Workflow for real-time simulation-based fatigue assessment in mobile machinery

Abstract

Heavy machinery components are prone to fatigue-related damage, and the trend of using high-strength steels in structural design makes fatigue assessment increasingly important. For mobile machinery, simulation-based fatigue assessment is traditionally carried out during the design stage. Digital twin technology, which adds real-time sensor data to simulations, unlocks an opportunity to integrate fatigue assessment results into the control system, but it also introduces new challenges because of the real-time requirement for underlying simulations and analyses. In this paper, a workflow is proposed for real-time simulation-based fatigue assessment specifically adapted to heavy mobile machinery, and applicability of methods available for practical implementation is discussed.

Introduction

Heavy mobile machinery plays a critical role in industrial applications ranging from construction and forestry to mining and logistics. These machines are typically custom-designed for specific operational environments, and they often function under harsh and highly dynamic conditions.^1,2

Heavy machinery is commonly built from steel plate weldments because they are easy to fabricate and offer excellent mechanical performance. However, welded joints are inherently prone to fatigue-related degradation. The welding process introduces geometric discontinuities, residual stresses, and potential defects that are ideal initiation sites for fatigue cracks. Under repeated loading cycles, even when stress levels are below the yield strength, these cracks can propagate and ultimately lead to structural failure. This vulnerability becomes especially critical in heavy machinery, where dynamic loads and operator-induced variability are inherent to the daily use of the equipment. Consequently, the estimation of cyclic load actions remains as the most uncertain factor in fatigue assessments, ³ an issue that is further exacerbated by modern design trends that favor larger and more efficient machines. This increased size and complexity elevates productivity per work cycle, but at the same time, it presents significant challenges in the design of lightweight yet durable structures. Traditional fatigue-resistant design often leads to overly stiff and heavy structures, which is contrary to the current objectives that seek to improve energy efficiency and reduce environmental impact.

A prominent direction in modern structural design is to replace conventional steels with high-strength steels (HSS). While HSS enables significant weight reduction and supports energy-efficient design, ⁴ it also introduces new fatigue-related challenges. The increased yield strength of HSS typically results in higher cyclic stress amplitudes. In the welded regions, however, fatigue resistance does not scale with the higher material strength. ⁵ As a result, fatigue failures may actually occur sooner. Accurately predicting fatigue life requires understanding three key inputs: material properties, structural and notch stress concentration effects (e.g. from structural members and weld geometry), and most critically, operational stress history. While material data and geometry are known, the accurate prediction of stress history remains difficult, especially for machines that are used under varying human-controlled and real-world conditions. ⁶

Multibody simulation-based techniques offer a promising solution to this problem. They allow engineers to model the machine’s dynamic behaviors and assess stress cycles before physical prototypes are built. Once deployed, real-time data collection and virtual sensing strategies can enhance fatigue assessments ⁷ and even guide adaptive control systems. ⁸ Digital twin technology, which links real-time sensor data with high-fidelity simulations, has already demonstrated its potential in aerospace and civil engineering for structural health monitoring.^9–11 The literature indicates that the preference for physics-based or physics-informed digital twins over purely data-driven approaches is often driven by limited availability of representative data and the need for physical interpretability.^10,12 Physics-based models for life prediction have been under active development also in such sectors as rotating machinery. ¹³ However, to fully realize the concept of a digital twin, physics-based computational models must operate in real time, continuously updating their predictions alongside the device operation. That is, essential to ensure that the digital twin remains a living dynamic representation of the real-world system and not just its static or delayed approximation.

In the context of mobile machinery, however, real-time fatigue assessment remains underdeveloped. Challenges such as complex interactions with the ground, systems with complicated actuation, and the effect of operator’s actions must be accounted for in any practical solution. To the best knowledge of the authors, continuous real-time fatigue assessment based on simulations has not yet been implemented for mobile machinery, and therefore, a comprehensive workflow is needed that integrates dynamic simulation, stress analysis, fatigue life estimation, and control strategies.

The objective of this paper is to propose a workflow for simulation-based real-time fatigue assessment that is specifically adapted to mobile machinery. The approach covers (1) methods for simulating machine dynamics and calculating stresses, (2) simulation techniques for local stress analysis using the finite element method (FEM), (3) fatigue life prediction strategies and novel assessment models, including the 4R method, ¹⁴ and (4) control approaches that utilize fatigue insights to support operation and extend structural life. This workflow is designed to enable real-time fatigue evaluation and serve as a technological foundation for integrating digital twins into heavy machinery applications.

