An approach to verifying and debugging simulation models governed by ordinary differential equations: Part 1. Methodology for residual generation

For dynamic simulations to be credible, verification of the computer code must be an integral part of the modelling process. This two-part paper describes a novel approach to verification through program testing and debugging. In Part 1, a methodology is presented for detecting and isolating coding errors using back-to-back testing. Residuals are generated by comparing the output of two independent implementations, in response to identical inputs. The key feature of the methodology is that a specially modified observer is created using one of the implementations, so as to impose an error-dependent structure on these residuals. Each error can be associated with a fixed and known subspace, permitting errors to be isolated to specific equations in the code. It is shown that the geometric properties extend to multiple errors in either one of the two implementations. Copyright (C) 2003 John Wiley Sons, Ltd.

An approach to verifying and debugging simulation models governed by ordinary differential equations: Part 2. Residuals analysis and a case study

In Part 1 of this paper a methodology for back-to-back testing of simulation software was described. Residuals with error-dependent geometric properties were generated. A set of potential coding errors was enumerated, along with a corresponding set of feature matrices, which describe the geometric properties imposed on the residuals by each of the errors. In this part of the paper, an algorithm is developed to isolate the coding errors present by analysing the residuals. A set of errors is isolated when the subspace spanned by their combined feature matrices corresponds to that of the residuals. Individual feature matrices are compared to the residuals and classified as 'definite', 'possible' or 'impossible'. The status of 'possible' errors is resolved using a dynamic subset testing algorithm. To demonstrate and validate the testing methodology presented in Part 1 and the isolation algorithm presented in Part 2, a case study is presented using a model for biological wastewater treatment. Both single and simultaneous errors that are deliberately introduced into the simulation code are correctly detected and isolated. Copyright (C) 2003 John Wiley Sons, Ltd.

Heat-induced changes in UHT milks - Part 1

Raw milk was stored for 0, 2 and 4 days and processed in a UHT pilot plant by either direct or indirect heating. The unstored raw milk was also pasteurised. The thermally induced changes resulting from these treatments were investigated by examining a number of indices of heat damage. Lactulose, furosine, total and free hydroxymethylfurfural (HMF) and acid-soluble beta-lactoglobulin were analysed by high performance liquid chromatography (HPLC) while soluble tryptophan was examined by fluorescence spectroscopy. The directly heated UHT milk showed less heat damage than the indirectly heated milk, while the pasteurised milk displayed the least heat damage. During storage of the UHT milk for 12 weeks at similar to20degreesC, the levels of lactulose remained constant, while the furosine concentration increased. Both the total HMF and undenatured beta-lactoglobulin contents showed a general decrease during storage; however free HMF values initially rose but then decreased after four weeks' storage. As the age of the milk at the time of UHT processing increased, the levels of some of the indicators decreased. It is concluded that lactulose is the most reliable index of heat treatment, as it is virtually unaffected by refrigerated storage of the milk before or ambient storage after UHT processing. Reliance on other indicators may give misleading information on the heat load that UHT milk has received during processing.