The ether group of the PEG molecular chain and the hydroxyl group of Mg(OH)2 can be combined by a hydrogen bond, which provides a "template" for the growth of Mg(OH)2. At the same time, the difference in growth mode and morphology will also affect the economic performance of electrolytic reactions. When the PEG content reaches 0.4 g/L, the particle size of the product is uniform, which can well reduce the polarization of the electrode plate. The cell potential of electrolytic reaction is small, and the economic benefit is high. When the content of PEG is low, it has a low impact on the product and the economic benefits of electrolytic reaction. When the PEG content is higher than 0.4 g/L, the electrode reaction is hindered, resulting in an increase in cell potential.The current research focuses on the mechanism of the surfactant polyethylene glycol (PEG) in the preparation of magnesium hydroxide by electrolysis of a salt lake bischite aqueous solution. The samples were analyzed by a scanning electron microscope (SEM), X-ray diffraction (XRD), Fourier transform infrared spectrometer (FT-IR) and laser particle size analyzer. The characterization results show that PEG plays an important role in adjusting the growth mode and morphology of Mg(OH) After pthan 96% .2 by alkaline neutralization [2 are low, but this method is often very difficult to precipitate and filter, and the heterogeneity of purity and morphology often affects the application field of products.With the shortage of resources and the improvement of human awareness of ecological resources protection, relevant experts and scholars began to focus on the treatment and application of bischofite resources. These research directions mainly include the preparation of metal magnesium by molten salt electrolysis and the preparation of Mg(OH)lization ,5,6. Mollization ,8. In ad2 by electrodeposition [2 thin films on metal substrates by electrodeposition with Mg(NO3)2 solution and MgCl2 solution as raw materials, respectively, and investigated the effects of different process parameters on the electrodeposition product Mg(OH)2 [2 thin films by electrodeposition with Pt as substrate and Mg(NO3)2 as raw material and investigated the effect of deposition potential on the morphology of the films [Compared with the alkaline neutralization method, magnesium hydroxide prepared by the electrolytic method has higher purity, controllable morphology and faster sedimentation rate, which cannot be achieved by other methods . Based oposition ,11. Kama Mg(OH)2 ,13,14. Lhe films .2 is very similar to that of the alkaline-chlorination process preparation of NaOH [− produced by electrolysis combined with free Mg2+ in the solution and formed Mg(OH)2. Moreover, the cathode plate served as the substrate for the growth of Mg(OH)2 nuclei. When Mg(OH)2 crystals grow to a certain extent, the H2 produced by electrolytic reaction peels off these Mg(OH)2 from the surface of the electrode plate, resulting in the rapid settlement of the product [2 is very intense. A large number of Mg(OH)2 crystal nuclei will adhere to the surface of the plate, reducing the number of active sites on the substrate [2 but also increase the cell potential and reduce the current efficiency.The reaction principle of electrolytic preparation of Mg(OH) of NaOH ,17. Near product ,19. Afteubstrate . It will2+ and Mg2+ in the solution. Therefore, the PEG macromolecule acts as a site for the growth of magnesium hydroxide crystals, which promotes the formation and sedimentation of Mg(OH)2.Polyethylene glycol (PEG) is a synthetic polymer with stable properties and good water solubility. It is widely used in medicine, paint, electroplating, pesticide, metal processing and food processing industries. Differences in PEG molecular weight often lead to differences in its physical and chemical properties. Among them, PEG-4000 is often used as a dispersant and emulsifier in industrial production to reduce product agglomeration. At the same time, PEG has strong water solubility. In the liquid medium, the ether bond in its molecule has a weak negative charge, which can be complexed with cations such as Ca2 was prepared by electrolysis with bischofite aqueous solution as a magnesium source. PEG-4000 was innovatively introduced as a surfactant to enhance the sedimentation performance of Mg(OH)2 and accelerate the stripping of products from the substrate surface. The action mechanism of PEG-4000 in the preparation of Mg(OH)2 by electrolysis was analyzed for the first time.In this study, Mg(OH)2. The bischofite was dissolved and filtered to obtain a clear aqueous solution. The composition was analyzed by atomic emission spectrometer and an atomic absorption spectrometer. The composition of bischofite is shown in In this experiment, bischofite was used as the raw material of electrolytic Mg(OH)PEG-4000 was the additive and was purchased from Shanghai McLean Biochemical Technology Co., Ltd. All the chemical reagents were of analytical grade purity without further purification, and the water used in the progress of the experiment was deionized water.2 by the electrolytic method was carried out in an electrolytic cell made of polyvinyl chloride. The device diagram is shown in The preparation of Mg(OH)2 by electrolytic bischofite aqueous solution can be expressed by the following electrode reaction.The basic principle of preparing Mg(OH)2 produced in the anode chamber reacts with water to produce HCl and HClO. These by-products will penetrate into the cathode chamber, consume H+ and hinder the progress of the cathode reaction. Therefore, compared with the anode electrolyte, a certain amount of Mg(OH)2 slurry and H2O2 need to be introduced to neutralize the generated acid. The purpose of water resource recycling was realized by regularly replacing electrolyte.The cathode electrolyte was the filtered and diluted bischofite aqueous solution. However, there were some differences in the composition of anode electrolyte. During long-time electrolytic treatment, Cl2+ in the electrolyte was controlled to 0.35 mol/L. During the experiment, the current density was adjusted to 0.05 A/cm2, and the reaction temperature was 25 °C.The dissolved and filtered bischofite was used as the magnesium source, and the concentration of MgA scanning electron microscope was used to characterize the morphology of the product , of which the working potential of the scanning electron microscope was 2 kV. The particle size of the product was measured by a laser particle size analyzer . Fourier transform infrared spectrometry spectrum was recorded by a Fourier transform infrared spectroscopy analysis . The phase composition of the product was characterized by an X-ray spectrometer , with Cu Kα1 radiation source, the excitation potential was 2.2 kV, the scanning range was 10°≤ 2θ ≤ 85°and the scanning speed was 0.2°/min.2), m is the quality of Mg(OH)2, S is the surface area of electrode plate.The peeling rate represents the mass of magnesium hydroxide peeled off per square centimeter of the cathode substrate surface per unit time (1 h). It should be noted that the measurement of the stripping rate needs to be carried out after the mass transfer process has reached equilibrium. The peeling rate represents the mass of magnesium hydroxide peeled off per square centimeter of the cathode substrate surface per unit time (1 h). It should be noted that the measurement of the peeling rate needs to be carried out after the mass transfer process has reached equilibrium. Moreover, in order to ensure the accuracy of the measurement and not destroy the mass transfer balance, it is necessary to use a syringe to suck out the magnesium hydroxide generated before the mass transfer balance. After completion of the reaction, the obtained magnesium hydroxide was sufficiently washed and then dried. The peeling rate can be calculated by the following formula.The trend of cell potential for electrolytic preparation of magnesium hydroxide is shown in 2 increases with the increase of PEG concentration initially. Magnesium hydroxide can be produced up to 0.055 g/cm2 per hour when the concentration of PEG-4000 is 0.4 g/L, which is the maximum under this system. When the PEG-4000 concentration in electrolyte is further increased, the peeling rate of Mg(OH)2 is significantly decreased. When the addition amount of PEG is 0.8 g/L and 1.0 g/L, the peeling speed of the product is lower than that of other conditions.2 crystal has sharp peaks, indicating that the Mg(OH)2 crystal has good crystallization properties. According to the spectrum, the product Mg(OH)2 has a stronger tendency to grow along the (101) crystal plane. This is understandable. In Mg(OH)2 crystal, the (101) plane is connected by a weak hydrogen bond and the (001) plane is connected by an ionic bond, so the (101) plane growth needs to break a higher potential barrier [ barrier .2 [2 film, which leads to the product presenting a curly sheet shape [2 particles curl and form the porous structure finally. Inevitably, this layer of magnesium hydroxide, which grows perpendicular to the surface of the plate, will be served as the substrate for secondary nucleation. It can be found that the Mg(OH)2 produced by secondary nucleation presents a flocculent shape under the condition of no PEG-4000 addition. Its existence will close the pores of network Mg(OH)2 and reduce the number of active sites on the substrate surface. It is the main reason for the rise of cell potential and the uneven particle size of Mg(OH)2. When the concentration of PEG-4000 was 0.2 g/L and 0.4 g/L, the Mg(OH)2 on the electrode surface still showed a dense and uniform continuous network morphology. The flocculent Mg(OH)2 produced by secondary nucleation disappears and is replaced by uniform flake products. When the concentration of PEG-4000 increased to 0.8 g/L, there was no significant change in the Mg(OH)2 initially grown on the surface of the electrode. Secondary crystallization occurs on the surface of the initial Mg(OH)2 crystal, and an irregular network structure with radial growth is obtained. When the PEG-4000 content in the electrolyte reaches 1.0 g/L, the surface morphology of the electrode is shown in 2 obtained from the nucleation of the electrode surface changed greatly. The electrode plate is covered by a grid-like distribution of Mg(OH)2 crystals and a film attached to the electrode surface in the grid, which is the factor that causes the non-uniform particle size distribution of the product. The film, which develops parallel to the plate surface makes the active sites on the plate surface reach the minimum, and the cell potential is also higher.2 ,23. The et shape . In orde2. There is no significant change in the size of the Mg(OH)2 crystal in the range of PEG 4000 content of 0–0.4 g/L, which is consistent with the results measured by the laser particle size analyzer. Since the crystal tends to grow along the (101) crystal plane, the product exhibits a flake shape. When the amount of PEG-4000 added was 0.6 g/L and above, the surface area of magnesium hydroxide was significantly increased. This can be attributed to the fact that the PEG-4000 provides the growth context for magnesium hydroxide, which has a positive effect on the expansion of the (101) crystal plane. At the same time, as the particle size of the flaky product increases, the stress effect inside the product is more significant. The flaky magnesium hydroxide crystals are thus distorted.