State-dependent Model Research Articles

The role of health in consumption and portfolio decision-making: Insights from state-dependent models

In this paper, we study an optimal consumption and asset allocation problem accounting for the fact that individuals’ utility differs across various health states. Our study is based on the assumption that an individual’s health status evolves through a semi-Markov process, where the transition probabilities are contingent on both the present state and the duration spent in that state. The optimal form of stock investment and of consumption is determined analytically. The optimal consumption level is significantly shaped by the integration of health-related factors and can be represented as the inverse of the marginal utility function with respect to time and state price density. Additionally, we introduce a Lagrangian multiplier that can be derived by solving a fixed point problem. While our optimal solutions are applicable to a wide range of utility functions, we provide numerical illustrations specifically using the power utility function in a model encompassing three distinct health states. Transition probabilities are estimated from real data collected by the China Insurance Regulatory Commission (CIRC), using a high-order polynomial Perks formula. We find that the investor’s consumption is higher when health is good, but lower when care is needed.

Collaborative train timetabling and passenger flow control in oversaturated metro lines considering state-dependence

Congestion downgrades the moving speed of passengers in trains and platforms. This in turn affects congestion. That is, the moving speed of passengers interacts with congestion. It is state-dependent and obeys the fundamental diagram. This interaction makes the system unstable and can result in substantial passenger delays and heightened security risks in oversaturated metro lines. This study aims to rectify this by developing a more realistic collaborative optimization approach. Firstly, we formulate a deterministic fluid queuing network model to accurately capture the dynamic propagation of congestion in oversaturated metro lines. This model incorporates the fundamental diagram, thereby effectively considering the interaction between passenger movement speeds and congestion. A recursive algorithm is devised to solve the fluid queuing network model. The complexity of the algorithm is independent of the capacities of the stations and trains. This provides the possibility of analyzing large-scale metro networks. Based on the queuing network model, a mixed-integer nonlinear programming model aimed at minimizing the total passenger waiting time is built. To solve the model effectively, we employ an alternating direction method of multipliers framework to decompose the model into nonlinear programming and integer nonlinear programming problems, which are respectively solved by improved simultaneous perturbation stochastic approximation and adaptive large neighborhood search algorithms. Finally, a small-scale case and a real-world case with data from Chengdu metro lines are implemented to demonstrate the performance and effectiveness of the proposed approach. The experimental results provide some interesting insights. (1) Without consideration of state-dependence, the queuing model underestimates the passenger waiting time and overestimates the service levels. (2) As demand increases, excluding extreme oversaturation scenarios, the optimized results of the state-independent model progressively deteriorate compared to our state-dependent model, with the largest percentage decline being 50.23%. This is especially noticeable when the train capacity is limited. (3) The contribution ratio of passenger flow control in mitigating congestion gradually surpasses that of train timetabling with increasing demand. In the small-scale case, the former contribution ratio to optimization rises from negligible to 98.19%.

Deformation and failure behavior of 2024-T42 sheet under impact loading

The deformation and failure behavior of 2024-T42 aluminum alloy sheet was investigated through a combined experimental-numerical method. Nine types of specimens were designed to cover a wide range of stress triaxialities and strain rates. Quasi-static and dynamic tests were carried out by electronic testing machine and split Hopkinson tensile bar respectively, and digital image correlation (DIC) method was introduced to measure the deformation. The phenomenological damage model GISSMO (generalized incremental stress state dependent damage model) and Johnson-Cook model were adopted to simulate all of the above tests and the load-displacement curves through numerical simulation were derived. An optimization method was developed to obtain all the model parameters by matching the load-displacement curves from simulation with those from tests by LS-OPT. Finally, drop weight tests and tensile tests of the central-hole plate were conducted. The applicability and accuracy of the damage models were verified by comparing the simulation results with the experiments, which indicates that GISSMO model predicts better the tests than the Johnson-Cook failure model.

Tree adaptive growth (TAG) model: a life-history theory-based analytical model for post-thinning forest stand dynamics.

