In this study, we developed a new saltiness sensor with the lipid/polymer membrane to quantify the saltiness enhancement effect of quinine by replacing a lipid that caused an unexpected initial drop in the previous study with another new lipid. As a result, the concentrations of lipid and ionophore were optimized to produce an expected response. Logarithmic responses have been found on both NaCl samples and quinine-added NaCl samples. The findings indicate the usage of lipid/polymer membranes on novel taste sensors to evaluate the saltiness enhancement effect accurately.The saltiness enhancement effect can be produced by adding specific substances to dietary salt (sodium chloride). This effect has been used in salt-reduced food to help people forge healthy eating habits. Therefore, it is necessary to objectively evaluate the saltiness of food based on this effect. In a previous study, sensor electrodes based on lipid/polymer membrane with Na Taste evaluation has been used in the development as well as the quality management of foods, beverages, and pharmaceuticals. Commonly, the sensory test and the chemical analysis are methods of quantifying the tastes of the products. However, the sensory test is affected by the physical and psychological conditions of testers, making the results subjective. The chemical analysis provides data on each substance in the food, but it can neither demonstrate the overall taste nor the taste-substance interactions.Under such conditions, sensors that can quantify or identify taste have been developed to solve the problems ,3,4,5,6.The taste sensor based on lipid/polymer membrane has been developed with the concept of global selectivity, which states for the selectivity to all chemical substances of individual taste so that the taste sensor is able to perceive the taste of any product ,11,12,13The main difference between the e-tongues and the taste sensors is that the result from the e-tongues demonstrates the information to differentiate types or states of food (such as beers and oils), while the result from the taste sensors is a quantity to show the intensity of the taste.The lipid/polymer membranes, which are made of lipids, plasticizers, and polyvinyl chloride (PVC), interact with the taste substances mainly based on electrical and hydrophobic properties. The electrical property originates from lipids because they dissociate in the membrane to contain charges. The hydrophobicity is from all of the components because they all contain hydrophobic groups. It is possible to quantify one taste quality selectively by changing the type and amount of lipids and plasticizers. For instance, sensor of saltiness taste CT0 contains a lipid called tetradodecylammonium bromide (TDAB) which is positively charged to make the sensor sensitive to chloride ions of NaCl, and a plasticizer called dioctyl phenylphosphonate (DOPP) which makes the membrane hydrophilic so that the sensor is not responsive to bitter substances which are hydrophobic.The taste sensor has been utilized in food and beverage manufacturing to control the taste of the food ,16,17 anThe tastes perceived by humans are defined as five basic tastes: saltiness, sourness, sweetness, bitterness, and umami (savoriness) . Each ofThe saltiness enhancement effect is the effect to intensify the salty taste by adding specific substances to salt (sodium chloride). Such substances, called saltiness enhancement substances, usually have other taste qualities even when the saltiness enhancement effect do not occur: umami taste substances such as monosodium glutamate (MSG), branched-chain amino acids BCAAs; sour taste substance such as tartaric acid and citric acid ,30,31,32Work has been done on the development of a taste sensor on saltiness enhancement effect . This taIn this study, a new lipid/polymer membrane was fabricated without the use of partially dissociated PADE to get rid of the initial potential drop problem. This sensor was expected to measure the saltiness enhancement effect produced by quinine, which contains a positively charged intramolecule  and hydr+ ionophore satisfied the requirements for measuring dietary salt sample and the quinine added saltiness enhancement sample.As a result, the taste sensor using the membrane comprising TFPB and NaWe performed a sensory test on the saltiness enhancement effect in collaboration with the Taste & Aroma Strategic Research Institute Co., Ltd.  in a similar way . Ten pan+ ionophore), TFPB, and polyvinyl chloride (PVC) were purchased from FUJIFILM Wako Pure Chemical Corporation , 2-nitrophenyl octyl ether (NPOE) and tetrahy-drofuran (THF) were purchased from Sigma-Aldrich Japan G.K. . The structures of these substances are shown in For the components of membranes, sodium ion selective ionophore bis[(12-crown-4)methyl] 2-dodecyl-2-methylmalonate , and sodium chloride (NaCl) were purchased from Kanto Chemical Co., Inc. (Tokyo Japan).+ ionophore (5 g) was dissolved in THF (5 mL). Later the calculated amount of Na+ ionophore solution was mixed into this vial snap. The lipid/polymer membranes were fabricated under the procedures as shown below:Prepare a 45 mm petri dish and a 20 mL vial snap;Dissolve TFPB, NPOE, and PVC with 10 mL THF in the vial snap;+ solution ionophore accordingly into the vial snap.Add NaStir the vial snap for 1 h and pour the content into the petri dish.Dry the petri dish for three days in a draft chamber with a temperature of 25 °C to let the THF be fully volatilized.First, NaA well prepared membrane was a transparent and colorless film about 300 μm thick.To test the response of the sensors, two kinds of samples were prepared: NaCl solution and NaCl + quinine solution. The NaCl solution was to test whether the sensor could respond to normal saltiness. The NaCl + quinine solution was to test whether the sensor could respond to the saltiness enhancement effect caused by quinine. The solutions were all made with deionized water. The details of the samples are shown in Additionally, a standard solution, made of 30 mM KCl and 0.3 mM tartaric acid, was prepared to initialize the sensor; a cleaning solution, made of 100 mL HCl and 30 vol% ethanol, was prepared to wash the samples left on the surface of the sensor after each measurement .For the preparation of working electrodes, the membranes made in Sensor electrodes were then connected to a unit of TS-5000Z Taste Sensing System, which is a commercialized taste sensing system from Intelligent Sensor Technology, Inc., Kanagawa, Japan. Each unit can connect to 4 working electrodes and 1 reference electrode ,14,33.The construction of this measuring system is as follows: Ag wire coated with AgCl|3.33 M KCl and sat. AgCl solution|membrane|sample solution|reference electrode (Ag/AgCl) in taste solution. Changes in potentials were measured and recorded in the taste sensing system.r). Then the sensor was immersed in the sample solution for 30 s to measure the sample potential (Vs). After that, the sensor was again immersed in the standard solution to obtain an adsorbed reference potential (Vr). Finally, the sensor was immersed in the cleaning solution to remove adsorbed substances on the membrane surface. The use of TS-5000Z Taste Sensing System is to automatize the measurement procedures [s and Vr is called the relative value, or response value, which is to quantify the initial taste. The difference of Vr and Vr is called CPA , which is to measure the taste produced by substances adsorbed on the membrane [The measurement procedures had four steps as stated in ,14. Firsocedures ,14. The membrane ,14. Thesmembrane .The steps mentioned above compose a cycle, and 5 cycles are performed in one measurement. The average and standard deviation of the second to fifth cycle was calculated as the response value .The saltiness enhancement effect of quinine was confirmed from the sensory test. The sensory test on the saltiness enhancement effect was performed in collaboration with the Taste & Aroma Strategic Research Institute Co., Ltd. . Ten well trained panelists  were enrolled in this study. The panelists were selected by their ability to detect taste substances with high sensitivity, and have been trained approximately once a week. The result is showed in From this result, the taste sensor on saltiness enhancement effect should produce a increasing response when quinine is added to low concentration NaCl solution, while staying unchanged when quinine is added to high concentration NaCl solution.+ ionophore, the responses to NaCl samples were tested on two types of membranes with the compositions listed in + ion-selective electrode (NaISE) is much better. The results were separated into two groups: the ones over 4.5 mg and the ones below 4.5 mg showed almost the same response respectively. The response of TFPB membrane is the same as reported [+ ionophore can dramatically improve the sensitivity of NaCl.Because it is needed to satisfy the basic function as a saltiness sensor and test the effect of the Nareported . This re+ ionophore was 4.5 mg to 1.125 mg, good sensitivity of the saltiness enhancement effect can be achieved. It is intriguing that the results are not clearly divided into two groups as in + ionophore nor the ones only with TFPB were able to measure the saltiness enhancement effect. Only the ones with Na+ ionophore lower than 4.5 mg showed the saltiness enhancement effect. The response of TFPB membrane started to increase from about 0.02 mM. However, as it is required to measure the saltiness enhancement effect with the concentration of quinine in The same type of membranes in  were use+ ionophore added and the TFPB membrane had large sensitivity to quinine. The result, on the other hand, showed that the concentration of NaCl in the solution can affect the sensitivity to quinine. We can conclude that the taste sensor composed of Na+ ionophore and TFPB can detect the saltiness enhancement effect at lower NaCl concentrations by comparing the two results in To make sure that the saltiness enhancement effect of quinine can only be detected at the relatively low concentration of NaCl, the measurement under high level concentration of NaCl (200 mM) has also been performed. The results are shown in + ionophore added succeed under 70 mM NaCl, the CPA value, which demonstrates the adsorption property of the membrane, is plotted in + ionophore added appeared to adsorb quinine on the membrane surface. This fact is considered to be a strong evidence that the increasing response is resulted from quinine.To explain why only the membranes with 2.25 and 1.125 mg Na+ ionophore is 2.25 mg, as it can determine the saltiness enhancement effect at the right concentration of NaCl. The response value and the CPA value of this membrane are shown in From the results in previous sections, it is reasonable to conclude that the best amount of the Na+ ionophore reached a low level (below 4.5 mg). The sensitivity increased as the amount of ionophore became lower. Without the use of Na+ ionophore, the sensor again failed to measure the effect. Therefore, it is the ionophore that handle the character of measuring quinine in the NaCl solution.In + ions accumulating on the surface of the membrane, thus repelling the quinine. The evidence can be found while finding the response of the sensor under a concentration of 200 mM of NaCl solution. As long as the concentration of Na+ ions increased in the solution, the amount of Na+ ions is greater, and the screening effect should be stronger. Thus, the saltiness enhancement effect appears at lower ionophore concentrations  in A similar phenomenon has also