Workflow of real-time simulation-based fatigue assessment for dynamic systems with control

To evaluate the durability and reliability of components subjected to cyclic loading, effective fatigue assessment is crucial. Fatigue assessment relies on statistical evaluations that are typically performed under specific loading assumptions. ¹⁵ By analyzing fatigue, it becomes possible to estimate an element’s remaining lifetime and predict potential failures. The accuracy of such assessments depends on the quality of input data, which includes stress and strain distributions, loading history, and environmental conditions. Different assessment methods are used based on the level of detail required and the availability of data.

The most reliable fatigue assessments can be made based on strain data coming from sensors installed on operating machinery. ¹⁶ However, implementing instrumentation comes at significant cost related to purchase, integration, measurement, data storage, and maintenance. Strain gauges, widely used in predictive maintenance, require meticulous installation and are highly sensitive to environmental factors such as temperature variations and humidity. While effective in controlled conditions, their application in heavy machinery is often impractical due to the inherent harsh operating environments.

For mobile machinery, fatigue assessment is typically performed as part of design. In the design phase, simulations are the only source of the stress and strain data necessary for fatigue assessment. The simulations typically include multibody dynamics simulations of machine operation followed by detailed finite element analysis (FEA) of the most critical parts. These traditional steps are depicted in Figure 1, where the top row shows two aspects of the simulations (boxes 1 and 2), and box 3 represents the fatigue assessment performed based on the simulation results.

Figure 1.

Workflow of the simulation-based real-time fatigue assessment for heavy machinery operations.

Digital twin technology offers a promising solution to extend fatigue assessment beyond the design stage and into the machine’s operational life. It is commonly defined as “a digital representation of a physical asset, linked with the physical counterpart by a flow of data enabling the real-time update of the digital model.” ¹⁷ By integrating high-fidelity simulations with real-time sensor data, digital twins allow engineers to predict performance degradation, monitor structural conditions, and optimize maintenance strategies in a simulated environment. ¹¹ As an application to fatigue life management, digital twins can continuously assess stress cycles and cumulative damage in mechanical structures and provide early warnings of fatigue failure. The aerospace and civil engineering sectors have been early adopters of digital-twin-based fatigue assessment. For example, the aircraft industry pioneered digital twin models of airframes that integrate flight sensor data (e.g. loads and temperatures) to predict local damage accumulation and material state evolution. ⁹ Similarly, civil infrastructure managers have begun deploying live digital twins that merge sensor measurements with numerical models to estimate the real-time fatigue condition of bridges and hydraulic structures. ¹⁰ Worth mentioning is also application of digital twin related to the fatigue assessment of wind turbine components and subsystems.^7,18 Taken together, the literature indicates that while the digital twin concept is broadly recognized across engineering domains, its effective implementation depends on application-specific requirements and therefore requires tailored solutions informed by domain knowledge. ¹⁹

However, in heavy machinery for large-scale construction, mining, and industrial equipment, real-time fatigue prognostics remains relatively underutilized. In these industries, fatigue monitoring during operation is still a challenge. It often relies on offline analyses and periodic inspections rather than simulations from integrated digital twins. ²⁰ This gap highlights an important opportunity to extend state-of-the-art digital twin fatigue assessment into heavy machinery to enable continuous health monitoring and more proactive maintenance of critical equipment. Because of the aforementioned challenges associated with using physical sensors in operating mobile machinery, deploying a digital twin technology for fatigue life management must mainly rely on data coming from simulations.

To address these challenges, we propose a novel simulation-based digital twin workflow for fatigue assessment shown in Figure 1. The workflow is based on a digital twin framework and integrates simulations with system control, either by informing the human operator or through automatic control algorithms (box 4 in Figure 1). This integration supports a closed-loop fatigue management process, where operational decisions can be guided by real-time insights into structural health.

The proposed workflow is composed of the following four interconnected phases:

1. Multibody simulation: This phase models the overall dynamics of the complete machine, including mechanical linkages, hydraulic systems, and interactions with the environment, such as tire-to-ground contact or grapple-log interactions in forestry machines. The multibody simulation generates time-dependent dynamic loads that serve as boundary conditions for the structural analysis in subsequent steps. The section “Simulations for mobile machinery” describes the details of this phase.