(101)/(001) values) of the samples prepared under different conditions, as shown in (101)/(001) obtained from the standard atlas (ICSD #165674) is equal to 1.887. The I(101)/(001) values of the obtained samples are significantly higher than that of the standard spectrum, indicating that the product is a flake product with the (101) crystal surface as the main exposed surface. It could be found that the I(101)/(001) of sample c  reached the minimum value of 2.061 among all samples. This means that the Mg(OH)2 has a high degree of crystallinity and low internal stress, as well as better dispersion properties [The X-ray diffraction patterns of the products are shown in operties . This is2 prepared under the condition of the PEG-4000 concentration of 0.8 g/L. The peak in the vicinity of 1088 cm−1 is the asymmetric expansion vibration peak of C-O-C in the PEG macromolecule, which indicates that the PEG-4000 is adsorbed on the Mg(OH)2 surface to a certain extent. The peaks at 2928 cm−1 and 2857 cm−1 belong to the asymmetric and symmetric vibrational peaks of -CH2, respectively. The peaks at 3440 cm−1 are derived from the hydroxyl vibrations of PEG [−1, 1358 cm−1 and 3700 cm−1 are respectively -OH bond of a water molecule and the stretching vibration of Mg(OH)2. The peak at 437 cm−1 is the stretching vibration peak of the Mg-O skeleton.s of PEG . The pea2 crystals (The ether group of the surfactant and the hydroxyl group of the Mg(OH)2 are bonded by hydrogen bonding.). When PEG-4000 was gradually added to the electrolyte until 0.4 g/L, the crystallization properties of magnesium hydroxide increased steadily. The product tends to grow along the (101) plane. When the PEG-4000 concentration reached 0.4 g/L, the particle size of the product did not increase significantly but was more uniform. The fine grains were significantly reduced, which was the main reason for the reduction of the cell potential and the rapid peeling of the product. When the concentration of PEG-4000 in the electrolyte reaches 0.6 g/L or above, PEG-4000 will be adsorbed on the surface of the electrode plate and hinder the occurrence of the electrode reaction. A large amount of Mg2+ forms complexes with PEG-4000 [− is also limited. According to Pauling’s first rule, the Mg(OH)64− negative ion formed by Mg2+ and OH− is an effective structural unit for the formation of flaky magnesium hydroxide [− generation leads to the existence of magnesium hydroxide, mostly with small nuclei or even amorphous, which further hinders the occurrence of electrode reaction. Since the electrode reaction is inhibited, there will be no hydrogen at these sites to exfoliate the electrode surface products in time. These reasons also lead to the high cell potential of the electrolysis reaction and the difficulty of peeling off the products on the substrate surface.According to the above results, it can be seen that the PEG molecular chain can serve as the base for the growth of Mg(OH)PEG-4000 . Howeverydroxide . The low2 can be combined by hydrogen bonding, which provides a "template" for the growth of magnesium hydroxide. Therefore, PEG plays an important role in regulating the growth mode, morphology and sedimentation performance of Mg(OH)2 crystals.(1) The ether group of the PEG molecular chain and the hydroxyl group of Mg(OH)(2) When the PEG concentration is low (no higher than 0.4 g/L), the crystallization and sedimentation properties of magnesium hydroxide are gradually optimized with the introduction of PEG. When the PEG content reaches 0.4 g/L, the grain size of the product is uniform, which can well reduce the polarization of the polar plate. The cell potential of the electrolysis reaction is smaller, and the economic benefit is higher.(3) Under the higher introduction amount, the role of PEG is more prominent in the aspect of crystal growth context and the promotion of crystal particle size increase. At the same time, it will also hinder the occurrence of electrode reaction, resulting in the rise of cell potential.


Under the condition of a laser energy density at 60 kJ/cm2, the macroscopic surface of the composite coating was continuously flat. The microstructure and phase of the cladding coating were analyzed by means of XRD and SEM. The reinforcements with nano-scale particle and micron-scale needle-like structures were in-situ synthesized in the cladding coating, and the content of the reinforcement phase decreased slightly from the coating surface to the substrate. The phase analysis results showed that the reinforcements included ZrB2 and SiC. When the content of the reinforcement was increased to 30 wt%, microhardness also increased from 48 HV0.2 to 309 HV0.2, which was about 5.6 times that of the copper matrix. The wear resistance of the composite coatings was characterized by current-carrying wear tests. By keeping the sliding speed and load constant, the wear rate decreased with an increase in the reinforcement content, and the wear mechanism changed from adhesive wear to abrasive wear. The wear rate of the composite coating with the current was higher than that without the current due to its electric ablation and high temperature.With the use of electrolytic Cu powder, Zr powder, Si powder and nickel-coated B On the one hand, because the reinforced phase, which possessed different sizes and shapes, showed different strengthening effects, and there was a synergistic strengthening effect between the reinforcements, the mechanical properties of the composite materials were significantly improved. On the other hand, two reinforcing phases with different morphology and different dimensions were uniformly distributed in the metal matrix, which could avoid the aggregation of the same kind of reinforcements and optimize the microstructure [It was noted that three kinds of reinforcing phases were simultaneously synthesized in situ in the copper matrix: the nano-scale particle SiC , the nano-scale needle-like ZrBtructure .0.2 to 167 HV0.2 with the increase of the laser energy density from 60 kJ/cm2 to 70 kJ/cm2. This was mainly due to the change in reinforcement size, which would have affected the mechanical properties of the composite coating. With the laser energy density increase from 60 kJ/cm2 to 70 kJ/cm2, the particle sizes of SiC increased from 25 nm to 40 nm; the length of ZrB2 increased from 35 μm to 80 μm. According to the dispersion strengthening mechanism [As shown in echanism , the sma2, due to the reduction of the size of the acicular ZrB2 ceramic reinforcing phase, the strengthening efficiency was increased, and the microhardness of the composite coating increased. The higher the content of the reinforcing phase, the more obvious the increase in hardness. For example, when the reinforcement content was 10 wt%, the increase in hardness was 18 HV0.2. When the content of the reinforcement was increased to 30 wt%, microhardness also increased from 48 HV0.2 to 309 HV0.2, which was about 5.6 times that of the copper matrix. For the composite coating prepared under the condition of a higher energy density (70 kJ/cm2), when the reinforced phase content was 10 wt%, the hardness of the composite coating (89 HV0.2) was 1.6 times higher than that of the original copper substrate (55 HV0.2). The microhardness of the composite coating increased rapidly with a further increase in the reinforcing phase content. When the content was 30 wt%, the microhardness of the coating reached 256 HV0.2, which was about 4.7 times that of the copper substrate. The in-situ synthesized ceramic reinforcing phase  was dispersed in the coating, and through component strengthening: load transfer, dispersion strengthening, thermal mismatch strengthening, grain refinement, etc. [nt, etc. ,24,25. TW is the wear rate of the material, k is the wear coefficient, P is the load, V is the sliding speed, and H is the hardness of the material. Therefore, the wear rate is proportional to the load P and sliding speed V and is inversely proportional to the hardness H of the material.The composite coating was prepared under the optimized process parameters with an energy density of 60 kJ/cm2. The change in wear rate is represented by the following formula:The reinforced phases in the composite coating were dispersed in the copper matrix and could play a significant role in the pinning enhancement during wear. Under the action of wear stress between the friction pairs, the addition of the harder phase distributes in the matrix increased the resistance of wear. The higher the reinforced phase content, the better the strengthening, so the cladding coating closer to the shear stress of materials obtained a lower wear rate. However, when a current was applied, the joule heat was generated because of the resistance between the friction pairs, which were superimposed with the heat generated by the tribological process and the heat impact was aggravated on the friction surface. Under the conditions of high-speed and the current load, the wear rate increased compared to that without current loading.The wear surface topography is shown in 2-SiC composite coating had high wear resistance and electric ablation resistance.The friction coefficient curves against time under the condition of being with or without a current are shown in (1).2-SiC/Cu composites underwent in-situ synthesis successfully onto the surface of the pure copper matrix by laser cladding.ZrB(2).2 with the reinforced phase content of 30 wt%, the surface of the composite coating was continuously flat, and no defect was observed at the interface.Under the condition of a laser energy density of 60 kJ/cm(3).2 gradually increased.The reinforcement morphology and microstructure in the coating were different. From the surface layer to the bottom, the size of the micron-scale ZrB(4).The wear rate decreased with an increase in the reinforcement content, and the wear mechanism changed from adhesive wear to abrasive wear.(5).2-SiC composite coating had a high wear resistance and electric ablation resistance.The wear rate was higher with the current than that without the current. The ZrB


