Maximum likelihood estimation for passive energy-based footstep localization

Zhao

Fatigue Fract Eng Mat Struct

2022

The fatigue life of natural rubber (NR) components under a constant‐amplitude load is dispersed. The dispersion can be reflected by establishing a probabilistic fatigue life prediction model (also called the P–S–N curve). However, the effect of strain ratio on fatigue life is typically ignored in conventional P–S–N curves. Aiming at improving the prediction accuracy of conventional models, a unified P–S–N curve for NR components is proposed in the present study, in which the strain ratio effect is considered in the calculations. Using the dumbbell‐shaped rubber specimen fatigue test data, a polynomial function is proposed to describe the correlation between the equivalent strain amplitude, strain amplitude, and strain ratio. Then a calculation model of equivalent strain amplitude is established. Furthermore, a unified P–S–N curve for NR is established with equivalent strain amplitude as the damage parameter. By comparing the measured and predicted fatigue life of NR under different reliabilities, the accuracy of the established unified P–S–N curve is verified.

“…Based on the test results, the maximum likelihood estimation method is used to determine the parameters. 26 The obtained results are shown in Tables 4-6.…”

Section: P-s -N Curve Based On the Logarithmic Strain Amplitudementioning

confidence: 95%

“…Accordingly, the reliability of the NR component can be calculated through the following expression:

P ((), N (|, S)) goodbreak= 1 goodbreak- \frac{1}{σ \sqrt{2 π}} \int_{‐ \infty}^{\ln N} \exp ([], goodbreak- \frac{{((), \ln N goodbreak- u)}^{2}}{2 σ^{2}}) d ((), \ln N),

Section: P–s–n Curve Based On the Logarithmic Strain Amplitudementioning

confidence: 99%

A unified probabilistic fatigue life prediction model for natural rubber components considering strain ratio effect

Zhao

Fatigue Fract Eng Mat Struct

2022

“…To emphasize the contributions of this study, it is essential to contrast our approach with the closest-related work, as encapsulated in [41]. While [41] initiates the exploration of the problem space by deriving probability density functions (PDFs) of the energy of the acquired vibro-measurement vectors, it does so with the simplifying assumption of neglecting the cross-terms as they are zero-mean random variables. Our work diverges fundamentally at this juncture, where we incorporate all terms in our derivation.…”

Section: Baseline Study and Overview Of The Fundamental Differencesmentioning

confidence: 99%

“…In light of their work, the authors assert that there is no evidence of a monotonic relationship between the amplitude or kurtosis of the measured signal and the propagation distance. Parametric energy-decay models highlight the potential for further improvement [41][42][43].…”

Section: Introductionmentioning

confidence: 99%

“…Along with parametric decay models, Poston et al [44], in an alternative attempt, moved the localization framework to a probabilistic framework by modeling the probability of detection and false alarm. Alajlouni et al [41] took a similar approach to localize the occupant by maximizing the sensor likelihood functions given the hypothesis of the sensor's time domain measurements and the energy-decay model proposed in their earlier work.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Multi-Sensor Stochastic Energy-Based Vibro-Localization Technique with Byzantine Sensor Elimination

Ambarkutuk,

Alajlouni,

Tarazaga

et al. 2023

Sensors

Self Cite

This paper presents an occupant localization technique that determines the location of individuals in indoor environments by analyzing the structural vibrations of the floor caused by their footsteps. Structural vibration waves are difficult to measure as they are influenced by various factors, including the complex nature of wave propagation in heterogeneous and dispersive media (such as the floor) as well as the inherent noise characteristics of sensors observing the vibration wavefronts. The proposed vibration-based occupant localization technique minimizes the errors that occur during the signal acquisition time. In this process, the likelihood function of each sensor—representing where the occupant likely resides in the environment—is fused to obtain a consensual localization result in a collective manner. In this work, it becomes evident that the above sources of uncertainties can render certain sensors deceptive, commonly referred to as “Byzantines.” Because the ratio of Byzantines among the set sensors defines the success of the collective localization results, this paper introduces a Byzantine sensor elimination (BSE) algorithm to prevent the unreliable information of Byzantine sensors from affecting the location estimations. This algorithm identifies and eliminates sensors that generate erroneous estimates, preventing the influence of these sensors on the overall consensus. To validate and benchmark the proposed technique, a set of previously conducted controlled experiments was employed. The empirical results demonstrate the proposed technique’s significant improvement (3~0%) over the baseline approach in terms of both accuracy and precision.

IEEE J. Transl. Eng. Health Med.

Probabilistic Estimation of Cadence and Walking Speed From Floor Vibrations

MejiaCruz,

Caicedo,

Jiang

et al. 2024

Objective: This research aims to extract human gait parameters from floor vibrations. The proposed approach provides an innovative methodology on occupant activity, contributing to a broader understanding of how human movements interact within their built environment.Methods and Procedures: A multilevel probabilistic model was developed to estimate cadence and walking speed through the analysis of floor vibrations induced by walking. The model addresses challenges related to missing or incomplete information in the floor acceleration signals. Following the Bayesian Analysis Reporting Guidelines (BARG) for reproducibility, the model was evaluated through twenty-seven walking experiments, capturing floor vibration and data from Ambulatory Parkinson’s Disease Monitoring (APDM) wearable sensors. The model was tested in a real-time implementation where ten individuals were recorded walking at their own selected pace.Results: Using a rigorous combined decision criteria of 95% high posterior density (HPD) and the Range of Practical Equivalence (ROPE) following BARG, the results demonstrate satisfactory alignment between estimations and target values for practical purposes. Notably, with over 90% of the 95% HPD falling within the region of practical equivalence, there is a solid basis for accepting the estimations as probabilistically aligned with the estimations using the APDM sensors and video recordings.Conclusion: This research validates the probabilistic multilevel model in estimating cadence and walking speed by analyzing floor vibrations, demonstrating its satisfactory comparability with established technologies such as APDM sensors and video recordings. The close alignment between the estimations and target values emphasizes the approach’s efficacy. The proposed model effectively tackles prevalent challenges associated with missing or incomplete data in real-world scenarios, enhancing the accuracy of gait parameter estimations derived from floor vibrations.Clinical impact: Extracting gait parameters from floor vibrations could provide a non-intrusive and continuous means of monitoring an individual’s gait, offering valuable insights into mobility and potential indicators of neurological conditions. The implications of this research extend to the development of advanced gait analysis tools, offering new perspectives on assessing and understanding walking patterns for improved diagnostics and personalized healthcare.Clinical and Translational Impact Statement: This manuscript introduces an innovative approach for unattended gait assessments with potentially significant implications for clinical decision-making. By utilizing floor vibrations to estimate cadence and walking speed, the technology can provide clinicians with valuable insights into their patients’ mobility and functional abilities in real-life settings. The strategic installation of accelerometers beneath the flooring of homes or care facilities allows for uninterrupted daily activities during these assessments, reducing the reliance on specialize...