Fast error estimates for indirect measurements: applications to pavement engineering

In ninny real-life situations, we have the fi~llowing problen|: we want it) know the vahle ~)f ~)n|e characteristic U that is diffiodt to measure directly (e.g., lifetin|e of a pavement, effidency of an engine, etc.). To esti|mate U, we mug know the relationship between 9 and aane directly measurable physical quamities X h . . . , xn. Fro|n this relationship, we extract an algorithm f that alh|ws us, given xi, to cmnpute p: 9 ---f ( x l . . . . ,xa). &~, we measure zi , apply an algorithm f , and get the d~sired estimate. Existing algorithms fi~r err .r ~timate (interval nmthematics, Monte-Carlo methods, nun|eri~l differentiadon, etc.} require cmnputation dine that is several times larger than the time necessary to compute Y = f ( x h . . . , x a ) . So, if an algorithm f is already time-consuming, error estimates will take t(x~ hmg. In ,many cases, this algorithm f consists of two parts: first, we use xi to determine the parameters zk of a nuMel that describes the measured object, and seomd, we use these parameters to estimate Y. The most tin|e-consunfing part is finding zk; this is done by ~dving a system of ram-linear equatkms; usually least squares method is used. We show that for such f , one can estimate errors repeating this time~msu|ning part of f only once. So, we can omlpute |xgh y and an em)r estimate fi,r U with practically m~ increase in total con|putadon dine. As an example of this m~htgtology, we give pavement lifetime estimates.