟶5$	0.083 (± 0.028)	0.111 (± 0.063)	0.146 (± 0.021)	0.080 (± 0.036)	0.086 (± 0.041)	0.055 (± 0.039)
$5⟶6$	0.194 (± 0.104)	0.116 (± 0.096)	0.181 (± 0.057)	0.056 (± 0.042)	0.197 (± 0.107)	0.053 (± 0.025)
$6⟶7$	0.425 (± 0.232)	0.089 (± 0.035)	0.212 (± 0.124)	0.066 (± 0.045)	0.426 (± 0.231)	0.064 (± 0.035)
$7⟶1$	0.0.439 (± 0.207)	0.161 (± 0.128)	0.264 (± 0.099)	0.283 (± 0.177)	0.438 (± 0.206)	0.254 (± 0.138)

). Yet, they followed similar moment requirements in a scaled proportion.

The observation in Figure 8 showed that Subject One had a stronger dependency on the left side of the body, and Subject Two was more evenly distributed with a slight bias to the right side of the body. The assessment from both the gait classification and moment prediction models demonstrated a fundamental breakdown in the analysis of walking movement and can be further implemented as a valuable tool for biometric technologies.

4. Conclusions

This paper proposes a machine learning method to identify the phase of gait from joint angle measurements and generalize a set of required joint moments between those phases of gait along the sagittal plane. We used the algorithms KNN, CART, and RNDM to yield an 82%, 87%, and 92% accuracy in gait phase classification with all available features or lower extremity joints. Our understanding of how feature reduction affected the confidence of our RNDM classification model (Table A6) indicated how reliable monitoring fewer joint angles could be. Figure 7 proved this analysis by showing how the amount of joints required for monitoring each subject affects the accuracy of gait phase prediction. It is clear that the more sensors or features monitored, the higher the confidence; however, the difference between tracking six joints to five joints (0.5%), or six joints to three joints (4.04%) has a very minimal drop-off in accuracy. This finding indicates that reducing the number of joints monitored for complex gait phase-reliant applications will yield promising results. It is important to note that flexibility of joints is entirely individualized, where age or gender might demonstrate their own significant variance. For this work, we focused on the relationship between the physical characteristics and angular displacement of joints for human subjects. The authors believe future applications of this work could include: biomechanic comparisons between age and gender [45], robotic assistive devices, and motion not confined to the sagittal plane.

We correlated the exact joint angle measurements and phases of gait to yield each subject’s moments. Figure 8 and Table A8 demonstrate how a smaller Subject One requires smaller moments to transition between phases of gait than a physically larger Subject Two. Generally, both subjects in Figure 8 follow similar trends, but differences like Phase 6 for the Right knee show a considerable uniqueness between persons. The difference between results demonstrated how body size affected the required maximum moments proportionally. Correlating the joint angle relationships between the two modes for gait prediction and moment transitions (Figure 4) can be used as a powerful tool for biometric applications. Using the same database for two different applications bridges the IK and ID area of biomechanic analysis proving the impact of joint angle measurement techniques. Implementing IMU sensors for biometric analysis reduces the cost, room-bounded configurations, and overall complexity of optical motion capture systems.