# Data-Driven Condition Assessment and Life Cycle Analysis Methods for Dynamically and Fatigue-Loaded Railway Infrastructure Components

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## Abstract

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## 1. Introduction

## 2. Aerodynamic Loading Acting on Railway Noise Barriers and Structural Interaction

_{1}, the speed of the train v

_{train}, the wall height h, and the eigenfrequency f

_{NB}of the NB construction as well as on the distance of the track axis to the surface of the noise barrier denoted as a

_{g}. Because of the impulsive sinusoidal shape of the air pressure and suction wave, a dynamic amplification of the NB deflection occurs [21], and its size is defined using the shock factor φ

_{dyn}given in EN 16727-2-2 [22]. The dynamic amplification can become a factor of up to φ

_{dyn}= 3.25 in the most unfavourable case. Until 2005, train-induced aerodynamic loading has not been adequately considered in the design of NB as well as in the applied calculation methods (pure static analysis with proof of load capacity) and in the relevant normative specifications given in Eurocode EN 1991-2 [23]. Causes for the resulting fatigue damage of NB components (aluminium panels) have been investigated in [24,25].

_{DS}based on the insufficient loading ±q

_{1,k}given in EN 1991-2 [23] as follows:

_{L}and φ

_{H}define the length and height factors (see [22] for details). According to RVE 04.01.01 [27], a minimum of three fatigue-relevant load cycles must be considered for a single train passage, i.e., in the case of 100 trains per day, a total of 5.475 Mio. load cycles occur within 50 years of the NB’s lifetime. Hence, in the design of NB constructions, a fatigue limit state analysis must be conducted according to EN 1993-1-9 [28], and the fatigue strength must be proofed for all fatigue-critical components of the NB (panels, steel posts, and fastening elements).

## 3. Data-Driven Condition Assessment and Life Cycle Analysis Framework

#### 3.1. General Details

#### 3.2. Established Visual Inspection Approach

_{V}) in a kind of school-grading system from 1 to 5, where grade 1 stands for a very good visual condition. This approach depends heavily on the experience of the inspecting engineer and, therefore, is very subjective. Since the process of fatigue in the fastening elements is progressing almost if not entirely hidden from the human eye, accessing this hidden mechanical state using new monitoring technologies and making use of the rapid development of computational power is a great advancement.

#### 3.3. Main Considerations of the Framework for Data-Driven Condition Assessment and Life Cycle Analysis

_{V}) and fatigue calculations, according to RVE 04.01.01 [27], currently carried out only in the design processes of new NB constructions. In a subsequent step, this calculated fatigue, or, in other words, the end of a lifetime, is put into a reliability index framework, which allows for the consideration of consequence classes. Finally, through discretisation into the mechanical condition classes ZK

_{M}1 to ZK

_{M}5, a maintenance strategy can be developed. With each model stage activation, the accuracy of the condition assessment and prediction of the remaining useful lifetime is increasing but so is the effort the infrastructure manager has to put in.

## 4. Discussion and Variation Studies in Selected Model Stages

_{V}), mechanical classes (ZK

_{M}) are additionally defined in a kind of school-grading system, with class grade 1 representing a good mechanical condition and class grade 5 representing a bad mechanical condition. The mechanical condition describes the state of fatigue in a deeper level of detail, which is not or barely detectable in a purely visual inspection. To make another comparison, visual condition classes contain visually detectable information, which is strongly dependent on the inspector’s experience and knowledge. On the other hand, the mechanical condition classes combine visual and monitoring information, information from experiments, applied standard calculations, and digital twins, from which a more stable and accurate solution is expected.

_{1}, where the train type ICE shows the most favourable, with k

_{1}= 0.6; train type RJ is medium favourable, with k

_{1}= 0.85; and train type FT, CJ, EC, and WB have the most unfavourable factor, with k

_{1}= 1.0. Starting with this typical load collective in case (a), the technical lifetime is calculated for four different scenarios numbered from 1 to 4. Scenario 1 describes a fastening system with visual condition class 1, which refers to sufficient preload force and, therefore, a maximum reduction in the stress variation range. Scenarios 2, 3, and 4 describe fastening systems with visual condition classes 2, 3, and 4, which, respectively, refer to a gradually reduced preload force to almost non-existent and, therefore, a minimum reduction in the stress variation range in the threaded bolts. The reduction factors, shown in Table 1, were roughly derived from the experiments conducted in [29]. Further laboratory, as well as numerical, experiments are necessary to calibrate these first approach factors.

