Nonlinear Data Research Articles

Assessment of hybrid machine learning models for non-linear system identification of fatigue test rigs

The prediction of system responses for a given fatigue test bench drive signal is a challenging problem, since highly dynamic loads from measurement campaigns must be reproduced accurately. Linear frequency response function models are commonly used for this system identification task, but energy intensive experimental iterations are required to account for system non-linearities. Two novel hybrid modeling strategies are suggested, which augment existing approaches using non-linear Long Short-Term Memory networks. These are trained and deployed on short subsequences of measurement data and recombined using a windowing technique, which enables their application to measurement data with high sampling rates. In addition to fatigue test bench commissioning, these hybrid models can also be employed in the field of virtual sensing. The approach is tested using non-linear experimental data from a servo-hydraulic test rig and this dataset is made publicly available. A variety of metrics in time and frequency domains, as well as fatigue strength under variable amplitudes, are employed in the evaluation. It is shown, that hybrid models can successfully use frequency response function models as a linear baseline estimate, which is further improved by Long Short-Term Memory networks to enable non-linear predictions.

Integrating Temporal and Feedforward Models for Solar Energy Prediction: LSTM and ANN Hybrid Approaches

The increasing reliance on renewable energy, particularly solar power, necessitates accurate models for predicting energy output to optimize storage and distribution systems. Traditional methods such as Long Short-Term Memory (LSTM) networks and Artificial Neural Networks (ANNs) offer unique strengths in forecasting photovoltaic (PV) system outputs. LSTM excels in capturing temporal dependencies in time-series data, while ANNs effectively model nonlinear relationships between variables. This study aims to develop and evaluate a hybrid LSTM-ANN model for improving the accuracy of PV energy output predictions, focusing on voltage, power, and irradiance. Using data collected from a solar-powered greenhouse in Talang Kemang, Indonesia, the model was trained and validated. The hybrid model demonstrated significant improvements in prediction accuracy. For voltage, the model achieved a Mean Absolute Error (MAE) of 0.1016 and a Root Mean Squared Error (RMSE) of 0.1417, while irradiance predictions resulted in an MAE of 0.0895 and RMSE of 0.1149. Power predictions also yielded strong results, with an MAE of 0.1506 and RMSE of 0.1954. These results highlight the hybrid LSTM-ANN model's effectiveness in combining temporal and nonlinear data processing capabilities, leading to superior accuracy in predicting PV system outputs. This approach can enhance the reliability of energy forecasting models, enabling better integration of solar power into electrical grids. The model holds promise for broader applications in renewable energy systems, improving their efficiency and sustainability

Hybrid intelligent framework for designing band gap-rich 2D metamaterials

An artificial intelligence machine learning-based design framework is proposed to design lattice-based metamaterials with hexagonal symmetry that deliver wide band gaps at user-desired frequency ranges between 0 and 1000 kHz. The design approach starts by selecting a traditional, easy-to-manufacture parent lattice-based material that does not necessarily exhibit wide or functional band gaps. Subsequently, the parent lattice is transformed into a band-gap-rich lattice by superposing periodic triangular-shaped perturbations (i.e., zigzag-sine-based curvatures) with controllable frequencies and magnitudes on its ligaments. Finally, the frequency and magnitude parameters needed to deliver a specific band gap between 0 and 1000 kHz are determined using a hybrid intelligent framework, developed based on an Adaptive Neuro-Fuzzy Inference Systems (ANFIS). The ANFIS network integrates fuzzy logic expert models and artificial neural networks’ machine learning capabilities. Such a hybrid network is known for its ability to model strongly nonlinear and complex data. The data used in training the ANFIS models is generated using parametric finite element-based simulations where band gaps corresponding to a wide range of perturbation frequencies and magnitudes are computationally determined. The parametric study showed a nonlinear and complex topology-band gap characteristic relation; however, the Adaptive Neuro-Fuzzy Inference System (ANFIS) proved capable of modeling the observed complex topology-band gap behavior efficiently. The accuracy of the ANFIS models exceeded 99 % in several design ranges (i.e., perturbation parameters ranges). These were designated as high-accuracy design regions and were highlighted in the proposed design approach. Using multiple case studies with different band gap requirements, the ANFIS-based design framework proved effective in delivering customized lattice-based metamaterials with user-defined band gap frequencies.

