Journal of Healthcare Engineering

Volume 2018, Article ID 4750104, 9 pages

https://doi.org/10.1155/2018/4750104

## Nonlinear Predictive Threshold Model for Real-Time Abnormal Gait Detection

Dipartimento di Automatica e Informatica, Politecnico di Torino, Turin, Italy

Correspondence should be addressed to Masoud Hemmatpour; ti.otilop@ruoptammeh.duosam

Received 28 December 2017; Accepted 1 April 2018; Published 26 June 2018

Academic Editor: Valentina Hartwig

Copyright © 2018 Masoud Hemmatpour et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Falls are critical events for human health due to the associated risk of physical and psychological injuries. Several fall-related systems have been developed in order to reduce injuries. Among them, fall-risk prediction systems are one of the most promising approaches, as they strive to predict a fall before its occurrence. A category of fall-risk prediction systems evaluates balance and muscle strength through some clinical functional assessment tests, while other prediction systems investigate the recognition of abnormal gait patterns to predict a fall in real time. The main contribution of this paper is a nonlinear model of user gait in combination with a threshold-based classification in order to recognize abnormal gait patterns with low complexity and high accuracy. In addition, a dataset with realistic parameters is prepared to simulate abnormal walks and to evaluate fall prediction methods. The accelerometer and gyroscope sensors available in a smartphone have been exploited to create the dataset. The proposed approach has been implemented and compared with the state-of-the-art approaches showing that it is able to predict an abnormal walk with a higher accuracy (93.5%) and a higher efficiency (up to 3.5 faster) than other feasible approaches.

#### 1. Introduction

Gait, that is, the manner of walking, is a unique personal trait that recognizes every individual [1]. By revealing the personal trait, gait analysis has numerous applications such as identification, authentication, and action recognition [2–4]. Abnormal gait detection is used in particular in pathological and rehabilitation processes, clinical assessment, automated surveillance, and falling systems [5–7]. In order to decrease fall occurrence and minimize their effects, international organizations advise improving health-care systems. This study focuses on abnormal gait/walk detection with the goal of predicting a fall risk. Fall-risk prediction out of abnormal gait detection is based on the relation between abnormal gait and risk of fall [8].

Critical consequences of falls include long-term disability, reduced mobility, injury, and even death. Physical injury due to a fall, in particular hip fracture, involves economical effects for the society [9]. Several fall risk factors have been identified but few successful approaches are adopted in real cases. Fall-related systems can be categorized into three different types: fall detection, prediction, and prevention systems.

Fall detection systems notify a user’s associate (e.g., caregivers or acquaintance) in case of fall occurrence [10–15]. These systems can be used to provide fast help after a fall, but they do not avoid it, so they are less effective than other systems. Several fall-risk prediction systems (FPSs) have been developed to estimate future fall risk through some clinical assessments. These tests often involve questionnaires or functional assessments of posture, gait, cognition, and other risk factors. These clinical assessments are subjective and qualitative and typically use threshold assessment scores to categorize people as fallers and nonfallers. Another kind of FPS aims to identify an abnormal gait pattern in order to estimate the probability of a real-time fall occurrence [16–19]. Real-time systems continuously assess the fall risk while the user is doing its daily activity. Fall prevention systems predict a fall and provide a solution for preventing real-time or future falls [20, 21]. Fall prevention systems are helpful in reducing the financial and health consequences of a fall [22].

Both prediction and prevention systems usually have some fundamental steps in common, in which prediction and prevention terms are interleaved: first, data are collected from sensors and are analyzed to compute the appropriate feature set; then, the risk of a possible fall is evaluated through some classification algorithms. Movement sensors are usually exploited to investigate the extrinsic parameters of a fall. In this study, common sensors, such as accelerometers (for measuring the acceleration) and gyroscopes (for measuring the angular rate around one or more axes of the space) are considered since they are easily accessible and do not disturb the privacy of the user (e.g., camera and sound sensors). The popularity of smartphones, the preciseness of the features extracted from embedded sensors [23–25], and their ability to easily engage to the IoT framework, motivates researchers to exploit smartphones in their studies. Although some studies employ additional sensors [18, 19], they bring inconvenience to the users such as wearing augmented shoes, belts, and so on. So, the proposed model only adopts the embedded sensors (i.e., accelerometer) in a smartphone to be convenient for the users.

