b-least-analysis

Analysis according to ISO 6143 and beyond

A comprehensive Python application for analysis modeling — both linear and nonlinear — with full uncertainty propagation, visual inspection, automated reporting (PDF/CSV), and model comparison. Supports a wide range of functions from polynomials and exponentials to sigmoids, and complies with ISO 6143 analysis methodology.

Features

• ISO 6143-compliant analysis

• Supports 14 different analysis models

• Full uncertainty propagation (incl. off-diagonal covariances)

• Automatic parameter estimation and robust fitting

• Intuitive GUI using Tkinter + CustomTkinter

• Visual output via Matplotlib (with confidence intervals)

• Export results as PDF (with graphs) or CSV

• Model diagnostics: RMSE, residual sum, Gamma (Γ)

• Weighted residual analysis

• Extensible architecture – easy to add new models or logic

GUI Overview

The main interface consists of three panels:

Left Panel: Data loading, model selection, and analysis controls

Center Panel: Results, fitted equations, uncertainties

Right Panel: Plot with calibration points, fitted curve, confidence band

Preview

Supported Models

Category	Model Name	Equation
ISO 6143 Compatible	Linear	$x = b_0 + b_1 y$
	Polynomial (order n)	$x = b_0 + b_1 y + \dots + b_n y^n$
	Exponential	$x = b_0 + b_1 e^{b_2 y}$
	Power Function	$x = b_0 + b_1 y^{(1 + b_2)}$
Exponential Growth	Simple Exponential	$x = b_0 e^{b_1 y}$
	Exponential w/ Offset	$x = b_0 + b_1 (e^{b_2 y} - 1)$
Saturation Models	Rational Function	$x = \frac{b_0 + b_1 y}{1 + b_2 y}$
	Hyperbolic Function	$x = b_0 + \frac{b_1}{y + b_2}$
Logarithmic Models	Logarithmic Function	$x = b_0 + b_1 \ln(b_2 y)$
	Log-Linear Function	$x = b_0 + b_1 \ln(y) + b_2 y$
Biological Curves	Gompertz Function	$x = b_0 \exp(-b_1 \exp(-b_2 y))$
	Sigmoid Function	$x = \frac{b_0}{1 + \exp(-b_1 (y - b_2))}$
Diffusion-like Models	Square Root Function	$x = b_0 + b_1 \sqrt{y}$

Installation

Requirements

• Python 3.9 or newer
• Recommended: use a virtual environment (venv or conda)

Install libraries

• numpy
• pandas
• matplotlib
• reportlab
• customtkinter

How to Use

Workflow

1. Load Calibration Data: CSV/TXT with columns x, u(x), y, u(y)

2. Load Measurement Data: CSV/TXT with columns y, u(y)

3. Select Function Model (e.g., polynomial, exponential, etc.)

4. Manually enter known covariances between calibration points (currently in beta)
Format: 2/4 0.0012, 3/4 0.0005
⚠️ Note: This feature is under development and may produce incorrect results in some cases.

5. Run Analysis

6. Review Results:

• Function equation + uncertainty per coefficient

• Residual analysis

• Fit quality metrics

7. Export:

• PDF Report with graph & optional model comparison

• CSV with full results and metadata

Example File Format

Supported delimiters: tab (\t), semicolon (;) and comma (,).

The delimiter is auto-detected from the first line of the file.

Calibration Data

x;u(x);y;u(y)
10.2;1.0e-1;5.0e-1;1.0e-2
11.8;0.1;1.0;0.01
13.5;0.1;1.5;1.2e-2

Measurement Data

y;u(y)
8.0e-1;1.0e-2
1.4;0.01

Analysis Options

• Weighted Residuals: both x- and y-direction

• Sum of Squared Residuals (SSR): compared to ISO acceptance threshold

• Goodness-of-Fit Γ: maximum normalized deviation

• Root Mean Squared Error (RMSE)

Export Contents

CSV Includes:

• Metadata (timestamp, selected function, user input)

• Calibration + Measurement Data

• Parameter estimates with uncertainties

• Covariance matrices (model parameters + predictions)

• Residuals + Diagnostics

PDF Includes:

• Summary report in fixed-width layout

• Full analysis equation + parameter table

• Model graph with:

  • Calibration points (± uncertainty)

  • Measurement predictions

  • 95% confidence band

• Optional model comparison (all models + RMSE/Γ/SSR)

Extensibility

The code is modular and extensible:

• Add your own models via compute_<model>() functions

• Extend GUI options with minimal changes

• All visualizations and exports are handled via standard libraries (matplotlib, reportlab)

License

Licensed under the MIT License.

Author

Tino Golub - Bundesanstalt für Materialforschung und -prüfung

Last updated: July 2025

Feel free to open issues or submit pull requests with suggestions or contributions.