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At least 433 records · Page 24

Leveraging explainable AI to characterize floating-point exceptions in linear solvers

Linear solver packages are central to many scientific, engineering, and machine learning applications. When floating-point exceptions occur in these solvers, e.g., division by zero or overflow, numerical results are compromised and become unreliable. Existing static and dynamic analysis tools can detect such exceptions, but they do not explain why the exceptions occur in terms of the solver inputs. Here, we present a study to characterize the inputs that cause numerical exceptions in linear solver packages. Our approach uses explainable AI (XAI) to find the most relevant characteristics of input matrices that explain the occurrence of exceptions in the solvers. Since training data in this domain is scarce, we perform extensive data gathering and data augmentation to obtain exception-inducing inputs. Our approach uses a repair strategy on the features blamed by XAI to validate that such features indeed explain the exceptions. We compare the LIME and SHAP XAI techniques using a dozen matrix features with three classifiers. We evaluate the approach on three widely used linear solver packages and find that some input characteristics can explain the occurrence of exceptions 100% of the time, in specific solvers and preconditioners.

Explainable AI↗

How structural differences influence cross-model consistency: An electric sector case study

Multiple models are often employed to describe a range of possible outcomes for one or more scenarios, yielding insights into causal relationships and their uncertainties. Electric sector capacity expansion scenarios are a common topic of such efforts due to the economic influence of the electric sector, but model results typically span a broad solution space despite efforts to harmonize input assumptions, making decision implications difficult to discern. This study investigates the relationship between input harmonization and cross-model scenario consistency under disparate electric sector scenarios. We compare cross-model consistency between two state-of-the-art electric sector capacity expansion models (GCAM-USA and ReEDS) for six electric sector scenarios comprising alternate assumptions about fossil fuel resource availability, technology innovation, and long-term economy-wide transitions under four harmonization configurations varying model representations of electricity demand, fuel prices, renewable resources, and capacity retirements. These comparisons reveal that cross-model consistency can vary across scenarios under a given harmonization configuration, suggesting that harmonization efforts must often be scenario-specific if comparable cross-model consistency is desired. Model structural differences can hinder consistency, and the impact of these differences can depend on the scenario. Ultimately, thorough harmonization can reveal insights into cross-model consistency, which can be used to tighten uncertainty bounds and improve the decision-making implications of multi-model activities.

Cohen, Stuart↗

Pareto-optimal target definition for multi-axis random vibration testing

In random vibration testing with multiple control channels, existing control laws require specification of a complete spectral density matrix at each control frequency. Spectral density matrices include autospectral densities on the diagonal and cross-spectral densities on the off-diagonal. In practice, the off-diagonal terms are often unknown, and recent vibration testing research has focused on fixing the diagonal and specifying the off-diagonal to minimize the required control energy, subject to a constraint that the target matrix is positive semidefinite. This paper shows that, even with a fixed diagonal, off-diagonal terms strongly affect control residuals. This overlooked effect occurs in both square and rectangular systems. By jointly considering input energy and control residuals, open-loop inputs are derived directly from the diagonal without specifying the off-diagonal terms. Vibration targets that can be used in closed-loop control are then derived using the optimal inputs, with positive semidefinite constraints applied during the derivation. The result is a set of Pareto-optimal control solutions. For each solution in the set, any other possible solution produces greater control error, greater input energy, or both. A balanced solution is selected automatically, though others can be chosen based on test needs. Simulations and experiments show that the proposed method outperforms state-of-the-art energy-minimizing approaches, achieving significant reductions in both control error and input energy.

Autospectral density↗

Respiration regimes in rivers: Partitioning source–specific respiration from metabolism time series

Respiration in streams is controlled by the timing, magnitude, and quality of organic matter (OM) inputs from internal primary production and external fluxes. Here, we estimated the contribution of different OM sources to seasonal, annual, and event-driven characteristics of whole-stream ecosystem respiration (ER) using an inverse modeling framework that accounts for possible time-lags between OM inputs and respiration. We modeled site-specific, dynamic OM stocks contributing to ER: autochthonous OM from gross primary production (GPP); allochthonous OM delivered during flow events; and seasonal pulses of leaf litter. OM stored in the sediment and dissolved organic matter (DOM) transported during baseflow were modeled as a stable stock contributing to baseline respiration. We applied this modeling framework to five streams with different catchment size, climate, and canopy cover, where multi-year time series of ER and environmental variables were available. Overall, the model explained between 53% and 74% of observed ER dynamics. Respiration of autochthonous OM tracked seasonal peaks in GPP in spring or summer. Increases in ER were often associated with high-flow events. Respiration associated with litter inputs was larger in smaller streams. Time lags between leaf inputs and respiration were longer than for other OM sources, likely due to lower biological reactivity. Model estimates of source-specific ER and OM stocks compared well with existing measures of OM stocks, inputs, and respiration or decomposition. Our modeling approach has the potential to expand the scale of comparative analyses of OM dynamics within and among freshwater ecosystems.