Understanding stand dynamics is essential for predicting future wood supply and associated ecosystem services for sustainable forest management. The dynamics of natural stands can be characterized by age-dependent growth and yield models. However, dynamics in managed stands appear somewhat different from that of natural stands, especially with difficulties in explaining the phenomenon of post-thinning overcompensation, based upon some long-term observations. Though overcompensation is an ideal outcome for the forest sector, it had been largely treated as an outlier and thus ignored or dismissed as "out-of-the-ordinary". We developed a life history theory-based, state-dependent model of Tree Adaptive Growth (TAG) to investigate this phenomenon and verified that overcompensation should be a common outcome in post-thinning forest stands when the stand growth over time is sigmoid shaped. TAG posits that individual trees will invest proportionately more into growth following thinning because it is evolutionarily adaptive to do so. Our investigation of the model's behavior unearthed diverse stand growth patterns similar to that which is observed in the empirical datasets and predicted by a statistics-based Tree's Compensatory Growth (TreeCG) model. A simple, theory-driven, analytical model, TAG, can reproduce the diverse growth patterns in post-thinning stands and thus assist addressing silviculture-related issues. The model can be applied to various jurisdictions even without detailed regional growth and yield relationships and is capable of incorporating the effects of other time sensitive factors like fertilization, pruning, and climate change.

State-Dependent Model Based on Singular Spectrum Analysis Vector for Modeling Structural Breaks: Forecasting Indonesian Export

Standard time-series modeling requires the stability of model parameters over time. The instability of model parameters is often caused by structural breaks, leading to the formation of nonlinear models. A state-dependent model (SDM) is a more general and flexible scheme in nonlinear modeling. On the other hand, time-series data often exhibit multiple frequency components, such as trends, seasonality, cycles, and noise. These frequency components can be optimized in forecasting using Singular Spectrum Analysis (SSA). Furthermore, the two most widely used approaches in SSA are Linear Recurrent Formula (SSAR) and Vector (SSAV). SSAV has better accuracy and robustness than SSAR, especially in handling structural breaks. Therefore, this research proposes modeling the SSAV coefficient with an SDM approach to take structural breaks called SDM-SSAV. SDM recursively updates the SSAV coefficient to adapt over time and between states using an Extended Kalman Filter (EKF). Empirical results with Indonesian Export data and simulation studies show that the accuracy of SDM-SSAV outperforms SSAR, SSAV, SDM-SSAR, hybrid ARIMA-LSTM, and VARI.

Research on state dependent differentiation field model based on pedestrian micro motion characteristics

Research on state dependent differentiation field model based on pedestrian micro motion characteristics

Among-individual behavioural variation in the ornamental red cherry shrimp, Neocaridina heteropoda.

Personality variation, defined as among-individual differences in behaviour that are repeatable across time and context, is widely reported across animal taxa. From an evolutionary perspective, characterising the amount and structure of this variation is useful since differences among individuals are the raw material for adaptive behavioural evolution. However, behavioural variation among individuals also has implications for more applied areas of evolution and ecology-from invasion biology to ecotoxicology and selective breeding in captive systems. Here, we investigate the structure of personality variation in the red cherry shrimp, Neocaridina heteropoda, a popular ornamental species that is readily kept and bred under laboratory conditions and is emerging as a decapod crustacean model across these fields, but for which basic biological, ecological and behavioural data are limited. Using two assays and a repeated measures approach, we quantify behaviours putatively indicative of shy-bold variation and test for sexual dimorphism and/or size-dependent behaviours (as predicted by some state-dependent models of personality). We find moderate-to-high behavioural repeatabilities in most traits. Although strong individual-level correlations across behaviours are consistent with a major personality axis underlying these observed traits, the multivariate structure of personality variation does not fully match a priori expectations of a shy-bold axis. This may reflect our ecological naivety with respect to what really constitutes bolder, more risk-prone, behaviour in this species. We find no evidence for sexual dimorphism and only weak support for size-dependent behaviour. Our study contributes to the growing literature describing behavioural variation in aquatic invertebrates. Furthermore, it lays a foundation for further studies harnessing the potential of this emerging model system. In particular, this existing behavioural variation could be functionally linked to life-history traits and invasive success and serve as a target of artificial selection or bioassays. It thus holds significant promise in applied research across ecotoxicology, aquaculture and invasion biology.

Who innovates? Abundance of novel and familiar food changes which animals are most persistent.