been found in PVC and DOPP membrane , where tThe TFPB membrane scarcely responded to quinine at coexistent 70 mM NaCl in + ionophore was modulated, so that the taste sensor can not only measure the saltiness enhancement effect correctly  but also sustains a large response region. The reason why the sensor was able to measure the effect only when the ionophore concentration was low is that the hydrophobicity of the membrane changed because of the ratio of ionophore to PVC and plasticizer is adjusted. The reason that the sensor failed to measure the effect under a high amount of Na+ ionophore has been discussed (decreased hydrophobicity and increased screening effect). The results from trials showed that the composition of 2.25 mg Na+ ionophore in the membrane is very suitable for the measurement of the saltiness enhancement effect produced by quinine. Because the mechanism of the saltiness enhancement effect has not been established, it is only possible to design a sensor which can imitate the saltiness enhancement effect obtained from sensory test. Currently, the salt-reduced foods using the saltiness enhancement effect produced from quinine have not been developed yet. The development of this sensor is assumed to be supportive to novel salt-reduced food products base on quinine. Future work can be done on investigating whether this sensor can measure the saltiness enhancement effect produced by commercialized substances.In this study, we showed that the saltiness enhancement effect can be produced from quinine when the concentration of NaCl was low, and we successfully developed a sensor to quantify the saltiness enhancement effect produced by quinine hydrochloride dihydrate. The sensor was designed to get rid of the use of the lipid PADE, owing to the initial drop problem. To increase the sensitivity and selectivity, the amount of Na


Hybrid composites, usually combining natural and synthetic reinforcing filaments, have gained a lot of attention due to their better properties than traditional two-component materials. For structural applications of hybrid composites, there is a need to precisely determine their mechanical properties on the basis of the mechanical properties, volume fractions, and geometrical distributions of constituent materials. The most common methods, such as the rule of mixture, are inaccurate. More advanced methods, giving better results in the case of classic composites, are difficult to apply in the case of several types of reinforcement. In the present research, a new estimation method is considered, which is simple and accurate. The approach is based on the definition of two configurations: the real, heterogeneous, multi-phase hybrid composite configuration, and the fictitious, quasi-homogeneous one, in which the inclusions are “smeared out” over a representative volume. A hypothesis of the internal strain energy equivalence between the two configurations is formulated. The effect of reinforcing inclusions on the mechanical properties of a matrix material is expressed by functions of constituent properties, their volume fractions, and geometrical distribution. The analytical formulas are derived for an isotropic case of a hybrid composite reinforced with randomly distributed particles. The validation of the proposed approach is performed by comparing the estimated hybrid composite properties with the results of other methods, and with experimental data available in the literature. It is shown that a very good agreement is obtained between experimentally measured hybrid composite properties and their predictions resulting from the proposed estimation method. The estimation errors are much lower than the errors of other methods. Hybrid composites are materials that consist of a matrix and at least two different types of reinforcement. They can be manufactured from a combination of a variety of organic or inorganic materials such as metals, ceramics, polymers, etc., to obtain the desired mechanical, thermal, electrical, or other properties. Virtually unlimited possibilities of combining several organic or inorganic constituents allow the designing of a huge number of new products with high precision, as well as modifying conventional composite materials.Hybrid composites usually exhibit properties that neither organic nor inorganic constituent materials can reach separately; they may be flexible and at the same time be characterized by high mechanical strength and thermal stability. Moreover, the resulting properties of the combination of several reinforcing materials may exhibit a synergistic effect . For exaIncreasing demand for eco-friendly materials encourages implementing agricultural waste as natural fibers, increasingly used as an addition or replacement to traditional synthetic fibers, which have harmful effects on the environment. For this reason, the hybrid use of natural and synthetic reinforcing materials has gained a considerable attention from researchers ,5. GenerConsidering other fields, Bagheri et al.  investigPanthapulakkal and Sain  investign) of reinforcing materials. The simplest classical models for the estimation of the average elastic moduli of a two-component composite are the Voigt [Following the expanding application of hybrid composites, it is necessary to extend the use of classical averaging methods for two-component composite properties to hybrid composites with a larger number  to conshe Voigt  used thehe Voigt  assumes he Voigt , who conhe Voigt , Gan et he Voigt , Liu et he Voigt , Würknerhe Voigt , Selvaduhe Voigt  and othePredicting the effective properties of hybrid composites becomes more complicated with a growing number of components, and so far, there has been little theoretical modeling of property relationships in these materials. In  the clasIn the majority of research papers, multi-step homogenization is applied. Hasanzadeh et al.  propose Although the classical Voigt’s rule of mixture was shown to result in significant discrepancies with the experimental results, especially in the case of natural fibers , it can The approach to predict the elastic properties of a hybrid composite presented in this research utilizes a concept of a fictitious quasi-homogeneous continuum , in whicThe first attempts to extend the CDM-based approach to a general case of thermodynamically based constitutive modeling were performed by Egner and Ryś ,40,41. TIn the present paper, this concept is further developed and applied for the first time to hybrid composite materials. A significant advantage of the method used in the presented research in comparison with the above-mentioned classical approaches is the simplicity of calculations and the possibility to predict with significantly better accuracy the effective properties of composite materials. What is more, there is no need to incorporate any multi-step procedures.Each inclusion within the RVE matrix is subjected to the same stress field derived from the external tractions applied at the boundary of this element.The effect of all other inclusions within the RVE matrix on the observed inclusion is measured through the change of effective composite stiffness or compliance.For the isotropic short fiber-reinforced composites the exact spatial correlation of the inclusions within the RVE has negligible influence on the effective composite properties defined within the element.The main assumption adopted in the considered homogenization method states that the effective properties of an isotropic composite can be described by volume averaging of the actual properties of its components (matrix and reinforcing inclusions) over a domain called the representative volume element (RVE) which maps a finite volume of the real heterogeneous hybrid composite material into a material point of the fictitious pseudo-homogeneous configuration. This effective quasi-homogeneous configuration method is based on the following assumptions:A transition between the microscale and the effective composite properties on the macroscale requires a proper selection of the RVE size, bounded by two constraints. On one hand, it must be large enough to include a sufficient number of reinforcing inclusions that justify homogenization within the RVE. However, on the other hand, the size of the RVE must be small enough for the stress state to be considered homogeneous. The existence of the RVE, which allows the material to be considered statistically homogeneous within the volume element, is the condition for the presented approach, in which there are no scale parameters involved. The true distribution of the inclusions within the RVE matrix, described by the  parameter rameters .The total strain energy equivalence (TEE) hypothesis can be described as follows ,42,43,44At any time, to an RVE in its real  configuration, described by the set of state variable pairs Accordingly, the definitions of effective stresses tion  and (5) and the Hooke law, the elastic stiffness tensor action ξ ,42,43:(6The above equation can be transformed with the use of Equation (3) into the following form:The details of the above transformations can be found in , and wilThe elastic properties estimation based on the hypothesis of total strain energy equivalence allows obtaining a very good agreement with the experimental data, while the calculations are relatively simple. There are some small discrepancies for the POM-CF composite, while for the other two materials, the predictions are excellent. It should be pointed out that the method proposed here, like all other homogenization methods, is based on simplifying assumptions and therefore approximate . Nevertheless, the errors in predicted values are very small in comparison with other classical methods. As it can be seen in The above-described concept will be further extended in the next section for the case of hybrid composites.In a general case of a hybrid composite, the volume fraction of reinforcement (4) can be decomposed as follows:In engineering practice, the most common are hybrid composites made of two types of reinforcement (1)(2)In the case of a three-phase hybrid composite, the unknown functions In the above expression (Taking into account expressions (7)–(9), the second boundary condition, (13), results in the following solutions for functions The first boundary condition therefore gives a single point solution:The simplest linear approximation of the functions The linear approximation between the boundary points together with the total strain energy equivalence hypothesis result in the second-degree polynomial description of the effective Lamé constants The approach may be furtherly developed by replacing in (18)–(19) the linear functions with more advanced interpolations.It should be underlined that the proposed method does not involve any model parameters that need to be identified experimentally. Parametric studies in this case concern therefore only the analysis of the model response (prediction of effective composite properties) for different volume fractions of the fillers. To perform such parametric studies the hybrid composite material described in  was selevariable b. SimilaThe obtained results were next compared with the Voigt and Reuss methods. Model validation was carried out for hybrid composites described in the available literature. The results for the (PA-AF-BF) composite described in the previous The space distribution of the Young modulus The same validation was performed with the use of another hybrid composite material available in the literature, which is a polylactide (PLA) reinforced with carbon (CF) and basalt (BF) fibers —see FiguThe validation results are summarized in The use of hybrid composites for semi-structural applications is increasing in many branches of industry. Hybrid composites are often more advantageous than classical two-component composites due to their environmental friendliness, weight reduction, and lower production costs. Structural applications of hybrid composites require knowledge of their mechanical properties, which result from the properties of constituent materials as well as their volume fractions and geometrical configuration. The commonly used estimation methods (for example the rule of mixtures) usually give results with a large error. For this reason, there is a need to develop a homogenization technique that would be accurate and preferably conceptually simple, not requiring complicated calculations.The paper describes a new method of hybrid composite properties estimation. The approach is based on the mechanical equivalence between a real, heterogeneous material, composed of a matrix and reinforced inclusions, and a fictitious pseudo-homogeneous configuration. The fictitious pseudo-homogeneous material is mechanically equivalent to the real composite in the sense of the total internal strain energy being the same for both materials.The proposed approach to properties estimation exhibits several important advantages in comparison with the most common homogenization methods. First of all, it has a physical, energy-based background. Additionally, the analysis is performed at the macro-scale, with the use of a mathematical formalism that does not require any assumptions about the exact size, type and distribution of reinforcing inclusions. The method can be used for an arbitrary number of composite components without any further simplifications or the need for multi-step calculations. The predictions are very close to the experimental values, which confirms that the physical assumptions of the approach are correct.One of the most important features of the proposed estimation method is its simplicity: there is no need to numerically homogenize the composite components. What is more, the estimates are given by the smooth analytical functions of the component material properties, while there is no need to identify any additional parameters. Such functions are convenient for example for optimization problems.In the present paper, the method was validated for isotropic short-fiber reinforced hybrid composites in the elastic range of response. However, it is possible to extend the approach to anisotropic materials. In that case instead of a scalar volume fraction parameter Finally, it should be pointed out that the proposed approach does not take into account some of the conditions that affect the effective properties of hybrid composites. For example, the influence of the reinforcing particle size is here disregarded, as well as the (surface) varying properties of interphases.


Aiming at the problems of the poor recognition effect and low recognition rate of the existing methods in the process of belt deviation detection, this paper proposes a real-time belt deviation detection method. Firstly, ResNet18 combined with the attention mechanism module is used as a feature extraction network to enhance the features in the belt edge region and suppress the features in other regions. Then, the extracted features are used to predict the approximate locations of the belt edges using a classifier based on the contextual information on the fully connected layer. Next, the improved gradient equation is used as a structural loss in the model training stage to make the model prediction value closer to the target value. Then, the authors of this paper use the least squares method to fit the set of detected belt edge line points to obtain the accurate belt edge straight line. Finally, the deviation threshold is set according to the requirements of the safety production code, and the fitting results are compared with the threshold to achieve the belt deviation detection. Comparisons are made with four other methods: ultrafast structure-aware deep lane detection, end-to-end wireframe parsing, LSD, and the Hough transform. The results show that the proposed method is the fastest at 41 frames/sec; the accuracy is improved by 0.4%, 13.9%, 45.9%, and 78.8% compared to the other four methods; and the F1-score index is improved by 0.3%, 10.2%, 32.6%, and 72%, respectively, which meets the requirements of practical engineering applications. The proposed method can be used for intelligent monitoring and control in coal mines, logistics and transport industries, and other scenarios requiring belt transport. Under intelligent work safety development, intelligent and safe production in coal mines is becoming increasingly important ,2. Belt At the present stage, there are mainly two types of detection methods, such as contact (sensor data-assisted method) and non-contact (image processing-based method), for the belt deviation detection problem. The contact belt deviation detection method is to install the sensor around the belt facility, trigger the belt deviation signal by detecting the abnormal deviation of the belt, feedback the signal to the terminal, and then complete the belt deviation detection. Fu et al.  proposedAn image processing-based belt deviation detection method is mainly based on image features and deep learning means to detect the belt deviation behavior. Bi et al. recognized the belt edge by Canny edge detection based on video images and judged the running status of the belt by comparing the edge line with the threshold line to accomplish the detection task ,8,9. LiuA representative of the edge connection-based line detection algorithms is Hough line detection. Duda et al.  proposedLine detection methods based on image gradient methods detect straight lines in an image with the gradient features of pixels. Von Gioi et al.  proposedDeep learning-based line feature detection methods have been widely used in wireframe detection, semantic line detection, and lane line detection, which are the main line feature detection methods nowadays. Zhou et al.  proposed(1)Initial belt edge line position estimation: This method utilizes contextual information and belt edge features to estimate the position of the belt edge line. This estimation is achieved by dividing the image from the line anchor  within t(2)Constraint using the first-order difference method: This method employs a first-order difference approach to constrain the belt edge features, ensuring a fast and accurate belt edge line determination.(3)This method involves constructing an industrial belt deviation detection dataset with multiple scenarios and angles from the collected field monitoring data.(4)In abnormal situations, this paper still shows a more accurate detection effect, such as in the case of the belt area shelter and excessive dust.(5)Advantages over conventional algorithms: Compared to traditional straight line detection algorithms, the proposed method excels in extracting belt edge straight lines with high accuracy and speed, avoiding false detection and missed detection. Advantages over sensor-based methods: In comparison to sensor-based belt deviation detection methods, RBDNet offers lower environmental adaptability requirements, reduced cost and maintenance, and improved detection accuracy. It performs better in harsh and complex environments, such as downhole scenarios.(6)Improvements over existing image processing-based methods: This method addresses the limitations of time-consuming detection and low detection accuracy that commonly exist in current image processing-based belt deviation detection methods. The visualization of the belt edge lines and threshold lines in the detection results enhances the recognition and effectively solves the issues of slow detection speed and low accuracy seen in previous methods.In general, the above methods have made some degree of progress in the field of belt deviation detection methods and line feature extraction. However, they cannot satisfy the universality of the scene of the application field, nor can they guarantee the detection accuracy with a real-time detection speed at the same time. This paper proposes a real-time belt deviation detection method based on depth edge features and gradient constraints (RBDNet). We summarize our contributions as follows:Overall, the proposed RBDNet method provides a real-time belt deviation detection solution that combines depth edge features and gradient constraints, offering higher accuracy, a faster detection speed, and improved visual representation compared to the existing approaches.The proposed method utilizes the residual network (ResNet) as the backbone network model. It focuses on retrieving edge features that are specifically related to the straight lines along both sides of the belt. By doing so, the model is optimized for speed and efficiency, leading to an improved inference speed in belt deviation detection. Once the edge features are obtained, the algorithm employs least squares linear fitting to accurately estimate the belt edge straight lines. These lines are then compared with a predefined deviation threshold to determine whether there is any belt deviation. The residual network (ResNet)  has a deThe method described in this paper utilizes a convolutional neural network (CNN) with four key modules: the input–output layer, convolutional layer, pooling layer, and fully connected layer. Here is an overview of the method’s architecture: (1) Input–Output Layer: The belt surveillance video images are standardized through the data input layer to ensure consistent formatting. (2) Convolutional Layer: The standardized data are fed into the convolutional layer for feature extraction. This layer applies convolutional operations to capture the relevant features from the input data. (3) Pooling Layer: The output results from the convolutional layer are standardized and then passed through the pooling layer using the rectified linear unit (ReLU) activation function. The average pooling (MaxPool) and maximum pooling (AvgPool) operations are performed on the extracted features to enhance their information. (4) Fully Connected Layer: The image features obtained are organized in a distributed manner in the fully connected layer. The learned distributed feature representation is mapped to the sample’s marker space. The cost calculation of the features is conducted to accurately detect the exact location of the belt edges. The detection results are visualized and displayed through the output layer. In summary, this method employs a CNN architecture with standardized inputs, feature extraction through convolutional and pooling layers, distribution-based organization of the features in the fully connected layer, and precise edge detection through cost calculation. The detection results are then presented via the output layer.The method described in this paper enhances the performance of focusing on belt edge feature information and suppressing unnecessary features in scenarios such as coal transport belts where factors such as lighting locations and dust can affect the lighting conditions. It achieves this by designing and applying a transformer mechanism in the mod module ,32.F is passed through the parallel MaxPool and AvgPool layers, changing the feature size from C × H × W to C × 1 × 1, where C is the number of image channels, H is the image height, and W is the image width. The shared MLP module first compresses the number of feature channels to 1/r (r is the reduction rate) times the original