Towards a more representative parametrisation of hydrologic models via synthesizing the strengths of Particle Swarm Optimisation and Robust Parameter Estimation

The development of methods for estimating the parameters of hydrologic models considering uncertainties has been of high interest in hydrologic research over the last years. In particular methods which understand the estimation of hydrologic model parameters as a geometric search of a set of robust performing parameter vectors by application of the concept of data depth found growing research interest. Bárdossy and Singh (2008) presented a first Robust Parameter Estimation Method (ROPE) and applied it for the calibration of a conceptual rainfall-runoff model with daily time step. The basic idea of this algorithm is to identify a set of model parameter vectors with high model performance called good parameters and subsequently generate a set of parameter vectors with high data depth with respect to the first set. Both steps are repeated iteratively until a stopping criterion is met. The results estimated in this case study show the high potential of the principle of data depth to be used for the estimation of hydrologic model parameters. In this paper we present some further developments that address the most important shortcomings of the original ROPE approach. We developed a stratified depth based sampling approach that improves the sampling from non-elliptic and multi-modal distributions. It provides a higher efficiency for the sampling of deep points in parameter spaces with higher dimensionality. Another modification addresses the problem of a too strong shrinking of the estimated set of robust parameter vectors that might lead to overfitting for model calibration with a small amount of calibration data. This contradicts the principle of robustness. Therefore, we suggest to split the available calibration data into two sets and use one set to control the overfitting. All modifications were implemented into a further developed ROPE approach that is called Advanced Robust Parameter Estimation (AROPE). However, in this approach the estimation of the good parameters is still based on an ineffective Monte Carlo approach. Therefore we developed another approach called ROPE with Particle Swarm Optimisation (ROPE-PSO) that substitutes the Monte Carlo approach with a more effective and efficient approach based on Particle Swarm Optimisation. Two case studies demonstrate the improvements of the developed algorithms when compared with the first ROPE approach and two other classical optimisation approaches calibrating a process oriented hydrologic model with hourly time step. The focus of both case studies is on modelling flood events in a small catchment characterised by extreme process dynamics. The calibration problem was repeated with higher dimensionality considering the uncertainty in the soil hydraulic parameters and another conceptual parameter of the soil module. We discuss the estimated results and propose further possibilities in order to apply ROPE as a well-founded parameter estimation and uncertainty analysis tool

The transmission of vertical vibration through seats: influence of the characteristics of the human body

The transmission of vibration through a seat depends on the impedance of the seat and the apparent mass of the seat occupant. This study was designed to determine how factors affecting the apparent mass of the body (age, gender, physical characteristics, backrest contact, and magnitude of vibration) affect seat transmissibility. The transmission of vertical vibration through a car seat was measured with 80 adults (41 males and 39 females aged 18–65) at frequencies between 0.6 and 20 Hz with two backrest conditions (no backrest and backrest), and with three magnitudes of random vibration (0.5, 1.0, and 1.5 m s-2 rms). Linear regression models were used to study the effects of subject physical characteristics (age, gender, and anthropometry) and features of their apparent mass (resonance frequency, apparent mass at resonance and at 12 Hz) on the measured seat transmissibility. The strongest predictor of both the frequency of the principal resonance in seat transmissibility and the seat transmissibility at resonance was subject age, with other factors having only marginal effects. The transmissibility of the seat at 12 Hz depended on subject age, body mass index, and gender. Although subject weight was strongly associated with apparent mass, weight was not strongly associated with seat transmissibility. The resonance frequency of the seat decreased with increases in the magnitude of the vibration excitation and increased when subjects made contact with the backrest. Inter-subject variability in the resonance frequency and transmissibility at resonance was less with greater vibration excitation, but was largely unaffected by backrest contact. A lumped parameter seat–person model showed that changes in seat transmissibility with age can be predicted from changes in apparent mass with age, and that the dynamic stiffness of the seat appeared to increase with increased loading so as to compensate for increases in subject apparent mass associated with increased sitting weight