## 5. Analysis of Installation Conditions Model Stage III on the Performance Assessment

_{a}

_{1}and F

_{a}

_{2}, with equal magnitude and equidistant from the bolt axis. Since the cross-section of interest “$i$” is engaging at the first loadbearing thread, the calculations of the internal forces are conducted at exactly that point. The action force ${F}_{a}$, which is centred in the case of ideal installation condition, results from the sum of F

_{a}

_{1}and F

_{a}

_{2}and equals the resistance force at the cross-section of interest ${F}_{r,i}$ via the equilibrium of forces. When the internal forces have been calculated, finally, the preload stress ${\sigma}_{\mathit{xx}}\left(z\right)$ is calculated with Equation (5), where ${A}_{i}$ is the area of the cross-section of interest. Since the forces act centrically, the bending stress term is omitted in Equation (5), leaving only the stress term of the normal force.

## 6. FEM-Digital Twin Studies of Installation Conditions “Model Stage III”

_{NORM}= 71 N/mm

^{2}, which leads to a failure of the threaded bolts after 7 × 10

^{5}load cycles. PL0 shows the highest stress variation range with around 200 N/mm

^{2}, resulting in failure after just 3 × 10

^{4}load cycles. The stress variation ranges of PL60 with around 23 N/mm

^{2}and PL100 with around 16 N/mm

^{2}are far below the standard calculations and result theoretically in an infinite technical lifetime since they are in the high-cycle fatigue domain.

_{NORM}= 71 N/mm

^{2}, which leads to a failure of the threaded bolts after 7 × 10

^{5}load cycles. PL0 shows that compared to the ideal installation condition with 0 kN preload force (Figure 10a), with 225 N/mm

^{2}, there is an even higher stress variation range, which results in failure after just 2 × 10

^{4}load cycles. The stress variation ranges of PL60 with around 26 N/mm

^{2}and a failure after 1 × 10

^{8}load cycles is very close to the endurance limit, which separates finite life fatigue and high cycle fatigue. The stress variation range of PL100 with around 17 N/mm

^{2}does not change very much compared to the ideal installation condition illustrated in Figure 11.

_{NORM}= 71 N/mm

^{2}, which leads to a failure after 7 × 10

^{5}load cycles. PL0 shows with 772 N/mm

^{2}a stress variation range almost 4 times higher compared to the ideal installation condition with 0 kN preload force (Figure 10a), which results in an immediate failure of the threaded bolts. The stress variation ranges of PL60 with around 1.5 N/mm

^{2}theoretically lead to an infinite lifetime for the threaded bolts. The stress variation range of PL100 with around 3.7 N/mm

^{2}theoretically leads to an infinite lifetime.

## 7. Data-Based Condition Assessment Using Bayesian Updating Techniques

_{IIa}) of the visual condition assessment and the likelihood information P(B

_{IIb}|A

_{IIa}) of the loading from the real train traffic actions (monitoring action side and load model) in order to obtain the posterior distribution P(A

_{IIa}|B

_{IIb}) of, e.g., the stress variation ranges in the anchor bolts.

_{IIb}) = P(A

_{IIa}|B

_{IIb}) and can be combined with the likelihood information on the resistance side, e.g., the preload degree in the bolted joints P(B

_{IIc}|A

_{IIb}) of Model Stage IIc, which leads to the posterior P(A

_{IIb}|B

_{IIc}).

_{IIc}|B

_{III}) in the stress ranges and, subsequently, using the Wöhler diagrams, into the posterior information P(A

_{II}|B

_{III}) of the remaining service life and the reliability level ZK

_{M}, which, in turn, can be correlated with the original ZK

_{V}. Thus, it is possible to consider a direct relation between the visual condition class ZK

_{V}and the mechanical condition class ZK

_{M}, taking into account the uncertainties of the different model stages. In this development of the correlations, it is not absolutely necessary to include all model stages in the Bayesian interference approach.