Most of the FPSs analyze the user’s posture or gait variables to investigate the characteristics of the movement. They typically exploit heavy mathematics which leads to high computational time. Since the complexity of an algorithm directly affects the performance, the trade-off between accuracy and complexity is an important consideration. In this paper, a Nonlinear AutoRegressive eXogenous (NARX) walking model is proposed in order to achieve both low complexity and high accuracy. This study is focused on the use of raw accelerometer data for real-time fall-risk prediction to analyze user’s data and assess fall risk during the walk. In the preliminary step, normal walking is modeled and stored based on the user’s acceleration signals out of the NARX identification technique. Then, the system monitors a sliding window of user acceleration and predicts the future behavior of the user gait in real time. If the predicted output can be distinguished from the normal gait pattern through a specified threshold, the system counts the gait as an abnormal walk. Result shows that this approach has higher accuracy up to 2.8% and lower computational time up to 3.5 times in comparison with the state-of-the-art approaches. In this study, the proposed method detects an abnormal gait while the user is walking in a normal manner on flat surface with casual footwear. The focus is finding a method with high accuracy and low performance in order to be feasible in real cases.

The remainder of the paper is organized as follows: Related works in the literature and complexities are reviewed in Section 2. The identification techniques are explained in Section 3. Gait-modeling formulation is presented in Section 4. Finally, some conclusions are written in Section 5.

#### 2. Background and Related Works

FPSs usually consider kinematic fall factors such as velocity, acceleration, tilt, stability, and symmetry. They exploit movement sensors to investigate the kinematic parameters of fall, that is, the characteristics of the movement of the body. Future fall-risk prediction systems estimate the user’s fall risk in an offline test such as Timed Up and Go (TUG), Berg Balance Scale (BBS), Sit To Stand (STS), and One-Leg Stand (OLS) [26–29]. If the fall risk is high, a probable future fall can be prevented through some exercises [30]. Typically, mentioned fall risk tests are applied by experts in clinical environments to evaluate balance and lower limb strength.

In the TUG test, the user is asked to rise from an arm chair, walk three metres away, turn, walk back to the chair, and sit down again. A performance higher than a threshold is identified as high risk of falls. However, the suggested threshold value varies in the literature [29].

The BBS test measures user’s balance by assessing the performance in carrying out a given task. It comprises a set of simple balance tasks. The degree of success in each task is given by a score, and the final measure is the sum of all scores [28].

In the STS test, firstly, the user sits in the middle of a chair, and he/she places his/her hands on the opposite shoulder crossed at the wrists. Then, he/she keeps the feet flat on the floor. Afterwards, he/she rises to a full standing position and then he/she sits back down again. Eventually, this test counts the number of full stands that are completed in 30 seconds. Since slowing of postural movements can be an indicator of the weak lower limb, a low number of full stands shows a high level of fall risk [26].

The OLS test is used to evaluate the user’s balance. The user stands, then he/she raises one leg, with the foot approximately six inches off the ground, keeping the foot raised up for 30 seconds. He/she can sway side-to-side or back-and-forth while maintaining the one-leg stand position. If a user puts his/her foot down some times during the 30-second period, then he/she will fail the test [27].

The drawback of the abovementioned tests is that they demand time and effort. These tests have to be conducted in a supervised environment and may therefore suffer from influences such as the Hawthorne effect, that is, the reaction in which the individual modifies his/her behavior due to his/her awareness of being observed. Unlike the clinical assessment tests, a real-time fall risk is predicted by recognizing an abnormal walking pattern, then the user is alerted [17–19, 31], or an external aid such as a walker or robot is exploited to prevent the fall [20, 21].

In the kinematic analysis of the real-time fall-risk prediction, some approaches detect abnormal gait for predicting a fall risk [17, 32, 33], while others consider the near-fall (i.e., stumble) instances [34]. It is conceivable because the near fall is an indication of a fall. However, a time analysis is missing in order to measure the time between the near-fall detection and the real-fall occurrence. This analysis is essential to check the feasibility of performing any recovery mechanisms before the fall occurrence. However, the main features adopted to detect abnormal gait/walk are explained [34]. In the following formulas, indicates the acceleration and , , and refer to its components along the 3 axes.

When a user significantly tilts in a direction, he/she assumes an abnormal posture, which can lead to a fall. The user tilt is evaluated with the combination of a gyroscope and an accelerometer [17].

*Hjorth parameters* and *energy* measurements of the tilt vector are computed as features of the user gait. Hjorth parameters are statistical measures of the signal, based on its variance in time domain [35]:(i) indicates the signal power.(ii) shows the smoothness of the signal curve.(iii) measures the irregularities in the frequency domain.

The of the acceleration signal specifies the amount of activity in the vertical and horizontal directions. It estimates the strength of the contact with the floor, so it can be used to recognize an abnormal walk pattern such as stumbling. The energy of the signal is computed as follows:

Acceleration-derived features can be used as a near-fall indicator [34]. Several features of the acceleration signal are presented in the following.

*Signal magnitude area* (SMA) is used to classify the user activities. It is computed aswhere is the monitored interval.

*Signal magnitude vector* (SMV) specifies the degree of the movement intensity and the resultant of the acceleration signal as follows:where is the number of samples.