number of channels and then reduces it to the original number of channels. The MaxPool and AvgPool layers are activated by the ReLU activation function to obtain the results. The two output results are summed element by element, and then the output result of the channel attention cM is obtained by the sigmoid activation function. cM is then multiplied by the element with the corresponding input features and restored to the dimension of C × H × W. The new belt feature, c(F)M, after the channel attention mechanism operation, is shown in Equation (1) below.The input belt feature c(F)M is passed through the MaxPool and AvgPool operations to obtain the corresponding two 1 × H × W belt features. The belt features of the two different operations are concatenated by the Concat (channel concatenation) operation, and the belt features are dimensionally reduced by the 7 × 7 convolution to transform the concatenated features into belt features with one channel. The new features sM are then obtained by sigmoid activation. Finally, sM is multiplied with the corresponding input features by the element to recover the C × H × W dimension. The final belt feature s(F)M after the spatial attention mechanism operation is shown in Equation (2).c(F)M and s(F)M after the channel attention and spatial attention processing are arranged serially to obtain the final feature descriptions as input to the fully connected layer.The final features In this paper, the belt edge line position is predicted accurately from top to bottom in different scenes and viewpoints. The approach for position prediction depends on the availability of the belt edge features. In scenes where the belt edge features are complete, the prediction is carried out using these features. These features provide sufficient information about the belt edge position, allowing accurate prediction. In scenes where there are belt edge features that are partially missing or obscured, global features are used for position prediction. Global features capture the overall information about the scene and do not rely solely on the belt edge. This helps to predict the position even when some belt edge features are unavailable or obscured. By utilizing both the belt edge features and global features, the position prediction method adapts to different scenarios and ensures accurate predictions regardless of the completeness of the belt edge information in the scene.The belt edge location prediction requires a line anchor for the area of the image where the belt is located. The anchors are selected from the main area of the image where the belt is located, i.e., the area where the belt edge features are relatively prominent, up to 70% of the image height. Scientific and reasonable row anchor delineation can help to predict the belt edge location more accurately, reduce the number of computational parameters, and reduce model complexity. The row anchor delineation in different scene images varies according to the position of the belt in the image, as shown in i,j:P is a w + 1 dimensional vector, indicating the probability of the ith belt edge line, on the jth row anchor, on the w + 1st grid cell, and then its calculation formula is as follows: C is the maximum number of belt edge lines, h is the number of row anchors, X is the global feature after pooling, and w is the number of gridded cells. ijf is used to select the classifier on the ith belt edge line, on the jth row anchor, for predicting where the belt edge line might be located. To improve the probabilistic prediction accuracy, this paper uses cross-entropy loss CEL in w + 1 dimensions for the loss of the belt edge lines. Assuming that i,jM is the label of the correct position with the highest probability, the prediction accuracy of the edge position clsL can be obtained by combining i,j:P with Formula (4) asTo improve the operating efficiency, after the row anchor division is completed, it is necessary to grid each row anchor into multiple cells where the edge position prediction is performed. Assuming that the grid point is the probability of the belt, As the probability of the belt edge position is predicted according to continuous linear features, the belt edge feature disappears in the presence of occlusion, and no direct position prediction can be made. Other methods result in false detections or false deviation warnings in this case. In this paper, masking is divided into two cases: one belt edge is masked (one-sided masking), and both belt edges are masked .i-P,j:1 can be obtained asl is the belt width obtained in advance in the video image when unmasked.Single-sided masking: First, the position of the unmasked edge on the other side is calculated by Equation (3) and combined with the continuity characteristics of the belt edge on the adjacent row anchor. Then, the probability of the belt edge position on the masked side iP,1j:1, the probability of a belt edge obtained by belt edge prediction within a grid point at the distal point location is iP,2j:2. To determine the belt edge location within the occlusion region, the contextual information of the belt edge needs to be known in advance. The maximum of iP,1j:1 and iP,2j:2 is taken as the most likely belt edge location at the endpoints Loc1 and Loc2:Bilateral masking: When both sides are masked, the positions of the two belt edges on the currently masked row anchors cannot be obtained and need to be predicted by the continuity characteristics of the belt edges on the adjacent row anchors. Assuming that the probability of a belt edge obtained by belt edge prediction within a grid point at the location of one edge at the proximal breakpoint is Loc1 and Loc2. By utilizing the belt edge continuity and the probability distribution of known locations, the probability of the belt edge points’ location in the occluded region can be reduced. The final prediction accounts for belt edge continuity in the line anchor and the geometry constraint of the belt width.Belt position prediction in the occlusion scenario is achieved by considering contextual information and using global features. The candidate points for the belt edge in the masked region are distributed near the line connecting This paper utilizes two loss functions to determine the mixed position relationship of the belt edge line points. The contextual information of the global features is employed in calculating both the local similarity loss and the belt edge shape loss. These loss calculations help constrain the belt edges and determine their positions. Subsequently, a feature aggregation method is applied to generate a set of candidate points for the belt edge.L1 parametrization of both. The similarity loss is defined asL1 parametrization.Similarity loss is mainly determined by a combination of continuity and similarity. The belt edge features are calculated within the row anchor region, which is continuous, thus guaranteeing the continuity condition for the belt edge feature continuity loss calculation. The similarity of the edge features is guaranteed because the similar row anchor area is divided by the entire belt, which has typical linear characteristics. The belt position probability obtained by using the feature variation, combined with the adjacent row anchor’s predicted belt edge probability, enables the similarity loss cost calculation by calculating the The belt edge line can be approximated as a straight line, so the consistency of the first-order difference equation can be used as a constraint on the shape of the belt edge line. When the shape is linear, the result of the first-order difference equation for the belt edge feature should be constant, i.e., the slope of the line at the edge remains constant, whereas if the difference equation is not constant, the feature is not consistent with the nature of the belt edge and can be discarded. In this paper, the belt edge feature is determined using a first-order difference equation, and all the functions within the equation should satisfy the condition of being differentiable, so the probabilities of different location image features are obtained using the differentiable softmax function, i.e., the predicted expectation as an approximation of the location feature, as shown in Equation (8):i,j,kProb denotes the probability of the belt edge being the location of falling on the ith belt edge line, the jth row anchor, and the kth unitized grid. The expectation of a discrete random variable from a probability distribution is used to determine the maximum expectation, i.e., the exact position of the belt edge line. In summary, the shape loss is defined asThe expectation of the location of the belt edge can be expressed astotalL ofUltimately, the combination of the belt edge position prediction, similarity loss, and shape loss cost calculation gives a final loss Based on the above constraints, the belt edge locations are determined in conjunction with the belt edge location predictions in f and its pixel values at N different belt edge candidates , , ),…, is given.A function a1,a2,a3n…,a of the unknown parameter set to derive the formula for the deviation ir of candidate point i:Determine the n-term coefficients N should be greater than the number of parameters n to reduce the influence of invariant errors in the input data. Assuming that the constant variance in the vertical coordinate iy of the candidate pixels satisfies a normal distribution, the Gaussian fitting principle or the least squares method is applicable according to probability theory. With minimum deviation, the following equations can be determined for the solution of each coefficient:The number of candidate points y = ax + b, and the fitting Formula (14) is as follows:In this paper, we choose to fit the belt edge points by the least squares fitting method, assuming that the equation of the belt edge line is The set of the identified belt edge candidate points is arranged in the direction of the belt edge line and the straight line fit is performed to the set of points to generate the belt edge line to be detected. Before performing the straight line fit, the deviation between the actual and predicted values needs to be estimated based on the pixel positions, and then a suitable fitting method needs to be determined, as follows:SD is the maximum belt offset in the image, STD is the actual maximum belt offset, BW is the actual width of the belt, xLPix is the pixel x-coordinate of the left edge of the belt in the image, and xLPix is the pixel x-coordinate of the right edge of the belt in the image. From this, the maximum offset of the belt in the image can be derived. The belt deviation threshold line is based on the pixel x-coordinate of the belt edge line plus (minus) the maximum offset when the belt is in normal operation (and in the middle of the carrier rollers), which is the pixel x-coordinate of the belt deviation threshold line. Based on the point-slope equation for a straight line, the belt deviation threshold line is obtained using the top left and bottom left, and the top right and bottom right points of the belt in the image are a basis. The left belt edge line Equation (16) shows thatthLy,thLy) is the set of points of the left edge line,  are the pixel coordinates of the upper left point of the belt, and  are the pixel coordinates of the lower left point of the belt.When the belt conveyor is in normal operation, the belt is in a closed loop, the upper and lower belts run at constant speed, and the center lines run parallel to each other. The offset in the belt width direction is to be kept within the specified limits. In