*2.4. Soil Enzymatic Activity*

Soil enzyme activity in the treatments was measured as follows:

## *2.5. Biological Index of Fertility (BIF)*

BIF was determined by employing dehydrogenase activity (DHA) and catalase activity (CAT) [24] using the formula: (DHA + kCAT)/2, where k is the proportionality factor (= 0.01).


**8. Conclusions**

Electrification systems based on the use of renewable energy sources are suitable for providing electricity to isolated communities autonomously. However, there are barriers that hinder this process and, between them, the major one is lack of local capacities. In this context, Practical Action (Peru), Engineers Without Borders (Spain), Universitat Politècnica de Catalunya (Spain) and Green Empowerment (USA) are promoting the CEDECAP, a capacity development center in Peru that support the implementation of energy projects and trains farmers, community leaders, policy makers and students of technical degrees and universities. In 2006-2009, 22 courses were developed with 484 participants and 22 educational materials.

The future challenge of CEDECAP is to strengthen and to consolidate its role within formal education, both in professional schools and universities, to increase professional's training, upgrade research and keep on working to insert renewable energy projects on the political agenda as a definitive step for promoting and improving their impact.


**Functional Nanomaterials in Biomedicine**

Editors

**Wansong Chen Jianhua Zhang**

MDPI ' Basel ' Beijing ' Wuhan ' Barcelona ' Belgrade ' Manchester ' Tokyo ' Cluj ' Tianjin

*Editors* Wansong Chen Chemistry and Chemical Engineering Central South University Changsha China

Jianhua Zhang Chemical Engineering Tianjin University Tianjin China

*Editorial Office* MDPI St. Alban-Anlage 66 4052 Basel, Switzerland

This is a reprint of articles from the Special Issue published online in the open access journal *Molecules* (ISSN 1420-3049) (available at: www.mdpi.com/journal/molecules/special issues/nanomater biomed).

For citation purposes, cite each article independently as indicated on the article page online and as indicated below:

LastName, A.A.; LastName, B.B.; LastName, C.C. Article Title. *Journal Name* **Year**, *Volume Number*, Page Range.

**ISBN 978-3-0365-6020-5 (Hbk) ISBN 978-3-0365-6019-9 (PDF)**

© 2022 by the authors. Articles in this book are Open Access and distributed under the Creative Commons Attribution (CC BY) license, which allows users to download, copy and build upon published articles, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications.

The book as a whole is distributed by MDPI under the terms and conditions of the Creative Commons license CC BY-NC-ND.


3.2.6. In Vivo Pharmacokinetic Studies

Additionally, in vivo studies were carried out in a porcine model to assess the local and systemic pharmacokinetics of FTS-loaded rings. To ensure that rings were properly placed in the proximal part of the esophagus, initial studies were carried out using placebo rings (without FTS). We have shown successful endoscopic ring implantation into the proximal esophagus of one set of five pigs. After successful implantation of placebo rings, FTS-loaded rings were fabricated using pre-loaded PCl700-DMA resin formulation. Additionally, a post-fabrication UV curing was implemented to fabricate rings with mechanical properties appropriate for esophageal implantation. These FTS-loaded rings were deployed in the proximal esophagus of two sets of five pigs each for a period of 7 days. A daily endoscopy was performed to monitor the placement of rings. During endoscopic screening, it was observed that the rings were not present in the proximal esophagus of pigs

after day 1. This observation was corroborated by the absence of FTS in esophageal tissue and plasma collected at euthanasia at day 7 post ring administration. As the pigs were provided with an ad lib diet during the study, we hypothesize that the rings slipped into the pig's stomach along with the food. The PK analysis showed no accumulation of FTS in the esophageal tissue and no detectable plasma levels at day 7. These studies demonstrated that rings can be successfully inserted in the proximal part of the esophagus; however, further optimization in order to keep these rings in place for a longer time is needed.