## 8. Conclusions

- It could be shown how the level of approximation and the level of detailing, as prescribed in the new guidelines of the Model Code 2020, can be implemented on a specific constructive detail and the required process of developing a deeper understanding of the detailing problem associated with the proposed holistic framework.
- It was also possible, based on the proposed holistic framework, to use a deeper understanding of the details of the initial visual inspection to adjust the conformity tests and quality control tests and to define further criteria or indicators that would allow a targeted control of the extension of the service life.
- Using the presented holistic approach ranging from visual inspection to monitoring elements to the creation of the digital twin, it became clear which elements can be used for an accurate service life assessment, maintenance control, and detail optimisation. From this holistic approach, it also became clear which model stage can be optimally applied to which needs.
- The presented approach also shows in which way the classical condition assessment with condition grades can be linked effectively with mechanical processes happening and the related reliability levels and lifetime assessments.
- Using this approach, we also demonstrated how the data-driven assessment can be implemented in detail, particularly not only by monitoring information from the resistance side but also by monitoring the impact situations of the degradation processes. Consequently, we also showed how these data-driven assessments can be used to link elements between the visual assessment and the digital twin assessment.
- Finally, this research project outlines how the uncertainties in the information available at each stage can be effectively addressed in the form of a Bayesian inference approach and used to consciously address the uncertainties in the evaluation process.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Aerodynamic loading situation over the height of the NB during train passage. (

**b**) Aerodynamic loading situation in the longitudinal direction of the NB during train passage.

**Figure 2.**Components and performance indicators of a noise barrier structure and the corresponding condition classes of visual inspection ZK

_{V}1.

**Figure 3.**Different designs and qualities of fixing the steel posts of NB to the concrete edge beam.

**Figure 4.**Holistic four model stages for condition assessment and service life prediction of railway structures.

**Figure 5.**(

**a**) Load collective 1 (

**left**), lifetime predictions of threaded bolts according to [23] with load collective 1 (

**right**); (

**b**) Load collective 2 (

**left**), lifetime predictions according to [23] with load collective 2 (

**right**); (

**c**) Load collective 3 (

**left**), lifetime predictions according to [23] with load collective 3 (

**right**).

**Figure 7.**(

**a**) Ideal installation condition; (

**b**) Deficient installation condition, displaced components; (

**c**) Deficient installation condition, inclined threaded bolts; (

**d**) Deficient installation condition, rough concrete surface; (

**e**) Deficient installation condition, deformed baseplate.

**Figure 8.**(

**a**) Stress distribution in eccentrically loaded threaded bolt. (

**b**) Stress distribution in eccentrically loaded threaded bolt.

**Figure 9.**Geometrical dimensions of the actual noise barrier design according to the standard regulations of the Austrian federal railway. Reprinted/adapted with permission from Ref. [32]. 2023, Michael Reiterer.

**Figure 10.**(

**a**) Ideal installation condition finite element model (

**left**), stress analysis (

**middle**), lifetime prediction (

**right**); (

**b**) Deficient installation condition 1 finite element model (

**left**), stress analysis (

**middle**), lifetime prediction (

**right**); (

**c**) Deficient installation condition 2 finite element model (

**left**), stress analysis (

**middle**), lifetime prediction (

**right**).

**Figure 11.**Bayesian inference procedure, to assign the reliability formats and remaining service life to the visual condition assessment.

**Table 1.**Defined visual condition classes and their corresponding reduction factors for the preload force in the threaded bolts derived from [29].

Visual Condition Class | ZK_{V} 1 | ZK_{V} 2 | ZK_{V} 3 | ZK_{V} 4 | ZK_{V} 5 |
---|---|---|---|---|---|

Reduction Factor ${\gamma}_{{ZK}_{V}}$ | 0.4 | 0.5 | 0.6 | 0.9 | 1.0 |

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**MDPI and ACS Style**

Granzner, M.; Strauss, A.; Reiterer, M.; Cao, M.; Novák, D.
Data-Driven Condition Assessment and Life Cycle Analysis Methods for Dynamically and Fatigue-Loaded Railway Infrastructure Components. *Infrastructures* **2023**, *8*, 162.
https://doi.org/10.3390/infrastructures8110162

**AMA Style**

Granzner M, Strauss A, Reiterer M, Cao M, Novák D.
Data-Driven Condition Assessment and Life Cycle Analysis Methods for Dynamically and Fatigue-Loaded Railway Infrastructure Components. *Infrastructures*. 2023; 8(11):162.
https://doi.org/10.3390/infrastructures8110162

**Chicago/Turabian Style**

Granzner, Maximilian, Alfred Strauss, Michael Reiterer, Maosen Cao, and Drahomír Novák.
2023. "Data-Driven Condition Assessment and Life Cycle Analysis Methods for Dynamically and Fatigue-Loaded Railway Infrastructure Components" *Infrastructures* 8, no. 11: 162.
https://doi.org/10.3390/infrastructures8110162