arXiv subjects

Tammam Bakeer

Publications and source records attributed to Tammam Bakeer.

4 recordsLinked to original sources

arXiv2026

Local Information Operators for Spatial Identifiability in Distributed-Parameter Inverse Problems in Computational Mechanics

In distributed-parameter inverse problems in computational mechanics, spatially varying fields are inferred from noisy, indirect, and heterogeneous observations. The relevant identifiability question concerns which spatial perturbation patterns of the field are distinguishable under a specified sensing and excitation programme. This paper develops a local information-operator framework for this purpose. Around a nominal parameter field, the parameter-to-observation map is linearized and the likelihood contribution to posterior precision is interpreted as an operator on parameter-field perturbations. For locally linearized Gaussian models with parameter-independent covariance, this operator is equivalently Fisher information, Gauss-Newton data-misfit curvature, and a noise-weighted sensitivity Gramian. The framework separates pointwise visibility from spatial identifiability. The diagonal gives a coordinate-dependent local information density, while the full kernel and metric- or prior-preconditioned spectra rank spatial patterns that are strongly visible, weakly visible, or locally invisible. Heterogeneous observation blocks are assembled in a common parameter space; information is additive only under conditional independence, whereas correlated errors require the full joint covariance. Model discrepancy, nuisance parameters, and prior information modify the same geometry through covariance inflation, Schur-complement information loss, and prior-preconditioned modes. Examples cover analytic beam kernels, two-span support coupling, static-dynamic fusion for flexural-rigidity identification, and two-dimensional damage-field reconstruction in a leading information subspace. The operator view supports interpretation of identifiability, sensor complementarity, and reduced reconstruction in distributed-parameter inverse problems.

cs.CE↗

arXiv2025

Sensor Informativeness, Identifiability, and Uncertainty in Bayesian Inverse Problems for Structural Health Monitoring

In Structural Health Monitoring (SHM), the recovery of distributed mechanical parameters from sparse data is often ill-posed, raising critical questions about identifiability and the reliability of inferred states. While deterministic regularization methods such as Tikhonov stabilise the inversion, they provide little insight into the spatial limits of resolution or the inherent uncertainty of the solution. This paper presents a Bayesian inverse framework that rigorously quantifies these limits, using the identification of distributed flexural rigidity from rotation (tilt) influence lines as a primary case study. Fisher information is employed as a diagnostic metric to quantify sensor informativeness, revealing how specific sensor layouts and load paths constrain the recoverable spatial features of the parameter field. The methodology is applied to the full-scale openLAB research bridge (TU Dresden) using data from controlled vehicle passages. Beyond estimating the flexural rigidity profile, the Bayesian formulation produces credible intervals that expose regions of practical non-identifiability, which deterministic methods may obscure. The results demonstrate that while the measurement data carry high information content for the target parameters, their utility is spatially heterogeneous and strictly bounded by the experiment design. The proposed framework unifies identification with uncertainty quantification, providing a rigorous basis for optimising sensor placement and interpreting the credibility of SHM diagnostics.

cs.CE↗

arXiv2025

Quality Control and Structural Reliability -- A Unified Framework for Integrating Conformity Assessment and Partial Safety Factors

Ensuring structural reliability remains a core concern in civil engineering, yet the quantitative effects of quality control measures on material variability and safety margins are not fully understood, especially for materials other than reinforced concrete. This study addresses this gap by presenting a probabilistic framework that integrates Bayesian updating, acceptance sampling, and operating characteristic (OC) curves to model conformity assessment as a probabilistic filter. In doing so, it refines prior distributions of key material and execution parameters based on quality control outcomes, linking reductions in the coefficient of variation directly to adjustments in partial safety factors. Applying the framework to a masonry wall example demonstrates how systematic quality control efforts, particularly those targeting parameters with higher importance such as masonry unit strength and execution quality-produce substantial gains in structural reliability. The analysis shows that combined quality control measures can lower the partial safety factor from a baseline of 1.5 to about 1.38, corresponding to an improvement factor of roughly 1.09 and material savings of approximately 8%. Conversely, controlling parameters with negligible influence, such as mortar properties, provides limited benefit. These findings encourage focusing quality control resources on the most influential parameters and integrating results into semi-probabilistic design methods. By offering a transparent, standards-compatible approach, the framework supports the refinement of design guidelines, promotes more efficient resource allocation, and enhances overall structural safety in the built environment.

stat.AP↗

arXiv2022

The theory of homogeneity of nonlinear structural systems -- A general basis for structural safety assessment

The paper develops a novel and general methodology to characterize the nonlinearity of structural systems and to provide a mathematically proven basis for applying partial safety factors to nonlinear structural systems. It establishes, for the first time since the development of limit-state theory, the necessary key relationship between the partial safety factor concept and the reliability theory of nonlinear structural systems. The degree of homogeneity has been introduced as a nonlinearity measure at the design point, allowing an efficient mathematical decoupling of the reliability index into nonlinearity-invariant partial reliability indexes. With this formulation, critical safety situations in extreme cases of nonlinearities have been identified in complex nonlinear structural systems. The theory resulted in two main outcomes based on the asymptotic behaviour of the reliability index. First, the reliability index of any nonlinear structural system remains always bounded between an upper and lower bound, which can be determined by the concept of nonlinearity-invariant partial reliability indexes. The second is nonlinearity-invariant critical partial safety factors, a concept that assures a reliability index greater than the target reliability index in any nonlinear structural system. Homogeneity analysis has been suggested to assess the safety of complex nonlinear structural systems. While it can be coupled with advanced computational methods available in structural mechanics, it is not specifically designed for engineering practice. The proposed theory is designed primarily to provide code writers with the necessary procedure for calibrating partial safety factors for nonlinear structural systems, and to identify the over-safe or under-safe cases in the codes of practice.

stat.AP↗