Novel behaviours are the raw material of cultural evolution, yet we do not have a clear picture of when they are likely to arise. I use a state-dependent model to examine how individual age and energy reserves interact with the abundance of known and novel prey to promote dietary innovation (incorporating a new food item into the diet). I measure innovativeness as persistence in attempting to capture novel prey. I find a trend towards greater persistence among younger individuals. Decreased abundance of known prey and increased abundance of novel prey also favour persistence. However, many exceptions to these trends occur. These exceptions are critical because they may explain inconsistencies among studies of animal innovation. Care must be taken in experiments to control for multiple factors relevant to an animal's energy budget and foraging opportunities. We may learn more about innovation in experimental contexts by (i) manipulating the abundance of novel and familiar food resources, (ii) directly measuring animal age and condition, and-where possible-(iii) fitting nonlinear models to innovative behaviour. Results indicate that selection for persistence may also favour neophilia.

Use of Linear Extrapolation to Estimate Critical State Void Ratio from Drained Triaxial Shear Tests on Dense Cohesionless Soil

Within the strain level attainable in drained triaxial tests, it is not uncommon for dense cohesionless soil to be sheared insufficiently to reach the critical state. Linear fitting of the correlative data from the maximum stress ratio or minimum dilatancy to the end of the test, and then extrapolating these fitted lines to the critical stress ratio or zero dilatancy has been frequently used to estimate the critical state void ratio. However, the linear extrapolation method is empirical and involves different choices of correlative test data, which leads to different estimates. Therefore, a series of simulations of drained tests on dense Toyoura sand are performed using a state-dependent model. Multiple data sets are generated, including void ratio e, volumetric strain εv, stress ratio η, and dilatancy D. The linear extrapolation accuracy of the e–η, e–D, and εv–D data sets is examined. It turns out that the e–η data set is best suited. The goodness of the e–η data set is examined against 18 sets of experimental data on dense sand. In addition, the selection of the start point for extrapolation is shown to influence the estimates. The latter 50% of the post-peak data is found to be reliable.

Application and effects of physics-based and non-physics-based regularizations in artificial intelligence-based surrogate modelling for highly compressible subsurface flow

Artificial intelligence (AI)-based surrogate reservoir models (SRMs) can provide computationally feasible and accurate approximations to numerical simulations. An AI-based SRM is trained to a set of parameters that significantly reduces its variance. This can be done by either supervised or semi-supervised learning. The latter involves regularization of the model’s parameters using non-physics-based, physics-based or a combination of both regularization terms.Effective enforcement of the physics-based and non-physics-based regularizations can significantly reduce the variance of AI-based SRMs. Little study has been reported on the application and effects of regularization terms. Also, for highly compressible subsurface flow where strong nonlinearities exist, well-constructed composite AI-based architectures and regularizations are necessary for learning.This paper applies and studies the effects of various regularization terms for highly compressible subsurface flow; it proposes unique and effective techniques in AI-based surrogate development and training. The learning utilizes the discretized domain and boundary physics with derivatives obtained from both finite difference methods (FDM) and algorithmic differentiation (AD). The regularizations are partly enforced as a hard constraint in the network architecture using a trainable layer and as soft constraints using a multi-cost function. The soft constraints exploit a tank material balance and time-discretization numerical errors, in addition to the domain, boundary and non-physics-based L2 regularization terms. The timely-trained AI-based surrogate predictions agree with those obtained from a numerical simulator.The regularization terms separately contribute to improved learning. The non-physics-based L2 norm if used in the right order of magnitude, improves grid block predictions. The tank material balance regularization term constrains the AI-based surrogate parameters to net domain accumulation, ensuring its reliability. The trainable hard enforcement layer enforces the initial condition and improves the predictions compared to other hard enforcement techniques. The discretized domain equation and time-discretization numerical errors allow for learning of variable timesteps, which give the best rounding-truncation error trade-off and improve the predictions compared to those of fixed timesteps. The AI-based surrogate, effectively trained by semi-supervision, can be reliably used as a state-dependent model in domain analysis like sensitivity and data assimilation.