59 BASIC BIOLOGICAL SCIENCES↗

Sensitive parameter identification and uncertainty quantification for the stability of pipeline conveying fluid

In this study, several uncertainty quantification and sensitivity analysis methods are used to determine the most sensitive geometric and material input parameters of a cantilevered pipeline conveying fluid when uncertainty is introduced to the system at the onset of instability. The full nonlinear equations of motion are modeled using the extended Hamilton’s principle and then discretized using Galerkin’s method. A parametric study is first performed, and the Morris elementary effects are calculated to obtain a preliminary understanding of how the onset speed changes when each parameter is introduced to a ± 5% uncertainty. Then, four different input uncertainty distributions, mainly, uniform and Gaussian distribution, are chosen to investigate how input distributions affect uncertainty in the output. A convergence analysis is used to determine the number of samples needed to maintain simulation accuracy while saving the most computational time. Then, Monte Carlo simulations are run, and the output distributions for each input distribution at ± 1%, ± 3% and ± 5% input uncertainty range are found and discussed. Additionally, the Pearson correlation coefficients are evaluated for different uncertainty ranges. A final Monte Carlo study is performed in which single parameters are held constant while all others still have uncertainty. Overall, the flow speed at the onset of instability is the most sensitive to changes in the outer diameter of the pipe.

36 MATERIALS SCIENCE↗

Latent map Gaussian processes for mixed variable metamodeling

Gaussian processes (GPs) are ubiquitously used in sciences and engineering as metamodels. Standard GPs, however, can only handle numerical or quantitative variables. Here we introduce latent map Gaussian processes (LMGPs) that inherit the attractive properties of GPs and are also applicable to mixed data which have both quantitative and qualitative inputs. The core idea behind LMGPs is to learn a continuous, low-dimensional latent space or manifold which encodes all qualitative inputs. To learn this manifold, we first assign a unique prior vector representation to each combination of qualitative inputs. We then use a low-rank linear map to project these priors on a manifold that characterizes the posterior representations. As the posteriors are quantitative, they can be directly used in any standard correlation function such as the Gaussian or Matern. Hence, the optimal map and the corresponding manifold, along with other hyperparameters of the correlation function, can be systematically learned via maximum likelihood estimation. Through a wide range of analytic and real-world examples, we demonstrate the advantages of LMGPs over state-of-the-art methods in terms of accuracy and versatility. In particular, we show that LMGPs can handle variable-length inputs, have an explainable neural network interpretation, and provide insights into how qualitative inputs affect the response or interact with each other. We also employ LMGPs in Bayesian optimization and illustrate that they can discover optimal compound compositions more efficiently than conventional methods that convert compositions to qualitative variables via manual featurization.

42 ENGINEERING↗

How does uncertainty of soil organic carbon stock affect the calculation of carbon budgets and soil carbon credits for croplands in the U.S. Midwest?