2. Finite element analysis: FEA provides high-resolution stress and strain fields in areas of interest, typically regions near welds, joints, or other geometric discontinuities where fatigue damage is likely to initiate. Although direct strain gauge measurements would offer the most accurate stress histories, as mentioned earlier, this approach is typically not available for mobile machinery. Consequently, the FEA stage ²¹ plays a critical role in generating the detailed stress or strain data required for accurate fatigue life estimation.

3. Fatigue assessment: Based on the stress histories obtained from FEA (or, in simplified cases, directly from the multibody simulation), this phase quantifies the accumulation of fatigue damage during operation. Accurate fatigue evaluation is essential for balancing modern lightweight design principles, which may exacerbate fatigue susceptibility, with the need for safe and durable machinery. The results of this analysis are then made available to both the operator and the control system. A more detailed discussion of the fatigue assessment methodology is provided in the section “Fatigue assessment methods.”

4. Control algorithm and operator interaction: The final phase involves using the fatigue assessment results to inform operational decisions. This information can be visualized for the operator to highlight damage accumulation and indicate which actions are contributing most significantly to fatigue. In automated systems, this data can also be used to adjust the control policy to enable motion planning that reduces or mitigates fatigue damage. The section “Control algorithms” discusses several control strategies that could leverage fatigue information.

Although Figure 1 presents the complete simulation cycle, various simplifications may be necessary to achieve real-time performance. The section “Simulations for mobile machinery” discusses some of the possible approaches to bypass the computationally expensive FEA stage.

For instance, in some applications, stress approximations from the multibody simulation may be used directly in fatigue assessment, which bypasses the computationally intensive FEA stage. Alternatively, surrogate models (e.g. machine learning-based predictors) may be used to replace the most time-consuming steps of the workflow while still maintaining acceptable accuracy.

Incorporating fatigue assessment into the control loop closes the digital twin cycle and enables real-time structural health management of dynamic systems operating in complex environments. However, achieving real-time performance imposes challenges on each step in the loop. These challenges and potential solutions are addressed in the following sections.

Simulations for mobile machinery

The accurate simulation of mobile machinery operations, as Figure 2 illustrates, may require modeling of elements such as flexible structures, hydraulics, ground-wheels (tracks) contact interactions, and complex dynamic loads.

Figure 2.

Schematic representation: computational challenges in the coupled simulation of flexible multibody system dynamics, hydraulics, dynamic loading, rough terrain and contact forces in heavy machinery operation.

Due to the complexity of the computational problem, it is usually not feasible, using a single mathematical model, to solve all the equations describing the mechanical behaviors of the system with the accuracy required for fatigue assessment. The problem is typically divided into two parts: flexible multibody dynamics simulation and detailed finite element analyses of the components relevant to fatigue assessment. In the following paragraphs, these simulation approaches, as well as possible methods for coupling them, are described in the context of fatigue assessment.

Flexible multibody dynamics simulations

The dynamics of a flexible system, such as that shown in Figure 2, can be described in a differential form using the classical formulations. These formulations are derived from the standard Lagrangian or Newton–Euler mechanics and include constraints in multibody system dynamics.^22–24 In general, the introduction of hydraulics, contact, and ground models in a flexible multibody system exhibit significant computational challenges for real-time simulation. Various approaches have been introduced to meet these computational challenges with reasonable accuracy.

Floating frame of reference formulation

A flexible body that deforms under load can be thought of as an infinite number of interacting particles. ²⁵ State-of-the-art flexible multibody modeling methods include the Finite Elements Method (FEM),^26,27 the assumed mode method, ²⁸ the transfer matrix method,^29,30 the lumped parameter model,^31,32 and Floating Frame of Reference Formulation (FFRF).^22,33 Simulation via these methods is limited by computational cost, the handling of complex geometries, ³⁴ the many degrees of freedom, ²⁶ and improper boundary conditions and modes.^35–37

Among these methods, the FFRF has demonstrated superior performance in many engineering applications that are characterized by large translations and rotations but small deformations.^22,33 Figure 2 showed flexible bodies in both undeformed and deformed configurations within a floating frame of reference. Several versions of the FFRF have been developed to enhance the computational efficiency of FEMs while maintaining reasonable accuracy.^22,23,38,39 However, the FFRF can become computationally expensive as the number of nodal degrees of freedom (DOFs) increases.

