Despite advances in computer capacity, the enormous computational cost of running complex engineering simulations makes it impractical to rely exclusively on simulation for the purpose of design optimization. To cut down the cost, surrogate models, also known as metamodels, are constructed from and then used in place of the actual simulation models. In this paper, we systematically compare four popular metamodelling techniques – polynomial regression, multivariate adaptive regression splines, radial basis functions, and kriging – based on multiple performance criteria using fourteen test problems representing different classes of problems. Our objective in this study is to investigate the advantages and disadvantages of these four metamodelling techniques using multiple criteria and multiple test problems rather than a single measure of merit and a single test problem.

Comparative studies of metamodelling techniques under multiple modelling criteria

Numerical Initial Value Problems in Ordinary Differential Equations

It is postulated that lane-changing vehicles create voids in traffic streams, and that these voids reduce flow. This mechanism is described with a model that tracks lane changers precisely, as particles endowed with realistic mechanical properties. The model has four easy-to-measure parameters and reproduces without re-calibration two bottleneck phenomena previously thought to be unrelated: (i) the drop in the discharge rate of freeway bottlenecks when congestion begins, and (ii) the relation between the speed of a moving bottleneck and its capacity.

Lane-changing in traffic streams

Structure and interpretation of computer programs

Despite the advances in computer capacity, the enormous computational cost of complex engineering simulations makes it impractical to rely exclusively on simulation for the purpose of design optimization. To cut down the cost, surrogate models, also known as metamodels, are constructed from and then used in lieu of the actual simulation models. In the paper, we systematically compare four popular metamodeling techniques —Polynomial Regression, Multivariate Adaptive Regression Splines, Radial Basis Functions, and Kriging —based on multiple performance criteria using fourteen test problems representing different classes of problems. Our objective in th is study is to investigate the advantages and disadvantages these four metamodeling techniques using multiple modeling criteria and multiple test problems rather than a single measure of merit and a single test problem.

Comparative studies of metamodeling techniques under multiple modeling criteria

Road roughness is gaining increasing importance as an indicator of road condition, both in terms of pavement performance, and as a major determinant of road user costs. This paper defines roughness measurement systems hierachically into four groups, ranging from profilometric methods (2 groups), through response type road roughness measuring systems (RTRRMS's), and, subjective evaluation. The International Roughness Index (IRI) is defined, and the programs for it's calculation are provided. The IRI is based on simulation of the roughness response of a car travelling at 80 km/h. The report explains how all roughness measurements can be related to this scale, also when travelling at lower speeds than 80 km/h. The IRI emerges as a scale that can be used both for calibration and for comparative purposes.

Guidelines for conducting and calibrating road roughness measurements

Introduction High-speed road profiling is a technology that began in the 1960's when Elson Spangler and William Kelly developed the inertial profilometer at the General Motors Research Laboratory. Some users still call high-speed profilers by their early name: GMR Profilometers. In the past decade, profiling instruments have become the everyday tools for measuring road roughness. The majority of States now own road profilers. A substantial body of knowledge exists for the field of profiler design and technology. There are also many proven methods for analyzing and interpreting data similar to the measures obtained from profilers. However, there has not been a single source of information about what you can do with a profiler. Users have instructions provided by the manufacturers to operate the equipment, but little else to go on. Road profiler users from different States met in 1989 and formed the Road Profiler User Group (RPUG). RPUG has been meeting annually since then to provide a forum for issues involving the measurement and interpretation of road profiles. From 1992 to 1995, the authors conducted a research project at The University of Michigan Transportation Research Institute (UMTRI) called " Interpretation of Road Roughness Profile Data. " The research was funded by the Federal Highway Administration (FHWA) and pooled State funds. At the 1994 RPUG meeting, representatives of the participating States suggested that a short course is needed to provide the necessary education. Dave Huft, inventor of the South Dakota profiler, proposed a " Little Golden Book of Profiling " in the spirit of the popular children's books. The National Highway Institute (NHI) of FHWA provided funding for the authors to prepare a short course called " Measuring and Interpreting Road Profiles. " The first session of the course was held in November 1995 in Ann Arbor, Michigan. In The Little Book, we try to cover three basic questions: 1. How do profilers work? 2. What can you do with their measurements? 3. What can you do to reduce errors? The material is targeted at users. Our intent is make the material no more technical than is needed to describe what the measures mean that you can get from a profiler. A profile is a two-dimensional slice of the road surface, taken along an imaginary line. Profiles taken along a lateral line show the superelevation and crown of the road design, plus rutting and other distress. Longitudinal profiles show the design …

The little book of profiling: basic information about measuring and interpreting road profiles

The high wheel loads of heavy trucks are a major source of pavement damage by causing fatigue, which leads to cracking, and by permanent deformation, which produces rutting. Among heavy trucks, all do not cause equal damage because of differences in wheel loads, number and location of axles, types of suspensions and tires, and other factors. Further, the damage is specific to pavement properties, operating conditions, and environmental factors. The mechanics of truck-pavement interaction were studied to identify relationships between truck properties and damage (fatigue and rutting). Computer models of trucks were used to generate wheel load histories characteristic of the different trucks and operating conditions. Influence functions, obtained from rigid and flexible pavement structural models, were used to predict responses along the pavement resulting from the truck motions. The pavement responses were evaluated to estimate overall pavement damage caused by each truck. The study assessed the significance of truck, tire, pavement, and environmental factors as determinants of pavement damage. Maximum axle load and pavement thickness have the primary influences on fatigue damage. Truck properties, such as number and location of axles, suspension type, and tire type, are important but less significant. High temperatures in flexible pavements and temperature gradients in rigid pavements adversely affect the damage caused by truck wheel loads with a fairly strong interaction. The report discusses and quantifies the influence of these variables.

Effects of heavy-vehicle characteristics on pavement response and performance

The international roughness index (IRI) was established in 1986 by the World Bank and based on earlier work performed for NCHRP. IRI is calculated from a measured longitudinal road profile by accumulating the output from a quarter-car model and dividing by the profile length to yield a summary roughness index with units of slope. Although IRI is used widely, there is no single, short reference document that describes what it is and how it is calculated. Instead, the critical information is spread over several large reports. A short, self-contained reference that defines IRI is provided, along with all the information needed to compute it from longitudinal road profile measurements. The development of the IRI is reviewed, the mathematical definition is presented, an algorithm for calculating IRI is derived, the performance of the algorithm is analyzed, tested Fortran source code for computing IRI is presented, and problems with IRI (and profile measurement in general) that have emerged since 1986 are identified.

On the calculation of international roughness index from longitudinal road profile

This report contains the results of an intensive study of response-type road roughness measuring systems (primarily Mays- and PCA-type road meters) for the purpose of developing calibration and correlation procedures. An artificial road bump approach is described as a simplified method for a calibration check of road meter systems. This method offers potential for calibrating systems over the moderate-to-rough range of the roughness scale. Currently available road meters are not generally suitable for assessing the roughness (smoothness) of newly constructed roads. The findings of this study will be of particular interest to highway and airport personnel responsible for collection and analysis of data on pavement surface characteristics, pavement rehabilitation and management programs, and testing and research activities.

Michael W. Sayers

Papers

Guidelines for conducting and calibrating road roughness measurements

The little book of profiling: basic information about measuring and interpreting road profiles

Effects of heavy-vehicle characteristics on pavement response and performance

On the calculation of international roughness index from longitudinal road profile

Calibration of response-type road roughness measuring systems