Good results from sensor data: Performance of machine learning algorithms for regression problems in chemical sensors

Accurately predicting unseen data, instead of mere memorization of training examples, is a critical goal of machine learning. This generalization is particularly important in the field of chemical sensors, where the ability to accurately predict the chemical properties or concentration levels of unknown samples is crucial. The paper presents a comprehensive yet accessible introduction to various machine learning concepts, highlighting the importance of model interpretability and generalization in ensuring reliable and accurate results in this context. Nonlinear sensor array data are utilized to introduce key concepts (e.g., bias-variance tradeoff) and techniques (linear models, partial least squares regression, support vector machines, k-nearest neighbors, decision trees, ensemble methods, automated machine learning, symbolic regression, and artificial neural networks), providing a solid foundation to make informed decisions when selecting machine learning techniques for sensor-specific regression applications. The results clearly indicate a number of conclusions. First, overparameterized deep feedforward neural networks show great accuracy and generalization when trained on a sufficiently large dataset. Second, symbolic regression models proved to be more accurate than deep feedforward neural networks and classical machine learning techniques on smaller datasets. Third, the performance of various machine learning models was dataset-dependent, showing the importance of comparative studies to determine the most suitable approach. It is clear that the optimal model cannot be known a priori. This paper aims to provide a starting point for investigations on the performance of different machine learning techniques in chemical sensor applications.

Random forests regression for soft interval data

Analyzing soft interval data for uncertainty quantification has attracted much attention recently. Within this context, regression methods for interval data have been extensively studied. As most existing works focus on linear models, it is important to note that many problems in practice are nonlinear in nature and the development of nonlinear regression tools for interval data is crucial. This paper proposes an interval-valued random forests model that defines the splitting criterion of variance reduction based on an L 2 type metric in the space of compact intervals. The model simultaneously considers the centers and ranges of the interval data as well as their possible interactions. Unlike most linear models that require additional constraints to ensure mathematical coherences, the proposed random forests model estimates the regression function in a nonparametric way, and so the predicted interval length is naturally nonnegative without any constraints. Simulation studies show that the new method outperforms typical existing regression methods for various linear, semi-linear, and nonlinear data archetypes and under different error measures. To demonstrate the applicability, a real data example is presented where the price range data of the Dow Jones Industrial Average index and its component stocks are analyzed.

Polyconvex neural network models of thermoelasticity

Machine-learning function representations such as neural networks have proven to be excellent constructs for constitutive modeling due to their flexibility to represent highly nonlinear data and their ability to incorporate constitutive constraints, which also allows them to generalize well to unseen data. In this work, we extend a polyconvex hyperelastic neural network framework to (isotropic) thermo-hyperelasticity by specifying the thermodynamic and material theoretic requirements for an expansion of the Helmholtz free energy expressed in terms of deformation invariants and temperature. Different formulations which a priori ensure polyconvexity with respect to deformation and concavity with respect to temperature are proposed and discussed. The physics-augmented neural networks are furthermore calibrated with a recently proposed sparsification algorithm that not only aims to fit the training data but also penalizes the number of active parameters, which prevents overfitting in the low data regime and promotes generalization. The performance of the proposed framework is demonstrated on synthetic data, which illustrate the expected thermomechanical phenomena, and existing temperature-dependent uniaxial tension and tension-torsion experimental datasets.