Component mode synthesis (CMS) reduces the system’s dimensionality by using a mode basis and boundary conditions through reduction techniques such as Guyan, ⁴⁰ Craig and Bampton ⁴¹ and Martinez et al. ⁴² The CMS allows the FFRF equations to be solved efficiently without sacrificing the accuracy of the dynamic behavior by representing the flexible body using a small set of component modes instead of the thousands of DOFs. Furthermore, modified versions of FFRF can bypass the unhandy inertia shape integrals,^39,43 which are typically the most computationally expensive part of the CMS-based FFRF formulation.

Using modal reduction techniques, the equations of motion in CMS can be further simplified based on eigenmodes to enhance computational efficiency with reasonable accuracy. ⁴⁴ Techniques such as modal reduction and mode selection enable structural flexibility to be represented without overwhelming computational resources. In such scenarios, including additional modes can enhance accuracy but also increase computational demands, potentially undermining real-time feasibility.

Hydraulics

Lumped fluid theory ⁴⁵ has been widely adopted to incorporate hydraulics into rigid multibody system models.^46–49 However, extending this approach to include flexible bodies introduces additional computational challenges. Modally reduced CMS has been coupled with hydraulics ⁵⁰ to model hydraulically actuated flexible systems while still ensuring reasonable computational efficiency and stability. Increasingly, analysts are using surrogate models, often based on reduced-order modeling, to further accelerate simulations in hydraulically actuated multibody systems.^51,52

For fatigue assessment, multibody simulation can determine loads, and fatigue can then be evaluated with the help of a precise finite element model. However, this approach is not sufficient in the event of non-typical requirements that require innovative solution variants such as real-time fatigue monitoring.^53,54

To make high-fidelity fatigue predictions based on multibody simulations and enable continuous, real-time monitoring, a balance must be reached between accuracy and computational performance. Two principal strategies emerge in this context: the monolithic (unified) approach and multirate integration:

• In the monolithic approach, the equations governing mechanical and other subsystems form a single system of coupled differential equations.^55–57 Numerous works reported in the literature adopted a monolithic framework to simultaneously solve the coupled mechanical and hydraulic equations in multibody dynamics simulations.^47,48,58,59 Several articles addressed the study of hydraulic cylinder models and the role of friction in making accurate predictions.^60,61 The dynamic simulation using a monolithic formulation of hydraulically driven mobile machinery was reported in several works.^62,63

• Multirate integration (including both co-integration^64,65 and co-simulation^66–68) offers an alternate path. It separates the system into distinct subsystems (e.g. mechanical and hydraulic) and integrates each one using a suitable time step. This can be especially advantageous for real-time applications where computational efficiency is paramount. Although high-frequency phenomena related to hydraulic or electromechanical actuators could be solved with finer time steps, lower-frequency mechanical dynamics might use larger intervals to reduce the overall simulation burden. Several works in the literature are devoted to co-simulation configuration^69,70 and multirate co-simulation, ⁷¹ which enable sophisticated subsystem-specific solvers to run concurrently and exchange boundary conditions or interface data at predetermined intervals.

In the context of simulation-based fatigue assessment for mobile machinery, both the monolithic and multirate schemes must incorporate flexible multibody formulations to capture significant deformations under cyclic loads.

Tire-to-ground interaction

In mobile machinery, the interaction between tires and the ground generates dynamic forces that are transmitted through the machine’s structural components. These forces can be highly variable, particularly in off-road conditions, and can significantly affect fatigue life by generating stress cycles in booms, joints, and other load-bearing elements. High-fidelity tire models are used to capture these effects precisely and predict transient stresses and local load peaks. By mirroring real-world conditions such as granular terrain, soil cohesion, and tire deformation, engineers can better identify fatigue-prone regions, optimize material usage, reinforce critical areas, and ultimately extend the service life of mobile machinery.

Classic treatments of the tire-to-road contact problem (see Pacejka ⁷² ), introduce both fundamental and advanced tire models and highlight the central role tires play in the overall dynamic behaviors of a vehicle. Nevertheless, for mobile machinery operating on granular soil, more complex approaches are needed. Computational feasibility varies with DEM resolution, and fatigue-relevant responses should be validated per system via sensitivity analysis. High-fidelity representations of deformable tires and granular terrain were proposed in Recuero et al., ⁷³ where three-dimensional finite element models of the tires incorporated layered, orthotropic materials and internal pressure. These were integrated into off-road vehicle multibody systems. In a similar vein, the physics-based mobility simulation frameworks reported by Serban et al.^74,75 included flexible tires modeled via nonlinear finite elements and granular soil captured as large collections of rigid particles that interacted via contact, friction, and cohesive forces. These advanced models are critical not only for predicting vehicle dynamics but also for identifying stress distributions and load cycles under realistic operational conditions. They enable more accurate fatigue assessment of vehicle structures operating in demanding off-road environments.

