A time-efficient continuous ramp protocol for data-driven walking energy expenditure estimation across multiple speeds

Abstract

Background

Recent research has sought to use data-driven models to estimate walking energy expenditure across multiple speeds via wearable devices. Many studies employ a discrete step protocol-repeatedly walking at a constant speed for several minutes-because indirect calorimetry depends on time-delayed respiratory responses. However, this approach becomes time-inefficient when constructing sufficiently diverse datasets for deep learning, which requires large amounts of distinctive data. To address this issue, we integrated a data-driven approach with a previously proposed continuous protocol wherein walking speeds are gradually increased within a single trial. The purpose of this study is to compare the effectiveness of such a continuous dataset for energy expenditure estimation against a conventional discrete approach.

Methods

Fourteen subjects walked on a treadmill wearing four IMUs, while energy expenditure was measured using an indirect calorimetry. In the continuous ramp protocol, subjects walked for 10 mins at speeds linearly increasing from 1.0 to 1.75 m/s. The discrete step protocol involved five speeds within the same range, each maintained for 6 mins. In the continuous ramp protocol, energy expenditure was mapped to each speed after compensating for respiratory delay, whereas in the discrete step protocol, we used averaged breath-by-breath measurements of the final 3 minutes. We compared the kinematics, kinetics, and energy expenditure between the two protocols. Subsequently, 13 additional subjects were recruited to compare a commercial smartwatch with linear and deep learning models trained on datasets from each protocol.

Results

After compensating for respiratory delays, no differences in energy expenditure were observed between the two protocols, although kinematic differences appeared at speeds above 1.5 m/s. These differences did not impair estimation accuracy: deep learning models trained on the discrete and continuous datasets showed comparable performance (13.1% vs. 10.7% mean error, respectively), both significantly outperforming the smartwatch. Furthermore, when trained on the more diverse data from the continuous ramp protocol, a deep learning model achieved uniformly low error across a broad speed range with only a single IMU.

Conclusion

The continuous ramp protocol can generate a valid walking motion-energy expenditure dataset in a time-efficient manner, improving model performance by providing richer data diversity. This approach is not limited to walking speed but can be applied to other continuously changing exercise intensities across various forms of locomotion, thus promoting efforts to replace indirect calorimetry, traditionally requires extensive laboratory experiments.

Background

Although monitoring energy expenditure is increasingly recognized as essential for modern health management and disease prevention [1–3], rigorous laboratory-based measurements using respiratory gas analysis are difficult to implement in daily life. Consequently, portable wearable sensors for estimating energy expenditure, also called metabolic rate or power, during daily activities have gained attention as a promising healthcare technology [4]. Walking energy expenditure is modulated by mechanical determinants, such as walking speed, stride frequency, swing-leg mechanical work, and gait asymmetry [5–8]. Recognizing that these variables can be inferred from lower-limb kinematics, recent studies have employed inertial measurement units (IMUs)–compact, inexpensive, and easily wearable sensors–to estimate metabolic cost [9–18]. To further enhance the accuracy of IMU-based energy expenditure estimation, recent studies have explored deep learning methods that directly extract features from signals, rather than relying on feature engineering grounded in domain expertise [11, 13, 15, 16, 18].

Deep learning models are highly effective at capturing the nonlinear relationships between IMU signals–which contain both motion and physiological information–and energy expenditure. However, constructing a dataset is a prerequisite for such models, and this step poses substantial practical challenges. In particular, energy expenditure must be measured via respiratory gas analysis in a laboratory, making data collection costly. Moreover, it is well established that large datasets are required to attain the high level of generalization typically associated with deep learning models [4, 19]. Publicly available or externally shared IMU–energy expenditure datasets are often difficult to reuse if the subjects’ pathological histories, sensor types, or sensor placements differ from those in the target study. Consequently, most researchers investigating IMU-based energy expenditure estimation have generated new datasets for each study [9–15, 17, 18]. Therefore, to enhance the performance of deep learning models, facilitate model architecture exploration, and optimize sensor placements, it is essential to develop more time-efficient methods for constructing IMU–energy expenditure datasets.

The time inefficiency in constructing IMU–energy expenditure datasets originates from the human physiological system’s delayed response [20]. Previous studies on data-driven approaches typically adopt a discrete protocol in which each exercise intensity (e.g., forward speed) is repeated for several minutes [10, 14, 16, 21–24]. When determining energy expenditure from respiratory gases, at least three minutes are required for gas exchange to reach steady-state [25, 26]. An additional 2–3 minutes are often needed to reduce respiratory noise, leading to approximately 5–6 minutes of measurement time per intensity level [27]. Prolonged exercise that induces peripheral fatigue can elevate energy expenditure through cardiopulmonary drift; therefore, experimental protocols should incorporate sufficient rest intervals [28]. Consequently, gathering wearable sensor and energy expenditure data across multiple intensities demands lengthy experiments. Significantly, a time-efficient protocol for measuring energy expenditure affects not only participant fatigue but also the quality of the dataset ultimately used for estimation.

Time efficiency becomes particularly important when constructing datasets across multiple exercise intensities for data-driven approaches. In designing a data collection process for machine learning, it is vital to include diverse scenarios to ensure adequate data variety [29–32]. A diverse dataset provides trained models with more discriminative information, potentially enhancing their generalization performance [30, 32]. The variety in IMU signals and energy expenditure increases with the range of exercise intensities and the number of clinical subjects: higher diversity in intensity level yields richer time-series features and corresponding energy expenditure measurements, while a larger pool captures a wider array of fitness levels and motion patterns. Because discrete protocols involve a small number of intensities and are time-consuming, they reduce dataset diversity; hence, a more time-efficient protocol for simultaneously collecting IMU signals and energy expenditure data is highly desirable.

