Fast and robust algorithm to compute exact polytope parameter bounds
Mathematics and Computers in Simulation - Parameter identifications with error bound
Membership-set estimation using random scanning and principal componet analysis
Mathematics and Computers in Simulation - Parameter identifications with error bound
Properties of least squares estimates in set membership identification
Automatica (Journal of IFAC)
Computing least trimmed squares regression with the forward search
Statistics and Computing
Uncertainty in the environmental modelling process - A framework and guidance
Environmental Modelling & Software
Environmental Modelling & Software
Scaling dispersion model for pollutant transport in rivers
Environmental Modelling & Software
Modelling Mediterranean landscape succession-disturbance dynamics: A landscape fire-succession model
Environmental Modelling & Software
Review: A review of surface erosion and sediment delivery models for unsealed roads
Environmental Modelling & Software
Power-Law Distributions in Empirical Data
SIAM Review
Environmental Modelling & Software
Set Membership identification of nonlinear systems
Automatica (Journal of IFAC)
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Power laws are used to describe a large variety of natural and industrial phenomena. Consequently, they are used in a wide range of scientific research and management applications. This paper focuses on the identification of bounds on the parameter and prediction uncertainty in a power-law relation from experimental data, assuming known bounds on the error between model output and observations. The prediction uncertainty bounds can subsequently be used as constraints, for example in optimisation and scenario studies. The set-membership approach involves identification and removal of outliers, estimation of the feasible parameter set, evaluation of the feasible model-output set and tuning of the specified bounds on model-output error. As an example the procedure is applied to data of scattered sediment yield versus catchment area (Wasson, 1994). The key result is an un-falsified relationship between sediment yield and catchment area with uncertainty bounds on its parameters. The set-membership results are compared with the results from a conventional least-squares approach with first-order variance propagation, assuming a zero-mean, symmetrical error distribution.