Ductile failure behaviour characterisation of HRT with GISSMO and crashworthiness optimisation design of VRB-HRT

In this paper, a generalised incremental stress state dependent damage model (GISSMO) is used to accurately characterise the ductile failure behaviour of hot formed steel under collision, which is the excellent material selection to improve the crashworthiness and lightweight level of car body frames. The deformation patterns, structural failure patterns, and key crashworthiness indexes of B1500HS hot-rolled tube (HRT) are validated by the comparative researches between experiments and simulations. To fully exploit the lightweight potential of HRT, a variable-thickness rolled blanks hot rolled tube (VRB-HRT) is proposed to perform its crashworthiness optimisation design with considering the ductile failure by the extended hybrid cellular automaton for VRB thin-walled structures (eHCA-VRB) algorithm. It is found that the optimal case of VRB-HRT with considering the ductile failure is easier to meet the actual performance constraints, even though possesses a lower weight reduction ratio. Therefore, the ductile failure of VRB-HRT should be considered to guarantee the structural reliability by a more reasonable optimal design.

Numerical modelling of shield tunnel face failure through a critical state sand plasticity model with nonlocal regularization

During shield tunneling in sand strata, variations in the state of sand can lead to localized instability and strength loss, which brings about numerical difficulties. This paper numerically investigates how nucleation and propagation of plastic deformation zones, including those leading to localized banding, possibly promote failure of shield tunnel faces excavated in sand. To this end, a material state-dependent model is used to capture the mechanical responses of sand. Nonlocal enhancement is introduced, through the volumetric strain increment that drives the change of void ratio and related material hardening/softening behavior, to regularize ill-posed boundary value problems caused by the activation of strain localization. Simulations of tunnel face failure indicate that lower initial void ratios result in more concentrated plastic deformation in the vicinity region near the face and a strain-softening trend in global deformation responses. Conversely, initial looser states drive the deformation zone to propagate spatially to the ground surface, and the resultant global deformation responses exhibit strain-hardening. The second-order work is used to explain the link between material instability around the tunnel faces and initial density. It was found that material instability usually occupies a fraction of plastic deformation regions, and shrinks as sand initial density increases.

High-velocity impact failure modeling of Armox 500T steel: Model validation and application to structural design

As an advanced fracture model, the Generalized Incremental Stress State dependent damage MOdel (GISSMO) provides non-linear damage accumulation formulation to better predict ductile fracture initiation associated with a wider range of material stress states. In this study, we simulate the high-velocity impact failure of Armox 500T steel through computational finite element modeling in the LS-DYNA/Explicit solver. Here, the GISSMO is used to describe the ballistic responses of the Armox 500T steel under dynamic impacts. Two sets of the most important parameters in the GISSMO (i.e., the fracture and instability surfaces) are determined for the Armox 500T steel. The GISSMO is calibrated in terms of the fade exponent and mesh regularization functions using the force–displacement curve of tensile tests extracted from the literature. The calibrated GISSMO is then scaled with the strain rate and validated by comparing quantitative measurements from ballistic experiments provided in the literature. Once validated, the model is then used to investigate the impact failure behaviors of Armox 500T steel by simulating bi-layer configurations consisting of an Armox 500T steel front plate and a rolled homogeneous armor (RHA) steel backing plate impact from a 20 mm fragment simulating projectile. The roles of the standoff distance and impact angle of obliquity on impact failure behaviors of bi-layered steel systems are explored. Altogether, results from this study provide new capabilities and insights into the design of armor structures with respect to lightweight and ballistic performance, and evaluation of impact failure behaviors of Armox 500T/RHA bi-layered systems.

Repercussions of the Russia–Ukraine war

Using the heteroscedasticity-based estimator of Rigobon and Sack (2005) to identify daily shocks of the Russia–Ukraine war, I assess and quantify the dynamic impact of the conflict on 86 open economies from January 2021 to November 2022. Within local projections, I show that war shocks caused considerable effects on macroeconomic conditions, financial markets, and global financial stability. Following a shock, weekly GDP fell significantly while inflation expectations and commodity prices soared, verifying the war’s nature as a contractionary supply shock. While global stock prices fell, the long-term government bond yields remained stable, implying the crisis had not triggered a flight of capital to the US, and governments remained able to borrow at the pre-war costs of funding. More concerning, a range of indicators – implied volatility, credit default swap spread, cross-currency basis – suggest a significant and sustained increase in systemic financial stress. Through a state-dependent model, I show that energy importers and nations that share borders or have close trade and military ties with the belligerents were more affected by war shocks. Taken together, these findings may inform policy responses and assist households and firms in preparing for possible contingencies arising from the war.