In recent studies, continuous protocols have been proposed to evaluate energy expenditure across various walking conditions more efficiently in time [20, 33, 34]. Briefly, a continuous protocol gradually varies exercise intensity while measuring respiratory gas exchange. Building on Selinger et al. [26], which approximates gas exchange kinetics as a first-order system, a continuous protocol determines energy expenditure at each exercise state (e.g., walking speed or stride frequency) using non-steady-state respiratory measures, thus saving time. Unlike a discrete approach, a continuous protocol collects respiratory data under continuously changing walking conditions and aims to derive an energy expenditure function. Felt et al. proposed a polynomial-fitting method that minimizes the difference between measured energy expenditure and the function’s output [20]. For data-driven approaches, continuous protocols can facilitate more efficient construction of motion–energy expenditure datasets. In this study, changes in exercise intensity refer to accelerating or decelerating walking speeds, and our dataset comprises motion–energy expenditure results over a continuous range of speeds.

Replacing a discrete protocol with a continuous one in constructing motion–energy expenditure datasets can lead to performance degradation due to motion and energy expenditure distortions arising from transient-state exercise, whereas steady-state conditions are typically the target for estimation. It is well established that domain adaptation–stemming from discrepancies between training and testing datasets–can weaken a model’s generalization performance [35]. Specifically, employing a continuous protocol to collect wearable signals during accelerated walking for motion–energy expenditure datasets containing multiple speeds may introduce distortions [36, 37]. Therefore, to build such datasets in a time-efficient manner, it is critical to evaluate how acceleration-induced motion and energy expenditure distortions affect both the dataset and subsequent estimation outcomes.

The aim of this study is to compare the effectiveness of a time-efficient continuous protocol for estimating energy expenditure via IMUs across multiple walking speeds, relative to a conventional discrete protocol. We propose the following hypotheses: (1) under low acceleration, the differences in lower-limb kinematics and kinetics between the discrete and continuous protocols are minimal; (2) when gas exchange kinetics are considered to compensate for delayed respiratory responses, energy expenditure measured by discrete and continuous protocols becomes comparable; and (3) when trained on a dataset featuring a diverse set of walking speeds, a predictive model can achieve high generalization performance with only one or two IMUs. First, to validate a continuous protocol as a dataset construction alternative, we compare motion and energy expenditure between the discrete and continuous protocols. Specifically, we assess differences in lower-limb kinematics and kinetics to identify potential discrepancies in IMU measurements and compare energy expenditure measured under the discrete protocol with that collected at three accelerations in the continuous protocol. Finally, we train both linear and deep learning models on the motion–energy expenditure datasets generated by the discrete and continuous protocols and evaluate differences in estimation error. Through this approach, we seek to determine whether a continuous protocol can enhance data-driven energy expenditure estimation models while improving time efficiency.

Methods

This section presents the experimental procedures for data collection and the data-driven approach for estimating energy expenditure from IMU signals. Specifically, we describe: (1) the experimental procedures for collecting training and test data with both discrete step and continuous ramp protocols, and (2) the architecture, training, and evaluation of a deep learning model designed to estimate energy expenditure from IMU-based indirect calorimetry measurements.

Subjects

A total of 27 healthy young male subjects (age  years; body mass  kg; height  cm; ) participated in this study. All experiments were approved by the Institutional Review Board (IRB) of KAIST (Approval No. KH2023-091), and subjects participated according to the IRB-approved protocol. Prior to the experiment, we provided subjects with a detailed explanation of the study objectives and protocol, and written informed consent was obtained. To collect training and test data, we randomly assigned subjects to two groups. The training data group (hereafter training group) consisted of 14 subjects (age  years; body mass  kg; height  cm; ), and the test data group (hereafter test group) consisted of 13 subjects (age  years; body mass  kg; height  cm; ). Data collected from subjects in the two groups were used to form the respective training and test datasets for the data-driven energy expenditure estimation. To prevent fatigue-induced increases in energy expenditure caused by prolonged walking, subjects were limited to a maximum of half an hour of walking per visit. Additionally, to reduce the thermic effect of food on energy expenditure, subjects were required to fast for at least two hours prior to the experiment.

Protocol

The training group visited the laboratory a total of three times over  days: once for the discrete step protocol and once for the continuous ramp protocol. Additionally, to examine repeated measurement variability, all training group subjects made one extra visit to perform three walking trials each at 1.2 m/s and 1.5 m/s under the discrete step protocol. In the discrete step protocol, subjects walked on a treadmill at five speeds (1.0, 1.25, 1.5, 1.625, and 1.75 m/s) for 6 minutes each, with a 3-minute rest between trials. The continuous ramp protocol involved walking at three constant accelerations (, , and ), starting at 1.0 m/s and ending at 1.75 m/s. These bouts lasted 7, 10, and 15 minutes, respectively, with rest periods of 3, 5, and 7 minutes proportional to their duration. The order of speeds in the discrete step protocol and accelerations in the continuous ramp protocol was randomized. Speed profiles of both protocols are shown in Fig. 1. To minimize excessive energy expenditure from accelerated walking, the continuous ramp accelerations were set at about of the acceleration (0.15 m/s²) known to induce a increase [37]. The test group visited the laboratory only once, participating solely in the discrete step protocol. Before each protocol, all subjects performed a 6 minutes warm-up at 1.25 m/s. At the beginning of each trial, the treadmill accelerated from rest to the target speed at 0.2 m/s². All sessions were conducted in an air-conditioned laboratory maintained at throughout the study.

Fig. 1.

Schematic of the experimental setup and the deep learning model for energy expenditure estimation. The motion-capture system was used for comparing biomechanical parameters between protocols (A) The subject wears four IMUs and a respiratory gas analyzer while walking on a treadmill. “Disc.” and “Cont.” indicate the discrete step and continuous ramp protocols, respectively. The graph shows the treadmill speeds over time for each protocol (excluding rest periods). Note that rest periods are omitted, and the graph only shows the 10-min continuous ramp protocol used to build the training dataset. B The deep learning model consists of two multi-layer perceptron (MLP) and a Transformer encoder. The model takes a time-series signals of length T and predicts a scalar energy expenditure value. Within the Transformer model, an estimation token () summarizes the time-series data; its summarized representation, , appears in the token-insertion position of the output sequence X?, from which the final estimation is made.

