Bridge with interval bars representing uncertainty.

Beyond Probability: How Interval Field Analysis Can Revolutionize Structural Engineering

Reese Marlowe in Tech & Innovation June 2025 • 4 min read.

"Uncover how a non-probabilistic approach is enhancing the safety and reliability of engineering designs by tackling uncertainties in new ways."

In the world of engineering, ensuring structures are safe and reliable is paramount. Traditional methods often rely on deterministic analysis, which assumes that all parameters are known and fixed. However, in reality, uncertainties are inherent in both the materials we use and the models we create.

To address these uncertainties, engineers have often turned to probabilistic approaches, which use statistical methods to quantify risk. Yet, these methods depend on having sufficient data to accurately define probability distributions—a requirement that is not always met. This is where a novel technique known as interval field analysis comes into play.

Interval field analysis offers a non-probabilistic way to deal with uncertainties that are spatially dependent. This means that instead of treating uncertainties as random variables, it models them as intervals with upper and lower bounds, reflecting the range of possible values. This approach is particularly useful when data is limited, providing a robust framework for analyzing structural behavior under uncertain conditions.

What is Interval Field Analysis and Why Is It Important?

Bridge with interval bars representing uncertainty.

Interval field analysis is a method used to model uncertainties in engineering systems, especially when those uncertainties vary across space. Unlike traditional probabilistic methods that require extensive data to define probability distributions, interval field analysis uses intervals—defined by upper and lower bounds—to represent the range of possible values for uncertain parameters. This approach is particularly beneficial when dealing with limited data or when precise statistical characterization is not feasible.

The core idea behind interval field analysis is to capture the spatial dependency of uncertain parameters. In structural engineering, this might involve the material properties of a beam or the load distribution on a bridge. By modeling these parameters as intervals, engineers can assess the range of possible behaviors of a structure under different conditions.

Deals with Limited Data: Interval field analysis is ideal when sufficient statistical data is unavailable.
Models Spatial Dependency: It effectively captures how uncertainties vary across different locations in a structure.
Provides Robust Bounds: Engineers can determine the extreme bounds of structural behavior, ensuring safety under worst-case scenarios.

One of the key advantages of interval field analysis is its ability to provide guaranteed bounds on the behavior of a system. By determining the extreme values that uncertain parameters can take, engineers can design structures that are robust and reliable, even under the most adverse conditions. This is particularly important in applications where failure could have catastrophic consequences.

The Future of Structural Engineering: Embracing Uncertainty with Confidence

Interval field analysis represents a significant step forward in how we approach uncertainty in structural engineering. By moving beyond traditional probabilistic methods, it offers a robust and reliable way to ensure the safety and performance of structures, even when data is limited. As our understanding of these techniques grows, we can expect to see even wider adoption and further innovation in the field, leading to safer and more resilient infrastructure for all.

About this Article -

This article was crafted using a human-AI hybrid and collaborative approach. AI assisted our team with initial drafting, research insights, identifying key questions, and image generation. Our human editors guided topic selection, defined the angle, structured the content, ensured factual accuracy and relevance, refined the tone, and conducted thorough editing to deliver helpful, high-quality information.See our About page for more information.

This article is based on research published under:

DOI-LINK: 10.1115/1.4041501, Alternate LINK

Title: Uncertain Structural Free Vibration Analysis With Non-Probabilistic Spatially Varying Parameters

Subject: Mechanical Engineering

Journal: ASCE-ASME J Risk and Uncert in Engrg Sys Part B Mech Engrg

Publisher: ASME International

Authors: Jinwen Feng, Qingya Li, Alba Sofi, Guoyin Li, Di Wu, Wei Gao

Published: 2019-04-17

Everything You Need To Know

What exactly is Interval Field Analysis, and why is it considered important in the field of structural engineering?

Interval field analysis is a method that models uncertainties in engineering systems, particularly when these uncertainties vary spatially. Unlike probabilistic methods needing extensive data, it uses intervals defined by upper and lower bounds to represent the possible values for uncertain parameters. This is especially useful when data is limited or precise statistical characterization isn't feasible. It seeks to capture the spatial dependency of uncertain parameters, such as material properties or load distribution, allowing engineers to assess a structure's behavior range under different conditions.

How do traditional methods and probabilistic approaches compare to Interval Field Analysis in handling uncertainties in structural engineering?

Traditional methods in structural engineering often rely on deterministic analysis, assuming that all parameters are known and fixed. When uncertainties are considered, probabilistic approaches are used, quantifying risk through statistical methods. However, these probabilistic methods require sufficient data to define probability distributions accurately, a condition not always met in real-world scenarios. Interval field analysis provides an alternative by modeling uncertainties as intervals with upper and lower bounds, useful when data is limited and offering a robust framework for analyzing structural behavior under uncertain conditions.

What are the main benefits of using Interval Field Analysis over other methods when designing structures?

One key advantage of interval field analysis is its ability to provide guaranteed bounds on the behavior of a system. By determining the extreme values that uncertain parameters can take, engineers can design structures that are robust and reliable, even under the most adverse conditions. This is particularly important in applications where failure could have catastrophic consequences, ensuring a higher level of safety and confidence in structural performance.

What are the limitations of Interval Field Analysis, and when might probabilistic methods be more appropriate despite their data requirements?

While Interval Field Analysis excels in situations with limited data by providing a range of possible values using intervals, it doesn't offer the detailed statistical insights that probabilistic methods provide when sufficient data is available. Probabilistic methods can offer a more refined risk assessment by describing the likelihood of different outcomes, while Interval Field Analysis focuses on defining the boundaries within which the solution is guaranteed to lie. Therefore, the choice between the two depends on the availability of data and the desired level of detail in the uncertainty analysis.

How does using Interval Field Analysis contribute to greater confidence and reliability in structural engineering designs for the future?

Embracing Interval Field Analysis allows for a more confident approach to structural engineering, especially when dealing with uncertainties and limited data. It ensures that structures are designed to perform safely within defined boundaries, even under the most adverse conditions. This leads to more resilient infrastructure that can withstand unexpected variations in material properties or environmental conditions, reducing the risk of failures and enhancing overall safety and reliability. The adoption of such advanced techniques marks a move toward a more robust and reliable future for structural engineering.