Multivariate statistical analysis and bespoke deviation network modeling for geochemical anomaly detection of rare earth elements

Rare earth elements (REEs), a significant subset of critical minerals, play an indispensable role in modern society and are regarded as “industrial vitamins,” making them crucial for global sustainability. Geochemical survey data proves highly effective in delineating metallic mineral prospects. Separating geochemical anomalies associated with specific types of mineralization from the background reflecting geological processes has long been a significant subject in exploration geochemistry. The processing of high-dimensional, non-linear geochemical survey data necessitates a systematic framework to address common issues, including missing values, the closure effect, the selection of appropriate multivariate analysis methods, and anomaly detection techniques in order to detect geochemical anomalies associated with mineral occurrences. The Curnamona Province in South Australia is considered an emerging REE province with significant REE mineralization potential. In this study, we use data from this region to evaluate the performance of a novel machine learning-based framework that incorporates data pre-processing, multivariate statistical analysis, and anomaly recognition to address challenges such as missing data, noise interference, data imbalance and high non-linearity. We utilize lithogeochemical data to map potential greenfield regions of REE mineralization. The primary advantages of our framework lie in its provision of an effective random forest-based data imputation method, utilization of isometric log-ratio transformation to eliminate the closure effect, and reduction of the impact of outliers on data interpretation through robust principal component analysis. Additionally, the framework utilizes a deviation network to learn anomaly scores from complex, non-linear data under imbalanced data conditions, identifying geochemical anomalies associated with REE occurrences by leveraging prior knowledge rather than those caused by data noise or anthropogenic factors. The anomalous areas identified by this framework delineate all known REE deposits and extend to the surrounding regions. Furthermore, a close spatial coupling relationship exists between these strongly anomalous areas and the felsic granite intrusions. The comprehensive workflow for processing geochemical data proposed in this study can effectively address common challenges in the geochemical exploration of critical minerals. The identified geochemical anomalies can provide important clues for subsequent exploration.

Population Pharmacokinetic-Pharmacodynamic Analysis of a Reserpine-Induced Myalgia Model in Rats.

(1) Background: Fibromyalgia syndrome (FMS) is a chronic pain condition with widespread pain and multiple comorbidities, for which conventional therapies offer limited benefits. The reserpine-induced myalgia (RIM) model is an efficient animal model of FMS in rodents. This study aimed to develop a pharmacokinetic-pharmacodynamic (PK-PD) model of reserpine in rats, linking to its impact on monoamines (MAs). (2) Methods: Reserpine was administered daily for three consecutive days at dose levels of 0.1, 0.5, and 1 mg/kg. A total of 120 rats were included, and 120 PK and 828 PD observations were collected from 48 to 96 h after the first dose of reserpine. Non-linear mixed-effect data analysis was applied for structural PK-PD model definition, variability characterization, and covariate analysis. (3) Results: A one-compartment model best described reserpine in rats (V = 1.3 mL/kg and CL = 4.5 × 10-1 mL/h/kg). A precursor-pool PK-PD model (kin = 6.1 × 10-3 mg/h, kp = 8.6 × 10-4 h-1 and kout = 2.7 × 10-2 h-1) with a parallel transit chain (k0 = 1.9 × 10-1 h-1) characterized the longitudinal levels of MA in the prefrontal cortex, spinal cord, and amygdala in rats. Reserpine stimulates the degradation of MA from the pool compartment (Slope1 = 1.1 × 10-1 h) and the elimination of MA (Slope2 = 1.25 h) through the transit chain. Regarding the reference dose (1 mg/kg) of the RIM model, the administration of 4 mg/kg would lead to a mean reduction of 65% (Cmax), 80% (Cmin), and 70% (AUC) of MA across the brain regions tested. (4) Conclusions: Regional brain variations in neurotransmitter depletion were identified, particularly in the amygdala, offering insights for therapeutic strategies and biomarker identification in FMS research.

A Hybrid Grey System Model Based on Stacked Long Short-Term Memory Layers and Its Application in Energy Consumption Forecasting

Accurate energy consumption prediction is crucial for addressing energy scheduling problems. Traditional machine learning models often struggle with small-scale datasets and nonlinear data patterns. To address these challenges, this paper proposes a hybrid grey model based on stacked LSTM layers. This approach leverages neural network structures to enhance feature learning and harnesses the strengths of grey models in handling small-scale data. The model is trained using the Adam algorithm with parameter optimization facilitated by the grid search algorithm. We use the latest annual data on coal, electricity, and gasoline consumption in Henan Province as the application background. The model’s performance is evaluated against nine machine learning models and fifteen grey models based on four performance metrics. Our results show that the proposed model achieves the smallest prediction errors across all four metrics (RMSE, MAE, MAPE, TIC, U1, U2) compared with other 15 grey system models and 9 machine learning models during the testing phase, indicating higher prediction accuracy and stronger generalization performance. Additionally, the study investigates the impact of different LSTM layers on the model’s prediction performance, concluding that while increasing the number of layers initially improves prediction performance, too many layers lead to overfitting.