Numerical modeling of the effect of loading rate on the tensile load capacity of offshore caisson foundations

Suction caissons are skirted foundations frequently used in offshore environments supporting various structures. Among those lie the offshore wind turbines (OWT), which are currently one of the most common renewable energy systems. In this paper we study the tensile capacity of caisson foundations of OWT in dense sands, where the generation of excess pore pressure is analyzed. The tensile capacity of suction buckets under various loading rates is investigated using a series of quasi-static axisymmetric finite element analyses with coupled flow-deformation formulation. DeltaSand model is utilized for the soil, which is an elasto-plastic state-dependent model capturing the response of sands at varying relative densities. Numerical results are validated with available test data of scaled physical model experiments. Particular emphasis is placed on the interaction between suction-bucket and the soil. Parameters governing the soil-caisson interface playing a key role in the uplift response are identified. Lastly, a case study that can be observed in offshore foundations is simulated. Results show that the developed numerical model is applicable to capturing the uplift response of bucket in an ocean environment. The outcome of this study will contribute to closing the gap in the design of suction caissons of OWT in existing standards.

Scenario-based multi-risk assessment from existing single-hazard vulnerability models. An application to consecutive earthquakes and tsunamis in Lima, Peru

Abstract. Multi-hazard risk assessments for building portfolios exposed to earthquake shaking followed by a tsunami are usually based on empirical vulnerability models calibrated on post-event surveys of damaged buildings. The applicability of these models cannot easily be extrapolated to other regions of larger/smaller events. Moreover, the quantitative evaluation of the damages related to each of the hazard types (disaggregation) is impossible. To investigate cumulative damage on extended building portfolios, this study proposes an alternative and modular method to probabilistically integrate sets of single-hazard vulnerability models that are constantly being developed and calibrated by experts from various research fields to be used within a multi-risk context. This method is based on the proposal of state-dependent fragility functions for the triggered hazard to account for the pre-existing damage and the harmonisation of building classes and damage states through their taxonomic characterisation, which is transversal to any hazard-dependent vulnerability. This modular assemblage also allows us to separate the economic losses expected for each scenario on building portfolios subjected to cascading hazards. We demonstrate its application by assessing the economic losses expected for the residential building stock of Lima, Peru, a megacity commonly exposed to consecutive earthquake and tsunami scenarios. We show the importance of accounting for damage accumulation on extended building portfolios while observing a dependency between the earthquake magnitude and the direct economic losses derived for each hazard scenario. For the commonly exposed residential building stock of Lima exposed to both perils, we find that classical tsunami empirical fragility functions lead to underestimations of predicted losses for lower magnitudes (Mw) and large overestimations for larger Mw events in comparison to our state-dependent models and cumulative-damage method.

Use of uncoupled ductile damage models for fracture forming limit prediction during two-stage forming of aluminum sheet material

In this paper, failure limits of aluminum AA5052 sheet material were experimentally investigated, and subsequently, these were predicted using various uncoupled ductile fracture models. In this context, three different sets of experiments, namely two-stage stretch forming, two-stage deep drawing, and single point incremental forming experiments, were performed to estimate the failure limits under several different strain paths. Both the isotropic von Mises and anisotropic Barlat Yld2000 yield criteria were used to calibrate eight different fracture models, and found that incorporating an anisotropic model enhanced the accuracy of prediction for most of the fracture models. Moreover, it was identified that the incorporation of anisotropic yield theory in the Bao-Wierzbicki (BW) fracture model predicted the experimental fracture surface strains precisely for as-received sheet materials. This BW model-based fracture forming limit diagram (BW-FFLD) was transposed into a path-independent polar effective plastic strain (PEPS) locus to estimate the onset of fracture during two-stage forming experiments. Furthermore, the BW model was incorporated as a fracture initiation model in the finite element (FE) software, LS-Dyna, using the generalized incremental stress state dependent damage model (GISSMO) platform to predict the fracture location and dome height through the element erosion technique. It was observed that the dome height and cup height were predicted within 7 % and 5 % error margins in the FE simulation of two-stage stretch forming and deep drawing experiments, respectively. Furthermore, the damage evolution contour indicated that the accumulation of the damage value was rapid, which was responsible for the massive drop in the dome and cup heights during two-stage stretch forming and deep drawing experiments.