Stress analysis for components of interest

The multibody dynamics simulations that describe machine movement do not reveal stresses acting within the machine’s components with the accuracies required for fatigue assessment. The following bullets summarize available techniques for calculating these stresses.

• Explicit dynamic simulations: In some cases, the dynamic behavior of the structure of interest can be simulated with FEA using explicit time integration. This approach is extensively used to simulate short processes, such as crash tests, ⁷⁶ and is typically extremely demanding of computational resources. ⁷⁷ To mitigate this, shell-element simulations are typically used. Stresses obtained in such simulations, as well as in equivalent static simulations, are used, for example, to assess fatigue in weld joints. ⁷⁸ However, because of the inherent computational difficulty, in practice, this approach cannot be used to simulate operational scenarios typical in mobile machinery without applying additional simplifications, for example, as described in the work. ⁷⁸

• Implicit finite element analysis and submodeling techniques: In most cases, FEA of the region of interest with very fine mesh is required for accurate fatigue prediction using advanced assessment methods. For mobile machinery, it is typically not feasible to keep the required level of details in a model used for simulating the whole structure, such as the ones discussed in the previous subsection. Instead, the analysis can be performed in several steps. In the first step, a multibody simulation of the machine is performed using flexible reduced order models as discussed in the subsection “Flexible multibody dynamics simulations.” Solution data obtained in this simulation is then used to formulate boundary conditions for a detailed finite element analysis based on implicit time integration and 3D solid elements. Quite often the complexity of the structures in mobile machinery requires this analysis to be carried out also in two steps. At first, a FEA of the entire component is done using joint forces from the multibody simulation as boundary conditions. In the second step, an FEA of a smaller region of the component is done based on an extremely detailed finite element model using interpolation of the displacement field from the first step as the boundary conditions. This is usually referred to as submodeling. ⁷⁹ This submodeling approach has proven reliable for the calculation of stresses with enough accuracy for fatigue assessment, but in practice its computational cost makes it unusable for real-time analysis.

• Recovering stress and strain fields from reduced order model simulations: Another approach is to determine stresses and stress fields based on a reduced-order model flexible multibody simulation. After carrying out this simulation, stresses and strains in the flexible parts of the model can be calculated in one of two ways:

Regardless of the exact technique used, recovering stress data from flexible multibody simulations makes it possible to avoid time-consuming finite element simulations. It is therefore essential for enabling real-time fatigue assessment. This approach, however, puts challenging requirements on the level of details of the model used to form the reduction basis.

Fatigue assessment methods

Different fatigue assessment methods are traditionally applied for systems of different types belonging to different industries. The following paragraphs review fatigue assessment methods relevant for mobile machinery, highlighting the benefits and disadvantages.

Fatigue design strategies

Fatigue design starts with the selection of a relevant strategy. The appropriate approach depends on which industry or type of machine is being analyzed. The likelihood for fatigue-critical flaws and defects, the load magnitudes and dynamics, and the consequences of failures are considerations. In general, fatigue design strategies for mechanical components can be subdivided into the following four different categories.^5,82

• Infinite life design: When structural components are expected to experience a very high number of cycles during the service period (usually the number of load cycles N ≥ 10⁷), fatigue assessment is carried out using concepts of fatigue limit or equivalent threshold limit for fatigue load actions.

• Safe life design: According to this strategy, fatigue crack(s) will not grow to critical crack size during the service period and load actions do not exceed the endurable stresses at desired number of cycles (i.e. N ≤ N_Rd at given load, where N_Rd is the design resistance of fatigue life).

• Fail-safe design: It is assumed that fatigue cracks might occur during the in-service lifetime, but they can be easily recognized, inspected and repaired before reaching the critical crack size. The fail-safe design strategy is mainly appropriate for components with readily-accessible components.

• Damage-tolerant design: Components are assumed to include initial cracks with minimum detectable size by non-destructive testing. Fracture mechanical crack growth analysis is conducted to design maximum allowable inspection periods ensuring that fatigue cracks do not reach the specified maximum allowable crack size between these inspection intervals.