Measurement

Four wireless IMUs (Opal, APDM, Portland, OR, USA; 100 Hz) were attached to the trunk and the right lower limb to measure the 3-axis linear accelerations and angular velocities of each body segment (Fig. 1). The IMUs on the trunk and dorsum of the foot were positioned over the sacrum and the lateral cuneiform, respectively, while the IMUs on the thigh and shank were placed at the lateral midpoint of each segment, aligned with the sagittal plane. All IMU signals were synchronized and recorded using Motion Studio 1.0 (APDM, Portland, OR, USA). We then applied a zero-lag, fourth-order Butterworth low-pass filter with a 6 Hz cutoff frequency to remove high-frequency noise from all IMU signals. Heel strike events were identified by detecting local maxima in the vertical acceleration of the foot-mounted IMU, and these events were used as references for calculating the gait phase. We measured oxygen consumption and carbon dioxide production breath-by-breath using a portable gas analyzer (K5, Cosmed, Rome, Italy) to indirectly estimate energy expenditure. The gas analyzer was calibrated according to the manufacturer’s guidelines once per subject visit, before initiating the walking trials, to ensure measurement accuracy. We then calculated breath-by-breath energy expenditure from the analyzed respiratory gases using the standard calorimetry equation [38]. Throughout this paper, we report gross energy expenditure, i.e., gross metabolic rate uncorrected for resting or upright resting metabolism. We also recorded the energy expenditure estimates provided by a smartwatch (Apple watch series 8, Apple Inc., Cupertino, CA, USA; watchOS 20T5y1) for the test group. Each subject wore the smartwatch on the right wrist, and we set the Workout app to indoor walking mode and tracked each walking session. Although the smartwatch’s energy expenditure estimation algorithm is undisclosed, it records values at 1 second intervals. Before the experiment, we reset the watch’s calibration and entered each subject’s information (age, height, weight) into the Health app. After completing all walking sessions, we extracted the recorded data through the paired smartphone (iPhone 11, Apple Inc., Cupertino, CA, USA; iOS 16.6.1). We analyzed lower-limb kinematics using a motion capture system equipped with 13 infrared cameras (MX T-40, Vicon Motion Systems, Oxford, UK; 200 Hz). A total of 28 passive reflective markers were attached to the feet, shanks, thighs, and pelvis, allowing us to capture 6-DOF (3 translational, 3 rotational) movements of each segment. Ground reaction forces were measured by two force plates (FP6012, Bertec, Columbus, OH, USA; 500 Hz) under a split-belt instrumented treadmill. All marker positions and analog signals were low-pass filtered with a fourth-order, zero-lag Butterworth filter at a 6 Hz cutoff frequency to remove high-frequency noise. We then calculated joint moments at the hip, knee, and ankle using Visual3D v6(HAS-Motion, Kingston, ON, Canada). For the discrete step protocol, we analyzed 50 steady-state walking steps per trial, while for the continuous ramp protocol, we analyzed all steps.

Data analysis

To construct a dataset for data-driven energy expenditure estimation using IMUs, we first mapped speed to energy expenditure, accounting for respiratory time delay. We then paired each IMU signal with the energy expenditure corresponding to the treadmill speed at the moment that signal was recorded. In the discrete step protocol, we assumed that breath-by-breath energy expenditure reached a steady state after the first 3 minutes of walking. Once a steady state was reached, we defined the average of all subsequent breath-by-breath measurements as the energy expenditure at each speed. For each trial under the discrete step protocol, we paired the IMU signals with the energy expenditure corresponding to that speed. In the continuous ramp protocol, subjects walked at increasing speeds, resulting in a non-steady state or time-delayed breath-by-breath energy expenditure response. We compensated for this delay using Instantaneous Cost Mapping (ICM) [20], assuming a 42-second time constant for the exercise gas exchange kinetics [26]. ICM approximates the speed–energy expenditure relationship with a second-order polynomial. For each IMU measurement, we paired the IMU signal with the corresponding approximated energy expenditure mapped to the treadmill speed at that moment. Each subject completed three accelerated walking trials, and we applied ICM to each trial individually to derive speed–energy expenditure functions. Unless otherwise noted, all subsequently reported energy expenditure is considered time-delay compensated.

Protocol comparison

To evaluate how accelerated walking in the continuous ramp protocol affects energy expenditure as well as kinematic and kinetic measures, we compared energy expenditure, joint range of motion (ROM), and peak moments with those obtained from the discrete step protocol. All comparisons were conducted at five walking speeds defined in the discrete step protocol. The energy expenditure from the continuous ramp protocol was fitted to a speed-dependent quadratic polynomial, and the values at each speed were compared with the discrete step protocol results. Joint ROM and peak moments were analyzed on a per-step basis. For the discrete step protocol, we used the average values from the analyzed steps. In the continuous ramp protocol, every measurement of ROM or peak joint moment was paired with its instantaneous walking speed and regressed using a third-order polynomial. The fitted curve was evaluated at the five target speeds, and the resulting values were compared with those obtained from the discrete step protocol [34]. This comparison procedure was only for 10-min continuous ram protocol and repeated for each subject.

We also estimated a subject-specific time constant for each subject and assessed how this personalization altered the energy-expenditure difference between protocols. For each subject, the time constant was optimized to minimize the sum of squared differences in energy expenditure between the discrete step and continuous ramp protocol (10 min). Optimization was performed with fmincon in MATLAB R2024a (MathWorks, Natick, MA, USA); upper and lower bounds were set to 80 sec and 20 sec, respectively, based on the range reported by [26]. We report the resulting personalized time constants as well as the corresponding energy expenditure differences between the two protocols.

