An adaptive Dendrite-HDMR metamodeling technique for high dimensional problems

High dimensional model representation (HDMR), decomposing the high-dimensional problem into summands of different order component terms, has been widely researched to work out the dilemma of “curse-of-dimensionality” when using surrogate techniques to approximate high-dimensional problems in engineering design. However, the available one-metamodel-based HDMRs usually encounter the predicament of prediction uncertainty, while current multi-metamodels-based HDMRs cannot provide simple explicit expressions for black-box problems, and have high computational complexity in terms of constructing the model by the explored points and predicting the responses of unobserved locations. Therefore, aimed at such problems, a new stand-alone HDMR metamodeling technique, termed as Dendrite-HDMR, is proposed in this study based on the hierarchical Cut-HDMR and the white-box machine learning algorithm, Dendrite Net. The proposed Dendrite-HDMR not only provides succinct and explicit expressions in the form of Taylor expansion, but also has relatively higher accuracy and stronger stability for most mathematical functions than other classical HDMRs with the assistance of the proposed adaptive sampling strategy, named KKMC, in which k-means clustering algorithm, k-Nearest Neighbor classification algorithm and the maximum curvature information of the provided expression are utilized to sample new points to refine the model. Finally, the Dendrite-HDMR technique is applied to solve the design optimization problem of the solid launch vehicle propulsion system with the purpose of improving the impulse-weight ratio, which represents the design level of the propulsion system.

Performance Characterization of Low-cost Air Quality Sensors for Off-grid Deployment in Rural Malawi

Low-cost gas and particulate sensor packages offer a compact, lightweight, and easily transportable solution to address global gaps in air quality (AQ) observations. However, regions that would benefit most from widespread deployment of low-cost AQ monitors often lack the reference grade equipment required to reliably calibrate and validate them. In this study, we explore approaches to calibrating and validating three integrated sensor packages before a 1-year deployment to rural Malawi using collocation data collected at a regulatory site in North Carolina, USA. We compare the performance of five computational modelling approaches to calibrate the electrochemical gas sensors: k-Nearest Neighbor (kNN) hybrid, random forest (RF) hybrid, high-dimensional model representation (HDMR), multilinear regression (MLR), and quadratic regression (QR). For the CO, Ox, NO, and NO2 sensors, we found that kNN hybrid models returned the highest coefficients of determination and lowest error metrics when validated; they also appeared to be the most transferable approach when applied to field data collected in Malawi. We compared calibrated CO observations to remote sensing data in two regions in Malawi and found qualitative agreement in spatial and annual trends. However, the monthly mean surface observations were 2 to 4 times higher than the remote sensing data, possibly due to proximity to small-scale combustion activity not resolved by satellite imaging. We also compared the performance of the integrated Alphasense OPC-N2 optical particle counter to a filter-corrected nephelometer using collocation data collected at one of our deployment sites in Malawi. We found the performance of the OPC-N2 varied widely with environmental conditions, with the worst performance associated with high relative humidity (RH > 70 %) conditions and influence from emissions from nearby biomass cookstoves. We did not find obvious evidence of systematic sensor performance decay after the 1-year deployment to Malawi; however, overall data recovery was limited by insufficient power and access to technical resources at deployment sites. Future low-cost sensor deployments to rural Sub-Saharan Africa would benefit from adaptable power systems, standardized sensor calibration methodologies, and increased regulatory grade regional infrastructure.

Optimization of twisted blade of pump as turbine based on high dimensional surrogate model

In order to improve the operation efficiency of the twisted blade pump as turbine (PAT), a medium specific speed PAT was selected as the research object. The variables of the twisted blade plane blade profile were defined, the twisted blade was transformed into three plane blade profiles, and the blade profiles were parameterized by MATLAB 9.7 software. MATLAB 9.7, CFturbo 2020 and Fluent 19.2 were used to build the support vector machine-high dimensional model representation (SVM-HDMR) surrogate model function for efficiency optimization of PAT. Genetic algorithm was run on MATLAB 9.7 to optimize the surrogate model function, and the optimized blade profiles were fed back. The optimization results were verified by numerical simulation and experiment. The results show that the simulation efficiency of the PAT after optimization at the design operating point is 3.51% higher than the efficiency of the PAT before optimization, and the output power is increased by 5.3%. The test efficiency of the PAT after optimization at the design operating point is 3.4% higher than the efficiency of the PAT before optimization, and the output power is increased by 5.1%.

Metamodel Approaches in Predicting the Seismic Response of Asymmetric Buildings

Asymmetry formed as a result of the eccentricity between the positions of Centre of Mass and Centre of Stiffness can cause undesired torsional coupling and can weaken the seismic performance of buildings and structures. This dynamic response is further affected by the randomness in material, geometric and loading properties caused as a result of uncertainties in construction and functioning. Stochastic analyses methods such as Monte Carlo Simulation have been found to accurately characterize this randomness and uncertainty, but are computationally intensive as well as expensive. This necessitates the need for alternative analyses methods that are much simpler and can fairly represent the uncertainties while preserving the similarity in results. The present investigation considers the various metamodel approaches in non-statistical stochastic analyses methods in determining the seismic response of asymmetric buildings. The study observes the efficiency of the High Dimensional Model Representation (HDMR) approach in accurately predicting the free vibration response of a reinforced concrete frame with the least number of samplings points as well as computational effort as compared to other response surface methods. For further validation, a non-linear reliability analysis was carried out at HDMR sampling points to obtain the seismic fragility of the building considered, the results of which satisfied the fragility obtained using conventional methods.