Effect of stress state on adiabatic shear banding in Al2024-T351

Cubic uniaxial compression and angled cubic biaxial shear-compression specimens are a preferable choice in the context of developing empirical data for models such as the Generalized Incremental Stress State Dependent Damage Model (GISSMO), with a strain-rate dependent extension. The angled cubic specimens introduce a multiaxial stress state of combined shear and compression. Al2024-T351 specimens have been impacted using a direct impact Hopkinson bar coupled with Digital Image Correlation (2D-DIC). 2D-DIC has been used to track the full-field strain evolution of all specimens and obtain the fracture strains for fractured specimens. The shear strain evolution related to failure along the shear planes can be acquired using 2D-DIC, and a quantitative measurement of fracture initiation is acquired from the DIC data. It is also highlighted that the transverse displacement contours can offer qualitative information about the effects of friction on proportional loading during uniaxial compression. Interrupted tests using stop rings are conducted for angled cubic specimens to identify the critical strains for the initiation of adiabatic shear bands (ASBs), which can be defined as the GISSMO instability strains. ASBs are confirmed using the optical microscope, and it is found that for a constant impact momentum, the specimens with a greater shear to compressive stress state exhibit a higher tendency to form ASBs at lower major axial strains. It is also found that ASBs are observed using the optical microscope with no loss of flow stress, and that angled specimens exhibit a lower flow stress than uniaxial compression specimens at higher strain rates. Lastly, pre-impact and non-fractured post-impact Vickers microhardness tests have been conducted, and it is found that for all specimens, the material is on average about 20% harder after impact in regions away from the ASB, and further that regardless of stress-state, the ASB is consistently about 30% harder than the pre-impact microstructure.

Importance of modelling hERG binding in predicting drug-induced action potential prolongations for drug safety assessment.

Reduction of the rapid delayed rectifier potassium current (I Kr) via drug binding to the human Ether-à-go-go-Related Gene (hERG) channel is a well recognised mechanism that can contribute to an increased risk of Torsades de Pointes. Mathematical models have been created to replicate the effects of channel blockers, such as reducing the ionic conductance of the channel. Here, we study the impact of including state-dependent drug binding in a mathematical model of hERG when translating hERG inhibition to action potential changes. We show that the difference in action potential predictions when modelling drug binding of hERG using a state-dependent model versus a conductance scaling model depends not only on the properties of the drug and whether the experiment achieves steady state, but also on the experimental protocols. Furthermore, through exploring the model parameter space, we demonstrate that the state-dependent model and the conductance scaling model generally predict different action potential prolongations and are not interchangeable, while at high binding and unbinding rates, the conductance scaling model tends to predict shorter action potential prolongations. Finally, we observe that the difference in simulated action potentials between the models is determined by the binding and unbinding rate, rather than the trapping mechanism. This study demonstrates the importance of modelling drug binding and highlights the need for improved understanding of drug trapping which can have implications for the uses in drug safety assessment.

Parameters Calibration of the GISSMO Failure Model for SUS301L-MT

With the development of the rail transit industry, more attention has been paid to the passive safety of rail vehicles. Structural damage is one of the main failure behaviors in a rail vehicle collision, but it has been paid little attention to in past research. In this paper, the quasi-static fracture experiments of SUS301L-MT under different stress states were carried out. The mechanical fracture properties of this material were studied, and the corresponding finite element simulation accuracy was improved to guide the design of vehicle crashworthiness. Through the tests, the fracture behavior of materials with wide stress triaxiality was obtained, and each specimen's fracture locations and fracture strains were determined. Parameters of a generalized incremental stress state dependent damage model (GISSMO) of the material were calibrated, and the model's accuracy was verified with test results from a 45° shear specimen. The GISSMO failure model accurately reflected the fracture characteristics of the material. The mesh dependency of this model was modified and discussed. The results show that the simulation agrees well with experimental data for the force-displacement curve after correction, but the strain distribution needs to be further studied and improved.