Different design strategies can be still implemented by applying the same fatigue assessment methods. To account for the applied approach in each strategy, different partial safety factors for the material and component fatigue resistances can be assigned. However, given the nature of the different design strategies, it is more appropriate to apply material defect-based assessments and fatigue limit models for infinite life design approaches. ⁸³ The damage-tolerant as well as fail-safe design strategies assume the existence of physical crack(s), and fracture mechanical crack growth analyses are conducted. ⁸⁴ For the structural elements in mobile machinery, such as boom and frame structures, a finite number of load cycles can usually be assumed. To avoid unfavorable fatigue failures, the manufacturing quality requirements in such components adhere to the principles of defect-free highly stressed areas. Section “Fatigue assessment Modeling techniques” gives a detailed review on the suitable stress- and strain-based assessments implemented within the safe life and fail-safe design strategies.

Fatigue assessment – Modeling techniques

The fatigue phenomenon, including crack initiation and propagation (See Figure 3), cannot be physically modeled using a single approach. Fatigue crack nucleation is governed by reversed plastic material strain at regions of high stress, followed by short crack growth. This phase is characterized by varying crack growth rates due to the crack arresting mechanism. When these incipient cracks reach a physical crack size, usually with crack depth of more than 50 µm, stable crack growth regime is reached. With a small amount of plasticity in the vicinity of the crack front, linear elastic fracture mechanics can be applied to assess crack growth behavior, for example, using the Paris model.

Figure 3.

Evolution of fatigue crack in different scales, and applications of different fatigue assessment models.

For dynamically loaded structural components, both design and manufacturing should aim to maximize the initiation and propagation phases. Consequently, fatigue modeling usually deals with total fatigue life concepts with continuum mechanics models without considering cracks. Real-time fatigue assessments subsequently incorporate either stress-based or strain-based assessments, depending on the redundancy of structure, allowance of existing fatigue crack and design strategy.

For welded joints and components, multiple different methods are used to assess the fatigue strength of welded steel structures. An overview of the most well-established concepts is presented here. Global concepts usually refer to the nominal stress approach, which yields maximum principal stress at nominal or macro geometric far field stress. The effect of different structural geometries and notch details is solely addressed in the relevant detail category or fatigue class, which usually refers to the fatigue strength at two million load cycles. Considering the elementary nature of the nominal stress method, it provides conservative assessments. However, it disregards many important factors contributing to fatigue performance and can only be applied for simple structural details and load cases.

Stress- or strain-based local concepts address the effects of structural details and notches in fatigue assessments. Use of such local concepts overcome the need to consider relevant detail category and evaluate global stresses in the complex structural details and stress fields. In particular, they can be easily adopted when computational FEM models are available.

Structural stress or strain methods use local stress or strain at structural detail without considering notch effects. Close field structural stresses or strain at “hot-spots” can be obtained, for example, by extrapolating from the reference points, linearizing stress over component thickness, and using stress at certain depth/distance points. ⁸⁵ The method employs few fatigue classes for different structural and notch details.

Notch stress-based assessments account for local notch stress concentrations. The benefit of these approaches lies in their consideration of local stress at actual fatigue-critical locations. The underlying methods for determining fatigue-effective stresses apply fictitious (reference) radius concepts (usually referring to effective notch stress approach) ⁸⁶ and effective stresses by the theory of critical distances.^87–90 Because the fatigue-effective stress is determined at the notch, the basic concept is that a single fatigue class can be applied regardless of joint or notch type. However, fatigue classes might involve corrections and stress ratio changes and/or post-weld treatments.

In simple assessment approaches, such as the nominal stress method, fatigue assessment models can directly incorporate cyclic stress or strain histories, extracted using the techniques introduced in the section “Simulations for mobile machinery.” However, when advanced local approaches are applied, nodal displacements or reaction forces can serve as inputs for FEM models including local geometries to obtain local stress or strain histories for fatigue assessments. For these histories, peak-valley analysis (see Figure 1) can be performed, and various cycle counting algorithms ⁹¹ can be applied to determine fatigue load actions and compare them with the fatigue capacity at the given load.

In addition to the selection of a suitable design strategy and fatigue assessment approach, variable in-service load magnitudes and dynamics and their effects on the fatigue design model must be considered. Conventionally, fatigue damage of variable amplitude load conditions is considered by accumulating a linear damage sum of individual load cycles with design principles similar to those given for constant amplitude load conditions. Varying mean stress conditions in variable amplitude loading can be treated with a modified damage sum. ⁵ However, recent experimental fatigue studies on high-strength steels have indicated that relevant damage parameters depend on the mean stress conditions. A linear damage sum of D >> 1.0 could be used in the case of low mean stress conditions. Under high mean stress conditions, the damage parameters seem to fall closer to D = 1 or below.^92–94 In mobile crane components, high mean stress under fatigue loading can occur, for example, due to the lifted mass.

