The motivation is stark. When the I-35W highway bridge in Minneapolis collapsed in 2007, killing 13 people, the subsequent National Transportation Safety Board investigation traced the failure to gusset plates whose load capacity had been compromised by a design error. Localized weakness had gone unnoticed until catastrophe. The aviation world offers similar warnings: reviews of aircraft fatigue accidents show that cracks frequently initiate at riveted joints and other stress-concentration interfaces, and the January 2024 in-flight separation of a door-plug panel on a Boeing 737-9 MAX underscored how elusive such vulnerabilities can be. In practice, sensors are rarely installed at every location of interest, so the quantities that matter most for fatigue assessment often remain unmeasured.

Existing approaches to this problem fall into two broad camps. Model-based structural health monitoring interprets measured responses through physics-based frameworks such as the eigensystem realization algorithm, subspace identification, augmented Kalman filtering, and Bayesian model updating. These methods are powerful but sensitive to modeling assumptions about material properties, connection stiffness, damping, and boundary conditions, and discrepancies between predicted and measured responses tend to be largest precisely near the local stress concentrations where failure begins. Data-driven methods, from convolutional and recurrent neural networks to sequence-to-sequence models with attention mechanisms, learn relationships directly from signals, but most still assume measurements from multiple distributed sensors or require strain-based inputs. Under truly sparse sensing, estimating internal responses becomes an underdetermined problem, because similar boundary measurements can correspond to different internal deformation states.

The new framework, developed by Jin Hyeok Seok, Ji Wan Seo, Yeong Kwan Jo, Sang Hu Park, Jae Hyuk Lim, and YunHo Kim, takes a different route. Rather than deepening the network to boost its representational capacity, the team split the prediction task into two sequential stages that mirror the physics of structural response. In the first stage, a shallow time-delay neural network converts boundary acceleration into boundary displacement. In the second stage, a second shallow network uses that estimated displacement to infer the internal strain. Each stage therefore learns only a reduced, physically consistent mapping, which keeps the model compact and trainable on limited experimental data while preserving sensitivity to the quantities that matter.

The choice of a shallow time-delay neural network, or TDNN, was deliberate. Each network consists of a single hidden layer with an input delay of eight time steps, allowing it to exploit short-term temporal dependencies in the vibration signal without the data appetite of deep sequence models. The first stage and the single-stage baseline used ten hidden neurons, while the second stage used five. Training employed the Levenberg-Marquardt backpropagation algorithm with full-batch optimization, validation-based early stopping, and a dataset of roughly 9,110 time-series samples split into training, validation, and test subsets at ratios of 70, 15, and 15 percent. A separate prediction dataset of about 121,291 samples, never seen during training, evaluated generalization.

The experimental validation was conducted on a commercial outdoor air-conditioning unit roughly 1.7 meters tall and weighing about 250 kilograms, mounted on an industrial rotary vibration system designed to reproduce transportation-type excitation conditions consistent with MIL-STD-810F guidance. Triaxial accelerometers with a 40 g range were rigidly bolted to the base structure to capture boundary acceleration, while strain gauges were attached to pipe sections inside the unit, locations that are structurally sensitive but sit in narrow spaces poorly suited to long-duration monitoring. Strain signals were initially recorded at 10 kHz and systematically downsampled; 500 Hz preserved the reference waveform with a similarity greater than 0.99 and was selected for training. Boundary displacement was obtained by numerically integrating acceleration with Simpson’s rule, with drift corrected by resetting displacement to zero at the end of each 3.5 Hz excitation cycle.

The results reveal both the promise and the subtlety of the approach. Over a 242-second prediction period, far longer than the training segments, both the one-stage and two-stage models produced stable strain estimates without divergence, adjusting smoothly when excitation intensity changed at around 125 seconds. Yet direct time-domain comparison produced negative coefficients of determination, at -0.66 for the one-stage model and -0.76 for the two-stage model, despite visually similar waveforms. The culprit was progressive phase drift: predicted peaks gradually shifted relative to measured peaks, with offsets growing from roughly 0.134 seconds early in the record to about 0.200 seconds later. After applying dynamic time warping, a post-processing alignment technique, both models achieved an R-squared of approximately 0.93, confirming that the overall waveform structure was faithfully reproduced once the timing offset was compensated.

Where the two architectures genuinely diverged was in peak reconstruction, and this is where the study carries real weight for fatigue engineering. Fatigue damage accumulation, particularly under cycle-counting methods such as Rainflow counting combined with the Palmgren-Miner rule, is dominated by peak amplitudes; if peaks are underestimated, remaining fatigue life can be significantly overestimated. The experimental mean peak strain was about 0.121 microstrain. The one-stage model captured only 68.60 percent of that value, while the two-stage model reached 80.99 percent, an improvement of roughly 12 percentage points. On the independent prediction dataset, peak accuracy fell to 68.94 percent for the one-stage network but rose to 80.67 percent for the two-stage network. The explanation lies in how mean-square-error training treats sparse events: a single-stage network forced to represent both global motion and local deformation in one mapping tends to sacrifice peak fidelity for overall waveform agreement, whereas the staged decomposition lets the second stage focus on local deformation behavior.