**1. Introduction**

Lithium-ion batteries are a key technology for electric vehicles, portable devices and stationary applications such as home-storage systems. With the increasing usage of lithiumion batteries in complex fields of application, the demand for battery models is growing as well. Battery models are necessary to predict the dynamic voltage and current behaviour and to monitor internal states, particularly the state of charge (SOC) and the state of health (SOH). There are many different types of battery models [1,2]. Depending on the required purpose, they can be selected as a compromise between accuracy and simplicity. We introduce here a grey-box (GB) modelling approach that uses a simple equivalent circuit model (ECM) as a basis.

Digitisation has been progressing rapidly in the past decades, and with it the amount of available data increases. This has boosted the development of artificial intelligence and especially neural networks. Neural networks are an important representative of blackbox (BB) models. They learn relations between inputs and outputs of systems based on data [3–6]. However, BB models require a huge amount of training data. Therefore, it is reasonable to consider other modelling techniques. White-box (WB) modelling uses prior physical, chemical or engineering knowledge in the form of mathematical equations to describe the behaviour of the corresponding system. WB models are therefore limited to the understanding of the underlying processes. GB models combine WB and BB modelling techniques to benefit from their respective advantages [3–6].

**Citation:** Brucker, J.; Behmann, R.; Bessler, W.G.; Gasper R. Neural Ordinary Differential Equations for Grey-Box Modelling of Lithium-Ion Batteries on the Basis of an Equivalent Circuit Model. *Energies* **2022**, *15*, 2661. https://doi.org/ 10.3390/en15072661

Academic Editors: Luis Hernández-Callejo, Sergio Nesmachnow and Sara Gallardo Saavedra

Received: 24 February 2022 Accepted: 25 March 2022 Published: 5 April 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

There are many examples in current research where neural networks are used to model lithium-ion batteries. In Ref. [7] a feedforward network with two hidden layers approximates the SOC of a battery based on the actual voltage, current and time. The authors of Ref. [8] predict the SOC of a battery with a recurrent neural network (RNN). The last three values of SOC, battery current, battery voltage and the values of four temperature sensors are taken into account. RNNs enable time series prediction. The authors of Ref. [9] perform online predictions of the remaining capacity of a lithium-ion battery with a long short-term memory network, a special form of RNN. The measured voltages during constant current (CC) charging above a certain battery voltage and the charge throughput till reaching the charge cut-off voltage serve as inputs. The authors of Ref. [10] use neural networks for battery design. They generate their training data with a pseudotwo-dimensional model of a lithium-ion battery by varying different design parameters. The first neural network classifies whether the given parameter combination leads to a possible battery configuration or not. A second neural network estimates the specific energy and the specific power of the battery with the chosen parameters. In Ref. [11] a feedforward network is used for end-of-line prediction. The unmeasured physical battery parameters are estimated by a neural network. The aforementioned approaches represent BB models. The following articles focus on GB modelling of lithium-ion batteries. The authors of Ref. [12] estimate the SOH of a battery with a neural network that takes the fitted parameters of an ECM as input. In Ref. [13] a reduced-order physics-based model is supplemented with two neural networks to predict what the authors call "nonideal voltages" of the positive and negative electrode. An additional Bayesian network approximates the influence of ageing on the battery resistance and the amount of cyclable lithium. The authors of Ref. [14] build GB models of dynamic systems including external variables with neural ordinary differential equations (NODEs). In contrast to the original contribution [15], they call the combination of NODEs and differential equations "universal differential equations". In Refs. [16,17] NODEs are used for GB modelling of lithium-ion batteries. The authors of Ref. [16] focus on physical battery modelling in combination with NODEs. They consider ageing effects such as solid electrolyte interface formation, lithium plating and active material isolation as well as the increase in the internal resistance. NODEs approximate the remaining deviation between the physical model and the experiment. In our previous work [17] an ECM serves as a basis for a GB model of a lithium-ion battery. NODEs model the voltage drop across the included resistor–capacitor (RC) circuit.

In the present contribution, we continue our previous work [17] by further improving the GB model. For this purpose, we increased the amount of physical knowledge in the model. In contrast to the former contribution, the focus of the current study is on modelling the dynamic properties of the battery. We used additional training data from charging and discharging with pulsed currents to train the time constant of battery dynamics. Furthermore, we tested the trained GB model against two test profiles covering more realistic battery operation. So far we have neither considered temperature dependencies nor ageing effects.

