# Investigating Bayesian Parameter Identification Using Non-Standard Laboratory Specimens
## 1 Introduction
In [38], hierarchical Bayesian identification was performed to identify the elastic parameters of the spring mass model in the dynamic test using acceleration measurements. Ultrasonic experiments were performed on a large aluminum plate containing a hole, where a semi-analytical numerical model in conjunction with the MCMC method was used to estimate transmission coefficients [39]. The Bayesian method was also applied to full-scale structures, such as a seven-story cross-laminated timber building [23], where gPCE and MCMC methods together with results of a vibration tests were used to identify elastic constants. Similarly, in [40], the elastic parameters of cultural heritage buildings were identified using a simplified finite element model, MCMC methods, and ambient vibration measurements. Furthermore, the elastic parameters of the concrete dams have been identified through gPCE and MCMC methods and by monitoring displacement data [41]. A hierarchical Bayesian approach combined with ambient vibration tests and gPCE was used in another dam study [42]. In [18], the goal was to identify mechanical model parameters based on existing damage patterns using the Bayesian inference method and a Gaussian process model. Several studies have also focused on the identification of fracture parameters. For instance, the elastic and strength parameters for FEM model of concrete tram poles were determined in [17] using a Kriging proxy model, MCMC, and vibration testing on pole specimens. In [43], the fracture properties of concrete and steel-concrete bond parameters were investigated using ED-FEM and X-FEM models, based on tensile tests on concrete beams. Here, gPCE and Kalman filtering were used alongside displacement measurements and cyclic fracture energy tests for parameter identification. Additionally, in [44], the parameters of a lattice model for mortar prisms reinforced with carbon fiber polymer plates were identified by double shear test, using gPCE and Kalman filtering with Digital Image Correlation (DIC) measurements. In [45], the focus was on identifying parameters of lattice models, specifically the mechanical properties of mortar and concrete, through unconfined compression cube tests and notched three-point bending tests by applying gPCE, MCMC, and Crack Mouth Opening Displacement (CMOD) measurements. The study presented in [46] focused on fracture parameters, such as strength and toughness in a phase-field model for elastic solids and brittle cement mortar, utilizing notched three-point bending tests with sequential updating, gPCE, and MCMC methods. Finally, the study presented in [47] addressed the identification of phase-field model parameters for metals through both synthetic and experimental measurements. For the experimental part, load-displacement measurements from I-shaped Al-5005 and Sandia Al-5052 specimens were used in combination with MCMC-based methods. Despite the progress made in identifying fracture parameters, these studies reveal some common challenges. Parameters associated with the later stages of failure tend to yield more uncertain results. Furthermore, the applicability of the identified parameters across different specimen geometries and stress states is not generally investigated. This study applies a Bayesian identification methodology to full-stage parameter identification in the mechanical testing of non-standard aluminum 6060 alloy specimens, covering the entire material response from elastic and plastic deformation to fracture and complete failure. The methodology uses the embedded discontinuity model (Q6 ED) with general polynomial chaos expansion (gPCE) as a proxy model. The Q6 ED model is capable of representing material plasticity with isotropic hardening and simulating crack initiation and propagation. Cracks are introduced within the elements as discontinuity lines (displacement jumps) with independent location and orientation, ensuring that the computed fracture energy dissipation remains independent of element size.