Fast Fourier Transform analysis added a mechanistic explanation. Acceleration and strain signals shared a dominant frequency near 6.98 Hz, while displacement was governed by a lower frequency of about 3.48 Hz. Crucially, the high-frequency components associated with rapid strain variations were preserved in the intermediate displacement prediction, meaning the first stage acted not merely as a motion estimator but as a feature-preserving transformation that passed peak-related cues to the second stage. The authors are careful to frame the limits of their work: the experiment covered a single repeated rotary excitation condition with a dominant cycle of about 3.5 Hz, the short 0.016-second input delay window may not capture longer time-varying phase relationships, and progressive loosening of the test fixture may have contributed to the observed phase drift. Real-time, phase-synchronous monitoring would require additional synchronization or phase-correction strategies.

Even within those constraints, the demonstration is striking. Once the relationship between boundary acceleration and internal strain is learned, the trained model can estimate strain at critical internal locations using only a handful of boundary sensors, without a finite element model, state-space formulation, or prescribed loading information. The researchers suggest the framework could support fatigue life evaluation, long-duration response prediction, and digital-twin-based structural state estimation, with future extensions potentially incorporating recurrent, attention-based, or physics-informed architectures while retaining the physically interpretable staged structure. For a field where the most dangerous stresses hide in the least accessible corners of a machine, the message is provocative: sometimes the boundary knows more than it lets on, and a small, well-structured network can be taught to listen.

Subject of Research: Data-driven reconstruction of internal structural strain from sparse boundary acceleration measurements using a two-stage shallow time-delay neural network

Article Title: Data-Driven Estimation of the Critical Structural Strain from Boundary Acceleration Using a 2-Stage Shallow Time-Delay Neural Network

Article References: Seok, J. H., Seo, J. W., Jo, Y. K., Park, S. H., Lim, J. H., & Kim, Y. (2026). Data-Driven Estimation of the Critical Structural Strain from Boundary Acceleration Using a 2-Stage Shallow Time-Delay Neural Network. International Journal of Aeronautical and Space Sciences. https://doi.org/10.1007/s42405-026-01244-1

Image Credits: AI Generated

DOI: 10.1007/s42405-026-01244-1

Keywords: structural health monitoring, time-delay neural network, virtual sensing, strain reconstruction, fatigue assessment, boundary acceleration, machine learning, vibration testing, digital twin, aerospace structures, peak strain prediction, dynamic time warping

The scientific rationale for a brief fatigue measure is rooted in how fatigue itself is understood. Researchers define fatigue as an overwhelming sense of tiredness, lack of energy, and a feeling of exhaustion associated with impaired physical or cognitive functioning. Its functional purpose is to suppress or terminate activity, and it operates through two complementary pathways. Peripheral mechanisms involve biochemical changes within working muscles that reduce activity independently of the central nervous system, while central mechanisms involve neurochemical changes that generate subjective sensations of tiredness and reduced motivation, prompting individuals to voluntarily stop what they are doing. Both pathways are considered essential to fatigue’s protective role in maintaining whole-body homeostasis, and the new study deliberately focused on the subjective experience, treating fatigue as a unidimensional and simple construct.

That conceptual choice matters because it justifies the use of a single-item scale. Although some scholars have argued that single-item measures are inferior to multi-item scales in reliability and validity, single-item instruments can perform equally well, or even better, when the construct being measured is simple and unitary. Long multi-item questionnaires administered to highly fatigued respondents can feel repetitive and redundant, evoking discomfort or disengagement and thereby degrading data quality. Existing Japanese fatigue scales, including a 24-item adolescent subjective fatigue measure, the 25-item Jikaku-sho shirabe developed for occupational settings, and the 20-item Japanese version of the Multidimensional Fatigue Inventory, are valuable but impractical when participants must respond during ongoing physical activity or work. A one-item rating scale sidesteps that burden entirely, requiring no specialized equipment or technical expertise, unlike physiological indicators such as electroencephalography or heart rate variability.

The validation process unfolded in three phases between July and November 2024. In the first phase, two native Japanese-speaking graduate students in psychology independently translated the original Rating of Fatigue scale into Japanese, one of them blind to the study’s purpose. Three native speakers then consolidated the translations into a single version, and three native English speakers proficient in Japanese, all unaware of the study’s aims, translated the Japanese version back into English following Brislin’s classic back-translation method. Four English speakers subsequently rated the comparability of language and the similarity of interpretability between each back-translated passage and the original on seven-point scales, adapting methodology from Sperber and colleagues. Items scoring above the threshold of 3 on either dimension are considered problematic, and only a single sentence describing the level moderately fatigued required revision, a mismatch traced to differences in the intensity of fatigue conveyed by the corresponding adjectives in the two languages.