The properties of the convergence region of the estimation error of a robust observer for second-order systems are determined, and a new algorithm is proposed for setting the observer parameters, considering persistent but bounded disturbances in the two observation error dynamics. The main contributions over closely related studies of the stability of state observers are: (i) the width of the convergence region of the observer error for the unknown state is expressed in terms of the interaction between the observer parameters and the disturbance terms of the observer error dynamics; (ii) it was found that this width has a minimum point and a vertical asymptote with respect to one of the observer parameters, and their coordinates were determined. In addition, the main advantages of the proposed algorithm over closely related algorithms are: (i) the definition of observer parameters is significantly simpler, as the fulfillment of Riccati equation conditions, solution of LMI constraints, and fulfillment of eigenvalue conditions are not required; (ii) unknown bounded terms are considered in the dynamics of the observer error for the known state. Finally, the algorithm is applied to a model of microalgae culture in a photobioreactor for the estimation of biomass growth rate and substrate uptake rate based on known concentrations of biomass and substrate. In the monitoring and control of biological and biochemical processes, it is crucial to have real-time knowledge of variables such as the concentrations of biomass, products or reactants; the growth rate of microorganisms; and the substrate consumption rate ,2,3,4. Oe output ; (ii) input see ,7);  put  input  a lack of knowledge in the dynamics of the observation error for the unknown state; (ii) an unknown term of the unknown state in the dynamics of the observation error for the known state ,20,21,22In , a tuninIn , an obseIn , a filteIn , a super−In , the dep−In , the wid−In , the widCi. The width of the convergence region of the observer error for the unknown state is expressed in terms of the interaction between the observer parameters and the disturbance in terms of the observer error dynamics. Thus, the desired estimation accuracy can be defined by the user by setting the observer parameters in accordance with this relationship. In contrast:Cii. The properties and limits of this width are determined. It was found that this width has a minimum point and a vertical asymptote with respect to one of the observer parameters, and their coordinates were determined. Then, the highest accuracy of the state estimation can be obtained by setting the observer parameters equal or similar to the coordinates of the minimum. In contrast, in ,23,25: Advantage A1. It involves a significantly simpler definition of observer parameters: the fulfillment of Riccati equation conditions, solution of LMI constraints, and fulfillment of eigenvalue conditions are not required, thus, reducing the trial-and-error effort. In contrast, the fulfillment of these conditions is commonly required in closely related observer strategies, for instance [instance ,23,26.(ii)Advantage A2. Different from [ent from ,20,21,22(iii)Advantage A3. The time derivatives of the disturbance terms of the plant model are not required to be bounded, whereas this condition is required in [uired in ,28,29,30(iv)Advantage A4. Different from [ent from ,31, discIn addition, the advantages of the proposed algorithm over closely related algorithms are: The work is organized as follows. The bioreactor model is presented in Consider the systemAssumption 1.The functionsandare known; the stateis measured, and the coefficientis known; the stateand the termsandare unknown.Assumption 2.The coefficient b is bounded away from zero:whereis an unknown positive constant.Assumption 3.The disturbance termsandare bounded.In this section, the observer equations and the bounds for the transient and asymptotic behavior of the observer error for the unknown state (led from . The detled from .The observer equations are :(3)dx^1dThe main mathematical definitions are given as follows. Mathematical definitions related to the function Mathematical definitions related to the overall Lyapunov function:Mathematical definitions of convergence regions: The combined state The Lyapunov function for Differentiating The overall Lyapunov function is:The time derivative of This indicates the asymptotic convergence of the observer error Remark 1.Thedefinition given after Equation (10) indicates that,andexist and are continuous. Thedefinition (7) indicates that,, andexist and are continuous. Consequently,, and the overall Lyapunov functionexist and are continuous. A detailed determination of,,,is given in [given in .Remark 2. The term ‘overall Lyapunov function’ is used for the Lyapunov function that results from the addition of several quadratic or positive forms and whose time derivative indicates the convergence result of some state. This term is also used in [. Notice that this condition is only fulfilled by, as follows from Equation (11). used in ,33. NotiFrom the definition of This leads toCombining the dynamics of Despite the fact that the convergence of Hence, In this section: (i) the width of the convergence region From the definition of From Equation (17) and the conditions on From these properties, it follows that Therefore, the relationship between Remark 3. The properties (21) of thefunction and its minimum (22) indicate that and a low  value leads to low , which implies a low width of the convergence region , and consequently, a high quality of  estimation, as follows from Equations (19) and (20).Remark 4. An overlargevalue fulfillingleads to: (i) fast convergence of the upper bound of, as follows from Equation (15); (ii) a largevalue, which implies a low quality ofestimation, as follows from Equations (19) and (20). Therefore, the choice ofmust take into account both the convergence rate and the width of the convergence region ofRemark 5. A lowvalue leads to low , since  increases with respect to , as follows from Equation (22). However, overly small  values lead to steeper slopes in the shape of the  signal (8) of the observer, which implies that the numerical solution of the differential equation must use a smaller step size.Remark 6. Thefunction (23) increases with , whereas  is independent of , as follows from Equation (22).In the case that Then, Equation (19) becomesThe resulting features of From these properties, it follows that Algorithm 1: Algorithm for setting the parameters of the observer (3)–(5).StepDescription1Cast the system model in the form (1)–(2) and identify the known state 2Obtain the values of 3−The time-dependent bound for the transient evolution of −The limit of the convergence region of  where Set the values of 4Set a high value of Set a high value of The algorithm presented in Algorithm 1 allows us to set the observer parameters Remark 7. The proposed algorithm and the observer (3)–(5) lead to a more practical and simpler real-time state estimation in either laboratory or industrial applications, according to the advantages A1 to A4, which are due to the observer of [. They can be applied to systems whose model can be cast in the second-order form (1) and (2), which includes a wide range of mechanical and physical systems. Some examples are:−Microalgae reactor represented by the Droop model: (i) estimation of specific bio-mass growth rate based on known biomass concentration; (ii) estimation of specific substrate uptake rate based on known substrate concentration—see ,23.−Anaerobic bioreactor for hydrogen production via the dark fermentation of glucose: estimation of influent glucose concentration based on known reactor glucose con-centration—see .−Fed-batch bioreactor for ethanol production: (i) estimation of the rate of enzymatic hydrolysis based on known substrate (starch) concentration; (ii) estimation of the glucose consumption rate based on known glucose concentration—see .−Membrane fuel cell: estimation of stack temperature based on known oxygen pres-sure—see .−Photovoltaic system: estimation of the power gradient based on known generated electric power—see .−DC-DC buck converter: estimation of the time derivative of the output tracking er-ror based on the known average output voltage—see .−Second-order underactuated mechanical system: estimation of the time derivative of the pole angle—see .erver of . They caRemark 8. The convergence rate and the width of theconvergence setcan be properly defined by setting the observer parameters,,,in accordance with the proposed procedure, with,values corresponding to the minimum point of, that is,,Remark 9. The proposed observer algorithm deals with the combined effect of disturbance terms and observer parameters on the width of the convergence region for the estimation error of the unknown state, as follows:a)(The convergence region is expressed as a function of the combined effect of observer parameters and disturbance terms—see Equations (19) and (20). Then, the desired estimation accuracy can be defined by the user by properly setting the observer parameters in accordance with this relationship.b)–(23). In turn, these properties allow choosing ω, ε values to avoid an undesired overlarge f_w value, and the lowest f_w value is obtained by using the coordinates of the minimum, that is, ω=ω^*, according to Equation (22). Thus, the highest accuracy of the state estimation is obtained by setting the observer parameters equal or similar to the coordinates of the minimum.The developed algorithm for setting parameters of the observer (3)–(5) is used to estimate the substrate uptake rate op model ,37:(27)dters are :(30){μ–(29) and the observer (3)–(5) was performed using Matlab software : the differential equations were numerically integrated using the ode45 routine. Although model (27)–(29) comprises three states, it leads to the following second-order subsystems:A)B)This approach is also considered in .The specific substrate uptake rate Additionally, the observer (3)–(5) provides the estimate of To examine the Low alue see b,d, whic−The observer error −The observer error  approx. a,b. −The observer error  approx. c,d. The −The low width of So that ved that :−The obsThe performed simulations confirm the adequacy of the parameter recommendations provided in the observer algorithm to achieve proper convergence speed and the width of the convergence region of The specific growth rate Additionally, the observer (3)–(5) provides the estimate of To examine the Low alue see b,d, whic−The observer error −The observer error fterward a,b. −The observer error  approx. c,d. The −A low width of So that ved that :−The obs−The main contributions over closely related studies of the stability of state observers are: −Ci. The width of the convergence region of the observer error for the unknown state is expressed in terms of the interaction between the observer parameters and the disturbance in terms of the observer error dynamics. Then, the user defines the desired estimation accuracy by properly setting the observer parameters in accordance with the aforementioned relationship.