Dataset preparation

All datasets contain IMU signals, body information (weight and height), and energy expenditure. IMU signals and body information serve as inputs to the estimation model, while energy expenditure is used as the label (or ground truth) during training and testing. In the following sections, the Discrete dataset and Continuous dataset refer to the datasets constructed from the discrete step and continuous ramp protocols, respectively. These datasets, collected from the training group, are used for training the deep learning model that estimates energy expenditure. The Discrete dataset includes IMU signals from the last 2 mins (50 steps) of walking at each of the 5 speeds, while the Continuous dataset includes IMU signals for every step during 10-min accelerated walking. To balance motion distortion and time efficiency, we constructed the dataset using a 10-min continuous ramp protocol with a moderate acceleration rate. IMU signals and energy expenditure were synchronized through the mapping process described previously. Finally, the Test dataset, collected from a test group following the discrete step protocol, is used to evaluate the final performance of the deep learning model trained on the training dataset. All datasets’ IMU signals were represented as multi-channel time series, treating each axis of linear acceleration and angular velocity as a separate channel. We then segmented these signals into 2-second windows to facilitate batch processing. The 2-second window length ensured that each sample contained at least one stride, and we did not allow any temporal overlap between samples. To balance the scale of different signal sources, we applied min–max normalization to each axis of acceleration and angular velocity. When constructing the training dataset, we tried to mitigate overfitting by augmenting the data through virtual rotation of the IMU signals [29]. For each batch, yaw, pitch, and roll angles were sampled within at random, a combined rotation matrix was formed, and this matrix was multiplied by the raw three-axis acceleration and angular velocity vectors.

Deep learning model

In this study, we designed a deep learning model for estimating energy expenditure during walking using IMU signals, based on a Transformer encoder, as shown in Fig. 1. The Transformer architecture follows the proposal by Vaswani et al. [39] and excels at capturing patterns that reflect long-term dependencies in time-series data. At the front end of the model, a multi-layer perceptron (MLP), referred to as MLP_emb, processes each time-step IMU signal individually to generate an embedding vector. The Transformer encoder then takes this sequence of embedding vectors as input, learning complex temporal patterns and extracting contextual features. Finally, MLP_est uses the encoder’s output to estimate energy expenditure as a scalar value. In the following section, we provide a detailed explanation of input signal processing, model architecture, and the training procedure. A single time sample , consisting of the 3-axis acceleration and angular velocity signals from IMUs, is combined with the gait phase as described in Eq. (1) and then fed into MLP_emb:

1

As described in Eq. (2), the output passes through a Layer Normalization [40], and is then concatenated with the normalized subject’s height and body mass to form a high-dimensional embedding :

2

Here, represents the dimension of the embedding vector, ensuring that the embedding can simultaneously represent both the temporal patterns of the IMU signals and the subject’s physical characteristics. Next, we append a learnable estimation token to the embedding sequence of length T, forming . The estimation token , created by concatenating a learnable vector with and , is fed into the Transformer encoder, where it summarizes the contextualized output [41]. The Transformer encoder implemented by Vaswani et al. [39] consists of a stack of blocks, each composed of a self-attention layer, sample-wise feed-forward neural networks. The self-attention layer considers the relationships between the entire embedding sequence X simultaneously, enabling each time-step’s representation to incorporate contextual information. The sample-wise, nonlinear feed-forward networks further enrich these contextual features. By repeating this block structure multiple times, the final output maintains the same length and channel dimension as the input sequence, while providing enhanced representations at each time step. In this output , the vector at the position where was inserted in the original X serves as a summary representation of the entire sequence. We feed into MLP_est as shown in Eq 3 to obtain the energy expenditure estimate :

3

MLP_est shares the same architecture as MLP_emb, except that its output layer consists of a single node.

Model training and evaluation

We employed the mean squared error (MSE) of energy expenditure as the loss function for training the deep learning model. Before training, all learnable parameters were randomly initialized. At each iteration, we computed the error between the estimated and measured energy expenditure, and performed gradient descent based on the parameter gradients obtained via backpropagation. During this process, we used the Adam optimizer with a learning rate of [42] and set the batch size to 256. To prevent overfitting and improve generalization performance, dropout () was applied to all layers except MLP_est[43]. The main hyperparameters for the energy expenditure estimation model were determined through a validation process. Validation was conducted independently for both the Discrete dataset and Continuous dataset, employing a five-fold cross-validation strategy with subject-wise splitting. From the validation results, we selected the hyperparameters: the maximum IMU rotation angle for data augmentation, the embedding vector dimension, the number of heads in the self-attention layer, and the number of blocks in the Transformer encoder. Based on a random search, we chose the hyperparameters that yielded the lowest mean absolute percentage error (MAPE). With the final chosen hyperparameters, the entire training dataset was retrained, and the model’s performance was evaluated on the Test dataset. We adopted MAPE as the evaluation metric for energy expenditure estimation. To reduce the variance caused by randomness in mini-batch sampling and parameter initialization, we trained 20 models and reported the average test results.

Linear model

To benchmark the deep-learning approach, we reproduced the data-driven linear model described by Slade et al. [10, 16). Its input vector contains the vectorized IMU signals concatenated with the subject’s height and weight, and estimated energy expenditure is expressed as a linear combination of these inputs plus a bias term. The model coefficients were fitted by ridge regression, which minimizes the sum of the mean-squared error on the training dataset and an L₂ penalty.