To account for the sequential effects of load cycles and overloads in association with the relaxation stress state, the 4R method simulates the local cyclic stress-strain response by accounting for elastic-plastic material behavior at the notch root. It determined the local stress ratio, which is applied in the mean stress corrections for each load cycle. Consequently The 4R method can significantly enhance the accuracy of fatigue predictions compared to other stress-based methods.^95,96 Assessments using the 4R method for different mean stress conditions have been experimentally validated for welded high-strength steel joints,^92–96 employing random Gaussian variable amplitude load spectra, typical for vehicles. ⁹¹

Control algorithms

The idea of accounting for mechanical fatigue in automatic control can be traced back to the 1990s when in their concept paper, Lorenzo and Merill introduced Life Extending Control (LEC). ⁹⁷ LEC was defined as a strategy to control the rates of change and the levels of some performance variables to minimize damage or damage rates of critical components while simultaneously maximizing dynamic plant performance. The authors emphasized a fundamental trade-off between the level of achievable performance and the ability to extend the life of system components generating that performance. In the following years, various applications of the concept were reported in the aerospace industry, and the term “damage mitigating control” was also introduced to describe similar approaches.^98,99 In Zhang et al., ¹⁰⁰ a design methodology of hybrid life-extending control was described for the structural durability and high performance of mechanical systems. The authors presented a two-tier architecture that used a variable-structure stochastic automaton on the lower tier to evaluate structural damage status. Overall system performance was maintained by the supervisory level discrete-event controller on the upper tier. In 2004, a NASA report was published with an overview of methods applied in the aircraft industry to monitor and extend engine life. ¹⁰¹

Another LEC application area is process control in manufacturing, chemical, and material processing plants. A review was presented in Zagorowska et al. ¹⁰² that discusses known approaches in this area. It considers a broader term of degradation defined as a detrimental change in physical condition with time, use, or external cause. Mechanical fatigue is an example of degradation. The paper considers degradation as a factor that affects system behaviors and therefore requires control-design attention. It proposes a classification of mathematical models of degradation to facilitate integrating of degradation modeling into control and optimization schemes. Besides process control, the paper mentions several applications where control design accounts for mechanical fatigue: a mass-beam system, an actuator cylinder, wind turbines, aircraft, and bearings.

A more recent review ¹⁰³ concludes that many studies from many industries report a negligible loss in control quality while still heavily reducing structural damage. The paper focuses on large-scale industrial facilities, such as power plants, other facilities associated with high pressure and/or temperature, and aircraft or spacecraft. It introduces “Life-Time Considering Control” (LTCC) as a more general term describing both LEC and damage mitigating control approaches.

Both of the aforementioned reviews state that optimal control via linear-quadratic controllers or model predictive controllers is the most applied method for degradation mitigation. These approaches allow the straightforward application of degradation models in constraints or directly in the objective function. An intrinsic feature of optimal control is that the objective function is calculated multiple times for each time step. As a result, the models must be simplified to ensure fast computation, or the controlled process must be slow enough to provide sufficiently long timeframes for real-time calculation with complex models. The latter is often the case for process control, but not for mobile machinery, where a common response time is one or several milliseconds. The reviews describe tens of applications, but mobile machinery is not present among them.

To develop life-time considering control for mobile machinery, the approaches used in the aerospace industry may be applicable because they also consider fast dynamics. A straightforward approach is to use intuitive LEC algorithms. ⁹⁷ Minimizing mean tensile stress, mean strain, and mean temperature, as well as minimizing the cyclic amplitude of stress, strain, and temperature should minimize damage. Minimizing the number of stress and strain cycles should also contribute to extending the life of critical components. These objectives can be achieved in a number of ways. One option is to use trajectory planning. For manual operation, operators should be trained to exercise smooth machine movements and follow trajectories of a certain type. Another option is to limit the maximum allowed value for the amplitude or the rate of the control signals provided by the operators. This approach was implemented and reported on in Roozbahani et al. ¹⁰⁴ As mentioned earlier, there is a trade-off to be considered between the desired level of performance and extended service life. To ensure the safety of human-machine interaction, LEC can be included in the system as an option that the operator is able to switch off if necessary. For autonomous machines, more freedom is available since a (semi)optimal trajectory can be built for each movement that takes into account the aforementioned variables. For example, for machines with simple mechanical structure, it is easy to construct trajectories that minimize forces and torques, and therefore strain. When the number of degrees of freedom and external loads increases, stress minimization requires a model that estimates stress at critical points. In this case, some form of optimal control can be used with the estimated stress in the objective function. To account for the trade-off between the performance and the life extension ability of the system, more advanced approaches should make use of performance variables in the optimization process and models for continuous degradation measurement or estimation.

