Purpose  This paper investigates the performance of a Damped Bipedal Inverted Pendulum model (Bipedal Model, for short) to represent the pedestrian body, focusing on applications in structural vibration problems due to human loads. The analysis compares experimental and numerical results, emphasizing the effects of simplifying the model to a single-degree-of-freedom (SDoF) system. It also examines how fixing the step length or attack angle influences ground reaction forces, step frequency, and overall model functioning. Methods Gait data were collected from individuals walking on a rigid surface under four conditions: slow, normal, free, and fast. Synchronized kinetic and kinematic data were used to extract Bipedal Model parameters and the key gait variables: walking speed (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(v\)</EquationSource> </InlineEquation>), step frequency (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(f_s\)</EquationSource> </InlineEquation>), and the first-harmonic Dynamic Load Factor (DLF1). These served as benchmarks for evaluating both one- and two-degree-of-freedom Bipedal Models. Results The models generally failed to reproduce all three parameters (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(v,f_s\)</EquationSource> </InlineEquation>, DLF1) simultaneously. When <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(v\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(f_s\)</EquationSource> </InlineEquation> were matched, DLF1 was generally overestimated, with errors increasing at higher speeds. This suggests a limitation of the Bipedal Model approach, likely due to its neglect of foot centre-of-pressure progression. The proportionality between v and DLF1 errors indicated that <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(v\)</EquationSource> </InlineEquation> had to be adjusted to match target DLF1 values. Conclusions No significant performance difference was found between the two Bipedal Models, favouring the simpler SDoF version, for which energy compensation is unnecessary. Moreover, although<InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(f_s\)</EquationSource> </InlineEquation> is not an input, it can be indirectly imposed in the SDoF model by setting a constant step length (<InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(d_s\)</EquationSource> </InlineEquation>), maintaining the relationship <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(v = f_s{d_s}\)</EquationSource> </InlineEquation>.

Evaluating SDoF and 2DoF Bipedal Models from Walking Tests on Rigid Surfaces

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发表日期：

2026年3月21日

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Rafaela L. Silva,
Roberto L. Pimentel,
Aleksandar Pavic

摘要

Purpose

This paper investigates the performance of a Damped Bipedal Inverted Pendulum model (Bipedal Model, for short) to represent the pedestrian body, focusing on applications in structural vibration problems due to human loads. The analysis compares experimental and numerical results, emphasizing the effects of simplifying the model to a single-degree-of-freedom (SDoF) system. It also examines how fixing the step length or attack angle influences ground reaction forces, step frequency, and overall model functioning.

Methods

Gait data were collected from individuals walking on a rigid surface under four conditions: slow, normal, free, and fast. Synchronized kinetic and kinematic data were used to extract Bipedal Model parameters and the key gait variables: walking speed ( \(v\) ), step frequency ( \(f_s\) ), and the first-harmonic Dynamic Load Factor (DLF₁). These served as benchmarks for evaluating both one- and two-degree-of-freedom Bipedal Models.

Results

The models generally failed to reproduce all three parameters ( \(v,f_s\) , DLF₁) simultaneously. When \(v\) and \(f_s\) were matched, DLF₁ was generally overestimated, with errors increasing at higher speeds. This suggests a limitation of the Bipedal Model approach, likely due to its neglect of foot centre-of-pressure progression. The proportionality between v and DLF₁ errors indicated that \(v\) had to be adjusted to match target DLF₁ values.

Conclusions

No significant performance difference was found between the two Bipedal Models, favouring the simpler SDoF version, for which energy compensation is unnecessary. Moreover, although \(f_s\) is not an input, it can be indirectly imposed in the SDoF model by setting a constant step length ( \(d_s\) ), maintaining the relationship \(v = f_s{d_s}\) .