Optimizing active distribution microgrids with multi-terminal soft open point and hybrid hydrogen storage systems for enhanced frequency stability

The recent increased interest in active distribution microgrids has complicated the process of reaching stable generation with the presence of distributed generators (DGs). These challenges can be handled by employing multi-terminal soft open points (SOPs), which can further boost system performance compared to the conventional two-terminal SOP, especially with present system disturbances. At the same time, hydrogen energy storage has drawn increased attraction to strengthen power grid stability and flexibility. This paper uses a hybrid-based energy storage device that employs an electrolyzer and fuel cell means with a hydrogen tank to absorb or generate power through multi-terminal SOP based on desired grid requirements. This work also offers a novel implementation of a hybrid jellyfish search and particle swarm optimization (HJPSO) applied to model predictive controllers (MPCs) to provide a solution regarding frequency control issues for multiple microgrids comprised of hybrid micro-turbines and renewable generators with the presence of storage devices. Furthermore, different forms of nonlinearity and actual data measurements for the implemented renewable generators are incorporated to attain further realistic analysis. The transient behavior of the studied microgrid is substantially augmented via the suggested control scheme. Referring to the modern grid codes and standards, the frequency operation limits in a specific range. This requirement has been preserved throughout the entire simulations, including uncertainty analysis, assessing the capabilities of multi-terminal SOP in providing frequency disturbance ride-through for the operating active hybrid distribution microgrid under various operating conditions.

Variational tensor neural networks for deep learning

Deep neural networks (NNs) encounter scalability limitations when confronted with a vast array of neurons, thereby constraining their achievable network depth. To address this challenge, we propose an integration of tensor networks (TN) into NN frameworks, combined with a variational DMRG-inspired training technique. This in turn, results in a scalable tensor neural network (TNN) architecture capable of efficient training over a large parameter space. Our variational algorithm utilizes a local gradient-descent technique, enabling manual or automatic computation of tensor gradients, facilitating design of hybrid TNN models with combined dense and tensor layers. Our training algorithm further provides insight on the entanglement structure of the tensorized trainable weights and correlation among the model parameters. We validate the accuracy and efficiency of our method by designing TNN models and providing benchmark results for linear and non-linear regressions, data classification and image recognition on MNIST handwritten digits.

Epileptic network identification: insights from Dynamic Mode Decomposition of sEEG data.

For medically-refractory epilepsy patients, stereoelectroencephalography (sEEG) is a surgical method using intracranial recordings to identify brain networks participating in early seizure organization and propagation (i.e., the epileptogenic zone, EZ). If identified, surgical EZ treatment via resection, ablation or neuromodulation can lead to seizure-freedom. To date, quantification of sEEG data, including its visualization and interpretation, remains a clinical and computational challenge. Given elusiveness of physical laws or governing equations modelling complex brain dynamics, data science offers unique insight into identifying unknown patterns within high dimensional sEEG data. We apply here an unsupervised data-driven algorithm, Dynamic Mode Decomposition (DMD), to sEEG recordings from five focal epilepsy patients (three with temporal lobe, and two with cingulate epilepsy), who underwent subsequent resective or ablative surgery and became seizure free. DMD obtains a linear approximation of nonlinear data dynamics, generating coherent structures ("modes") defining important signal features, used to extract frequencies, growth rates and spatial structures. DMD was adapted to produce Dynamic Modal Maps (DMMs) across frequency sub-bands, capturing onset and evolution of epileptiform dynamics in sEEG data. Additionally, we developed a static estimate of EZ-localized electrode contacts, termed the Higher-Frequency Mode-based Norm Index (MNI). DMM and MNI maps for representative patient seizures were validated against clinical sEEG results and seizure-free outcomes following surgery. DMD was most informative at higher frequencies, i.e. gamma (including high-gamma) and beta range, successfully identifying EZ contacts. Combined interpretation of DMM/MNI plots best identified spatiotemporal evolution of mode-specific network changes, with strong concordance to sEEG results and outcomes across all five patients. The method identified network attenuation in other contacts not implicated in the EZ. This is the first application of DMD to sEEG data analysis, supporting integration of neuroengineering, mathematical and machine learning methods into traditional workflows for sEEG review and epilepsy surgical decision-making.