Statistical analysis

To investigate differences between the discrete step and continuous ramp protocols, we compared the biomechanical parameters and energy expenditure collected under both conditions (Table 1). At five walking speeds under the discrete step protocol, repeated-measures ANOVA was performed to assess differences in lower-limb joint ROM, peak moment, walking frequency, stride length, and energy expenditure. In the case of energy expenditure, additional conditions were included in which different walking accelerations were applied or ICM was not used in the continuous ramp protocol, thereby examining how acceleration and respiratory time-delay compensation affect errors. If a significant difference was found, Tukey’s honestly significant difference (HSD) test was conducted as a post-hoc analysis to identify differences among conditions. To test differences in the errors of various energy expenditure estimation methods, we conducted repeated-measures ANOVA on each walking speed and the overall average, followed by post-hoc analyses using Tukey’s HSD. In addition, the linearity between measured and estimated energy expenditure was evaluated by comparing the subject-wise first-order regression line with the line of identity (); slope and intercept were analyzed using paired-sample t-tests. Likewise, repeated-measures ANOVA and Tukey’s HSD were applied to the errors obtained by varying the number of IMUs in training deep learning models with each Discrete and Continuous datasets. When one to three IMUs were used, we included only the combination that exhibited the lowest MAPE among possible combinations. All statistical analyses were conducted using MATLAB R2024a (MathWorks, Natick, MA, USA), with a significance level () of 0.05.

Table 1.

Comparison of biomechanical parameters and energy expenditure between the discrete step and continuous ramp protocols

Values are “Disc.” and “Cont.” refer to the discrete step protocol and the 10-minute continuous ramp protocol, respectively. “7 min” and “15 min” rows indicate energy expenditure measured during the 7-minute and 15-minute continuous ramp protocols. Boldface values denote statistically significant differences between the two protocols ().

Results

The deep learning model trained on the Continuous dataset showed comparable or slightly superior energy expenditure estimation performance compared to the Discrete dataset-based models across most walking speeds (Fig. 2). Notably, although the Continuous dataset required only about one-quarter of the collection time compared to the Discrete dataset, the deep learning model’s estimation accuracy remained comparable. When comparing the deep learning models trained on the two datasets at each walking speed, the model trained on the Discrete dataset showed significantly lower errors at 1.5 and 1.625 m/s (). However, overall, the estimation errors between the two deep learning models– and , respectively–were not statistically significant (). Similarly, the linear model trained on the Discrete dataset exhibited significantly larger errors at walking speeds of 1.0 m/s, 1.5 m/s, and 1.625 m/s compared to the deep learning model trained on the Continuous dataset (). However, although the deep learning model exhibited a mean error that was lower than the linear model across all walking speeds, the difference in errors was not statistically significant (). Meanwhile, the deep learning model based on the Continuous dataset demonstrated significantly lower errors than the smartwatch across all walking speeds ().

Fig. 2.

Energy expenditure estimation errors of four methods at various walking speeds. The bars represent mean absolute percentage errors (MAPE) between indirect calorimetry measurements and estimates obtained from a smartwatch (gray), a linear model trained on the Discrete dataset (sky blue), a deep learning model trained on the Discrete dataset (navy), and a deep learning model trained on the Continuous dataset (red). Error bars represent standard deviations, and asterisks (*) indicate statistically significant differences ().

We compared biomechanical parameters and energy expenditure between discrete step and continuous ramp protocols across walking speeds from 1.0 to 1.75 m/s (Table 1, Fig. S1). Within the proposed acceleration ranges, most kinematic and kinetic parameters, as well as energy expenditure, exhibited consistent patterns between the two protocols. A statistically significant difference in ROM was observed only at the ankle at 1.75 m/s (). Spatiotemporal gait parameters also remained consistent across both protocols, except that the discrete step protocol exhibited a significantly lower cadence at 1.625 and 1.75 m/s, as well as a significantly shorter step length at 1.75 m/s ().

Energy expenditure increased consistently with speed in both protocols, showing no significant differences between the discrete step and continuous ramp protocols (Fig. 3). The mean percentage error (MPE) between protocols was (), and no significant differences were found across speeds (). Without ICM, the continuous protocol significantly underestimated energy expenditure (MPE , ). By speed, significantly lower energy expenditure was observed at 1.0, 1.625, and 1.75 m/s (). This highlights the importance of ICM for accurate measurements while retaining the time efficiency of the continuous ramp protocol. Moreover, among the three acceleration levels, only the walking with the highest acceleration (), which ended after 7 mins, showed a significantly lower energy expenditure at the lowest speed ().

Fig. 3.

Comparison of energy expenditure between discrete step and continuous ramp protocols. Navy dots with error bars and red lines with shaded areas indicate the results of the two protocols, respectively (). The dashed navy line represents a quadratic polynomial regression of discrete step protocol data, while the solid green line shows continuous ramp protocol data with no ICM applied. Asterisks denote statistically significant differences compared to the discrete step protocol, and the color of each asterisk corresponds to the protocol being compared.

In both protocols, energy expenditure steadily increased with walking speed, and no statistically significant difference was observed between the discrete step and continuous ramp protocols (Fig. 3). No walking speed showed a statistically significant difference in energy expenditure (). The mean percent error (MPE) was (). These results suggest that the continuous ramp protocol, when ICM is applied, offers comparable accuracy in energy expenditure estimation relative to the discrete step protocol.

In addition, when the 7-min and 15-min continuous ramp protocols were compared with the discrete step protocol, no significant differences were found in energy expenditure (). However, when ICM was not applied, the MPE of the continuous ramp protocol was (), significantly differing from the ICM-applied condition () and indicating an underestimation of energy expenditure. Specifically, energy expenditure was significantly underestimated at 1.0 m/s, 1.625 m/s, and 1.75 m/s (). Therefore, while accelerated walking in continuous ramp protocols does not substantially increase overall energy expenditure, ICM is critical for correcting underestimation and ensuring measurement accuracy.

Optimizing the time constant for each subject to minimize the energy expenditure mismatch between the discrete step and continuous ramp protocols yielded a mean time constant of , which did not differ significantly from the assumed fixed value of . Recalculating energy expenditure with these individual time constants reduced the total inter-protocol mean absolute percentage error by  (), indicating a significant improvement in agreement between the two protocols.