−Cii. The properties and limits of this width are determined; it was found that this width has a minimum point and a vertical asymptote with respect to one of the observer parameters, and their coordinates were determined. Thus, the highest accuracy of the state estimation is obtained by setting the observer parameters equal or similar to the coordinates of the minimum.−The main challenges encountered in this research work are:−Choosing the idea of contributions Ci and Cii as the core topics of the paper required identifying contributions and limitations of high-quality works addressing observer design and stability analysis, mainly ,25. ThisThe statement of the procedure for determining the constants that satisfy Equation (18). Based on several literature studies, we finally concluded that they could be obtained by the simulation of In this work, a new algorithm is proposed for setting parameters of a robust observer for second-order systems, considering persistent but bounded disturbances in the two observation error dynamics. As the main contribution over closely related studies of the stability of state observers, the width of the convergence region of the observer error for the unknown state is expressed in terms of the interaction between the observer parameters and the disturbance terms of the observer error dynamics. Moreover, the properties and the minimum of this relationship were determined.The proposed observer algorithm leads to a more practical and simpler state estimation in either laboratory or industrial applications. It can be used for systems whose model can be cast in second-order form, for instance, mechanical, chemical, and biochemical systems. Moreover, it can be used for multiple state estimation, in cases of several second-order systems. The choice of the observer parameters must consider both the convergence rate and width of the convergence region of the estimation error of the unknown state. Choosing the observer parameter values to be similar or equal to the values for the minimum leads to a high quality of state estimation. The performed simulations confirm the adequacy of the parameter recommendations provided in the observer algorithm to achieve the proper convergence speed and width of the convergence region of the observer error for the unknown state.Future work will include: (i) extending the observer and the algorithm to system models of third order; (ii) extending the observer and the algorithm to system models of general nth order; (iii) considering noise in the measurement of the known state.


The reuse of steel slag, a large-scale solid waste from steel production, has good social and environmental benefits. The application of a steel slag asphalt mixture is mainly hindered by its volume expansion in water. The expansion of steel slag can be inhibited by oxalic acid. The expansion rate and adhesion of steel slag were investigated, and the immersion stability of steel slag and its asphalt mixture was evaluated by water erosion. By means of XRD, XRF, TG, SEM, etc., the influence mechanism of oxalic acid and water erosion on the properties of steel slag and its asphalt mixture was discussed. The results show that oxalic acid can not only inhibit the expansion of steel slag but also improve its crush resistance, with a reduction in the expansion rate of steel slag by 53%. Oxalic acid is able to leach alkaline metal elements, reducing its adhesion with asphalt. After 10 days of water erosion, the rutting stability and bending crack resistance of the treated steel slag mixture decreased by 37% and 43.2%, respectively. Calcium oxalate is generated on the surface of treated steel slag, which improves the surface compactness, effectively inhibits the expansion of steel slag caused by water erosion, and improves the performance of steel slag and its asphalt mixture. Water erosion can accelerate the hydration and shedding of calcium-containing substances on the surface of steel slag, reduce the adhesion of steel slag, and lead to degradation in the performance of steel slag and its asphalt mixture. Oxalic acid is able to effectively inhibit the expansion of steel slag, and the treated steel slag can be used as recycled aggregate in asphalt mixture, effectively solving the problems of road aggregate deficiency and environmental pollution caused by steel slag. Steel slag accounts for a large amount of the solid waste produced by steel making. With the development of China’s steel industry, the output of steel slag in China was as high as 100 million tons in 2021, and the total accumulated amount is as high as 1 billion tons at present. The multipurpose use rate of steel slag in China is less than 30%, of which less than 10% is used in building materials. Most steel slag is regarded as industrial waste, so it is filled or accumulated, resulting in ecological environmental pollution and other problems ,5. At th2) leads to the expansion and cracking of steel slag. There is a close relationship between f-CaO and the expansion of steel slag, and f-CaO on the surface of steel slag is more likely to cause expansion and cracking than that inside [The steel slag accumulated and produced in China has the property of volume expansion. The main factor affecting the expansion of steel slag is free calcium oxide (f-CaO), which undergoes a slow hydration reaction when coming into contact with water. The process of generating calcium hydroxide (Ca(OH)t inside ,11. Roadt inside ,13,14. Tt inside ,16. The t inside ,18,19. Tt inside ,21. ThesTo solve the problem of the volume expansion of steel slag caused by water, and to evaluate the immersion stability of treated steel slag and its asphalt mixture, an oxalic acid solution was used to treat steel slag aggregate. This paper analyzes the mechanism of influence of oxalic acid and water erosion in the performance of steel slag and its asphalt mixture, evaluates the applicability of steel slag and its asphalt mixture following treatment with oxalic acid, and provides engineering suggestions and theoretical guidance for the practical application of steel slag in asphalt mixture.2H2O4·2H2O and a reagent content of not less than 99.6%, as a colorless transparent crystal or powder. The chemical composition of the selected steel slag, and its basic physical properties, are shown in 3. This is mainly because there is a large amount of iron in steel slag, which is one of the main reasons for the high density of steel slag [BOF steel slag aggregate, limestone aggregate, and SBS(I-D) polymer modified asphalt were used as raw materials. The raw material used for treatment was a self-prepared oxalic acid solution; oxalic acid was produced by Tianjin Chemical Three Plant Co., Ltd. with the chemical formula C2 and water in the air influencing the treatment process, the treatment process was sealed after stirring for 3 min, and the treatment time was 84 h. Treated steel slag can be used after being dried at 105 °C. The specific treatment process is as follows , the basic physical properties of steel slag and limestone were tested. The basic index of SBS-modified asphalt, the road performance index of the steel slag asphalt mixture, and the mix design of steel slag asphalt mixture were adopted with reference to the Standard Test Methods of Bitumen and Bituminous Mixtures for Highway Engineering (JTG E20-2011). There are three index samples in each group tested by steel slag and its asphalt mixture, and the indexes of the samples need to meet the specifications. The experimental results are the average of the results of the three samples. The water stability of the mixture is tested by a Universal testing machine (UTM-30), including the Marshall stability test and freeze-thaw splitting test. The sample in the Marshall stability test needs to be kept in a water bath at a constant temperature of 60 °C for 30–40 min and 48 h, respectively. After the heat preservation is completed, it is put into a fixture for testing, and the loading rate is 50 mm/min. For the samples in the freeze–thaw test, the molded samples are divided into two groups. One group is stored at room temperature, and the other group is kept in a vacuum for 16 h. After taking out, the samples are kept in a water bath at 60 °C for 24 h. Finally, the samples of both groups are kept in a water bath at 25 °C for 2 h, and then taken out for testing. The loading rate is 50 mm/min. The rutting stability of the mixture is tested by a rutting tester (SYD-0719B). The formed sample is kept in a 60 °C incubator for 5 h, and then put into a test bench for testing. The test will be stopped when the test time is 1 h or the maximum deformation is 25 mm.d10 is the final reading of the dial indicator, mm; d0 is the initial reading of the dial indicator, mm.The mineral composition and phase composition of steel slag have a great influence on the properties of steel slag. To ensure the average of the selected steel slag, selected the original steel slag by the quartering method and ground it to below 0.075 mm. The material was tested by X-ray diffraction (XRD), the diffraction pattern was analyzed, the mineral composition of the steel slag was obtained, the equipment used in this experiment is Ultima IV, with the parameters of X-ray Cu Kα Radiation Diffraction Meter, wavelength of 0.15406 nm, voltage of 40 KV, current of 40 mA, testing speed of 5°/min, and testing angle of 10–90. X-ray fluorescence (XRF) is used to test the elements and substance composition in steel slag, and the equipment model is PANalytical Axios. Moreover, the microstructure of the steel slag is observed using a scanning electron microscope (SEM), its equipment model is Hitachi Regulus8100. Ethylene glycol differential thermal analysis—EDTA-TG—is an effective current method that is accurate and simple for measuring the content of f-CaO in steel slag. After grinding the steel slag selected by the quartering method to below 0.075 mm, the free total calcium in the steel slag is determined by titration with ethylene glycol, and the free total calcium content obtained using this method includes the content of calcium hydroxide. The content of calcium