A novel global modelling strategy integrated dynamic kernel canonical variate analysis for the air handling unit fault detection via considering the two-directional dynamics

As an indispensable component of air-conditioning system, the air handling unit (AHU) always exhibits strong nonlinearity and two-directional dynamics (time-wise and batch-wise dynamics). However, existing monitoring strategies cannot adequately figure out the AHU's two-directional dynamics from the nonlinear data. To boost the AHU's fault detection performance, a novel global modelling scheme integrated dynamic kernel canonical variate analysis (GDKCVA) is developed in this paper. The first contribution is to collect datasets from various days to develop a three-way training dataset and then normalize it along the batch-wise to suppress the batch-wise dynamics and variables' correlations. The second contribution is to establish the dynamic kernel CVA by integrating autoregressive moving average exogenous framework to more effectively confront the time-wise dynamics and variables' nonlinear relationships. The kernel matrices of augmented batch dataset are determined utilizing the kernel trick that transforms nonlinear data into high-dimensional linear space by leveraging kernel function. The third contribution is to propose a novel global modelling strategy to further eliminate the batch-wise dynamics by computing the total average kernel matrices from all the normal batch datasets. Finally, experiments and comparisons on the ASHRAE RP-1312 datasets are carried out to assess the suggested GDKCVA's fault detection capability. Compared with the kernel CVA (KCVA), the three-way training dataset based CVA (TCVA) and the three-way training dataset based KCVA (TKCVA), the proposed GDKCVA has the highest fault detection rates and its average fault detection rates of three monitoring statistics for eleven fault patterns reach 99.38 %, 99.15 % and 100 %, respectively.

Forecasting mooring tension of offshore platforms based on complete ensemble empirical mode decomposition with adaptive noise and deep learning network

The tension sequence data of offshore platforms mooring cables exhibit randomness, strong nonlinearity, and nonsmoothness. Previous studies have shown that single neural network models, such as long short-term memory (LSTM) and recurrent neural network (RNN) models, can effectively predict nonlinear data. Dealing with nonstationary data presents several challenges, nevertheless, like a noticeable delay in forecast outcomes and significant prediction errors. Aiming to address the aforementioned challenges, this article proposes an innovative hybrid prediction model named CEEMDAN-CLL for predicting mooring tension in semi-submersible platforms based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), frequency-domain analysis, convolutional neural network–long short-term memory (CNN-LSTM), and LSTM. The data used in this study are those monitored during the operation of “DeepSea One”, which is the first deepwater semi-submersible production platform in the South China Sea, is taken as the research object and cover a wide range of orientations and sea states.

Nonlinear dynamic transfer partial least squares for domain adaptive regression

Aiming to address soft sensing model degradation under changing working conditions, and to accommodate dynamic, nonlinear, and multimodal data characteristics, this paper proposes a nonlinear dynamic transfer soft sensor algorithm. The approach leverages time-delay data augmentation to capture dynamics and projects the augmented data into a latent space for constructing a nonlinear regression model. Two regular terms, distribution alignment regularity and first-order difference regularity, are introduced during data projection to address data distribution disparities. Laplace regularity is incorporated into the nonlinear regression model to ensure geometric structure preservation. The final optimization objective is formulated within the framework of partial least squares, and hyperparameters are determined using Bayesian optimization. The effectiveness of the proposed algorithm is demonstrated through experiments on three public datasets.

