System representations in subspaces of finite-sample signals and their application to data-driven fault detection
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914488781897728 |
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| author | Li, Linlin Ding, Steven X. Wang, Jiahao Zhong, Maiying Cheng, Wei |
| author_facet | Li, Linlin Ding, Steven X. Wang, Jiahao Zhong, Maiying Cheng, Wei |
| contents | This paper deals with system representations in finite-sample signal subspaces and their application to data-driven fault detection. The first part addresses concepts of finite-sample image and kernel system representations and, associated with them, image and residual subspaces of finite-sample signals. On this basis, the equivalence between the fundamental lemma and finite-sample image subspace is demonstrated. While the image representation models the nominal system dynamics, the residual representation describes uncertainties in the input-output data and is essential for fault detection. This result extends the fundamental lemma and builds the basis for exploring data-driven fault detection. In the second part, a data-driven projection-based fault detection approach is developed. By means of a singular value decomposition, orthogonal projections onto the image and residual subspaces are realized in the context of a low-rank matrix approximation, leading to projection-based residual generation and evaluation. Finally, analysis of detection performance in the framework of matrix perturbation theory and comparison with existing data-driven fault detection methods are explored. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_17444 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | System representations in subspaces of finite-sample signals and their application to data-driven fault detection Li, Linlin Ding, Steven X. Wang, Jiahao Zhong, Maiying Cheng, Wei Systems and Control This paper deals with system representations in finite-sample signal subspaces and their application to data-driven fault detection. The first part addresses concepts of finite-sample image and kernel system representations and, associated with them, image and residual subspaces of finite-sample signals. On this basis, the equivalence between the fundamental lemma and finite-sample image subspace is demonstrated. While the image representation models the nominal system dynamics, the residual representation describes uncertainties in the input-output data and is essential for fault detection. This result extends the fundamental lemma and builds the basis for exploring data-driven fault detection. In the second part, a data-driven projection-based fault detection approach is developed. By means of a singular value decomposition, orthogonal projections onto the image and residual subspaces are realized in the context of a low-rank matrix approximation, leading to projection-based residual generation and evaluation. Finally, analysis of detection performance in the framework of matrix perturbation theory and comparison with existing data-driven fault detection methods are explored. |
| title | System representations in subspaces of finite-sample signals and their application to data-driven fault detection |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2604.17444 |