The target battery studied here is a large-format 180 Ah prismatic commercial lithiumion cell with lithium iron phosphate (LFP)/graphite chemistry. This type of cell is used in stationary storage systems. We have previously investigated the experimental properties of this cell in great detail [18]. LFP cells are attractive for stationary storage applications because they have shown a high cyclic and calendaric lifetime [19,20]. However, their state diagnosis is challenging due to a flat, plateau-like discharge voltage curve and charge– discharge voltage hysteresis [21]. One of the goals of the present study is therefore to investigate the applicability of GB models to this type of cell.

The paper is organised as follows. In Section 2, we describe the fundamentals of the ECM, the NODEs and the combination of both for GB modelling of lithium-ion batteries. In Section 3, we show and discuss the application of the proposed GB model to the simulation of lithium-ion batteries. The training and test results are given as well as their dependencies on hyperparameters, the user-defined parameters of a neural network. Hyperparameters such as the learning rate or the number of hidden layers of a neural network control the learning process. At the end of the paper, we summarise the results and give an outlook.

The measurement data and the code are available in Zenodo. See 'Data Availability Statement' for further information.


**Juan Claver 1,\*, Amabel García-Domínguez 1, Lorenzo Sevilla 2 and Miguel A. Sebastián 1**

Received: 31 October 2018; Accepted: 10 January 2019; Published: 14 January 2019

**Abstract:** Any research in any field needs an initial background, and in the same way, any decision should be supported by previous knowledge and study of the problem and its context. In the case of the industrial heritage, both the study of the typology and the decision making about the actions of conservation and reutilization of its assets must be based on a deep knowledge of the set of elements that the typology includes. All of that refers to the corresponding territory being analyzed, since the intensity and productive tradition will be different between each territory, region, or country. In that context, this paper represents the continuation of the main research line of the authors, and exposes their efforts to develop a useful tool for the study, management, and cultural promotion of the assets related to industrial heritage in Spain through the development of a multi-criteria catalogue of assets. Thus, based on the initial catalogue developed by some of the authors, this paper significantly increases the number of assets considered. In addition, it includes new classification criteria, reviews the observed trends, and establishes the future lines of work and suitable strategies for these kinds of initiatives.

**Keywords:** industrial heritage; cataloguing; methodology; multi-criteria; Andalusia; Spain


*2.1. Materials*

Moxifloxacin (molecular weight of 437.9 Da) was received as an in-kind gift from Zydus Cadila Ltd., Ahmedabad, India with a purity of 99.99%. Soluphor® P was generously supplied by BASF, Ludwigshafen, Germany. Tween 80 was purchased from S.D Fine Chem, Mumbai, India and ethyl oleate was purchased from Central Drug House Pvt. Ltd., Mumbai, India. All other chemicals used were of analytical grade.


*2.5. Expression Analysis of SlBAG Genes*

Seeds of *Solanum lycopersicum* cv. Ailsa Craig were sterilized and sown in the solid Murashige and Skoog (MS) medium at 25 ◦C/20 ◦C, and 20-day-old seedlings were used for the following treatments. For *SlBAG* gene expression under stresses, tomato seedlings were cultured in liquid MS medium for 24 h, then exposed to salt, drought, high temperature, cold, cadmium, H2O2, and ABA treatment for 1, 3, 6, 12, 24, and 48 h. Tomato plants were transferred to liquid medium containing 100 mM NaCl, 20% polyethylene glycol-6000, 50 uM cadmium, 100 uM ABA, and 10 mM H2O2, respectively.

For HT and cold, the seedlings were exposed to HT (42 ◦C) or 4 ◦C conditions. All real leaves were collected, frozen, and preserved at −70 ◦C for RNA extraction. For organsspecific expression of *SlBAG* genes, organs from root, stem, leaf, flower, green fruit, and red fruit of different stages were collected according to the method of Ding et al. [23]. The transcription levels of *SlBAG* genes were determined by quantitative real-time PCR (qRT-PCR).