accordance with the safety standards for belt machines, a belt with a deflection of more than 5% of the belt width is considered to have deviation. In accordance with the above conditions, the deviation threshold line is defined in this paper by the following equation:thRy, thRy) is the set of points of the left edge line,  are the upper right point pixel coordinates of the belt, and  are the lower right point pixel coordinates of the belt.The right belt edge line Equation (17) shows thatThe algorithm in this paper was first compared with ultrafast structure-aware deep lane detection (UFSLD) , L-CNN , LSD 1818, and tIn this paper, the model was trained by combining a self-labeled dataset with the TuSimple dataset. Due to the relatively small size of the experimental dataset compared to the Tucson dataset and the less diverse scene data, a specific dataset suitable for mining belts was created. This dataset underwent data augmentation techniques, including flipping, rotation, random color adjustments, contrast enhancement, and brightness adjustment. These techniques were applied to overcome adverse conditions such as varying lighting and to adapt the model to the complex environments encountered in mining areas.Mining belt conveyors are typically long, requiring monitoring of multiple sections to assess their real-time operational status. To acquire on-site data, the video data from cameras positioned at different angles were used as a reference. The monitoring videos were then processed frame by frame, and the extracted belt images were manually annotated using “LabelMe” software to create labeled belt edge lines. The real images and the corresponding labeled data and binary images with labels were compiled into a cohesive dataset. Finally, the data augmentation techniques were applied to further enhance the dataset. The model in this paper was trained using the Adam  optimizeThe experiments were conducted using three different backbone networks: ResNet18, ResNet34, and ResNet50. Real-time video streams were used for these experiments, and the performance of each backbone network was evaluated in the detecting surveillance videos. The inference time of each network model was measured, and the evaluation was based on the processing results of one minute of stable operation. The accuracy and F1-measure of the network models using different backbone networks were calculated. The results of these calculations are presented in Based on the information provided in the table, it appears that ResNet18 met the requirement for real-time processing as its inference speed was satisfactory. Additionally, ResNet18 demonstrated a comparable accuracy rate to ResNet34 and ResNet50. However, the inference speeds of ResNet34 and ResNet50 were relatively slower, which may result in blockages in real-time monitoring video streams. Consequently, ResNet18 was selected as the backbone network for practical application.The effectiveness of RBDNet was verified through three sets of ablation experiments. The results of the quantitative analysis can be found in Based on the observations in clipC is the number of correctly predicted belt edge points and clipS is the total number of actual location belt edge points in each image. The cross union (IoU) between the true and predicted belt edge location values was then calculated. Predictions with an IoU greater than 0.5 were considered to be true positives. The evaluation index F1-measure was calculated as follows:The accuracy, F1-measure, and inference time of the different algorithms were evaluated for accuracy and speed detection. The accuracy was calculated as follows:According to the information provided in RBDNet utilized belt edge position prediction based on the feature belt edge position to swiftly locate the belt edge position. The belt edge attention mechanism ensures accurate belt edge extraction. Including the first-order difference constraint reduced the program time consumption, ultimately improving the detection speed while maintaining detection accuracy. Consequently, the detection speed of RBDNet reached 41/s.The algorithm accuracy indices and the UFSLD and L-CNN methods in this paper are not much different from those of RBDNet, but they do not represent their practical application effects. Therefore, the proposed RBDNet was visualized and compared with UFSLD and L-CNN and the other line feature detection methods in different scenarios, and the detection results were then analyzed to verify the realistic performance of the different methods. The final detection results are shown in From the description of the experimental results in In contrast, the L-CNN algorithm performed well in various scenarios except for coal mines. In the coal mine scenarios, L-CNN struggled to discriminate straight lines due to the complex environment, lack of light, dust, and other unusual factors. The method relied on identifying straight line segment endpoints, which were difficult to determine accurately in coal mines. While the extraction effect was better for other facilities within the scene, the detection performance for the belt edge line was not satisfactory in terms of accuracy and practical requirements.These observations highlight the limitations and challenges faced by UFSLD and L-CNN in detecting belt edge lines in coal mine scenarios, indicating the need for alternative methods, such as the proposed RBDNet, to address these issues effectively.In application scenarios such as coal transport belts, there is inevitably the influence of factors such as dust and large foreign objects obscuring the belt edge, resulting in weakened belt edge information. In addition, staff may work in the vicinity of the coal transport belt, and shadows caused by light can lead to reduced or even indistinguishable contrast at the belt edges in this area. Therefore, in this paper, the detection effect under shading conditions was verified for possible shading and dust phenomena in the belt operation. The UFSLD algorithm in In this paper, belt edge line detection in the scenarios with area occlusion and heavy dust is discussed. In the case of area occlusion, the detection result was slightly affected, resulting in a deviation in the belt edge line from the actual position. However, by utilizing contextual information, a priori knowledge obtained during training, and unobscured edge lines, the algorithm can generate belt edge lines by constraining the features of the remaining belt edge lines. This helps to mitigate the impact of area occlusion on the overall detection performance.Regarding heavy dust, the method proposed in the paper effectively overcame its effects on belt edge detection. Dust did not significantly impair the detection results.The deviations in the belt edge line were primarily attributed to the prediction of the edge information in the single-sided and double-sided masking regions based on the contextual and location information. The deviation occurred due to candidate point displacement and subsequently affected the fitted belt edge line. The double-sided masking area generally exhibited slightly larger deviations compared to the single-sided masking area.In summary, the proposed method addresses the challenges posed by area occlusion and heavy dust in belt edge detection, providing more accurate results despite slight deviations in the edge line under certain conditions.(1)Lighter ModelFirst, this paper provides a further analysis and comparisons to evaluate the effectiveness of the RBDNet method. The key findings are described as follows:The experiments conclude that using ResNet18 as the backbone network results in a slightly lower accuracy compared to ResNet50 but with a significantly faster processing speed. This tradeoff is suitable for belt deviation detection scenarios that have stricter requirements in both accuracy and speed. The video stream detection speed is increased by 2 fps, 14 fps, 32 fps, and 35 fps compared to the other algorithms.(2)Improved AccuracyCompared to the other algorithms such as UFSLD, L-CNN, LSD, and Hough transform, the RBDNet method demonstrates a higher accuracy in belt edge line detection. This paper reports an improvement of 0.4%, 15.9%, 45%, and 78.8% in belt edge line detection accuracy compared to these algorithms. Similarly, the F1-measure also improve by 0.3%, 9.9%, 32.6%, and 72%, respectively. Verification using video stream data from coal mine conveyor belt operations confirms the requirements in terms of accuracy and speed.(3)Scene AdaptabilityThe RBDNet method exhibits better adaptability to various scene conditions compared to other algorithms. It can handle poor lighting conditions, dust, and occlusion by foreign objects. Poor illumination and dust minimally impact the detection results, while regional occlusion may slightly affect the performance. The algorithm can extract belt edges effectively throughout different times of the day, overcoming variations in illumination. The experiments with area masking also show positive results without compromising speed or accuracy. In contrast, algorithms such as UFSLD are less effective in detecting belt edges under abnormal conditions, further validating the superiority of the proposed algorithm and its improvement strategy.These findings highlight the advantages of the RBDNet method, including its balance between accuracy and speed, superior performance compared to other algorithms, and robustness in handling adverse conditions.(1)In the different sizes of the ResNet network models, ResNet18 guarantees the detection accuracy under the premise of improving the detection speed. The detection reaches 41 frames/s, and the detection accuracy is 96.21 percent.(2)The belt edge position constraints based on the feature classification, edge attention mechanism with first-order differential loss can effectively improve the accuracy of detection, and the accuracy rate can reach 96.21 percent.(3)Compared with UFSLD, L-CNN, LSD, and the Hough transform, the accuracy of the proposed REDNet is improved by 0.4%, 13.9%, 45.9%, and 78.8%, and the F1 scoring index is improved by 0.3%, 10.2%, 32.6%, and 72%, respectively, and the accuracy, precision, and speed of RBDNet are optimal.(4)The proposed RBDNet is well adapted to scenarios such as insufficient light, occlusion of the belt area, and excessive dust in the detection area, and accurate detection results can be obtained.Aiming at the existing belt deviation methods that cannot be practically applied in industry, this paper proposes a real-time belt deviation detection method based on the depth edge feature and gradient constraint (REDNet). The feature extraction is carried out with ResNet18 as the backbone network, the global feature analysis is carried out through the softmax classifier in the fully connected layer, the prediction of the model is achieved by using the first-order difference constrained belt edge, the accurate belt edge straight line is obtained by linear fitting through least squares and compared with the threshold value, and the real-time runaway detection of the belt is realised. Based on the monitoring video actually collected on site, the industrial belt deviation detection dataset was established. By comparing and analyzing the results of various experiments, the following conclusions are drawn:The proposed method has been practically applied in REDNet with good results. In the future, we will build a more lightweight model to achieve edge computing at the camera end near the belt to reduce the requirement of hardware performance and improve the applicability of the model.