Manifold learning localization based on local tangent space alignment for wireless sensor networks

At present, nodes localization in wireless sensor networks are one of the focuses of many scholars' research. But now the current localization algorithms usually face the problems of low localization accuracy and high computation. Since the information captured by wireless sensor networks is essentially nonlinear, thus this paper proposes a localization algorithm based on manifold learning algorithm local tangent space alignment for wireless sensor networks. It can process nonlinear data to achieve good positioning effect, and the variables in the algorithm have little impact on the localization effect. Two types of positioning data are considered for localization: the measurement distance and the signal strength between sensor nodes. Firstly, the local k-neighborhoods of the localized data points can be found for determining the low-dimensional geometric structure of their local tangent spaces by principal component analysis. Next, the local tangent space of the localized sample points is aligned to obtain the relative locations of the sensor nodes. Then, the physical locations of the sensor nodes can be get by lining up the relative positions with anchor points. Finally, the ending of the paper by doing simulation experiments demonstrate that the algorithm has good precision and few variables in performing nodes localization.

AI-driven modelling approaches for predicting oxygen levels in aquatic environments

Reliable water quality models are crucial for better water management and pollution control. Biochemical oxygen demand (BOD) and dissolved oxygen (DO) are the widely recognized indicators used to examine the quality of water. Stakeholders often face challenges when it comes to monitoring water quality indicators daily. The conventional approach for testing is laborious and costly. Therefore, there is a need to incorporate alternate concepts for predicting water quality parameters. This article proposes a novel approach “Autoencoder-Deep-Autoregressive (AE-DeepAR)” to predict the concentration of BOD and DO using in-situ measurable water quality parameters as input. The autoencoder is employed to utilize a latent space that accurately captures the fundamental characteristics of the nonlinear data. On the other hand, the DeepAR model is utilized to produce point predictions. This approach is being implemented in the Mahanadi River system for the first time. It is found that conductivity, total suspended solids (TSS), turbidity, and ammoniacal nitrogen (NH3-N) are correlated with BOD. Likewise, turbidity, temperature, and total dissolved solids (TDS) correlate significantly with DO. The performance of the AE-DeepAR model in predicting BOD surpasses that of other models at all stations. The R2 range from 0.90 to 0.93, mean absolute error (MAE) varies from 0.061 to 0.147, mean squared error (MSE) lies between 0.005 to 0.028, and mean absolute percentage error (MAPE) differs from 9.20% to 19.95%. All stations show a greater degree of sensitivity. The uncertainty observed is less in most circumstances, but the unpredictability of the values caused by the occurrence of outliers in severe events may influence the outcome. The PICP value varies between 87 % to 95 % in BOD and 89 % to 95 % in DO. The results reveal that AE-DeepAR can be used as an alternative approach to predict BOD and DO with a high degree of accuracy.

Online nonlinear data reconciliation to enhance nonlinear dynamic process monitoring using conditional dynamic variational autoencoder networks with particle filters

In the chemical plants, data-driven process monitoring serves as a vital tool to ensure product quality and maintain production line safety. However, the accuracy of monitoring hinges directly upon the quality of process data. Given the inherently slow and complex nature of chemical processes, coupled with the potential for gross errors in process data leading to inaccuracies in model predictions, this paper proposes a method called Conditional Dynamic Variational Autoencoder combined with a Particle Filter (CDVAE-PF) for data reconciliation and subsequent process monitoring. CDVAE-PF leverages the capabilities of Conditional Dynamic Variational Autoencoder (CDVAE) to effectively model chemical process data in the presence of noise. This probabilistic model serves as the foundation for the Particle Filter (PF), which is employed for data reconciliation. Moreover, CDVAE-PF incorporates mechanisms to detect and rectify gross errors in process data, further enhancing its efficacy in data reconciliation. Subsequently, monitoring indices based on CDVAE are established to facilitate process monitoring. Through numerical simulations of a two-to-one variables Continuous Stirred Tank Reactor (CSTR) example and a fifteen-to-one variables dichloroethane distillation process from an actual chemical plant, CDVAE-PF demonstrates its effectiveness by reducing mean absolute error to 7.8 % and 12.8 % respectively in gross error data reconciliation. Moreover, in terms of monitoring performance, CDVAE-PF successfully mitigates misjudgments caused by gross errors, thereby significantly enhancing the reliability of process monitoring in chemical plants.