*5.3. Atmospheric Particulates*

Aerosols are small particles suspended in the atmosphere and play an important role in the earth's radiation balance, air quality and cloud microphysics. They directly affect the regional and global climate by absorbing and scattering solar and terrestrial radiation, and indirectly affect the global climate by altering cloud formation characteristics. Ambient aerosol particles are mainly derived from anthropogenic activities and natural sources, such as residential heating, automobile exhausts, open-air combustion and volcanic activities [81]. The Asian monsoon brought in aerosols from biomass burning in southeast Asia, which were mixed with moist air particles in southern China, eventually reaching high aerosol concentrations in the spring, which reached the lowest concentration in winter [82]. There was a significant negative correlation between O3 and particulate matter in the margin of Tarim Basin, indicating that the effect of dust on solar transmittance in the atmosphere lead to a decrease in net O3 productivity [83]. The concentration of O3 was influenced by the nonuniform chemical processes occurring on the surface of particles, so increasing the concentration of PM2.5 could weaken the atmospheric radiation. This would allow the O3 level to be suppressed by eliminating ultraviolet light, which was consistent with the conclusions of Wang et al. [22] and Qu et al. [84]. In 2017, 338 main cities in China were selected to sample ambient air for 365 days to compare the concentrations of O3, NO2, SO2, particulate matter and CO in the atmosphere [85]. The results showed that O3 concentrations were significantly correlated with PM10 in 238 cities, among which, the coefficients in 142 cities were positive whereas those in 96 cities were negative. Most cities with positive correlations were mainly located in the south and northeast, while most cities with negative correlations were mainly located in the north of China. There was no significant correlation between O3 concentration and PM10 concentration in 100 cities. O3 concentrations were significantly correlated with PM2.5 in 250 cities, among which, the coefficients in 117 cities were positive and those in 133 cities were negative. Most cities with positive correlations were mainly located in the south, while most cities with

negative correlations were mainly located in the north. There was no significant correlation between O3 concentration and PM2.5 concentration in 88 cities. The possible reason for the above results was that NOx and VOCs would simultaneously increase significantly on the particulate matter (PM) pollution days in many cities, and the increase in these precursors influences the atmospheric O3 concentration more than the particulates. Atmospheric O3 was usually used as a tracer for photochemical reactions. A large amount of O3 was used as an oxidant to enrich the secondary components of PM2.5 through a secondary photochemical process, so higher PM2.5/PM10 usually indicated the existence of more active photochemical reactions. To some extent, PM2.5/PM10 could be used as a reference index for the types of air pollution, that is, higher or lower PM2.5/PM10 indicated the complicated pollution types related to photochemical reaction [86].

The main fixed sources of PM2.5 and PM10 are smoke and dust produced by fuel combustion and gas oil during heating in industrial enterprises, such as power generation, oil and printing. The main moving source is exhaust gas emitted by road traffic vehicles into the atmosphere. The temporal characteristics of PM2.5 in Anhui province showed that PM2.5 decreased from January to July, and increased from July to December, that is, the concentrations of PM2.5 were lower in summer and higher in winter [87]. Some studies showed that PM2.5 and PM10 were positively correlated with NO2 and CO, and weakly correlated with O3. The high concentration of O3 in highly oxidized air in hightemperature seasons promoted the formation of secondary particulate matter, which made PM2.5 positively correlated with O3 [88]. Several studies have found that reducing PM2.5 might lead to an increase in atmospheric O3, and reducing emissions of NOx and VOCs is required to overcome this effect. A more important factor affecting O3 trends in the North China Plain (NCP) from 2013 to 2017 was the reduction in PM2.5, which slowed down the sink of hydroperoxy radicals, thus speeding up O3 production [89]. In addition, atmospheric particles could directly affect the scattering and absorption of radiation, consequently changing the intensity of incident ultraviolet radiation, and affecting the production of O3. The formation of O3 decreased with the decrease in UV radiation or light scattering associated with PM2.5 [90].