Signal Evaluation Using Detrended Fluctuation Analysis
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional methods for air pollution forecasting in urban areas, particularly from road traffic, often rely on weather conditions and fail to accurately account for temporal fluctuations in immission measurements, leading to inadequate or premature measures.
Innovation Solution
A method utilizing Detrended Fluctuation Analysis (DFA) to analyze time series data of immissions, allowing for the identification of long-term correlations and short-term changes, enabling more precise and localized forecasting and countermeasure implementation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional forecasting methods relying on weather conditions are used, then the forecasting process is simple, but the accuracy of emission forecasts deteriorates
Solution Approach 1:
The patent applies preliminary action by calculating the fluctuation exponent from historical immission time series data in advance. This pre-computed exponent characterizes the temporal fluctuation pattern and is stored for later use in forecasting. When forecasting is needed, this pre-calculated exponent is combined with current weather forecasts to generate emission predictions, avoiding the need to re-analyze historical data each time and improving both accuracy and efficiency.
Solution Approach 2:
The fluctuation exponent serves as an intermediary parameter that bridges historical immission data and future emission forecasts. Instead of directly using complex historical time series or simple weather conditions, the patent introduces this intermediate metric that captures the essential temporal fluctuation characteristics. This intermediary enables the combination of historical patterns with weather predictions to produce accurate forecasts without requiring direct analysis of the full historical dataset.
2Measurement precision
If hourly or daily mean values are calculated for monitoring purposes, then the monitoring process is simple, but the temporal resolution of immission measurements deteriorates
Solution Approach 1:
The patent extracts the fluctuation exponent as a specific characteristic from the complex immission time series data. Instead of processing the entire detailed time series or calculating simple mean values, it extracts this single parameter that captures the essential temporal fluctuation pattern. This extracted exponent can then be used for forecasting without needing to retain or process the full high-resolution historical data, thus maintaining temporal resolution benefits while simplifying storage and computation.
3Area of stationary object
If decentralized distributed solutions are used to measure larger areas, then the spatial coverage is improved, but the complexity of evaluation increases
Solution Approach 1:
The patent transforms complex spatial-temporal immission data into a simplified parameter - the fluctuation exponent - that characterizes temporal patterns. By applying this transformation to data from multiple decentralized measuring points, each location generates its own exponent that captures local temporal behavior. This parameter transformation simplifies the evaluation of decentralized measurements, allowing complex spatial patterns to be represented through comparable exponent values from different locations.
Data Source
Figure 1
Figure 2
Figure 3
AI summary
Method for evaluating at least one signal representing a time series of measured values, wherein the measured values relate to emissions, wherein the at least one signal is evaluated using a trend-correcting fluctuation analysis, so that a trend-corrected signal is obtained, which in turn is evaluated to detect a temporal change in the fluctuation of the measured values and to evaluate this temporal change.