It is well-established that energy expenditure exhibits inherent variability even within the same subject performing identical activities [44, 45]. During the discrete step protocol, three repeated measurements of energy expenditure each at 1.2 m/s and 1.5 m/s walking speed yielded a coefficient of variation of , , respectively. When comparing the mean of these three measurements from walking at 1.5 m/s to a measurement from a different day, the MAPE was . The MAPE between discrete step and continuous ramp protocols was , though this difference was not statistically significant (). Thus, the differences observed between the discrete step and continuous ramp protocols were comparable to intra-subject variability levels. In addition, the coefficient of variation for breath-by-breath energy expenditure on steady-state walking was , significantly higher than the intra-subject variability (), confirming that averaging at least 2–3 mins effectively attenuates respiratory noise.

Notably, energy expenditure in the discrete step protocol closely followed a quadratic relationship with walking speed. Regression analysis of data from the discrete step protocol using first-, second-, and third-order polynomials revealed that the quadratic function provided statistically significant coefficients () and achieved a high coefficient of determination (). This finding supports our assumption of using a quadratic function to represent the speed-energy expenditure relationship in ICM.

All energy expenditure estimation methods effectively capture the tendency for energy expenditure to increase with walking speed and estimate values close to the steady state immediately after the onset of walking (Fig. 4). This stands in contrast to the transient responses observed in indirect calorimetry, largely because these methods leverage IMU signals that quickly settle into a steady state after changes in walking speed. Meanwhile, the smartwatch showed smooth estimation results overall; it exhibited delayed convergence to steady state. Both IMU-based linear and deep learning models exhibited sharp fluctuations in their energy expenditure estimates, reflecting the stride-to-stride variability in IMU signals.

Fig. 4.

Energy expenditure estimation of four methods at various walking speeds. Each row illustrates energy expenditure estimates: A–C a smartwatch; D–F a linear model; G–I a deep learning model trained on the Discrete dataset; J–L another deep learning model trained on the Continuous dataset. The columns display representative subjects for each method, ordered from the case with the lowest error on the left to the case with the highest error on the right. We also show breath-by-breath energy expenditure (gray line) and the 3-minute average (black line), which serves as the ground truth. The horizontal axis indicates walking time; rest intervals are omitted, and trials have been reorganized in ascending order of speed for clarity.

The deep learning model trained on the Continuous dataset effectively estimated increases and decreases in energy expenditure in response to changes in walking speed (Fig. 5). Analyzing the subject-specific Pearson correlation coefficients between the energy expenditure measured via respiratory gas analysis and the model’s estimated values revealed a high correlation (). In addition, both the slope () and intercept () showed no statistically significant difference from the line of identity () (). A similar trend was also observed in the deep learning model trained on the Discrete dataset. Although the smartwatch estimates likewise exhibited a high correlation (), the slope () significantly differed from the line of identity (). In contrast, the linear model using the Discrete dataset showed a relatively lower linearity (), and its intercept () also exhibited a statistically significant difference from the line of identity ().

Fig. 5.

Correlation between measured and estimated energy expenditure. The measured values were obtained using indirect calorimetry, while the estimates were generated by a deep learning model trained on the Continuous dataset. Each circular marker represents measured and estimated energy expenditure at five test speeds, with the color corresponding to each subject. The solid lines indicate the linear regression results for each subject, while the gray dashed line represents the line of identity ().

The pattern of estimation error in the deep learning model with respect to the number of IMUs showed smaller errors when fewer IMUs were used, regardless of the dataset (Fig. 6). Overall, the model trained on the Discrete dataset exhibited a reduction in average error when using only 2 IMUs, while the model trained on the Continuous dataset showed a reduction when using only 1 IMU. However, despite these reductions in average error, no IMU combination showed statistically significant differences in error ().

Fig. 6.

Energy expenditure estimation errors of the deep learning model according to the number of IMUs. Panels A and B show the results obtained using the Discrete, and the Continuous dataset. Each row displays the estimation errors when using one to four IMUs in order. For cases where one to three IMUs were used, only the combination that achieved the lowest error among all possible sets.

The deep learning model trained on the Discrete dataset exhibited large errors at certain walking speeds depending on the IMU combination used. When the shank IMU was included, the model showed significantly higher errors at 1.5 m/s compared to when it was excluded (). At 1.625 m/s, it also showed significantly higher errors compared to the combination with the lowest mean error (). In contrast, the model trained on the Continuous dataset showed minimal differences in error across all walking speeds, depending on the IMU combination, and no IMU combination showed statistically significant differences (). These results suggest that the Continuous dataset is able to train a model less sensitive to specific IMU placements, resulting in more consistent performance across all speeds.

Discussion

In this study, we propose a time-efficient method of utilizing a continuous ramp protocol to estimate walking energy expenditure based on lower-limb kinematics measured by IMUs. Conventional discrete step protocols, which measure energy expenditure by waiting for delayed respiratory gas exchange to stabilize at each constant walking speed, are time-consuming and can induce fatigue in subjects. To address these limitations, we introduced a continuous ramp protocol that reduced experimental time by over compared with the conventional protocol, while achieving comparable levels of energy expenditure estimation accuracy (Fig. 2). This result suggests that our accelerated walking protocol induces only minimal distortion in both energy expenditure and kinematic aspects compared to constant-speed walking (Table 1), aligning with recent biomechanics studies. Wade et al. [36] reported that accelerated walking alters lower limb kinematics and kinetics; however, at the acceleration level used here, the resulting changes were small, indicating minimal motion distortion. Koller et al. [33] and Malcolm et al. [34] confirmed that appropriately designed continuous ramp protocols yield similar energy expenditure measurements to those of discrete step protocols. Our energy expenditure estimation accuracy maintained comparable levels to Slade et al. [10], whose lower limb IMU-based study employed discrete step protocols while significantly reducing data collection time. These findings demonstrate that human movement itself contains valuable information about energy expenditure, and data-driven methods can effectively extract this information. Furthermore, a continuous ramp protocol based on exercise gas exchange kinetics can serve as a time-efficient approach for developing data-driven methods when attempting new sensor placements or workloads.