Revolutionizing semantic integration of maintenance cost prediction for building systems using artificial neural networks

The maintenance cost management for building services has significantly advanced with the advent of computational techniques and semantic web technologies. Building services, including HVAC, plumbing, firefighting, and electrical systems, ensure building safety and efficiency. However, predicting maintenance costs is challenging due to the complexity and variability in usage patterns and environmental conditions. To address this challenge, this study introduces a Semantically Integrated Knowledge-based Artificial Neural Network (SIKB-ANN) framework. The SIKB-ANN framework integrates Semantic Web Technology (SWT) and Artificial Neural Networks (ANN) to improve the accuracy of maintenance cost predictions. SWT enhances data interoperability and standardization, while ANN manages complex non-linear data relationships. The model was trained with historical maintenance data from a firm (2017–2022) and validated using metrics such as Coefficient of Determination (R2), Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and Mean Absolute Error (MAE). The model achieved high predictive accuracy, with R2 values of 0.986 for the test set and 0.944 for the training set, indicating its robustness and reliability. An essential contribution of this research is the innovative integration of semantic ontologies with ANN, significantly enhancing predictive capabilities and providing a structured data management framework. This approach improves prediction accuracy and supports better decision-making and resource allocation in building management. The study highlights the potential of combining semantic technologies with machine learning to address complex predictive challenges in the built environment. Future research should consider integrating real-time data streams, advanced machine learning techniques, and broader applications in facility management.

Comparison of Approaches for Assessing Linearity of Impedance Measurements

There are two experimental methods available to assess the linearity of electrochemical impedance measurements. Observation of current as a function of potential, known as Lissajous plots, provides an instantaneous visual representation of the data.1 Deviation from an elliptical shape suggests a perturbation amplitude that is too large, resulting in nonlinear impedance data. A second approach is to measure, along with the fundamental, the higher harmonics of the measurement signal. Under potentiostatic control, the harmonics of current that exceed the noise level suggest nonlinear behavior. These harmonics may be expressed in terms of a frequency-dependent total harmonic distortion, THD, written as the ratio between the sum of the root mean square of the harmonic magnitude and fundamental frequency magnitude for electrochemical applications.The impedance was measured for a model system consisting of a Pt disk immersed in an electrolyte containing 0.01 M potassium ferricyanide, 0.01 M potassium ferrocyanide, and 1 M KCl. Measurements were performed using a Gamry Reference 3000 with THD measurement enabled and disabled. Low-frequency (10 mHz) Lissajous plots were recorded to facilitate comparison of the two methods for assessing linearity. The impedance measurements with THD enabled or disabled were in good agreement, including the frequency-dependent stochastic error structure, the shapes of Lissajous curves, and the values of the impedance. Both the low-frequency THD and the low-frequency Lissajous plots gave similar sensitivity to nonlinear behavior. Perturbation amplitudes of 1, 5, and 10 mV rms yielded elliptical Lissajous plots with THD values on the order of the background noise. Interestingly, the THD for the 10 mV perturbation was slightly above the background noise with a value of 0.01 (or 1 % of the fundamental). Perturbation amplitudes of 20, 60, and 100 mV rms yielded both non-elliptical Lissajous plots and low-frequency THD values much larger than the background noise.The regression of the measurement model 2 to the imaginary part of the impedance was applied to assess the consistency of the measured data to the Kramers-Kronig relations.3 Data measured at amplitudes of 1, 5, 10, and 20 mV rms were found to be consistent with the Kramers-Kronig relations, and data collected with amplitudes of 60 or 100 mV rms were found to be inconsistent with the Kramers-Kronig relations. As the measurement with a 20 mV rms amplitude was found to be nonlinear by observation of non-elliptical Lissajous plots and a THD of 4.2% at a frequency of 10 mHz, the post-measurement analysis of consistency with the Kramers-Kronig relations was found to be less sensitive than experimental observation of Lissajous plots and calculation of THD. Comparison of Lissajous plots to THD values suggests that experiments with THD less than 1% of the fundamental may be considered to be linear.