The problems of flexible planning of the design of logistics systems for the collection of food products such as raw milk can result in a decrease in the performance of critical indicators for their performance. This paper proposes a new efficient methodology for robustly designing a first-mile logistics system for storing and refrigerating milk as a perishable product considering decisions related to open facilities and the flow of products, including sustainability indices. The proposed approach is modeled as a bi-objective problem by considering the minimization of greenhouse gas emissions (CO2) produced by milk transportation canteens and the maximization of the system configuration's net present value (NPV). We have analyzed and determined the most robust configuration for the first time and explained the robustness-NPV and robustness-CO2 relationships. The proposed mathematical model is solved by the Epsilon constraints method, and the robustness is calculated considering an extension of the FePIA methodology for multiobjective problems. A novel contribution is a balance in the possible future values generated by the company related to its cash flows and the generation of CO2 emissions when using a motorized transport frequently used in the shipment of raw milk considering a new important aspect such as the volume of product transported and the slope of the path between the production farm and the storage cooling tanks. StudiesIn 2021, the value of the dairy market worldwide was estimated to be about 871 billion U.S. dollars, projected to grow to 1,128 billion dollars by 2026 . Milk pThe design of a production system is recognized as a critical factor in achieving competitive advantages since its management allows the systematic integration of innovation processes and the strengthening of business strategy ,13). If . If 13])One more challenge is achieving a logistics system's sustainability . Among robust solution to a problem as an immune strategy to manage the uncertainty of the data. Besides )Likewise, studies have analyzed two objective functions for the design of sustainable logistics systems . LogistIn order to balance economic issues with environmental and social disturbances in the supply chain network design, the idea of a resilient and sustainable supply chain network design offers a viable solution. In order to allocate raw materials or finished goods to suppliers, manufacturers, distributors, and retailers, a supply chain network must be strategically and tactically designed. One proposal of this work is to present a systematic and bibliometric overview of the idea and term "supply chain network design." We consider 155 papers from 2010 to 2022 assessed and categorized using the VosViewer software. Research objectives, keywords, highly referenced papers, productive journals, and attributes considered for each sustainability factor were analyzed. The visualization of bibliometric literature reviews is performed using VosViewer. Future academic and professional work on supply chain network design will benefit from the findings of this study.Several authors have recently examined real-world applications of sustainable, reliable supply chain design. The design of a sustainable lead-acid battery supply chain network is covered by Ghalandari et al. . A two-sAlshurideh et al.  investigRecently, multi-objective sustainable supply chain design problems have been studied by Refs. ,108. AliThere is a need to develop generic models to solve real problems related to the design of logistics systems, generating value for all those involved and emitting fewer greenhouse gases from used vehicles for transportation. This aspect is the main objective of the present work, where a generic model is intended to inform decision-makers who manage these logistics systems and who can participate in tenders to acquire funds that make their businesses more competitive. The flexible model can be extended to logistics systems with similar characteristics.3The development of this research extends the methodology described by Ref.  for the 3.1This section describes the base problem for formulating the proposed robust design of a sustainable raw milk collection system. The problem seeks to decide strategic (open tanks for producer-associated) and tactical decisions (flow and inventory of products) related to the supply chain design of raw milk. The network considers several periods, a single product, and a network of farmer producers. The milk supply chain involves different farmers and raw milk collection tanks, which could be located in the same locations as the producers to facilitate handling and maintenance. Thus, the system network consists of a single type of node. Any producer whose property does not have a cooling tank must transport the milk to an assigned tank in two modes: a motorcycle with a wheelbarrow for transporting canteens or on foot. As there are producers associated with tanks, these groups are known as a "cluster" in this work.2 emissions from motorcycles. Each node was assigned a number to label each producer, and the coordinates were collected in situ using a global positioning system (GPS) for the case study. Additionally, the use of slopes for transporting raw milk on motorcycles was taken into account in such a way that the work carried out by the engine is considered for calculating CO2 emissions.The proposed model contains two types of binary variables. One variable determines whether a cluster is created, while the other specifies whether a producer belongs to a created cluster, including whether the cooling tank is installed on their property. The model seeks to maximize the Net Present Value (NPV) of all money flows in various periods and minimize CO3.23.2.1•A single product is considered.•The model considers the flow of the only product in the network forward, considering strategic and tactical decisions.•Cooling tank storage capacity constraints are considered. It is assumed that a cooling tank could be located in any producer location.•Tanks have a limited capacity.•There are multiple periods for making decisions.•The locations of the farmer producers are specified.•All milk supply from suppliers must be transported to some tank.•Producers can only be linked to a single cluster.•Scarcity is not allowed.•All costs considered are deterministic and known a priori.The proposed model considers the following assumptions:The problem is of great interest because the location of a specific tank implies the opening of facilities. This situation forces dairy companies to seek design or redesign strategies for their logistics systems based on optimization tools to maintain high competitiveness and seek sustainable development. In this paper, the model considers the number of cooling tanks to locate, their capacity, and the location, which raises the following questions: How many tanks should be used? Where is it convenient to open the tanks? Is an expansion (open more tanks) or contraction (remove tanks) convenient? Is it possible to find an optimal configuration of the milk collection logistics system considering the robustness of changes in raw milk supply and its selling prices?The following indices, parameters, and variables were defined to solve the problem:3.2.23.2.33.2.4VariablesCO2: Total emissions (kilogram/km)VPN: Net Present Value (COP)Binary Variables3.2.5We proposed a multiobjective model considering the variability and relationship between economic and environmental aspects .Net profit (5) is the result of the difference between gross profit and taxes:Constraints (6)–(7) show operating and gross profits calculation. Equations Equation We have considered the sales costs associated with the inventories of concentrate for the animals and fertilizer for pastures, employee salaries, financial obligations and the cost of transportation used to transport the milk to the enabled cluster, the refrigeration costs of stored milk, and depreciation costs (12).Equations Equation Constraints (18) allow controlling the location of tanks with smaller capacity with the offer generated by each producer belonging to each cluster. In particular, the offer in each cluster is sought less than the enabled tanks' capacity.Equation Constraints (20) indicate the cluster to which each producer Constraints (21) indicate that open clusters could have only one tank. Constraints (22) ensure the epsilon constraint approach for objective function (3).3.3The main objective of this research is to design a model for the sustainable evaluation of a raw milk collection system. This methodology can be defined as a series of steps that provide a way to measure the robustness of any system considering its system resources, operational characteristics, and the effects of previously defined disturbance parameters.i.Definition of the robustness requirements system.ii.Definition of the system's operating characteristics regarding the system robustness requirements and tolerances.iii.Determination of the disturbance parameters.iv.Determination of the effect of the disturbance parameters upon the different operating characteristics.v.Determination of the effect of disturbance parameters upon the different requirements of disturbance of the system.FePIA methodology  to analyze the robustness of a system was proposed by Ref. . The proThe FePIA methodology selects the robustness requirement  where each one has a defined offer by the annual milk production  must be analyzed through experimentation and intentionally controlled variation of the disturbance parameters (Π). Finally, the effect of the intentional controlled variation of the disturbance parameters on the established robustness requirement  and (30) to determine the minimum value of 2 emissions from transporting raw milk, supported by Equation 2 emissions. Equation Another robustness requirement for the system is the system's CO3.3.3The performance characteristics must have a limited variation to meet the robustness requirements described above. Three performance characteristics were considered for the model described above: 1. Installed Milk Collection Capacity (lts/year), 2. Cost of energy for cooling tanks (COP/year), and 3. Utilization of storage capacity of cooling tanks. Equation Equation Equation 2 relationship. In addition, the methods to use the tanks for the four scenarios concerning the different values of π are established. Compared to the evaluation stage of the impact of We defined a final stage considering a tactical plan for using the installed tanks for the best-established configuration by the robustness-NPV and robustness-COConstraints (19) are deleted because the use of minimum tank capacity is no longer tactically needed. During periods of low milk production, certain tanks would not be used or would only be filled to a small percentage of their actual capacity.According to the previous methodology, we present a general scheme for measuring raw milk collection system robustness :Fig. 1Fe4Step 1The disturbance parameters Introduced a new known parameter 2)Constraints (19) are removed because the minimum tank capacity is no longer tactically necessary. During periods of low milk production, certain tanks would not be used or would only be filled to a small percentage of their actual capacity.3)Constraints (12) are updated by Constraints (38) since Constraints (37–38) have been added to the optimization model forcing it to adopt each configuration selected from the previous step. Subsequently, for each configuration, the disturbance parameters  also increase. Each is analyzed for each scenario proposed to determine the most robust configuration. The results show that the system's performance varies depending on the analyzed robustness requirement  to the most optimistic . 