hydroxide in steel slag is determined by TG, and its equipment model is TA. The content of f-CaO is obtained by subtracting the content of calcium hydroxide from the free total calcium . The 10-S is the anti-stripping percentage of asphalt, m1 is the original mass of asphalt aggregate, m2 is the original mass of aggregate, and m3 is the loose loss mass of the aggregate surface.The application process of steel slag and its asphalt mixture is greatly affected by water, which also directly causes steel slag expansion. To intuitively evaluate the changes in the performance of steel slag and its asphalt mixture under the action of water, the water erosion method is adopted ,11. WateAt present, there are many specifications of asphalt mixture, and AC asphalt mixture is widely used in pavement. AC-13c is the main type in most experiments . AC-13c As oxalic acid cannot directly affect the particle size of steel slag, the gradation curves of steel slag before and after treatment show little difference. However, in order to better standardize the experimental results, designed two gradations under the condition of meeting the lower limit of gradation. The specific gradation curves are shown in This section mainly discusses the gradation design and the best asphalt–aggregate ratio of steel slag asphalt mixture before and after treatment. The gradation curve of steel slag asphalt mixture before and after treatment has little difference. It is worth noting that the best asphalt–aggregate ratio of steel slag asphalt mixture after treatment has decreased by 0.4%. All calculated data are the average value from three tests.2 content of steel slag before and after treatment, respectively. After treatment with oxalic acid, the content of f-CaO decreased from 4.551% to 2.225%, and the expansion rate decreased from 3.59% to 1.69%. The mass loss of Ca(OH)2 at 400~550 °C was calculated by TG analysis. The mass loss of water in steel slag at 400–550 °C can be expressed as the loss of calcium hydroxide [2, causing volume expansion. With the passage of time, the hydration reaction weakened, the content of f-CaO decreased, and the growth trend of expansion rate decreased [The main factors causing the volume expansion of steel slag are f-CaO, free magnesium oxide (f-MgO), and RO phase. f-CaO, the f-CaO caused volume expansion corresponding to 91.7% ,29. Becaydroxide . After tydroxide . In the ecreased . In the 2+, Mg2+, Al3+, Fe3+, and Mn2+ on the surface of steel slag. In the process of its combination with asphalt, it can react with some substances in asphalt, such as asphaltene groups, to generate bituminous acid salt, and form an adsorption layer on the surface of steel slag, which has high chemical strength. Therefore, steel slag and asphalt have good adhesive force [2O3) in the steel slag decreases, while the content of silicon dioxide (SiO2) changes little, and the content of other metal oxides decreases slightly. After treatment, the basicity of steel slag decreases slightly, but it is still higher than that of limestone. The adhesive force between aggregate and asphalt is one of the main factors determining the performance of the mixture. Because steel slag is a basic aggregate, there are a lot of metal cations such as Cave force ,32. The 2. During the erosion process, the pH value changes obviously, and CO2 in the air reacts with Ca(OH)2 to generate calcium carbonate (CaCO3), resulting in a white coating on the surface of the aqueous solution [2, the volume of steel slag aggregate expands, micro-cracks appear on the surface and pores of steel slag, and water immerses into the cracks, providing further hydration. However, due to the slow hydration process, only the surface can be hydrated, resulting in a slight decrease in the strength of the steel slag aggregate [At present, most countries use abrasion to express the anti-crushing ability of aggregate, but the importance of crush value in the asphalt mixture cannot be ignored. Therefore, in this section, the abrasion value and the crush value are used to jointly characterize the anti-crushing ability of the aggregate. solution , as showggregate . Under c2, resulting in the expansion of the steel slag [eel slag , therebyeel slag , which lUnder the same conditions with respect to gradation, aggregate, and asphalt type, the rutting stability of the mixture is mainly related to its strength and compactness. The higher the strength and compactness of the mixture, the higher its dynamic stability and the better its rutting stability ,40. Figu3SiO5), dicalcium silicate (Ca2SiO4), calcium ferrite (Ca2Fe2O5), and RO. After the steel slag is treated with oxalic acid, the diffraction peak of calcium oxalate (CaC2O4) appears. Some of the Ca2SiO4 and Ca3SiO5 diffraction peaks disappear and decrease. The diffraction peak of CaO disappears and changes to Ca(OH)2. The presence of oxalic acid breaks the acid–base balance of the original system of steel slag, and some silicate minerals on the surface of the steel slag, such as Ca2SiO4 and Ca3SiO5, react with oxalic acid to form the CaC2O4 complex. During the treatment of steel slag, the hydration speed of f–CaO accelerates, and Ca(OH)2 is generated. Under the closed treatment condition, CO2 in the air fails to participate in the reaction, so there is Ca(OH)2 after the treatment, which is consistent with the quality loss analysis results Ca(OH)2 described above. 3), accompanied by a large number of loose network structures [2C2O4 crystals [2 [2O4 complexes on the surface and in the pores. The weak particles and reticular structure on the surface of the untreated steel slag are replaced and filled by the generated CaC2O4, resulting in precipitation transformation. The surface compactness of the steel slag increases and the strength of the steel slag increases slightly [ructures . A largecrystals ,46, accostals [2 . Steel sslightly . Oxalic 2C2O4:During the treatment of steel slag with oxalic acid, a large number of calcium ions dissolve out and react with oxalic acid to generate CaOxalic acid can also promote the hydration of f-CaO:In Ding et al.’s research , oxalic 2Fe2O5, Ca2SiO4, and Ca2C2O4, decrease obviously, and are almost invisible in the XRD diffraction patterns. Most minerals on the surface of the steel slag can hydrate to form hydrated calcium silicate (C-S-H) during the process of water erosion, especially Ca2SiO4 and Ca3SiO4, which are invisible in the XRD diffraction patterns because of their amorphous forms [2 [2 and floc C-S-H on the surface of untreated steel slag become more and more obvious, and at the same time, a few microcracks appear. However, the surface of the treated steel slag is mostly massive Ca2C2O4, and water erosion can accelerate the shedding degree of Ca2C2O4. Moreover, floc C-S-H was not found on the surface of steel slag, which was due to the existence of a large amount of Ca2C2O4 blocking the C-S-H. With increasing shedding degree of Ca2C2O4, a small amount of fashioned Ca(OH)2 begins to appear on the surface of the steel slag, which indicates that the f-CaO on the surface of the treated steel slag has been basically eliminated, which is in agreement with the previous experimental results.us forms ,50,51. Tforms [2 ,53,54. W2C2O4 present on the surface of the treated steel slag is free in aqueous solution due to the action of water erosion. With increasing water erosion time, the degree of Ca2C2O4 that is free and falling off increases, resulting in a slight decrease in the strength of the steel slag. At the same time, the shedding of the asphalt layer and the lack of basic metal content on the surface of steel slag have a great influence on adhesion, which leads directly to the obvious downward trend of the adhesion in the mixture with the action of water erosion, and the downward trend of the performance of the mixture [Most of the Ca mixture ,56.(1)Oxalic acid is able to promote the hydration reaction of f-CaO on the surface of steel slag, eliminate some f-CaO in steel slag, and inhibit the volume expansion of steel slag. However, due to the leaching of alkaline ions, the adhesion decreases. After 7 days of water erosion, the crush resistance of treated steel slag tends to be stable. Water erosion has little effect on the crush resistance of steel slag.(2)After oxalic acid treatment, the performance of the steel slag asphalt mixture is improved, but in the process of water erosion, its performance decreases obviously, especially with respect to rutting stability and bending crack resistance. The performance of the steel slag asphalt mixture after treatment is greatly reduced after being subjected to low temperature, and its low-temperature performance needs further consideration.(3)2C2O4. It can promote the hydration of f-CaO, filling the surface and most pores of the steel slag, effectively inhibiting the expansion effect of f-CaO hydration on the surface of steel slag after water erosion, and improving the strength of the steel slag.Water erosion is able to accelerate the hydration of calcium silicate and f-CaO on the surface of steel slag, leading to the slight expansion of the steel slag surface, decreased adhesion, and a decline in the performance of the steel slag asphalt mixture. Oxalic acid can react with calcium silicate and f-CaO on the surface of steel slag to produce Ca(4)2C2O4 complex. With increasing water erosion time, the shedding degree of Ca2C2O4 increases. Most basic metal elements on the surface of steel slag are leached out, and the adhesion between steel slag and asphalt decreases more obviously, which finally leads to a decline in the performance of the asphalt mixture. After a long duration of water erosion, the properties of steel slag treated with oxalic acid and its asphalt mixture are similar to those of untreated steel slag, indicating that it is feasible to apply steel slag treated with oxalic acid in asphalt mixtures.The surface of steel slag treated with oxalic acid mostly consists of the Ca(5)This work solves the problem that steel slag is difficult to apply due to volume expansion, and the treated steel slag can be widely used in asphalt mixtures. This provides a solution to the excessive accumulation and output of steel slag at present, in China, and solves the environmental problems caused by steel slag and the lack of natural aggregates in China. It is worth noting that whether the performance of steel slag asphalt mixture changes under the long-term action of water erosion and how the performance changes under actual application conditions are the factors that determine whether the steel slag asphalt mixture can ultimately be applied. In future research, it is worth our continued consideration.In this study, a self-prepared oxalic acid solution was used to treat steel slag with the aim of inhibiting its expansion, and the steel slag and its asphalt mixture were subjected to water erosion at different times before and after treatment. Then, the basic properties of the steel slag and its asphalt mixture were tested by means of comparison. The mechanisms of influence of oxalic acid and water erosion on the mixed properties of steel slag and its asphalt mixture were discussed. The potential of steel slag treated with oxalic acid in an asphalt mixture was evaluated. The following conclusions were drawn:


This paper presents the results of physical modelling of the process of multi-pass rolling of a wire rod with controlled, multi-stage cooling. The main goal of this study was to verify the possibility of using a torsion plastometer, which allows conducting tests on multi-sequence torsion, tensile, compression and in the so-called complex strain state to physically replicate the actual technological process. The advantage of the research methodology proposed in this paper in relation to work published so far, is its ability to replicate the entire deformation cycle while precisely preserving the temperature of the deformed material during individual stages of the reproduced technological process and its ability to quickly and accurately determine selected mechanical properties during a static tensile test. Changes in the most important parameters of the process  were analyzed for each variant. After physical modelling, the material was subjected to metallographic and hardness tests. Then, on the basis of mathematical models and using measurements of the average grain size, chemical composition, and hardness, the yield strength, ultimate tensile strength, and plasticity reserve were determined. The scope of the tests also included determining selected mechanical properties during a static tensile test. The obtained results were verified by comparing to results obtained under industrial conditions. The best variant was a variant consisting of physically replicating the rolling process in a bar rolling mill as multi-sequence non-free torsion; the rolling process in an NTM block (no twist mill) as non-free continuous torsion, with the total strain equal to the actual strain occurring at this stage of the technological process; and the rolling process in an RSM block (reducing and sizing mill) as tension, while maintaining the total strain value in this block. The differences between the most important mechanical parameters determined during a static tensile test of a wire rod under industrial conditions and the material after physical modelling were 1.5% for yield strength, approximately 6.1% for ultimate tensile strength, and approximately 4.1% for the relative reduction of the area in the fracture and plasticity reserve. Providing a required strain value, strain rate, and temperature during physical modelling that is similar to those occurring during the actual process ensures the high accuracy of obtained results [The wire rod rolling process in modern rolling mills is characterized by high dynamics with the linear speeds of the rolled band reaching values of 120 m/s or more [ results ,4. In a The most commonly used methods for the physical modelling of rolling processes are the compression test ,6,7,8,9 Most of the work concerning the physical modelling of the rolling processes published so far focuses on the assumption that the microstructure and properties of the final product are mainly determined by the few final passes, and the impact of the earlier stages of the technological process is less important . As showHowever, during physical modelling of the rolling process during a torsion test using a torsion plastometer, a limitation may be the low value of the strain rate. Apart from the standard free or non-free torsion tests, modern torsion plastometers enable testing in the course of multi-sequence torsion , tensile, and compression tests, and in the so-called complex strain state test (simultaneous torsion with compression or simultaneous torsion with tensile tests). Furthermore, they enable precise temperature control during individual stages of the reproduced technological process, and a sole torsion test allows for much greater deformation values than a compression test.Most of the works published so far on the physical modelling of real technological processes in torsion tests refer to the rolling of sheet metal bars ,23,24,25This paper presents the results of physical modelling of the process of multi-pass wire rod rolling with controlled, multi-stage cooling. The main objective of the study was to verify the possibility of using a torsion plastometer, enabling testing with the use of a variable strain scheme to physically reproduce the technological process of rolling a wire rod.The advantage of the research methodology proposed in the paper in reference to the works published so far is the possibility of reproducing the entire strain cycle , precisely preserving the temperature value of the deformed material during individual stages of the reproduced technological process, and the possibility of quickly and accurately determining selected mechanical properties during a static tensile test directly from the material after physical modelling.The tests presented in the paper were carried out on several variants with the use of the STD 812 torsion plastometer , which, For each variant, changes in the most important process parameters  were analyzed in detail. After physical modelling, each time the material was subjected to metallographic tests at characteristic points in order to assess the microstructure of the tested steel and the average ferrite grain size. In addition, Vickers hardness tests were also carried out. Then, based on the available mathematical models and using the measurements of the average ferrite grain size, chemical composition, and hardness ,29, the Basing on the obtained research results, it has been determined that the best variant is a variant consisting of physically reproducing the rolling process in a bar rolling mill as multi-sequence non-free torsion; the rolling process in an NTM block (No-Twist Mill) as non-free continuous torsion, with the total strain equal to the actual strain occurring at this stage of the technological process; and the physical modelling of the rolling process in an RSM block (reducing and sizing mill) as a tension, while maintaining the total strain value in this block. The differences between the most important mechanical parameters determined during a wire rod static tensile test under industrial conditions and during tensile tests of material after physical modelling were 1.5% for the yield strength, approximately 6.1% for the ultimate tensile strength, and approximately 4.1% for the relative reduction of area at fracture and the plasticity reserve.According to the authors, such high accuracy between the research results obtained under industrial and experimental conditions results mainly from inducing a high level of yield stress during the final stage of physical modelling of the analyzed process (RSM block), by changing the deformation state from torsion to tension. The level of yield stress obtained in such a manner is close to the value of the yield stress occurring in the actual technological process, which is crucial for activating the microstructure rebuilding processes.The research presented in the paper was carried out for low-carbon cold upsetting steel of the 20MnB4 grade, with a chemical composition in accordance with PN-EN 10263-4:2004  17,21,3,321,30.Physical modelling tests were carried out for the entire production cycle of rolling a wire rod with a final diameter of 5.5 mm, for an exemplary combined-type rolling mill (a combination of a bar rolling mill and a wire rod rolling mill) . The rolHowever, during tests it is necessary to take into consideration the temperature increase caused by the deformation of the material in the RSM block with a high strain rate, which for the tested steel grade was about 50 °C. Therefore, during the tests, the temperature of the rolled band in the RSM block was 850 °C. After the rolling process, the material was cooled in two stages. During the first stage of the controlled cooling process, the 20MnB4 steel was cooled from the rolling end temperature to 500 °C at a cooling rate of approx. 10 °C/s, while during the second stage of cooling, the tested material was cooled to 200 °C at a cooling rate of 1 °C/s.Several different tests were carried out in this paper with the use of the STD 812 torsion plastometer , which, r is the sample radius, L is the sample length, N is the number of sample twists (revolutions), M is the torque.In order to determine the actual strain value, the relation (1) was used, the actual strain rate was determined based on the relation (2), while the yield stress was calculated according to the Formula (3) ,37:(1)ε=Research concerning the physical modelling of the wire rod rolling process was carried out in three variants, differing mainly in the method of applying deformation.Variant 1 (V1): Physical modelling of the analyzed process in this variant was carried out during non-free torsion tests, as a cycle of 31 individual deformations at a certain temperature with specified intervals between successive deformations, and taking into account multi-stage controlled cooling during the individual stages of the technological process:-17 individual deformations as non-free torsion, representing the rolling process in a continuous bar rolling mill;-10 individual deformations as non-free torsion, representing the rolling process in an NTM block of a wire rod rolling mill;-4 individual deformations as non-free torsion, representing the rolling process in an RSM block of a wire rod rolling mill.Variant 2 (V2): The physical modelling of the analyzed process in this variant was carried out in non-free torsion tests, as a cycle of 19 deformations at a certain temperature with specified intervals between following deformation cycles, and taking into account multi-stage controlled cooling at individual stages of the technological process:-17 individual deformations as non-free torsion, representing the rolling process in a continuous bar rolling mill;-1 deformation reproducing the rolling process at an NTM block of a wire rod rolling mill, as non-free torsion, with a total strain value equal to the actual strain value occurring at this stage of the technological process;-1 deformation reproducing the rolling process at an RSM block of a wire rod rolling mill, as non-free torsion, with a total strain value equal to the actual strain value occurring in