The second phase tested face validity and concurrent validity in a questionnaire survey of 85 Tohoku University students, 36 men and 49 women with a mean age of 20.27 years, recruited in October 2024. Participants rated their agreement with six face-validity items drawn from the original scale’s development, both before and after receiving instructional text accompanying the ROF-J, and completed a battery including the Jikaku-sho shirabe, an established Japanese fatigue questionnaire covering five symptom domains: drowsiness, instability, uneasiness, dullness, and eyestrain. Statistical analyses, powered a priori using G*Power and conducted in jamovi with a two-tailed significance level of 0.05, compared responses between the instructed and uninstructed conditions and correlated ROF-J scores with each subscale of the occupational fatigue questionnaire.

The results broadly supported the instrument. Participants generally agreed that the ROF-J measured fatigue, and the score on the item asking whether the instructions were helpful in understanding the scale rose significantly above the midpoint of the rating range, indicating that instructional text improved comprehensibility. Descriptive components and overall understandability did not differ between conditions, echoing patterns seen in the original English scale and its validated French counterpart. One result diverged from the earlier studies: rather than strengthening the perception that the scale measures fatigue while weakening the perception that it measures exertion, the instructions in this sample significantly reduced agreement that the scale represents exertion without significantly changing agreement that it represents fatigue. The authors suggest that because high-exertion tasks frequently produce fatigue, a strict subjective separation of the two experiences may be difficult, and future users should apply the scale with that caveat in mind.

Concurrent validity emerged clearly in the correlation analyses. ROF-J scores showed significant positive correlations with all five subscales of the Jikaku-sho shirabe, meaning that students who reported greater overall fatigue also reported more drowsiness, instability, uneasiness, dullness, and eyestrain. This covariation with an established, widely used Japanese fatigue instrument provides reassurance that the translated scale is tapping the same underlying phenomenon rather than an idiosyncratic construct. An independent-samples t-test also found no significant gender difference in ROF-J scores, with men averaging 3.89 and women 4.57 on the rating scale, supporting the instrument’s comparability across respondent groups at least within this sample.

The third phase examined convergent validity in a real-world athletic setting. Thirty-five members of Tohoku University varsity teams, 18 players from a men’s volleyball team and 17 from a women’s lacrosse team, rated their fatigue on paper immediately before and after regular practice sessions in November 2024. The volleyball squad trained in a gymnasium from seven to nine in the evening, progressing from serving and receiving drills to small-sided match play, while the lacrosse squad practiced at an athletic stadium from early morning, combining passing and shooting drills with sub-team matches. A repeated-measures mixed analysis of variance revealed a significant main effect of measurement time, with a large effect size, no significant effect of team affiliation, and no interaction between the two. Bonferroni-corrected post hoc testing confirmed that ROF-J scores rose significantly after exercise, exactly as observed in the original English validation and the French translation.

Together, the three lines of evidence, translational equivalence, agreement that the scale measures what it claims, correlation with an established domestic questionnaire, and sensitivity to the fatigue induced by physical exercise, indicate that the ROF-J possesses adequate validity for research and applied use. The authors acknowledge important limitations that shape the roadmap ahead. Convergent validity was tested only against physical exercise, leaving open whether the scale is equally sensitive to mental fatigue produced by cognitive tasks, desk work, or other low-intensity repetitive activities. The samples consisted exclusively of university students, so generalization to workers, children, older adults, and clinical populations remains untested. Concurrent validity was established against another self-report measure rather than objective fatigue indices such as performance decrements or physiological markers, a gap that future studies should close.

Even so, the practical significance of the work is considerable. Japan faces a documented fatigue burden: epidemiological survey data indicate that 17.2 percent of Japanese adults consider themselves easily fatigued and 13.2 percent experience residual fatigue that persists without signs of recovery, while national nutrition survey figures show that roughly 38.5 percent of men and 43.6 percent of women sleep fewer than six hours per night, with the burden concentrated among middle-aged adults. Overwork-related deaths from cardiovascular disease and suicides tied to overwork-related mental disorders have risen in recent administrative data, and industries such as road freight transport and care services figure prominently in recognized fatal cases. A brief, validated, single-item Japanese fatigue scale offers occupational health practitioners, sports scientists, and researchers an accessible quantitative tool that can be deployed repeatedly during ongoing activity, supporting intervention design, monitoring, and the broader advancement of fatigue science in Japan and beyond.

Subject of Research: Validation of a Japanese-language, single-item subjective fatigue rating scale for use during ongoing activity

Article Title: Validation of the Japanese Version of the Rating of Fatigue Scale

Article References: Suzuki, K., & Arai, T. (2026). Validation of the Japanese Version of the Rating of Fatigue Scale. Sports Medicine – Open, 12(1), Article 134. https://doi.org/10.1186/s40798-026-01108-8

Image Credits: AI Generated

DOI: 10.1186/s40798-026-01108-8

Keywords: fatigue, Rating of Fatigue scale, ROF-J, scale validation, psychometrics, cross-cultural translation, Japan, exercise, sports science, occupational health, sleep deprivation, karoshi