4.4.1The analysis of this robustness requirement shows that for the different scenarios analyzed, the total profit per product in one year varies from COP 17,453,166 , the distance traveled increases as the scenarios are analyzed to increase the amount of produced milk. Configuration F has the shortest distance traveled by partners in manual raw milk transport (or transport on foot) in scenario All configurations were analyzed to increase the distance traveled to transport raw milk canteens. As the weight of canteens full of raw milk increases, the logistics system does not allow motorcycles to be used to reduce CO4.4.5The general average of distances traveled in the transport of milk is lower in configuration E. The results can be observed in Three performance characteristics have been considered for the proposed model, each of which is a global performance indicator for the company. The milk collection and refrigeration tank's installed capacity  is selected since it has all of the different cash flows in a more extended review period than one year. The results for all configurations in all scenarios analyzed (Π) are shown in The results of the analysis of the performance characteristics of system (Φ) are inconclusive since it is contrary to the result of the robustness requirements (Φ): configuration E has the worst results in the selected performance characteristics. This situation occurs because as a configuration that reduces COAs the supply of raw milk increases, the NVP of configuration E improves. This situation is due to the absorption of costs to use resources such as transport modes for milk canteens, use of the infrastructure with a lower depreciation cost, and lower payment of interest on loans for the purchase of infrastructure. In the scenarios 4.6This work proposed a novel efficient approach to the robust design of sustainable logistics systems for collecting and processing raw milk. The obtained results show the efficiency of making decisions related to strategic decisions, such as the location of facilities (cooling tanks) and assignment of producers to each facility, and tactical decisions, such as the flow of products between nodes (distribution flows). Besides, the paper covers a significant gap related to the analysis of several objectives considering a multiobjective scheme for a sustainable logistics system for collecting and processing raw milk based on environmental and economic aspects. Indeed, the performance of the sustainable logistics system should be based on financial, environmental, and social aspects generating a realistic analysis to support decision-making.Note that considering the vehicles' load and the road's slope confirm the improvement of the social aspects related to human effort. These aspects highlight a broader social and environmental point of view rather than just considering the economic issues of primary raw milk production. In addition, the results show the collaborative framework's efficiency for decision-making, improving the Sustainable Development Goals (SDG). The need to reduce carbon emissions in agricultural systems has increasingly shown the logistics system's configuration in the spotlight as an effective measure for this problem. In this way, the location of raw milk collection tanks has attracted attention to the sustainable management of these systems. In addition, this location is expected to address the management problem for the long term, as it is a robust configuration. However, the relevant literature shows that researchers have focused more on the robust optimization problem than on integrating robustness metrics in configuring sustainable logistics systems. Additionally, agro-industrial systems that sell products in their first mile have yet to calculate carbon emissions as a corporate strategy.There must be more than this approach to guarantee carbon reduction throughout the dairy supply chain, as carbon reduction policies must be directly involved with methodology development. Since locating cooling tanks for milk storage is not easy and there is a need to involve additional components in the logistics network, such as the distances traveled by producers, the design faces a more severe uncertainty and consequently a higher cost and increased risk of variation of the supply. Therefore, it is necessary to provide a more comprehensive approach to logistics network design, considering the uncertainty of raw milk supply as a determining factor in a robust way. The interaction between the producers' offer, different used modes of transportation, the capacity of the raw milk collection tanks, and performed investment in its acquisition and maintenance versus the economic risk and generated emissions should be examined. For this logistics system, both dimensions affect the configuration and the network's economic, social, and environmental performance.Despite the importance of the subject, there needs to be more exhaustive research on first-mile agro-industrial logistics systems integrating all studied characteristics for an appropriate methodology. This paper addresses this research gap by developing a bi-objective MILP model and its solution approach using the FePIA procedure as a robustness metric. The results show that the design of the logistics network, when changing the milk supply, strongly affects the configuration of the network. This effect can be seen in open clusters using different transport modes and storage capacities. The impact on the network configuration directly affects the robustness requirements  interrelated with its robust design.The numerical experiments showed that the implemented methodology serves to select a robust logistic system despite the change in the disturbing parameters of "normal" conditions. Despite changes in disturbing parameters for system performance, decision-makers can use the methodology to choose a system configuration adequate to manage disturbances. Furthermore, this study sheds light on how to manage first-mile logistics networks for perishable products.5This work has been motivated by the need for small dairy producers to generate strategies to guarantee the quality of the product from the beginning of the chain, meeting the requirements of the final customer demanded by dairy company processors. This work demonstrated the possibility of evaluating the robustness of a raw milk collection chain by using the FePIA methodology through a multi-objective analysis based on social, environmental, and economic aspects. Considering the effects on strategic and tactical decisions, farmers must compel those small producers to stay in the market to sell raw milk.This research is limited and can be expanded in several ways. In this research, the attention was focused on the transportation and distribution of raw milk in small companies. At the same time, other perishable products can be addressed by modifying the optimization model and the robust design methodology of the proposed logistics system. The calculation of emissions from fuel use has been developed from a mathematical model that can be applied to other scenarios, different from the use of motorcycles for transporting perishable products. A limitation of the study is that the parameters of the raw milk collection of a supply chain may be uncertain. Therefore, these values can be considered for the future development of the model. Besides, Euclidean distance was used to calculate the distance between raw milk producers and tanks. Given the closeness between producers, this value is a good approach. However, the distance must be calculated with greater precision for logistics network designs at interregional scales.2 emissions from transporting milk through motorcycles. Furthermore, it is essential to note that the solutions obtained by the present approach indicate that the model can provide Pareto curves to assess trade-offs between economic and environmental objectives. The decisions of location (strategic), use of transportation modes , use of cooling tank capacities , and distribution  guarantee a better performance of the global system.The results show that the performance of the sustainable logistics system, based on financial, environmental, and social aspects, provides a more realistic analysis to support decision-making. From this analysis, it is concluded that the configuration of a sustainable logistics system for the company's formation is feasible. This conclusion is based explicitly on the high impacts of the analysis of CO2 emissions) aspects can be selected from the Pareto efficient frontier through a decision-making process based on the methodology FePIA. One of the most interesting conclusions of this study is that using more motorcycles can generate excellent fuel economy in the long term and, therefore, fewer emissions and less use of human force in transporting raw milk canteens. From the point of view of environmental impact, more motorcycles that make short paths transporting raw milk from primary producers with more excellent supply are the appropriate strategy.The multi-objective approach to this problem is appropriate since the balance between economic (NPV) and environmental (CO2 emissions. Finally, developing more efficient, robust supply methodologies is essential to obtain better financial and environmental results, guaranteeing better income in the long term. In addition, other transportation modes must be included, such as vans or small tank trucks. Future research can consider different types of uncertainty for the input parameters. Additionally, planning decisions for tactical and operational first-mile logistics systems can be approached under the sustainability paradigm by expanding the current approach. Likewise, the present work can deal with uncertainty for food supply chains. Finally, new robustness metrics can be tested to incorporate the study of the first-mile logistics system and the supply chain design.The results of this study show that dairy companies can make the best decisions for their first-mile logistics system for the storage, facility location, and refrigeration of raw milk, obtaining profitable solutions and guaranteeing good economic results, and reducing COFinally, although the proposed methodology is generic, the analysis results are limited to the time, location, and specific characteristics of the case studied and cannot be generalized to other cases. Therefore, a series of comprehensive experiments with other food product pickup systems may shed more light on the proposed methodology for the robust design of first-mile product pickup logistics systems and the results in future research. Future research must be addressed regarding the problems generating the disturbance of the supply chain and defining each possible scenario's occurrence probability. Besides, several objectives must be considered as the key performance of the supply chain, such as those proposed by Refs. . FinallyAndrés Polo Roa: Conceived and designed the experiments; Performed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.John Willmer Escobar: Conceived and designed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data.María Paula Montoya: Conceived and designed the experiments; Contributed reagents, materials, analysis tools or data; Wrote the paper.Data will be made available on request.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.