Compensating for the time-delayed respiratory response through instant cost mapping (ICM) [33] played a crucial role in ensuring the accuracy of our continuous speed protocol. As walking speed or exercise intensity changes, the respiratory response is delayed by the time required for oxygen delivery and utilization in muscle activity and metabolic processes. By incorporating the first-order system characteristics with a time constant of 42 seconds, we significantly reduced the differences in energy expenditure between continuous and discrete protocols at equivalent speeds (Fig. 3). This finding reaffirms earlier results showing that respiratory changes in response to walking speed can be described as a first-order system [26]. The subject-specific time constant that best minimized the energy expenditure disagreement between protocols did not differ statistically from the empirically derived reference value of . However, the optimized time constants showed a greater coefficient of variation, likely because breath-by-breath noise was not reduced through repeated-trial averaging. Nevertheless, the marked error reduction achieved with personalized constants underscores substantial inter-individual variability in gas-exchange kinetics, demonstrating that tailoring these kinetics can further improve ICM accuracy in the continuous protocol. Because larger time constants have been noted in older adults and in disease conditions [25], identifying an individual’s kinetics will be important for extending our findings to broader populations. Moreover, cycling studies have reported time constants as low as 26 s, underscoring the need for caution when applying gas-exchange kinetics assumptions [45]. Finally, adopting higher-order models of respiratory kinetics offers a promising route to more accurately characterize gas-exchange dynamics [46, 47].

The continuous ramp protocol proposed in this study not only enhances time-efficiency in data-driven research but also addresses limitations of the conventional discrete approach for experiments aimed at examining biomechanical characteristics at multiple speeds. Human gait varies in joint kinematics, kinetics, and energy expenditure according to walking speed, necessitating experiments across a broad range of speeds to capture these properties. However, discrete step protocols can induce fatigue, potentially confounding the measurements with factors beyond the speed effects. In contrast, a continuous speed protocol with an appropriate acceleration, such as one employed here, minimizes differences in joint kinematics relative to constant speed walking and reduces fatigue. For instance, continuous protocols can serve as a time-efficient and precise alternative in studies seeking optimal cost of transport (COT) speeds. Determining an individual’s optimal COT speed under various walking conditions–such as different loads and inclines–requires testing at multiple speeds. Yet, discrete step protocols are constrained by respiratory delays, as measuring energy expenditure at multiple speeds demands considerable time, typically limiting tests to around five speed conditions and thus limiting accuracy in estimating optimal COT speed [48, 49]. The continuous ramp protocol overcomes these limitations: as shown in Fig. 7, the optimal COT speed ( m/s) obtained from the training group closely matched that of the discrete protocol ( m/s) (). Moreover, as accelerated walking involved in the continuous protocol induces negligible changes in joint kinematics and kinetics, it is also applicable to studies examining relationships between energy expenditure and biomechanical parameters–such as mechanical work and mechanical efficiency–across different walking speeds [6, 50].

Fig. 7.

Speed-dependent cost of transport (COT) derived from the discrete step and continuous ramp protocols. The navy dotted and red solid lines indicate the average COT () for the discrete step and continuous ramp protocols, respectively, and both are fitted with a second-order polynomial. The arrows mark the optimal COT speeds. “n.s.” denotes the absence of a statistically significant difference.

When collecting a dataset for energy expenditure estimation, employing a continuous ramp protocol not only offers time efficiency but also yields high generalization performance under various conditions, such as different speeds and numbers of sensors. This indicates that, in training deep learning models, the sheer amount of data is as crucial for generalization as data accuracy. Although the discrete step protocol provides accurate energy expenditure measurements by stabilizing respiratory responses considering gas kinetics, it yields limited data points due to time constraints. In this study, training a deep learning model on the Discrete dataset resulted in decreased performance at certain speeds depending on the IMU used (Fig. 6). In contrast, the Continuous dataset, which captures relationships between motion and energy expenditure across a wide range of speeds mitigated overfitting and bias, achieving high generalization performance for all tested speeds and IMU configurations [30]. Notably, the shank IMU degraded model performance under the Discrete Dataset but proved effective–even as a single sensor–when using the Continuous dataset. This suggests that, although shank kinematics contain essential features for estimation, low speed diversity can hinder robust generalization even with an optimally positioned sensor.

The deep-learning model reduced MAPE by at least relative to the linear model when estimating energy expenditure (Fig. 2). This performance advantage was consistent across models trained on both Discrete and Continuous Datasets. We attribute the improvement to the hierarchical, non-linear representation learned by the model, which combines self-attention with a sample-wise MLP. This approach captures higher-order correlations, such as stride-to-stride variability and the interaction between lower-limb kinematics and anthropometric factors, thereby minimizing residual error. The accuracy gain persisted even when the model was compared with a feature-engineered regression proposed by [51]. The linear regression model, which predicts mass-normalized energy expenditure from height-normalized walking speed squared, yielded a MAPE of , exceeding the error of the smartwatch. These findings align with earlier work [10, 15, 18], which reports that data-driven, non-linear models offer superior accuracy compared to feature-engineering-based approaches.

Neither the Discrete nor the Continuous dataset produced the highest estimation accuracy when all available IMUs were used (Fig. 6). This implies that some sensors provide redundant features, adding little to training data diversity. Moreover, the tendency for errors to increase when using more sensors reflects not only feature redundancy but also overfitting arising from an increased number of model parameters. These findings align with prior studies on accelerometer-based motion classification studies reporting performance declines as sensor counts increase [52, 53]. They also highlight the necessity of optimizing sensor placement to minimize redundant information [54]. When heuristic search for the optimal placement is challenging, adopting a continuous ramp protocol can be highly advantageous for constructing a prototype dataset with minimal experimental time.