An efficient inverse method for structural identification considering modeling and response uncertainties

The inverse problem analysis method provides an effective way for the structural parameter identification. Due to the coupling of multi-source uncertainties in the measured responses and the modeling parameters, the inverse of unknown structural parameter will face the challenges in the solving mechanism and the computational cost. In this paper, an uncertain inverse method based on convex model and dimension reduction decomposition is proposed to realize the interval identification of unknown structural parameter according to the uncertain measured responses and modeling parameters. Firstly, the polygonal convex set model is established to quantify the uncertainties of modeling parameters. Afterwards, a space collocation method based on dimension reduction decomposition is proposed to transform the inverse problem considering multi-source uncertainties into a few interval inverse problems considering response uncertainty. The transformed interval inverse problem involves the two-layer solving process including interval propagation and optimization updating. In order to solve the interval inverse problems considering response uncertainty, an efficient interval inverse method based on the high dimensional model representation and affine algorithm is further developed. Through the coupling of the above two methods, the proposed uncertain inverse method avoids the time-consuming multi-layer nested calculation procedure, and then effectively realize the inverse uncertainty quantification of unknown structural parameters. Finally, two engineering examples are provided to verify the effectiveness of the proposed uncertain inverse method.

Implementation and Performance Evaluation of a Bivariate Cut-HDMR Metamodel for Semiconductor Packaging Design Problems with a Large Number of Input Variables

A metamodeling technique based on Bivariate Cut High Dimensional Model Representation (Bivariate Cut HDMR) is implemented for a semiconductor packaging design problem with 10 design variables. Bivariate Cut-HDMR constructs a metamodel by considering only up to second-order interactions. The implementation uses three uniformly distributed sample points (s = 3) with quadratic spline interpolation to construct the component functions of Bivariate Cut-HDMR, which can be used to make a direct comparison with a metamodel based on Central Composite Design (CCD). The performance of Bivariate Cut-HDMR is evaluated by two well-known error metrics: R-squared and Relative Average Absolute Error (RAAE). The results are compared with the performance of CCD. Bivariate Cut HDMR does not compromise the accuracy compared to CCD, although the former uses only one-fifth of sample points (201 sample points) required by the latter (1045 sample points). The sampling schemes and the predictions of cut-planes and boundary-planes are discussed to explain possible reasons for the outstanding performance of Bivariate Cut HDMR.

AN ITERATIVE HDMR APPROACH FOR ENGINEERING RELIABILITY ANALYSIS

Engineering reliability analysis has long been an active research area. Surrogate models, or metamodels, are approximate models that can be created to replace implicit performance functions in the probabilistic analysis of engineering systems. Traditional 1st-order or second-order high dimensional model representation (HDMR) methods are shown to construct accurate surrogate models of response functions in an engineering reliability analysis. Although very efficient and easy to implement, 1st-order HDMR models may not be accurate, since the cross-effects of variables are neglected. Second-order HDMR models are more accurate; however they are more complicated to implement. Moreover, they require much more sample points, i.e., finite element (FE) simulations, if FE analyses are employed to compute values of a performance function. In this work, a new probabilistic analysis approach combining iterative HDMR and a first-order reliability method (FORM) is investigated. Once a performance function is replaced by a 1st-order HDMR model, an alternate FORM is applied. In order to include higher-order contributions, additional sample points are generated and HDMR models are updated, before FORM is reapplied. The analysis iteration continues until the reliability index converges. The novelty of the proposed iterative strategy is that it greatly improves the efficiency of the numerical algorithm. As numerical examples, two engineering problems are studied and reliability analyses are performed. Reliability indices are obtained within a few iterations, and they are found to have a good accuracy. The proposed method using iterative HDMR and FORM provides a useful tool for practical engineering applications.

AN RBF BASED HIGH-DIMENSIONAL MODEL REDUCTION APPROACH IN BUILDING OPTIMIZATION

Building optimization has gained importance with the recent push to create the most economical and efficient buildings possible. As the effects of optimization are a function of the building size, it is crucial to understand and further develop optimization techniques for large-scale building structures. Practical structural optimization of buildings requires the use of a structural analysis software package and an iterative optimization procedure. As a result, finite element (FE) software shall be linked with an optimization solver. It is an expensive process which requires extensive computer coding. Alternative methods are available, including metamodeling methods, which are used to create simple and approximate functions based on complex FE simulations. In this study, the approximate functions are generated using a high-dimensional model representation (HDMR) framework. The HDMR framework is a model reduction approach and is found to be very accurate for different functions. The component functions of HDMR are expressed using augmented radial basis functions (RBFs). To further improve the numerical efficiency of the metamodels and reduce the total required number of structural analyses, a few different HDMR sampling approaches are investigated, including one static approach and two iterative strategies. An existing nonlinear programming (NLP) solver is employed in the design process. To illustrate the proposed approach, a three-dimensional building structure is selected as a numerical example. The numerical optimization is conducted to reduce the torsional response of the building. The proposed optimization method works very well and the results from different HDMR techniques are compared.