this block.Variant 3 (V3): The physical modelling of the analyzed process in this variant was carried out during non-free torsion and tensile tests, as a cycle of 19 deformations at a specific temperature with specified intervals between successive deformation cycles, and taking into account multi-stage controlled cooling during individual stages of the technological process:-17 individual deformations as non-free torsion, representing the rolling process in a continuous bar rolling mill,-1 deformation reproducing the rolling process in an NTM block of a wire rod rolling mill, as non-free torsion, with a total strain value equal to the actual strain value occurring at this stage of the technological process and,-1 deformation reproducing the rolling process in an RSM block of a wire rod rolling mill, as tension, while maintaining the total strain value in this block.The general diagram of thermo-mechanical treatment, reproducing the entire rolling process of a 20 MnB4 steel wire rod with a diameter of 5.5 mm, is shown in Before the deformation process, the material was heated to a temperature of 1165 °C, corresponding to the temperature in the equalizing zone of a heating furnace . Then, in order to unify the temperature distribution in the entire sample working zone, the 20MnB4 steel was heated for 300 s. The following stage consisted of cooling for 30 s to a temperature of 1086 °C, replicating the cooling of the band during its transport from the furnace to the first rolling pass stand. Then, the tested samples were deformed over 17 cycles with strain parameters in accordance with After physical modelling, changes in the most important parameters of the process  were analyzed in detail.During the second stage of work, samples were cut out from the material for metallographic tests after physical modelling using an EDM 32 wire electro-driller, and then metallographic microsections (nitrile etching) were prepared .The locations of characteristic points where metallographic analyses and hardness measurements were carried out are presented in An assessment of the microstructure of the tested steel was carried out using light microscopy (Nikon Eclipse MA-200 microscope with NIS-Elements software) . The aveYS), ultimate tensile strength (UTS), and plasticity reserve were determined.HV is the Vickers hardness; %Mn, %Si, %P, %Cu, %N, %Ni, and %C are the content in mass percent of manganese, silicon, phosphorus, copper, nitrogen, nickel, and carbon, respectively, in the steel; and αD is the ferrite grain size in μm.In the following stage, on the basis of available mathematical models and using measurements of average ferrite grain sizes, chemical composition, and hardness ,29, the The scope of research carried out in terms of the work also included determining selected mechanical properties directly during the static tensile test using a Zwick Z/100 strength machine .During the final stage of the work, the obtained research results were verified under industrial conditions.The general course of temperature and plasticizing yield stress during the physical modelling of the rolling process of 20MnB4 steel round bars in a medium continuous rolling mill is shown in The most important parameters of the deformation process during the physical modelling of rolling of round bars made of 20MnB4 steel in a medium continuous rolling mill, which have been tested, determined, and verified in previous works ,21, are When analyzing the data presented in −1, with values of individual deformations of 0.5–0.6, resulted in exceeding the strain value. According to published data, among others, in the paper [Analyzing the data in he paper , despitehe paper .The minimum time between deformations achievable by a torsion plastometer was 0.9 s. After the last deformation in the rod rolling mill (No. 17), in accordance with the industrial conditions, the material was cooled to a temperature of about 851 °C, required before the first deformation in an NTM block of a wire rod rolling mill . AccelerThe general course of temperature and yield stress during the physical modelling of a 20MnB4 steel wire rod rolling process in NTM and RSM blocks of a wire rod rolling mill for the V1 test variant is shown in The most important parameters of the deformation process during the physical modelling of rolling a 20MnB4 steel wire rod with a diameter of 5.5 mm in NTM and RSM blocks of a wire rod rolling mill according to the V1 test variant are presented in Analyzing the temperature changes during the deformation reproducing the rolling process in an NTM block (No. 18–27), it is possible to observe a continuous increase in temperature caused mainly by short intervals between successive deformations. Comparing the nominal (set) and obtained temperature values during the physical modelling of the 20MnB4 steel rolling process in an NTM block, a high accuracy of this analyzed parameter was found. The biggest error between the set temperature value and the obtained value occurred for passes No. 18 and 22, at 0.2%.The course of yield stress during the first five deformation sequences at this stage of the physical modelling process is somewhat unusual. As the temperature increases, the yield stress decreases and then slightly increases. This may result from an uneven temperature distribution after the process of accelerated cooling between the continuous rolling mill and the NTM block. During subsequent cycles of deformations simulating the rolling process in an NTM block, the course of yield stress is typical, i.e., as the temperature of the deformed material increases, the yield stress value of the deformed steel decreases.The minimum possible time between deformations achieved by the torsion plastometer was 2 s. After the final deformation in an NTM block (No. 27), in accordance with industrial conditions, accelerated material cooling to a temperature of about 845 °C was required before the first deformation in an RSM block of a wire rod rolling mill was applied . The accAnalyzing the temperature changes during the deformation reproducing the rolling process in an RSM block (No. 28–31), it is possible to observe (similar to the case of deformation in the NTM block) a continuous increase in temperature caused mainly by short intervals between successive deformations. By comparing the values of the nominal (set) temperature and that obtained during the physical modelling of the 20MnB4 steel rolling process in an RSM block, a high accuracy of this analyzed parameter was found. The largest error between the set temperature value and the obtained value occurred for pass No. 28 and was 0.4%. Despite an increase in temperature during the first two deformation sequences (No. 28 and 29), the yield stress increased , which mThe general course of temperature and yield stress during the physical modelling of 20MnB4 steel wire rod rolling process in NTM and RSM blocks of a wire rod rolling mill for the V2 test variant is shown in −1, whereas in the case of the RSM block it was 10 s−1. In turn, this had a positive impact in that it increased the value of the yield stress. In relation to the V1 test variant, the yield stress in the NTM block increased in value to about 223 MPa, while in the case of the RSM block, the yield stress value increased to approximately 145 MPa. During the physical modelling of the rolling process in NTM and RSM blocks according to the V2 test variant, the increase in temperature in these blocks was also programmed. Taking into account the inductive method of heating the samples and the shape of the inductive exciter itself  the speed of accelerated cooling was increased between the continuous rolling mill and the NTM block as well as between the NTM and RSM blocks, and the resistance immediately after accelerated cooling was abandoned. This facilitated an increase in temperature as a result of the rapid thermal conductivity from areas with higher temperatures towards the central part of the samples. The error between the temperature assumed after deformation in the NTM block and the temperature obtained during physical modelling was 7.4%. In the case of the RSM block, the error between the temperature assumed after deformation and the temperature obtained during physical modelling was less than 2%.Replacing the sequence of individual deformations in NTM and RSM blocks of a wire rod rolling mill with single deformations with strain values equal to the actual strain value occurring in these blocks (similar to the case of variant V2) allowed using a higher value of the strain rate in relation to the V1 test variant. In the case of the NTM block, the strain rate was 40 sIt was found that the obtained level of yield stress, as a result of replacing the sequence of individual deformations in NTM and RSM blocks with one deformation and changing the strain state in the RSM block, is similar to the value of yield stress occurring in the actual technological process , which iThe general course of changes in yield stress for all analyzed variants is shown in Examples of the 20MnB4 steel microstructure after the physical modelling process according to the V1–V3 variants are shown in α ferrite grain size was between 8.14 and 5.48 μm. The average Dα ferrite grain size was 6.43 μm  to the value achieved as a result of modelling in accordance with the V1 variant and was at 6.62 μm . Moreover, the value of yield stress during the physical modelling of the deformation process in the NTM block in this variant in relation to the V1 variant was also higher   , it was α ferrite grain size in a cross-section of the samples , it is possible to observe a relatively high homogeneity in size. This may result from the high value of the total strain value (14.32) and the small length of the sample’s measured part , whereas by analyzing the grain size at individual measurement points  and those presented in earlier works ,21 with In the future, we have planned to carry out the physical modelling of the analyzed process with the use of a complex deformation scheme (simultaneous tension and torsion) during the modelling of the rolling stages in NTM and RSM blocks of a rolling mill. The purpose of these tests is to create a strong deformation (neck) location in the deformed samples. Based on the results of many experimental and theoretical studies, it has been proven that the deformation speed in the neck during a tensile test is higher than the average speed calculated on the basis of changes in the measurement length of samples . Taking An increase in the deformation speed in the analyzed process should positively affect the stress and activation of microstructure reconstruction processes and consequently increase the accuracy