Cropland carbon budget depicts the amount of carbon flowing in and out of agroecosystems and the changes in carbon stocks of soil and living biomass during the same period. Soil carbon credit is the additional change in soil carbon stock under certain farming practices compared with the business-as-usual practices. Accurately calculating cropland carbon budget and soil carbon credit is critical to assessing climate change mitigation potential in agroecosystems. The calculation of cropland carbon budget and soil carbon credit is sensitive to local soil and climatic conditions, especially initial soil organic carbon (SOC) stock, which is determined by both SOC concentration (SOC%) and bulk density (Bulk_Density). SOC stock data are either from soil sampling or gridded public survey data. In agroecosystem models, SOC stock data are a key model input for quantifying cropland carbon budget and soil carbon credit. However, various types and degrees of uncertainties exist in SOC stock datasets, which propagate to the quantification of SOC stock change. In particular, a large discrepancy is found in two widely used SOC stock datasets — Rapid Carbon Assessment dataset (RaCA) and Gridded Soil Survey Geographic Database (gSSURGO) — in the U.S. Midwest, with a relative difference (quantified using Normalized Root Mean Square Error, NRMSE) of 48.0% for 0–30 cm SOC stock between the two datasets. It remains largely unclear how uncertainty in SOC stocks affects the calculation of cropland carbon budget and soil carbon credit. To address this question, we used a well-validated process-based agroecosystem model, ecosys, to assess the impacts of SOC stock uncertainty on carbon budget and soil carbon credit calculation in the U.S. Midwestern corn-soybean rotation systems. Our results reveal the following findings: (1) A sizable discrepancy exists in simulated cropland carbon budget between using gSSURGO and using RaCA for their SOC% and Bulk_Density as model inputs, with a Pearson correlation coefficient (r) of only 0.4 for simulated change of SOC stock (ΔSOC) using these two different soil datasets. (2) Simulated cropland carbon budget components were more sensitive to initial SOC% than to Bulk_Density. For example, the upper and lower quartiles of multi-year averaged ΔSOC were –29.8 and 4.8 gC/m 2 /year for the selected counties respectively, with an uncertainty of 13.7 and 0.7 gC/m 2 /year induced by uncertainties in initial SOC% and Bulk_Density, respectively. (3) Both simulated ΔSOC and its uncertainty were negatively correlated with initial SOC%, whereas ΔSOC was negatively correlated with air temperature, and ΔSOC uncertainty was positively correlated with air temperature. (4) The uncertainty of calculated soil carbon credits was much smaller compared with the uncertainty of calculated absolute carbon budgets assuming the same SOC stock uncertainty level in the inputs. Specifically, in our assessment comparing planting cover crops vs no cover crop, the uncertainty of calculated soil carbon credits induced by initial SOC% uncertainty was less than 4% (relative to the quantified value of the soil carbon credits) for 90% of the cases. Our analysis highlights that high accuracy measurement of SOC% as inputs is needed for the calculation of cropland carbon budgets; however, soil carbon credit quantification is much less sensitive to the initial SOC% inputs, and the current publicly available soil datasets (e.g., gSSURGO) are largely suitable for the calculation of soil

54 ENVIRONMENTAL SCIENCES↗

Soil carbon change in intensive agriculture after 25 years of conservation management

Changes in soil organic carbon (SOC) and nitrogen (SON) are strongly affected by land management but few long-term comparative studies have surveyed changes throughout the whole soil profile. We quantified 25-year SOC and SON changes to 1 m in 10 replicate ecosystems at an Upper Midwest, USA site. We compared four annual cropping systems in maize (Zea mays)-soybean (Glycine max)-winter wheat (Triticum aestivum) rotations, each managed differently (Conventional, No-till, Reduced input, and Biologically based); in three managed perennial systems (hybrid Poplar (Populus × euramericana), Alfalfa (Medicago sativa), and Conifer (Pinus spp.); and in three successional systems (Early, Mid- and Late succession undergoing a gradual change in species composition and structure over time). Both Reduced input and Biologically based systems included winter cover crops. Neither SOC nor SON changed significantly in the Conventional or Late successional systems over 25 years. All other systems gained SOC and SON to different degrees. SOC accrual was fastest in the Early successional system (0.8 ± 0.1 Mg C ha –1 y –1 ) followed by Alfalfa and Conifer (avg. 0.7 ± 0.1 Mg C ha –1 y –1 ), Poplar, Reduced input, and Biologically based systems (avg. 0.4 ± 0.1 Mg C ha –1 y –1 ), and Mid-successional and No-till systems (0.3 and 0.2 Mg C ha –1 y –1 , respectively). Over the most recent 12 years, rates of SOC accrual slowed in all systems except Reduced input and Mid-successional. There was no evidence of SOC loss at depth in any system, including No-till. Rates of SON accrual ranged from 64.7 to 0.8 kg N ha –1 y –1 in the order Alfalfa ≥ Early successional > Reduced input and Biologically based ≥ Poplar > No-till and Conifer > Mid-successional systems. Pyrogenic C levels in the Conventional, Early, and Late successional systems were similar despite 17 years of annual burning in the Early successional system (~ 15 % of SOC to 50 cm, on average, and ~40 % of SOC from 50 to 100 cm). Results underscore the importance of cover crops, perennial crops, and no-till options for sequestering whole profile C in intensively managed croplands.

60 APPLIED LIFE SCIENCES↗

N-induced soil acidification triggers metal stimulation of soil methane oxidation in a temperate steppe ecosystem

Methane (CH 4 ) is a potent greenhouse gas, and it is well established that low nitrogen (N) stimulates- and high N suppresses CH 4 oxidation in grassland ecosystems. Here, in this study, we examined the response of CH 4 uptake to long-term (>10 years) multi-level N additions in a temperate steppe of northern China. The N impacts on CH 4 uptake transitioned from positive to negative at the N addition rate of 4 g N m -2 y -1 . However, the high-N suppression on CH 4 uptake was partially relieved when the continuous (>10 years) high N inputs (16 g N m -2 y -1 to 64 g N m -2 y -1 ) caused soil pH drop to < 5.7. Further experiments revealed that continuous high-N inputs acidified soil to pH < 5.7 that released metal ions to stimulate monooxygenase enzyme activity; therefore, the CH 4 oxidation suppression was partially relieved under continuous N loading. Structural equation model results confirmed that metal ions, such as Iron (Fe 3+ ), Manganese (Mn 4+ ), and Copper (Cu) desorbed by soil particles, were negatively correlated with soil pH while positively correlated with CH 4 oxidation under high N inputs. These analyses suggested that continuous high N inputs-induced soil acidification can release previously bounded metal elements that partially alleviated the N suppression on CH 4 uptake. The N-induced soil acidification impacts on CH 4 uptake might play a critical role in global CH 4 cycling and deserve further investigation as external N inputs continue climbing.

59 BASIC BIOLOGICAL SCIENCES↗

Turn-key constrained parameter space exploration for particle accelerators using Bayesian active learning

Abstract Particle accelerators are invaluable discovery engines in the chemical, biological and physical sciences. Characterization of the accelerated beam response to accelerator input parameters is often the first step when conducting accelerator-based experiments. Currently used techniques for characterization, such as grid-like parameter sampling scans, become impractical when extended to higher dimensional input spaces, when complicated measurement constraints are present, or prior information known about the beam response is scarce. Here in this work, we describe an adaptation of the popular Bayesian optimization algorithm, which enables a turn-key exploration of input parameter spaces. Our algorithm replaces the need for parameter scans while minimizing prior information needed about the measurement’s behavior and associated measurement constraints. We experimentally demonstrate that our algorithm autonomously conducts an adaptive, multi-parameter exploration of input parameter space, potentially orders of magnitude faster than conventional grid-like parameter scans, while making highly constrained, single-shot beam phase-space measurements and accounts for costs associated with changing input parameters. In addition to applications in accelerator-based scientific experiments, this algorithm addresses challenges shared by many scientific disciplines, and is thus applicable to autonomously conducting experiments over a broad range of research topics.

43 PARTICLE ACCELERATORS↗

Network-level encoding of local neurotransmitters in cortical astrocytes

Abstract Astrocytes, the most abundant non-neuronal cell type in the mammalian brain, are crucial circuit components that respond to and modulate neuronal activity through calcium (Ca 2+ ) signalling 1–7 . Astrocyte Ca 2+ activity is highly heterogeneous and occurs across multiple spatiotemporal scales—from fast, subcellular activity 3,4 to slow, synchronized activity across connected astrocyte networks 8–10 —to influence many processes 5,7,11 . However, the inputs that drive astrocyte network dynamics remain unclear. Here we used ex vivo and in vivo two-photon astrocyte imaging while mimicking neuronal neurotransmitter inputs at multiple spatiotemporal scales. We find that brief, subcellular inputs of GABA and glutamate lead to widespread, long-lasting astrocyte Ca 2+ responses beyond an individual stimulated cell. Further, we find that a key subset of Ca 2+ activity—propagative activity—differentiates astrocyte network responses to these two main neurotransmitters, and may influence responses to future inputs. Together, our results demonstrate that local, transient neurotransmitter inputs are encoded by broad cortical astrocyte networks over a minutes-long time course, contributing to accumulating evidence that substantial astrocyte–neuron communication occurs across slow, network-level spatiotemporal scales 12–14 . These findings will enable future studies to investigate the link between specific astrocyte Ca 2+ activity and specific functional outputs, which could build a consistent framework for astrocytic modulation of neuronal activity.

Science & Technology - Other Topics↗

An adaptive approach to machine learning for compact particle accelerators

Abstract Machine learning (ML) tools are able to learn relationships between the inputs and outputs of large complex systems directly from data. However, for time-varying systems, the predictive capabilities of ML tools degrade if the systems are no longer accurately represented by the data with which the ML models were trained. For complex systems, re-training is only possible if the changes are slow relative to the rate at which large numbers of new input-output training data can be non-invasively recorded. In this work, we present an approach to deep learning for time-varying systems that does not require re-training, but uses instead an adaptive feedback in the architecture of deep convolutional neural networks (CNN). The feedback is based only on available system output measurements and is applied in the encoded low-dimensional dense layers of the encoder-decoder CNNs. First, we develop an inverse model of a complex accelerator system to map output beam measurements to input beam distributions, while both the accelerator components and the unknown input beam distribution vary rapidly with time. We then demonstrate our method on experimental measurements of the input and output beam distributions of the HiRES ultra-fast electron diffraction (UED) beam line at Lawrence Berkeley National Laboratory, and showcase its ability for automatic tracking of the time varying photocathode quantum efficiency map. Our method can be successfully used to aid both physics and ML-based surrogate online models to provide non-invasive beam diagnostics.

97 MATHEMATICS AND COMPUTING↗

Dynamics of photosynthetic light harvesting systems interacting with N-photon Fock states

Here, we develop a method to simulate the excitonic dynamics of realistic photosynthetic light harvesting systems, including non-Markovian coupling to phonon degrees of freedom, under excitation by N-photon Fock state pulses. This method combines the input–output and the hierarchical equations of motion formalisms into a double hierarchy of density matrix equations. We show analytically that under weak field excitation relevant to natural photosynthesis conditions, an N-photon Fock state input and a corresponding coherent state input give rise to equal density matrices in the excited manifold. However, an N-photon Fock state input induces no off-diagonal coherence between the ground and excited subspaces, in contrast with the coherences created by a coherent state input. We derive expressions for the probability to absorb a single Fock state photon with or without the influence of phonons. For short pulses (or, equivalently, wide bandwidth pulses), we show that the absorption probability has a universal behavior that depends only upon a system-dependent effective energy spread parameter Δ and an exciton–light coupling constant Γ. This holds for a broad range of chromophore systems and for a variety of pulse shapes. We also analyze the absorption probability in the opposite long pulse (narrow bandwidth) regime. We then derive an expression for the long time emission rate in the presence of phonons and use it to study the difference between collective vs independent emission. Finally, we present a numerical simulation for the LHCII monomer (14-mer) system under single photon excitation that illustrates the use of the double hierarchy equations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Enhancing Monte Carlo Workflows for Nuclear Reactor Analysis with Metamodel-Driven Modeling

Monte Carlo codes are essential components of many reactor physics simulation workflows as high-fidelity continuous-energy neutron transport solvers. Among Monte Carlo radiation transport codes, MCNP is particularly notable due to its diverse simulation capabilities, large user base, and long validation history. Despite being a powerful simulation tool, MCNP provides limited capabilities to allow automated execution, model transformation, or support for user-defined logic and abstractions that limit its compatibility with modern workflows. Here, to better integrate MCNP into a modern scientific workflow, we have developed an intuitive yet full-featured MCNP Application Program Interface (API) in Python, named MCNPy, which provides a specialized set of classes for MCNP input development. Moreover, to guarantee that our reading, writing, and modeling capabilities remain self-consistent (and to render the huge scope of the MCNP API manageable), we have adopted a strategy of model-driven software development in which a generalized model of the MCNP input format has been created. From this generalized model, or “metamodel,” problem-specific implementations such as an engine for input validation or a codebase for programmatic operations may be automatically generated. Since MCNPy primarily acts as a Python front-end to the underlying Java API that directly interfaces with the metamodel, it is intrinsically linked to the metamodel and thus remains maintainable. With MCNPy, users can programmatically read, write, and modify any syntactically valid MCNP input file regardless of its origin. These capabilities allow users to automate complicated tasks like design optimization and model translation for nuclear systems. As examples, this work demonstrates the use of MCNPy to find the critical radius of a plutonium sphere and to translate a 9000+ line MCNP input file into a corresponding OpenMC model.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Leveraging observed soil heterotrophic respiration fluxes as a novel constraint on global-scale models

Microbially-explicit models may improve understanding and projections of carbon dynamics in response to future climate change, but their fidelity in simulating global-scale soil heterotrophic respiration (RH), a stringent test for soil biogeochemical models, has never been evaluated. We used statistical global RH products, as well as 7,821 daily site-scale RH measurements, to evaluate the spatio-temporal performance of one first-order decay model (CASA-CNP) and two microbially-explicit biogeochemical models (CORPSE and MIMICS) that were forced by two different climate datasets. CORPSE and MIMICS did not provide any measurable performance improvement; instead, the models were highly sensitive to the meteorological input data used to drive them. Spatial RH variability was generally well simulated except in the northern middle latitudes (~50°N) and arid regions; models captured the seasonal variability of RH well, but showed more divergence in tropic and arctic regions. Our results demonstrate that the next generation of biogeochemical models shows promise, but also needs to be improved for realistic spatio-temporal variability of RH. Finally, we emphasize the importance of net primary production, soil moisture, and soil temperature inputs, and that jointly evaluating soil models for their spatial (global scale) and temporal (site scale) performance provides crucial benchmarks for improving biogeochemical models.

Jian, Jinshi↗

Drought Reduces Formation, but Enhances Persistence, of Mineral‐Associated Organic Matter in a Grassland Soil

Drought effects are pervasive in terrestrial ecosystems, yet there is limited understanding of how drought impacts the transformation of plant carbon (C) inputs to mineral-associated organic matter (MAOM)—the largest and slowest-cycling pool of soil organic carbon (SOC). In a 12-week 13 C-CO 2 greenhouse labeling experiment, we tracked the formation of MAOM derived from the two dominant sources of plant C input to the mineral soil—living root inputs ( 13 C-rhizodeposits) and decaying root inputs ( 13 C-root detritus)—under normal moisture and droughted conditions in a semiarid grassland soil. At the end of the 12-week period, we also measured the persistence of 13 C-MAOM formed from rhizodeposits versus root detritus via a subsequent persistence assay. Drought reduced the formation of MAOM derived from living roots by decreasing rhizodeposits, reducing microbial growth rates, and altering the composition of organic matter, lipids, and metabolites. Drought initially delayed the formation of MAOM derived from root detritus by slowing the early stages of root litter decomposition (week 4–8), but did not decrease total MAOM formation by the end of the 12-week period. Notably, drought enhanced the persistence of MAOM derived from root detritus, but did not influence the persistence of MAOM derived from rhizodeposits. Our results provide some of the first direct evidence that drought can reduce the formation of MAOM in a grassland soil, but may enhance its persistence, based on the source of plant input from which MAOM is derived.

13C- labeling↗

Future roots for future soils

Abstract Mechanical impedance constrains root growth in most soils. Crop cultivation changed the impedance characteristics of native soils, through topsoil erosion, loss of organic matter, disruption of soil structure and loss of biopores. Increasing adoption of Conservation Agriculture in high‐input agroecosystems is returning cultivated soils to the soil impedance characteristics of native soils, but in the low‐input agroecosystems characteristic of developing nations, ongoing soil degradation is generating more challenging environments for root growth. We propose that root phenotypes have evolved to adapt to the altered impedance characteristics of cultivated soil during crop domestication. The diverging trajectories of soils under Conservation Agriculture and low‐input agroecosystems have implications for strategies to develop crops to meet global needs under climate change. We present several root ideotypes as breeding targets under the impedance regimes of both high‐input and low‐input agroecosystems, as well as a set of root phenotypes that should be useful in both scenarios. We argue that a ‘whole plant in whole soil’ perspective will be useful in guiding the development of future crops for future soils.

Lynch, Jonathan P.↗

Unexpected Scaling of Peak Acceleration for a Yielding Mass-Spring System Subjected to a Triangular Base Acceleration Pulse

The use of bounding scenarios is a common practice that greatly simplifies the design and qualification of structures. However, this approach implicitly assumes that the quantities of interest increase monotonically with the input to the structure, which is not necessarily true for nonlinear structures. This paper surveys the literature for observations of nonmonotonic behavior of nonlinear systems and finds such observations in both the earthquake engineering and applied mechanics literature. Numerical simulations of a single degree-of-freedom mass-spring system with an elastic–plastic spring subjected to a triangular base acceleration pulse are then presented, and it is shown that the relative acceleration of this system scales nonmonotonically with the input magnitude in some cases. The equation of motion for this system is solved symbolically and an approximate expression for the relative acceleration is developed, which qualitatively agrees with the nonmonotonic behavior seen in the numerical results. The nonmonotonicity is investigated and found to be a result of dynamics excited by the discontinuous derivative of the base acceleration pulse, the magnitude of which scales nonmonotonically with the input magnitude due to the fact that the first yield of the spring occurs earlier as the input magnitude is increased. The relevance of this finding within the context of defining bounding scenarios is discussed, and it is recommended that modeling be used to perform a survey of the full range of possible inputs prior to defining bounding scenarios.

42 ENGINEERING↗