Generation of Spatial Road Profile Spectra for Various Road Classes

In the fields of road engineering and vehicle simulation, road profile spectra serve as mathematical tools to describe surface irregularities, typically expressed as functions of spatial frequency. For various applications (such as vehicle vibration analysis or autonomous driving testing), there's a need to generate spatial road profile spectra that comply with specific classification standards (such as classes A-H in ISO 8608).

The core methodology consists of three key components: Road Class Mapping: Establishing correlations between internationally recognized road classifications and power spectral density (PSD) values. For instance, Class A roads (high-speed smooth surfaces) exhibit the lowest spectral density amplitudes, while Class H roads (extremely rough surfaces) demonstrate the highest amplitudes. This mapping can be implemented through lookup tables or mathematical relationships defined in standardization documents. Random Process Generation: Converting target power spectral densities into elevation sequences using inverse Fourier transform techniques. By incorporating random phase components, this approach simulates the spatial distribution characteristics of real-road surfaces. In code implementation, this typically involves generating complex random numbers with specified spectral properties and applying inverse FFT operations. Parameter Customization: Supporting adjustable wavelength ranges (e.g., 0.1m to 100m) and segmented stationarity to accommodate different testing scenarios (such as long-wave undulations or short-wave bumps). This flexibility can be achieved through configurable filter parameters and windowing functions in the spectral generation algorithm.

In extended applications, the methodology can be enhanced by integrating terrain data or measured samples for improved realism. Alternatively, time-space conversion models can be employed to generate dynamic road profile spectra for real-time vehicle simulations, where velocity-dependent transformations convert spatial profiles to time-domain excitations.