Principal Component Analysis of Building Structural Resilience Indicators from Material and Geometry Parameters

Project info

• Field of studyCivil Engineering and Transportation
• LevelUndergraduate thesis (S1)
• Method typeDimensionality Reduction
• Estimated build time± 3 working days
• Toolsscikit-learn PCA, StandardScaler; matplotlib
• PriceUS$19 - US$125

Research goal

Reduce the dimensions of concrete strength and column dimension related to structural resilience using Principal Component Analysis (PCA) to summarise the main pattern.

Variables

Example result

• 41.884PC1 variance %
• 32.932PC2 variance %
• 74.816PC1+PC2 %
• 4Components for 90%
• 2.949Largest eigenvalue
• 0.51Max |PC1 loading|

PCA condenses 7 indicators (including Structural resilience, Concrete strength and Column dimension) into 4 components for 90% of the variance; PC1 alone carries 41.9%.

Computed from illustrative synthetic data, not from a real study.

About Principal Component Analysis (PCA)

PCA transforms correlated variables into uncorrelated principal components ordered by variance. It is used to reduce dimensionality, lessen multicollinearity, and visualise multivariate data.

Steps

1. 1Standardise numeric variables
2. 2Fit PCA with all components
3. 3Inspect variance ratio and the scree plot
4. 4Choose the number of components (for example 90 percent cumulative variance)
5. 5Inspect loadings to name the components
6. 6Plot scores on the first two components

Assumptions to check

• Variables are on comparable scales (standardised)
• Relations among variables are roughly linear
• Large variance is assumed to carry important information

Reading and reporting the results

Report the variance explained by each component and the number retained with the reason. Interpret components through dominant variable loadings.

Example Python code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

import numpy as np
import matplotlib.pyplot as plt
from sklearn.decomposition import PCA
from sklearn.preprocessing import StandardScaler

rng = np.random.default_rng(20)
n = 300
f1 = rng.normal(size=n)
f2 = rng.normal(size=n)
concrete_strength = f1 + rng.normal(0, 0.3, n)
column_dimension = f1 + rng.normal(0, 0.3, n)
x3 = f2 + rng.normal(0, 0.3, n)
x4 = f2 + rng.normal(0, 0.3, n)
x5 = rng.normal(size=n)
structural_resilience = np.column_stack([concrete_strength, column_dimension, x3, x4, x5])

Z = StandardScaler().fit_transform(structural_resilience)
pca = PCA().fit(Z)
cum = np.cumsum(pca.explained_variance_ratio_)
print("Variance ratio:", pca.explained_variance_ratio_.round(3))
print("Cumulative:", cum.round(3))
k = int(np.searchsorted(cum, 0.90) + 1)
print("Components for 90%:", k)
print("Loadings (PC1, PC2):\n", pca.components_[:2].round(2))

scores = pca.transform(Z)
fig, ax = plt.subplots(1, 2, figsize=(10, 4))
ax[0].plot(range(1, 6), pca.explained_variance_ratio_, marker="o")
ax[0].set_title("Scree plot"); ax[0].set_xlabel("Component")
ax[1].scatter(scores[:, 0], scores[:, 1], s=10)
ax[1].set_xlabel("PC1"); ax[1].set_ylabel("PC2")
plt.tight_layout()
plt.show()

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

• Payment: 50% down payment before work starts, balance after the deliverables are handed over
• Tax: Prices exclude 11% VAT
• Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
• Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions