Initial Parameter Estimates Research Articles

Analytical and numerical investigation of natural rubber bearings incorporating U-shaped dampers behaviour for seismic isolation

Although Natural Rubber Bearings (NRBs) constitute a reliable and cost-effective conventional bearing system, they are rarely used for seismic isolation because of their low damping. There are various seismic isolation systems based on NRB, but they mostly have multiple drawbacks (cost, capacity, environmental, etc.). The U-shaped damper (UD) is an efficient energy dissipating device used in seismic-resistant design. However, no guidelines or procedures are available to understand its behaviour nor for design purposes. This paper presents an analytical and numerical investigation of the cyclic behaviour of the NRB system combined with UDs that allow to increase the systems’ damping capacity and seismic performance. An analytical study of the UD is performed to predict its initial elastic parameters and numerical models are developed to study the nonlinear behaviour of the NRB-UDs, under large cyclic loadings. A set of UDs and NRBs subjected to cyclic loadings are then studied to investigate their behaviour and the effect of different geometric, loading and design parameters. Results show that the UD significantly dissipates vibration energy based on its large plastic deformations and achieves comparable and predictable performances corresponding to the in-plane and out-of-plane loading directions. Its cyclic behaviour depends on geometrical parameters and material yield stress. The developed analytical formulas provide a reliable estimation of initial elastic parameters of UD, which is essential for the selection and sizing of preliminary designs of the devices. The NRB-UDs systems show a high energy dissipation capacity with stable hysteresis behaviours in any direction. Further, the performance of these devices can be easily adjusted by varying the geometry, number and cross-section of UDs, making them an effective solution that meets a wide range of seismic isolation design requirements in high and moderate seismic areas.

A Novel Recursive Non-Parametric DBSCAN Algorithm for 3D Data Analysis with an Application in Rockfall Detection

The density-based spatial clustering of applications with noise (DBSCAN) algorithm is a well-known algorithm for spatial-clustering data point clouds. It can be applied to many applications, such as crack detection, rockfall detection, and glacier movement detection. Traditional DBSCAN requires two predefined parameters. Suitable values of these parameters depend upon the distribution of the input point cloud. Therefore, estimating these parameters is challenging. This paper proposed a new version of DBSCAN that can automatically customize the parameters. The proposed method consists of two processes: initial parameter estimation based on grid analysis and DBSCAN based on the divide-and-conquer (DC-DBSCAN) approach, which repeatedly performs DBSCAN on each cluster separately and recursively. To verify the proposed method, we applied it to a 3D point cloud dataset that was used to analyze rockfall events at the Puiggcercos cliff, Spain. The total number of data points used in this study was 15,567. The experimental results show that the proposed method is better than the traditional DBSCAN in terms of purity and NMI scores. The purity scores of the proposed method and the traditional DBSCAN method were 96.22% and 91.09%, respectively. The NMI scores of the proposed method and the traditional DBSCAN method are 0.78 and 0.49, respectively. Also, it can detect events that traditional DBSCAN cannot detect.

Aerobic fitness as a parameter of importance for labour loss in the heat

ObjectivesTo derive an empirical model for the impact of aerobic fitness (maximal oxygen consumption; V̇O2max in mL∙kg−1∙min−1) on physical work capacity (PWC) in the heat. DesignProspective, repeated measures. MethodsTotal work completed during 1 h of treadmill walking at a fixed heart rate of 130 b∙min−1 was assessed in 19 young adult males across a variety of warm and hot climate types, characterised by wet-bulb globe temperatures (WBGT) ranging from 12 to 40 °C. For data presentation and obtaining initial parameter estimates for modelling, participants were grouped into low (n = 6, 74 trials), moderate (n = 8, 76 trials), and high (n = 5, 29 trials) fitness, with group mean V̇O2max 42, 52, and 64 mL∙kg−1∙min−1, respectively. For the heated conditions (WBGT 18 to 40 °C), we calculated PWC% by expressing total energy expenditure (kJ above resting) in each trial relative to that achieved in a cool reference condition (WBGT = 12 °C = 100% PWC). ResultsThe relative reduction in energy expenditure (PWC%) caused by heat was significantly smaller by up to 16% for the fit participants compared to those with lower aerobic capacity. V̇O2max also modulated the relationship between sweat rate and body temperature changes to increasing WBGT. Including individual V̇O2max data in the PWC prediction model increased the predicting power by 4%. ConclusionsIncorporating individual V̇O2max improved the predictive power of the heat stress index WBGT for Physical Work Capacity in the heat. The largest impact of V̇O2max on PWC was observed at a WBGT between 25 and 35 °C.

Evaluating pedestrian interaction preferences with a game theoretic autonomous vehicle in virtual reality

Localisation and navigation of autonomous vehicles (AVs) in static environments are now solved problems, but how to control their interactions with other road users in mixed traffic environments, especially with pedestrians, remains an open question. Recent work has begun to apply game theory to model and control AV-pedestrian interactions as they compete for space on the road whilst trying to avoid collisions. But this game theory model has been developed only in unrealistic lab environments. To improve their realism, this study empirically examines pedestrian behaviour during road crossing in the presence of approaching autonomous vehicles in more realistic virtual reality (VR) environments. The autonomous vehicles are controlled using game theory, and this study seeks to find the best parameters for these controls to produce comfortable interactions for the pedestrians. In a first experiment, participants’ trajectories reveal a more cautious crossing behaviour in VR than in previous laboratory experiments. In two further experiments, a gradient descent approach is used to investigate participants’ preference for AV driving style. The results show that the majority of participants were not expecting the AV to stop in some scenarios, and there was no change in their crossing behaviour in two environments and with different car models suggestive of car and last-mile style vehicles. These results provide some initial estimates for game theoretic parameters needed by future AVs in their pedestrian interactions and more generally show how such parameters can be inferred from virtual reality experiments.

Multi-phase algorithm design for accurate and efficient model fitting

Recent research applies soft computing techniques to fit software reliability growth models. However, runtime performance and the distribution of the distance from an optimal solution over multiple runs must be explicitly considered to justify the practical utility of these approaches, promote comparison, and support reproducible research. This paper presents a meta-optimization framework to design stable and efficient multi-phase algorithms for fitting software reliability growth models. The approach combines initial parameter estimation techniques from statistical algorithms, the global search properties of soft computing, and the rapid convergence of numerical methods. Designs that exhibit the best balance between runtime performance and accuracy are identified. The approach is illustrated through nonhomogeneous Poisson process and covariate software reliability growth models, including a cross-validation step on data sets not used to identify designs. The results indicate the nonhomogeneous Poisson process model considered is too simple to benefit from soft computing because it incurs additional runtime with no increase in accuracy attained. However, a multi-phase design for the covariate software reliability growth model consisting of the bat algorithm followed by a numerical method achieves better performance and converges consistently, compared to a numerical method only. The proposed approach supports higher-dimensional covariate software reliability growth model fitting suitable for implementation in a tool.

Инженерная оценка минимальной циклической долговечности при заданном уровне вероятности ее реализации

Object and purpose of research. This paper discusses structural materials under cyclic load. The purpose is to determine the minimum fatigue life corresponding to a certain non-exceedance probability of this value. Materials and methods. The study was performed on three structural materials: steel 15ХМ, steel 08Kh18N10Т and titanium alloy PТ-7М. Initial estimate of fatigue life distribution parameters relied on the data about guaranteed maximum and minimum values of temporary resistance and relative cross-section tapering. The assessment was performed as per a common curve “conditionally elastic stress amplitude versus number of cycles to failure” taking into account the mechanical prop-erties of given material. The values of minimum fatigue life were obtained as per two different methods: statistical simulation of the random values following the Weibull distribution law and the analytical expression for probability density of the lows for given distribution function of random value and fixed scope of sampling. Main results. The lows yielded by statistical simulation are more conservative than those yielded by the analytical formula. The margin in terms of the number of cycles to failure stipulated as 10 in several regulatory documents seems to be somewhat unsubstantiated. This margin is too great in the low-cycle domain and too small in the high-cycle one. Conclusion. This paper postulates the existence of guaranteed maximum and minimum values for mechanical properties of structural materials, namely temporary resistance and relative cross-section tapering. These values were applied to well-known analytical curves of fatigue, which finally yielded possible variation ranges for fatigue life at various amplitudes of conditionally elastic reduced stresses, assuming the existence of a certain shift in the sensitivity limit of fatigue life distribution. These data were further used to establish standard deviations and mathematical expectations for the number of cycles to failure.

A dimensionless number for predicting universal processing parameter boundaries in metal powder bed additive manufacturing

One of the main challenges facing selective laser melting processes is finding suitable process parameters to achieve maximum density (pore-free) parts. In this letter, two newly discovered dimensionless numbers are presented that correlate process parameters to a part’s density allowing for an initial estimation of suitable process parameters without the need for extensive modeling or experimentation. The prediction is achieved by utilizing the Buckingham-Π theorem and the implementation of Pawlowski’s matrix transformation method. The universality of the new dimensionless numbers is verified by applying them to selective laser melting data for eight different metals and alloy systems, obtained both experimentally and gathered from the literature. The dimensionless numbers allow for identification of process parameters that will result in a maximum density regime in the as-built part. Finally, a universal scaling law is introduced that can aid in quantitative prediction of process parameters that result in the highest as-built density.

Evaluating computational performances of hyperelastic models on supraspinatus tendon uniaxial tensile test data

Accurate modelling of the mechanical behaviour of tendon tissues is vital due to their essential role in the facilitation of joint mobility in humans and animals. This study focuses on the modelling of the supraspinatus tendon which helps to maintain dynamic stability at the glenohumeral joint in humans. It is observed that in sporting activities or careers that involve frequent arm abduction, injuries to this tendon are a common cause of discomfort. Therefore, this paper evaluates the relative modelling capabilities of three hyperelastic models, namely the Yeoh, Ogden and Martins material models on the tensile behaviour of three tendon specimens. We compare their fitting accuracies, convergence rates during optimisation, and the different forms of sensitivities to data-related features and initial parameter estimates. We find that the Martins model outperforms the other models in fitting accuracies; the Yeoh model has the most stable performance across all initial parameter estimates (with correlations above 99 %) and has the fastest convergence rates (above 20 and 8 times as fast as the Ogden and Martins models’ rates, respectively); and that the Ogden model does not depend on differences in the topological features of the test data. The material parameters of relevant constitutive model may be used for further development of computational models.

An estimation method for the fuel burn and other performance characteristics of civil transport aircraft during cruise: part 2, determining the aircraft’s characteristic parameters

ABSTRACTA simple yet physically comprehensive and accurate method for the estimation of the cruise fuel burn rate of turbofan powered transport aircraft operating in a general atmosphere was developed in part 1. The method is built on previously published work showing that suitable normalisation reduces the governing relations to a set of near-universal curves. However, to apply the method to a specific aircraft, values must be assigned to six independent parameters and the more accurate these values are the more accurate the estimates will be. Unfortunately, some of these parameters rarely appear in the public domain. Consequently, a scheme for their estimation is developed herein using basic aerodynamic theory and data correlations. In addition, the basic method is extended to provide estimates for cruise lift-to-drag ratio, engine thrust and engine overall efficiency. This step requires the introduction of two more independent parameters, increasing the total number from six to eight. An error estimate and sensitivity analysis indicates that, in the aircraft’s normal operating range and using the present results, estimates of fuel burn rate are expected to be in error by no more than 5% in the majority of cases. Initial estimates of the characteristic parameters have been generated for 53 aircraft types and engine combinations and a table is provided.

A Bayesian Approach to Autonomous Analysis of Electrochemical Impedance Spectra

Electrochemical impedance spectroscopy (EIS) is a valuable characterization tool for a wide variety of materials due to its ability to probe transport and reaction pathways over a broad range of timescales. Recently, developments in experimental techniques have increased the use of EIS in high-throughput materials characterization. However, extraction of meaningful insight from high-volume EIS data streams is often stymied by the complexity of processing and analyzing impedance spectra. To address this challenge, we present a framework for fully autonomous analysis of EIS data leveraging Bayesian methods to obtain both the distribution of relaxation times (DRT) and equivalent circuit fits.The predominant quantitative method for EIS analysis is equivalent circuit modeling, which requires careful selection of equivalent circuit elements to represent physical processes in the system under study. However, the last decade has seen increasing interest in the DRT, which enables detailed EIS analysis without a priori construction of equivalent circuits. Deconvoluting the DRT is an ill-posed problem which may be tamed by imposing constraints upon the solution (regularization), but the solution is highly sensitive to the nature and severity of such constraints, which are challenging to calibrate. We demonstrate the application of Bayesian inference to determine the optimal regularization level and accurately deconvolute the DRT. The Bayesian approach identifies both smooth features (e.g. dispersed ZARCs) and sharp features (e.g. RC and Gerischer elements) in the DRT, is highly robust to noise, and is self-calibrating. We also explore the connection between the DRT and equivalent circuit modeling, illustrating how well-calibrated estimates of the DRT can both enable empirical selection of equivalent circuit models and provide initial parameter estimates for complex non-linear least squares fitting of these models. We apply these methods to both synthetic spectra and experimental data from high-throughput characterization of fuel cells and batteries to demonstrate their validity and utility. The software is published in an open-source Python package to enable broad usage and further development.Acknowledgments:This work was supported by the Advanced Research Projects Agency-Energy (ARPA-E) through the REFUEL program (Award No. DE-AR0000808) and the Army Research Office under Grant No. W911NF-17-1-0051.

Calibration method for the electrically tunable lens based on shape-changing polymer.

In this paper, a calibration method for the camera system with electrically tunable lens (ETL) based on shape-changing polymer (SCP) is proposed to improve the accuracy, robustness and practicality of the system. The camera model of the ETL based on SCP is proposed based on the analyses of its optical properties. The calibration strategy, including initial estimation of camera parameters and bundle adjustment is presented. To eliminate the influence of temperature on ETL in machine vision applications, a real-time temperature compensation method is proposed. The proposed method makes use of the existing calibration hardware without adding new components to the system. Both simulations and experiments are conducted to evaluate the effectiveness and accuracy of the proposed camera model and calibration method. The measurement error with the proposed calibration method is below 20 microns at high magnification, whose measurement accuracy is improved by five times than the existing method at high magnification. With the proposed calibration method for the camera system with ETL based on SCP, the calibration workload is reduced and accurate calibration at high magnification is achieved. It also benefits the development of autofocusing 3D measurement technology.

Using an ensemble Kalman filter method to calibrate parameters of a prediction model for chemical transport from soil to surface runoff.

Water pollution from surface runoff is an important non-point pollution source, which has been a great threat to our environment. The model proposed by Gao et al. (2004) is of great significance to solve the non-point source pollution problem, which is a numerical advection-diffusion equation (ADE) model for chemical transport from soil to surface runoff. The ensemble Kalman filter (EnKF), the data assimilation (DA) method, is easy to be implemented and widely used in hydrology field. In this study, we use the EnKF method to update model state variables such as chemical concentrations in surface runoff and calibrate model parameters such as water transfer rate in Gao et al. (2004) under different study cases, while other model parameters are assumed to be known. The observations are generated from the simulation results based on synthetic real parameters. The objective of this study was to extend the application of the EnKF to the ADE-based prediction model of chemical transport from soil to surface runoff. The results of the predicted chemical concentration in the surface runoff with EnKF are greatly improved than those without EnKF in comparison with the observations, and the updated parameters are close to the real parameters. We explored feasibility of the EnKF method from six factors, including the initial parameter estimate, the ensemble size, the influence of multi-parameters, the assimilation time interval, the infiltration boundary conditions, and the relationship between the standard deviations of the observation error and initial parameter. Different study strategies are proposed for different factors. For assimilation time interval, the key observation can reduce the assimilation frequency. With the situation of much larger observation error covariance than the prediction covariance, we analyzed influences of the standard deviation of the observation error and initial parameter on the feasibility of the EnKF method. According to the study results, it is concluded that the EnKF is efficient to update the parameter for the ADE-based prediction model of chemical transport from soil to surface runoff.

Test Verification of Two-Stage Adaptive Delay Compensation Method for Real-Time Hybrid Simulation

Real-time hybrid simulation (RTHS) is a versatile testing technique for performance evaluation of structures subjected to dynamic excitations. Research revealed that compensation for the delay induced by the dynamics of the loading system and other factors is a critical issue for obtaining reliable test results. Lately, a two-stage adaptive delay compensation (TADC) method was conceived and performed on the benchmark problem of RTHS. For this method, the main part of the system delay is coarsely compensated by the classic polynomial extrapolation (PE) method; the second stage represents a fine remedy for the remaining delay with adaptive compensation based on a discrete model of the loading system. As an extension of this study, this paper aims to further verify and reveal the performance of this method through real tests on a viscous damper specimen. In particular, loading tests with a swept signal and RTHS with sinusoidal and seismic excitations were carried out. Investigations show that the TADC method is endowed with smaller parameter variation ranges, simple yet effective initialization or a soft-start process, less dependence on initial parameter estimation accuracy, and best compensation performance.

A novel method for estimating the fractional Cole impedance model using single-frequency DC-biased sinusoidal excitation.

The Cole model is a widely used fractional circuit model in electrical bioimpedance applications for evaluating the content and status of biological tissues and fluids. Existing methods for estimating the Cole impedance parameters are often based on multi-frequency data obtained from stepped-sine measurements fitted using a complex non-linear least square (CNLS) algorithm. Newly emerged numerical methods from the magnitude of electrical bio-impedance data-only do not need CNLS fitting, but they still require multi-frequency stepped-sine data. This study proposes a novel approach to estimating the Cole impedance parameters that combines a numerical and time-domain fitting method based on a single-frequency DC-biased sinusoidal current excitation. First, the transient and steady-state voltage response along with the current excitation are acquired in electrical bio-impedance measurement. From the sampled data, a numerical method is applied to provide the initial estimation of the Cole impedance parameters, which are then used in a time-domain iterative fitting algorithm. The accuracy of the algorithm proposed is tested with noisy electrical bio-impedance simulations. The maximum relative error of the estimated Cole impedance parameters is 1% considering 2% (34 dB) additive Gaussian noise. Experimental measurements performed on a 2R-1C circuit and some fruit samples show a mean difference less than 1% and 5% respectively compared to the Cole impedance parameters estimated from a commercial electrical bio-impedance analyzer performing stepped-sine measurements and CNLS fitting. This is the first method that allows estimating the Cole impedance parameters from single-frequency electrical bio-impedance data. The approach presented could find broad use in many applications, including single-frequency body impedance analysis.

Initial Tracking Parameter Estimation of Magnetic Ship Based on PSO

We consider the problem of tracking a surface magnetic ship as it travels in a straight line path with the exertion of a magnetometer located at the seabed. Note that the initial filter parameters are prior information and the tracking performance depends on the initial filter parameters, and traditional estimation of initial filter parameters is to apply the filter bank algorithm, but there are several obvious defects in this method. In this paper, a novel algorithm based on the particle swarm optimization (PSO) algorithm is proposed to estimate initial parameters of the filter, and the model of uniformly magnetized ellipsoid is adopted to fit the magnetic field of the ship. The simulation results show that, under the condition of no prior information, the estimated ship parameters based on the observation of the single-observer are invalid, whereas the estimated ship parameters based on the observation of the double-observer are valid. Further, the estimated results of real-world recorded magnetic signals show that the ship parameters estimated by PSO based on the double-observer are also valid, as the estimated parameters are used as the initial parameters of the unscented Kalman filter (UKF), and a ship can be tracked effectively by the UKF filter. Moreover, the estimated half focal length can be used as a feature to distinguish noise environment, ships with different sizes, and mine sweepers.

Improved genetic algorithm for intrinsic parameters estimation of on-orbit space cameras

Computer vision plays a key role to measure the relative posture and position between the spacecrafts, especially in various important space tasks. As one of the essential steps for computer vision, camera calibration is important for obtaining precise three-dimensional contours of the space target. However, it is impossible to use the traditional calibration targets to calibrate the space camera in orbit. To solve this problem, in this paper, we attack the on-orbit space camera calibration problem by using two steps. First, we only use two images of the solar panel, which is a commonly used element of majority human-made spacecraft, to generate an approximate initial estimation of the camera intrinsic parameters. In order to improve the robustness and accuracy of our method, the second step optimizes the initial solution by using an improved genetic algorithm (IGA). Simulated and real experiments prove that the proposed method is accurate and flexible, and shows good robust performance. Therefore, our method has realistic significance for various space tasks.

Initialization effects in two-component second-order multivariate calibration with the extended bilinear model

Bilinear decomposition of an augmented data matrix is usually complicated by the phenomenon of rotational ambiguity. If the latter is significant, quantitative and qualitative information of the recovered profiles may be less useful. Although constraints can reduce the extent of feasible regions and the degree of rotational ambiguity, the estimation of initial parameters to start the decomposition is an important phase in multivariate curve resolution-alternating least-squares (MCR-ALS) studies. Dealing with a bilinear decomposition of an augmented data matrix where rotational ambiguity persists, the question remains whether it is possible to still develop a successful calibration protocol. Indeed, literature reports indicate that various analytical systems have been experimentally developed, in which substantial rotational ambiguity exists, yet the experimental results confirmed that accurate analyte quantitation was possible. In this research, we further investigate on the effect of the initialization step for a two-component second-order multivariate calibration with the extended bilinear model. It is shown that the selection strategy based on the so-called purest variables can be helpful in achieving a correct profile resolution, depending on which data direction it is applied. Finally, some data-driven guidelines for analytical chemists are suggested, to identify the potential degree of rotational ambiguity and the correct choice of the initialization strategy.

Calibration routine for a telecentric stereo vision system considering affine mirror ambiguity

A robust calibration approach for a telecentric stereo camera system for three-dimensional (3-D) surface measurements is presented, considering the effect of affine mirror ambiguity. By optimizing the parameters of a rigid body transformation between two marker planes and transforming the two-dimensional (2-D) data into one coordinate frame, a 3-D calibration object is obtained, avoiding high manufacturing costs. Based on the recent contributions in the literature, the calibration routine consists of an initial parameter estimation by affine reconstruction to provide good start values for a subsequent nonlinear stereo refinement based on a Levenberg–Marquardt optimization. To this end, the coordinates of the calibration target are reconstructed in 3-D using the Tomasi–Kanade factorization algorithm for affine cameras with Euclidean upgrade. The reconstructed result is not properly scaled and not unique due to affine ambiguity. In order to correct the erroneous scaling, the similarity transformation between one of the 2-D calibration plane points and the corresponding 3-D points is estimated. The resulting scaling factor is used to rescale the 3-D point data, which then allows in combination with the 2-D calibration plane data for a determination of the start values for the subsequent nonlinear stereo refinement. As the rigid body transformation between the 2-D calibration planes is also obtained, a possible affine mirror ambiguity in the affine reconstruction result can be robustly corrected. The calibration routine is validated by an experimental calibration and various plausibility tests. Due to the usage of a calibration object with metric information, the determined camera projection matrices allow for a triangulation of correctly scaled metric 3-D points without the need for an individual camera magnification determination.

An approach to computer analysis of the ligand binding assay data on example of radioligand assay data.

As a rule, receptor-ligand assay data are fitted by logistic functions (4PL model, 5PL model, Feldman's model). The preparation of the initial estimates for parameters of these functions is an important problem for processing receptor-ligand interaction data. This study represents a new mathematical approach to calculate the initial estimates more closely to the true values of parameters. The main idea of this approach is in using the modified linear least squares method for calculations of the parameters for the 4PL model and the Feldman's model. In this study, the convergence of model parameters to true values is verified for the simulated data with different statistical scatter. Also, the results of processing real data for the 4PL model and the Feldman's model are presented. A comparison is made of the parameter values calculated by the presented and a nonlinear method. The developed approach has demonstrated its efficiency in calculating the parameters of the complex Feldman"s models up to 4 ligands and 4 sites.

A procedure for ranking parameter importance for estimation in predictive mechanistic models

We begin with a mechanistic model that is considered to be a reasonably good predictor of the real-life system with a set of parameters determined from prior biophysical studies and expert knowledge. For complex mechanistic growth models, it is usually advantageous to numerically estimate a subset of the ‘most important’ parameters (i.e., those that most influence dynamic model behavior) based on data and fix the others at their estimated a priori values. Determining a reduced-order parameter subset for end-user estimation can be challenging, often relying heavily on expert knowledge and trial-and-error. A straightforward but oversimplified method relies on one-at-a-time (OAT) sensitivity of model outputs to changes in individual parameters. However, this commonly used method fails to account for how simultaneous changes in multiple parameters can significantly impact model outputs in unpredictable ways due to model nonlinearities. Additionally, hidden relationships between parameters can prevent consistent identifiability of parameters from different initial estimates. Rather than analyzing the effect of individual parameter variation on the model outputs, we evaluate the importance of parameters to the curvature of the quadratic cost function (sum squared difference between reference and model output sequences). This analysis is carried out by calculating the matrix of second-order partial derivatives of the cost function (aka Hessian matrix) with respect to the model parameters. Calculating the cost function Hessian allows analysis of changes in multiple parameters simultaneously. The method is presented as an analytic, reproducible procedure for determining a ranking for parameter importance. The procedure is demonstrated on a limited version of the Yield-SAFE predictive agroforestry growth model. For the analysis, 12 model parameters are considered with their nominal values set to those given in a published implementation of Yield-SAFE. The Hessian was calculated at 212 ( = 4096) locations systematically selected in the neighborhood of the nominal parameter setting, each generating a parameter ranking determined by the relative contribution of each parameter to the cost function curvature. The top ranked 6 parameters were the same for 4091 of 4096 locations, suggesting that this procedure has potential to guide modelers in recommending the most important parameters for estimation given reasonably good initial parameter estimates and real data.