By virtually altering subjects’ body weight and height, we observed changes in the deep learning model’s energy expenditure estimates that closely aligned with established findings in the biomechanics literature (Fig. 8). Because deep learning models–often described as “black boxes”–incorporate numerous parameters and nonlinear operations, their inference processes are not readily interpretable. Thus, we adjusted anthropometric measures in the model’s input and examined the resulting outputs to verify whether the model had learned how body size influences energy expenditure. Consequently, when evaluating Test dataset in which body weight and height were varied, the output changes showed trends consistent with previous biomechanical research. Specifically, when the deep learning model trained on the Continuous dataset received inputs representing 80–120% of the original weight or height, the estimated energy expenditure changed from to and from to , respectively. These findings align with a simpler model proposed in prior studies [55], which uses weight, height, and walking speed to predict energy expenditure–incorporating terms proportional to body weight and inversely proportional to the square root of height. Thus, even in the absence of conventional feature engineering or explicit mathematical modeling, the deep learning model appears to capture the relationship between anthropometric factors and energy expenditure in its inference process. However, when trained on the Discrete dataset, changes in weight and height did not exhibit clear increases or decreases. This outcome implies that differences in generalization–arising from the broader diversity of walking speeds in the Continuous dataset–indeed affect the model’s inference process.

Fig. 8.

Comparison of the deep learning model’s results under synthetic changes in body size. The model was trained on the Continuous dataset. The plotted values (mean ± SD) show changes in estimated energy expenditure () when the subject’s weight () and height () are modified. Asterisks (*) indicate statistically significant differences ().

The effectiveness of data augmentation–implemented to ensure robust energy expenditure estimation under varying IMU attachment orientation–differed according to model complexity and capacity. When augmentation was performed through random IMU rotation, the linear model’s estimation errors decreased, whereas the deep learning model showed only minimal changes. As the maximum random rotation angle about the axis perpendicular to the skin increased from to , the MAPE of the linear model trained on the Discrete Dataset steadily declined from to . In contrast, the deep learning model’s error increased slightly from to , and similarly minimal changes were observed when trained on the Continuous dataset. This suggests that the deep learning model learns patterns from modestly rotated data that remain largely consistent with the original dataset–an outcome that can be interpreted as an effect of its high expressiveness, which is capable of representing complex functional relationships. Considering that the data augmentation functions as a regularization method to generalize sensor attachment orientation, one can infer that the linear model was particularly prone to overfitting during training. Moreover, for the linear model, the random rotation angle selected in the validation stage was the one that minimized error, indicating that validation is an effective means of mitigating overfitting.

This study has the following limitations. First, the comparison between the discrete and continuous protocols involved a relatively small number of subjects, which may have contributed to the absence of observed statistically significant differences. Accordingly, we do not assert that the discrete step protocol should be replaced entirely; rather, we emphasize that our purpose was to examine the potential benefits and drawbacks of employing the time-efficient continuous ramp protocol. Second, the small sample size limits the statistical power required to fully elucidate the impact of the training dataset and the number of IMUs on performance. Third, although weight and height were used alongside IMU signals for energy expenditure estimation, these anthropometric measures have limitations in reflecting physical capabilities such as muscle mass, body fat percentage, and maximal oxygen uptake. Previous studies mentioned that integrating physiological signals (heart rate, skin temperature, SpO2, etc.) with motion data (accelerometer, EMG) yields more accurate energy expenditure estimation than relying on motion data alone [23]. However, considerable inter-individual variability in heart rate can lead to systematic overestimation of energy expenditure, so HR-based methods must be employed with caution [10, 56]. Because physiological signals, like respiration, also exhibit delayed responses, incorporating them into the continuous protocol via signal-specific kinetics could further enhance energy expenditure estimation accuracy. Finally, at high intensities, the growing contribution of anaerobic metabolism leads to lactate-associated increases in energy cost, limiting the applicability of the continuous ramp protocol [57].

Conclusion

In this study, we employed a continuous ramp protocol to collect IMU signals and energy expenditure during accelerated walking within a greatly shortened time, capturing a broad range of speeds. From the resulting dataset, we obtained a data-driven estimation model that exhibited consistently low estimation errors over a wide speed range. The accuracy for new subjects surpassed that of a commercial smartwatch and matched the outcomes of the more time-consuming discrete protocol. Moreover, when trained on the dataset from the continuous ramp protocol featuring dense speed coverage, a deep learning model achieved uniformly low errors with only a single IMU. These findings suggest that motion and energy expenditure distortions induced by acceleration remain minimal, particularly when employing low accelerations and compensating for the time-lagged respiratory response.

The continuous ramp protocol can be extended to locomotion-based energy expenditure estimation studies that have lengthy laboratory experiments. For instance, IMU–energy expenditure datasets can be constructed for running, inclined walking, or stair climbing at various intensities, providing sufficient training scenarios for deep learning models while limiting experimental overhead. The shorter duration of high-intensity exercise is advantageous for tasks such as stair climbing, where fatigue can significantly restrict data collection. Furthermore, the continuous variable used for walking speed in this study can be extended to define torque profiles in exoskeleton assistance [20, 34]. If paired with a sufficiently accurate, real-time energy expenditure estimation technique, continuous ramp protocols may eventually replace indirect calorimetry for optimizing exoskeleton assistance. However, caution is warranted regarding potential long-term training effects and short-term motion adaptations in users. In this regard, our findings serve as a benchmark for understanding how motion and energy expenditure distortions affect estimation performance and may encourage further research into data-driven methods to replace laboratory-based indirect calorimetry.

Author contributions

All authors conceived the research questions. HHJ designed and performed the experiment. All authors analyzed and interpreted the data. All authors prepared the manuscript. All authors reviewed, edited, and approved the final version of the manuscript.

Funding

This work is supported by the National Research Foundation of Korea(NRF) grant funded by the Korea Government (MSIT) (No. RS-2024-00356657).

Data availability

No datasets were generated or analysed during the current study.

Declarations

Ethics approval and consent to participate

All participants provided written informed consent prior to participating in the study. The study was approved by the Institutional Review Board (IRB) of KAIST (Approval No. KH2023-091).

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12984-025-01707-8.