Reservoir simulations for subsurface processes play an important role in successful deployment of geoscience applications such as geothermal energy extraction and geo-storage of fluids. These simulations provide time-lapse dynamics of the coupled poromechanical processes within the reservoir and its over-, under-, and side-burden environments. For more reliable operations, it is crucial to connect these reservoir simulation results with the seismic surveys . However, despite being crucial, such integration is challenging due to the fact that the reservoir dynamics alters the seismic parameters. In this work, a coupled reservoir simulation and time-lapse seismic methodology is developed for multiphase flow operations in subsurface reservoirs. To this end, a poromechanical simulator is designed for multiphase flow and connected to a forward seismic modeller. This simulator is then used to assess a novel methodology of seismic monitoring by isolating the reservoir signal from the entire reflection response. This methodology is shown to be able to track the development of the fluid front over time, even in the presence of a highly reflective overburden with strong time-lapse variations. These results suggest that the proposed methodology can contribute to a better understanding of fluid flow in the subsurface. Ultimately, this will lead to improved monitoring of reservoirs for underground energy storage or production. Reservoir simulations allow us to accurately predict fluid flow inside a reservoir, based on a combination of geological, geophysical and borehole data5. Geophysical methods, such as seismic monitoring, are able to observe time-lapse changes of dynamic properties like pressure and fluid saturation, everywhere in a three-dimensional subsurface. Seismic monitoring relies on the fact that changes in the reservoir will translate into changes in the seismic reflection response. The fluid flow inside the reservoir can then be imaged by comparing a baseline seismic survey with a monitor survey, recorded over the same location at a later point in time9.Understanding fluid flow in subsurface reservoirs is crucial to predict underground processes related to the energy transition, such as geothermal energy10 or migration of injected 12. These types of studies rely on reservoir simulations to predict the movement of the fluids in the reservoir. Although this methodology provides accurate estimates of the time-lapse changes inside the reservoir, it does not predict geomechanical changes in the overburden. However, these changes can have large effects on the repeatability of time-lapse experiments, as overburden time-shifts might be mistaken for changes inside the reservoir13. Generally, an independent geomechanical model is used to compute the time-lapse changes in the layers above the reservoir15. Recently, multiphase poromechanical models were introduced as an all-in-one solution to link fluid flow, transport and deformation in the subsurface16. Traditionally, these models are used to predict induced seismicity due to fluid injection in the subsurface19. Additionally, poromechanical simulations can, in theory, also be used to model both time-lapse changes inside the reservoir and overburden at once for seismic monitoring applications.Feasibility studies aim to assess the seismic detectability of fluid movement inside a hydrocarbon reservoir21. This isolation is based on the 3D Marchenko equations that describe all orders of multiple scattering inside the medium24. After this Marchenko-based isolation is applied to the seismic data, the reflections related to the reservoir are clearly visible in the seismic response. Next, the primary reflection from the top of the reservoir is used as a reference event that contains all the delays of the overburden. This reference event is then combined with events originating from the reservoir’s base to retrieve time-lapse differences that are solely dependent on the changes inside the reservoir21.In addition to time-lapse overburden effects, static overburden effects can also obstruct the reservoir signal in the baseline and monitor seismic surveys, due to the presence of highly reflective layers in the overburden. Both the static and dynamic overburden effects can be accounted for by isolating the reservoir responseIn this work, a poromechanical simulator is proposed to model time-lapse changes in density and compressional velocity due to fluid injection in a subsurface reservoir. Since multiphase fluid flow as well as geomechanics are included in the formulation, the changes in the overburden and reservoir are modelled all at once. Next, the velocities and densities are computed at a number of time-steps during the simulation, which are used to model the seismic response for the seismic baseline and different monitor studies. Finally, time-lapse changes are retrieved. These changes are then independently assessed both before and after isolation of the reservoir response from the total seismic response . In the next section, we will first discuss the governing equations behind the poromechanical model, the connection with seismic parameters and the retrieval of time-lapse traveltime differences. Secondly, the methodology is tested on a simple as well as a complex model. To conclude, we discuss the results and possible future improvements and extensions to the method.This section discusses the background on how time-lapse changes can be extracted from a modelled reservoir. The constitutive equations related to poromechanics are first reviewed, then these equations are related to seismic properties, which can be used to model the seismic response at different times in the simulation. These responses are compared to one another to find seismic time-lapse traveltime differences between the different surveys.25), and conservation of mass describes flow of immiscible fluids through a reservoir (Eqs. 26). This gives the following system of equations:m, q, are the fluid mass per unit volume, density, velocity and sinks/sources, respectively. The subscripts t denotes time, 27. Moreover, the mass per unit volume of each phase is related to it’s saturation, density and the porosity  and 2 (P2) returns the timelag  is first computed for each of seismic study using Eq.  are now revealed in the reflection response. Similarly, the isolation is applied to the remaining monitor surveys as well as the baseline survey. Next, the correlations are interpolated from 4 to 1 ms via the frequency domain for improved resolution. Subsequently, the correlations between P1 and P2 are computed, which will be used to find the time differences of the reservoir layer.The evolution of the saturation is shown in the left column of Fig. P1 and P2 of the baseline and monitor surveys. Lastly, the gray lines show the results of computing the time-differences from the full medium responses (i.e. without isolation, Fig. Once again, the time-lapse traveltime differences inside the reservoir are computed according to Eq. ; the resIn the previous section it was shown that poromechanical modelling can add valuable insights to seismic reservoir monitoring, specifically because overburden changes are predicted together with fluid flow. In this section possible improvements upon both the poromechanical and the seismic part of the method are discussed.48. However, this time dramatically increases on a grid with finer discretization. One solution to this problem is to apply a preconditioner to improve convergence of the equations, allowing to still achieve high resolution simulations16. Alternatively, a multiscale approach could be used in order to limit the size of the problem, thus speeding up the simulations51.Firstly, poromechanical simulations are computationally expensive, which sets practical limitations on their use. Currently, the simulation takes around 8 h, when using 8 CPUs on the Delft High Performance Computer52. It would also be interesting to include a third fluid to the simulator, in order to account for solution and dissolution of gasses into fluid due to the pressure changes inside the reservoir.Additionally, the simulator could be improved by extending the formulations to include fractures. This is especially relevant as fractures can unexpectedly block the fluid or bypass impermeable zones. Another feature that is currently missing from the simulator is the ability to model cyclic storage, which is required to accurately monitor temporary storage of hydrogen or other gasses in the subsurface53. Ideally, a combination of both amplitude and traveltime differences is used to recover the dynamic fluid parameters from the seismic data54.In the current seismic study, only timelapse time-differences were considered. Future developments should also consider seismic amplitude variations of the signal. Recent work investigated how angle-dependent amplitude information can be retrieved with the Marchenko methodThis work developed a multiphase poromechanical simulator that is tightly coupled with a seismic survey simulator, through the update of the seismic parameters. This integrated simulator allows to instantly resolve time-lapse changes not only inside the reservoir but also in its overburden. The simulator was used to test the feasibility of a novel methodology to extract time-lapse travel time changes after Marchenko-based isolation of the reservoir response. This methodology solves the repeatability issue of time-lapse seismic surveys by identifying and utilizing a reference reflection above the reservoir. Future developments should focus on inverting the seismic time-lapse changes back to the dynamic reservoir properties, in order to close the loop between reservoir simulations and seismic monitoring.These results are a significant step to achieve higher resolution monitoring of subsurface reservoirs. A better understanding of fluid flow in these reservoirs will improve predictions of underground processes related to geothermal energy, subsurface storage of gasses like hydrogen, and sequestration of Supplementary Information.