The peak and peak-to-peak are useful measurements of data changing over time. The peak is the maximum value of the signal over the period of time, and the peak-to-peak is the difference between minimum and maximum values of the signal. Moreover, the derivative of the acceleration can be used to indicate the vibration of a user movement. Another feature used in FPSs relies on the relative frequency in data distribution [32].

A co-occurrence matrix is a square matrix that shows the scattering of similar adjacent values at a given offset. Normally, it is applied to the image [36], but its application in fall-risk prediction has been investigated to analyze the acceleration and gyroscope values [32]. Let be the element of the co-occurrence matrix to the sum of all the elements. , , , , and of the co-occurrence matrix [36] are used as features of the user gait [32]:(i)*Contrast* shows the intensity between a cell and its neighbors:(ii)*Homogeneity* measures the spatial closeness of the distribution of elements to the diagonal of the co-occurrence matrix:(iii)*Correlation* shows how a value is related to its neighbors:

where , , and are computed as follows:(iv)*Uniformity* computes the sum of the squares of the elements:(v)*Maximum probability* measures the highest value of the co-occurrence matrix.

The principal component analysis is a mathematical procedure based on an orthogonal transformation of data. The output of the transformation from the accelerometer and gyroscope signals is a set of eigenvectors, which can be used as a feature of walking [33].

##### 2.1. Complexity Analysis

The complexity of an algorithm can be presented as a numerical function of the input () to the algorithm. In this section, the time complexity of the fall-risk prediction algorithms (i.e., feature extraction and the classification) are discussed [17, 32–34].

A combination of average, fixed size matrix multiplication, variance, derivative, and trapezoidal rule is used to compute the feature set [17]. The dominant complexity among the mentioned computation is . Moreover, decision tree (DT) is adopted to predict a fall. The complexity of the classification is related to the number of analyzed features: it is plus the complexity of the classification algorithm that depends on the depth of the built tree [37]. In the presented analysis, is the number of features in the decision tree and is the input size of the algorithm.

The best feature set of acceleration signal for abnormal gait detection is extracted from derivative, trapezoidal rule, peak-to-peak, and average [34]. Among these computations, peak-to-peak exploration has the highest complexity equal to .

The co-occurrence matrix, average, relative frequency, and standard deviation are adopted to compute the feature set and a neural network to detect abnormal walk [32]. The dominant complexity of the feature set extraction is the calculation time for the co-occurrence matrix which is [38], and the complexity of the neural network is , where *L* is the number of layers and *W* is the average number of nodes in each layer.

Principal component analysis of the co-occurrence matrix is adopted as a feature set, and random forest classification is exploited to classify the normal and abnormal walks [33]. The classification complexity of this study increases by a factor of *m* (the number of decision trees in random forest) respecting [17] due to the adoption of random forest classification instead of decision tree.

#### 3. ARX and NARX Identification

An identification technique is commonly used in many engineering areas to build a function that finds a relation between variables in a system. Generally speaking, finding a mathematical model that adequately describes a system is part of the system identification. Most of the physical activities in nature can be described by a dynamic system, where the output depends on the input history. System identification adopts statistical methods to build a mathematical model from measured data of the dynamic system. A three-step procedure is used in preparing the model: firstly collecting data, then building a convenient model, and finally validating the model. In more detail, the mathematical model is based on a function that depends on a set of unknown parameters *θ*:where represents the input and output history and specifies the coefficient parameters. A model can describe either a linear or nonlinear system. In general, the estimation of nonlinear systems is more complex than linear models due to the complex relation among the variables of the model.

AutoRegressive eXogenous (ARX) is a simple, frequently used identification model based on linear difference equation [39]. It describes the input effects on the process output as follows:where the current output relates to a finite number of past outputs and inputs . The model is thus entirely defined by three integers , , and , where is the number of poles and is the number of zeros, while is the pure time-delay in the system.

NARX is a system identification method for discrete nonlinear systems exploiting past input and output data [40]. The NARX model regresses the next output with the previous values of input and output. The mathematical expression of a NARX model iswhere and represent input and output values of the system at time step *t*; *m* and represent the input and output delays, and represents a nonlinear mapping function.where is the set of unknown coefficients , and is a *basis function*. Every continuous function can be represented as a linear combination of a particular function called *basis function*. The main problem is finding a good estimation of function with low identification error. Since each estimation has some noise *ε*, a general equation can be presented as follows:where is the measured output, is a function of , and is the prediction error. Parameter can be estimated by means of the prediction error (PE) method:where and presents the least square. strives to minimize the squares of the errors between real and estimated values. It should be considered that is nonconvex so the solution may be a local optimum instead of the absolute one.

NARX is based on a neural network to approximate the function , as can be seen in Figure 1. The complexity of this part is the same as creating a neural network, but it occurs only once in the training step, and using in real time has a linear complexity.