Conclusions

A comprehensive workflow has been proposed for simulation-based real-time fatigue assessment specifically tailored to mobile machinery. It integrates multibody dynamic simulation, stress analysis, fatigue life estimation, and control strategies. As a schematic reference of the complete methodology, Figure 1 illustrates the full workflow and serves as the central diagram summarizing the proposed approach. The workflow has been designed to serve as a technological foundation that can be used to integrate digital twins into heavy machinery applications.

The proposed workflow begins with the multibody simulation of machine operation. Accurate simulations of high-fidelity models of mobile machines may require modeling of flexible bodies, hydraulics, ground–tire contact interaction, and complex dynamic loads. The FFRF enables accurate modeling of flexible components undergoing large translations and rotations. Generalized CMS, which is an advanced version of FFRF, can be used to model 3D flexible systems. Using modal reduction techniques, the equations of motion in the CMS can be further simplified based on eigenmodes, which enables computational efficiency while maintaining reasonable accuracy. Hydraulic actuation can be incorporated either through a monolithic set of coupled mechanical–hydraulic equations or via co-simulation schemes. In addition, high-fidelity tire-to-ground interaction models are included to reproduce the variable off-road loads transmitted through the machine’s structural components.

Once the multibody dynamic simulation based on reduced order models is complete, stresses are computed for accurate fatigue assessment. In the context of mobile machinery, continuous real-time computation of stresses in the regions of interest can be reliably achieved using direct stress recovery based on stress modes or recovered displacement field. The main disadvantage of this method is the necessity to include all design features important for the distribution of stresses, in the models used in model order reduction process. In case, that is, too challenging but local stresses are needed for fatigue assessment, submodeling techniques can be considered as another option.

Fatigue assessment begins with the selection of an appropriate fatigue design strategy. For mechanical components, common approaches include infinite life, safe life, fail-safe, and damage-tolerant design strategies. For structural elements in mobile machinery such as boom and frame structures, a finite number of load cycles is typically assumed. Once a strategy is defined, a suitable modeling technique must be selected. The selected fatigue assessment method will consider variable amplitude loads, which are characteristic of real-world work cycles for mobile machinery. Recent HSS research supports using modified damage parameters or sequence-sensitive techniques such as the 4R method to better capture overload-induced residual stress relaxation effects resulting from peak and variable amplitude loading.

Finally, a control algorithm is implemented. LTCC and LEC are well documented control strategies for aerospace, power-plant and other process industries. However, no implementations for mobile machinery are reported in the surveyed literature. Optimal control frameworks typically used for degradation mitigation, such as linear-quadratic or model predictive control, often involve computation times that are incompatible with the millisecond-level update rates required by mobile equipment. To adapt LTCC concepts to this domain, engineers can adopt intuitive LEC rules to minimize mean and cyclic stresses, strains, and temperatures. They can also reduce the number of high-load cycles, either through operator training or by generating smooth motion trajectories that limit force and torque peaks. For machines with many degrees of freedom and complex external loading conditions, effective stress minimization requires fast surrogate models capable of estimating stress at critical locations. These stress estimates can then be integrated into the control objectives without violating real-time constraints.

In future work, the proposed workflow will be validated through real-world case studies involving off-road mobile machinery, such as agricultural and construction equipment. To enable real-time monitoring and predictive maintenance, integration within a comprehensive digital twin environment may also be explored. Experimental validation based on sensor data acquired from machines operating under real field conditions would be essential to assess the accuracy of the fatigue predictions. In parallel, the practical workability of the workflow could be further investigated by assessing its computational performance and real-time capability, using the real-time factor (RTF), defined as the ratio between computation time and simulated time, as a key performance indicator. The influence of numerical integration settings, such as absolute and relative solver tolerances, on execution speed and real-time feasibility will be systematically analyzed. In addition, machine learning techniques may be investigated to enhance surrogate modeling or to enable direct fatigue life prediction from sensor signals. Finally, future developments may include operator feedback systems aimed at promoting operational practices that extend component lifetime.