of the results of physical modelling  in relation to the results of industrial tests. However, this will require designing a new geometry of samples, as the current geometry leads to a deformation location outside the research area, which disqualifies it for further analysis . The locIn addition, we have planned to carry out tests of the analyzed process with alternating torsion and alternating compression and tensile tests.The speed of implementing the results of theoretical calculations and laboratory scale tests in industry determines the development and dissemination of new technologies. Industrial research constitutes the final and very costly part of the implementation process, costly due to involving significant levels of production, amounts of manpower and materials, and the consumption of utilities. The costs of implementing new technologies can be significantly reduced and the process itself can be simplified and accelerated with the use of modern research methods. Physical modelling of the dynamic wire rod rolling in modern rolling mills is a complicated issue. This is due to, among others, high deformation speeds in individual rolling stands and short intervals between successive deformations. Therefore, during physical modelling of this process, it is necessary to take advantage of certain simplifications, for example, by replacing the sequence of several deformations with a single deformation. In the case of the analyzed, dynamic plastic treatment processes, such a solution is acceptable, as evidenced by the research results published, among others, in works ,40.Results of the parameters of the deformation process from physical modelling that are similar to those occurring in actual processes ensures the high accuracy of the obtained results, and they affect the shape and nature of changes in the plasticizing stress of the tested material and consequently the microstructure and properties of the finished product. In this paper, a similar value of plasticizing stress to that occurring in the actual rolling process  was achiThe best variant is the V3 variant, which consists of physically replicating the rolling process in a bar rolling mill as multi-sequence non-free torsion; the rolling process in an NTM block (No-Twist Mill) as non-free continuous torsion, with the total deformation equal to the actual deformation occurring during this stage of the technological process; and the rolling process in an RSM block (reducing and sizing mill) as a tension, while maintaining the total deformation value in this block;The difference between the ferrite grain size measured in the cross-section of a wire rod and obtained as a result of physical modelling according to the V3 technological variant was 4.3%, whereas the error between the ferrite grain sizes measured in the longitudinal cross-section of a wire rod and obtained as a result of physical modelling for this technological variant was 11.2%. On this basis, it can be concluded that the average ferrite grain size in a wire rod obtained under industrial conditions is similar to the grain size obtained in samples after physical modelling of the rolling process according to variant V3;The differences between the most important mechanical parameters determined during a static tensile test of a wire rod under industrial conditions and material after physical modelling were 1.5% for the yield strength, approximately 6.1% for the tensile strength, and approximately 4.1% for the constriction and plasticity reserve;The developed research methodology (variant V3) allows for replicating the entire deformation cycle while precisely preserving the temperature value of the deformed material during individual stages of the analyzed technological process and allows for quickly and accurately determining the most important mechanical properties during a static tensile test;Using a variable deformation scheme increases the research possibilities of modern torsion plastometers in terms of physical modelling of dynamic thermal and plastic treatment processes.On the basis of the results presented in the paper, the following conclusions can be drawn:


The aim of the study is to observe the difference in progression between type 1 and type 2 Bietti crystalline dystrophy (BCD) using multimodal imaging.  A retrospective clinical study was performed with six BCD patients who underwent multimodal imaging twice in Hebei Provincial Eye Hospital from October 2015 to December 2020. Multimodal imaging includes color fundus photography, fundus autofluorescence (AF), infrared autofluorescence (IRAF), fundus fluorescein angiography (FFA), and spectral domain optical coherence tomography (SD-OCT). The fundus lesion progression difference was observed in 3 patients with type 1 BCD and 3 patients with type 2 BCD.  In type 1 BCD, the range of hypoautofluorescence (hypo-AF), hypoinfrared autofluorescence (hypo-IRAF), and hypofluorescence in the posterior pole was enlarged, and FFA showed that the lesions in the posterior pole and periphery extended to the middle periphery. SD-OCT revealed retinal and choroidal thinning, progressive loss of the outer nuclear layer and ellipsoid zone, and reduction of the choroid macrovascular diameter. In type 2 BCD, the range of hypo-AF was enlarged, but there was no significant change in the macula area. The uniform hypo-IRAF in the posterior pole showed no significant change. FFA showed no significant change with the progression of the disease in the macula area and the hypofluorescence around it expanded. SD-OCT revealed no obvious change in the macula area.  The retinal choroid atrophy in the macula area of type 1 BCD continued to worsen, and the choroid great vessels became narrower. The macular lesions of type 2 BCD can remain unchanged for a long time. Bietti crystalline dystrophy (BCD) was first reported by Bietti et al. in 1937 . CurrentThe implementation of all research methods in this study followed the provisions of the Helsinki Declaration, the Ethics Committee of Beijing Tongren Hospital and the Ethics Committee of Hebei Provincial Eye Hospital. This study included 6 BCD subjects who underwent fundus color photography, autofluorescence (AF), infrared autofluorescence (IRAF), FFA, and spectral domain optical coherence tomography (SD-OCT) twice in Hebei Provincial Eye Hospital from October 2015 to December 2020. The clinical features and imaging changes of these patients were retrospectively analyzed.Written informed consent was obtained from each patient before peripheral venous blood was drawn for genomic DNA extraction and mutation screening of the CYP4V2 gene by direct sequencing. The 6 subjects were unrelated Chinese patients, and all diagnosed with BCD by genetic testing.For convenience of description, the 6 patients are referred to as P1, P2, P3, P4, P5, and P6. The interval between the two multimodal imaging was 1 year for P1 and P2, 3 years for P3, and 2 years for P4–P6.Our previous study divided BCD into two types based on the observation of FFA progression in 12 patients with BCD . In typeAll patients underwent a complete ophthalmic examination, including the best corrected visual acuity (BCVA), slit lamp microscopy, Goldman flattening tonometry dilated fundus examination, and fundus photography . AF, IRAF, and FFA images were obtained with a confocal scanning laser ophthalmoscope  with a 55 × 55° field lens.SD-OCT images were obtained by spectral-domain optical coherence tomography . Central macular thickness (CMT) and subfoveal choroid thickness (SCT) were measured in the B-scan flat through the macula fovea. Two large choroid vessels that easily measured were selected for measurement of the vessel diameter, one at the nasal side and one at the temporal side of the choroid below the fovea. The difference of vessels' diameter between the first and last examination was calculated, and the change of vessels' diameter was calculated. The ellipsoid zone (EZ) of the fovea in the right eye of P1 was missing, but the remaining EZ was visible in the temporal side of the fovea. Therefore, the distance between the Bruch membrane of the fovea and the residual EZ of the temporal side was measured, and the difference between the first and last measured values was calculated . A smallThe age of six patients ranged from 30 to 46 years at initial diagnosis. The BCVA of the type 1  and type 2  BCD patients decreased significantly. The genetic data of the patients are shown in With the progression of the disease, the crystalline deposits in the posterior pole fundus of patients with type 1 BCD decreased significantly Figures . In typeThe AF and IRAF of both eyes of the BCD patients were basically the same. The range of hypo-AF in P1–P6 expanded. The hypo-AF region is formed by the combination of multiple small patches of hypo-AF Figures . In typeThe IRAF images of type 1 patients showed hyper-IRAF spots at the edge of the hypo-IRAF, and there were fewer hyper-IRAF spots than hyper-AF spots Figures . The posThe regularity of FFA progression in BCD patients has been reported in detail in our previously published paper . The speμm greater than the first, indicating that EZ was also lost progressively in the right eye of P1. In type 2 patients, the EZ, the interdigitation zone, and part of the RPE were absent in the macular area, and the external limiting membrane was clearly visible . There was no EZ residue in the fovea of the right eye of P1, so the distance between the remnant of the EZ at the temporal side of the fovea and the Bruch membrane at the fovea was measured. The last distance was 165  visible . Except  changes .The 6 patients observed in this study ranged in age from 30 to 46 years, which is the common age of BCD onset. The results of gene mutation of the 6 patients were all BCD-related gene mutation sites , 12.Color fundus photographs of type 1 BCD showed a decrease in crystalline deposits with the progression of disease, consistent with previous reports . The yelIt is known that AF mainly reflects the fluorescence of lipofuscin . The locRetinal and choroidal atrophy in the last FFA examination of 6 BCD patients was significantly worse than that in the first FFA examination, which was consistent with previous reports , 9. BothIn this study, the changes in the retina and choroid in BCD patients were quantified by SD-OCT. In type 1 patients, both the retina and choroid thinned significantly, and the diameters of choroidal great vessels narrowed. Studies have reported that the blood flow density of choroidal capillaries in BCD patients decreases as measured by optical coherence tomography angiography . AccordiThe limitation of this study was that the number of eyes included was small and the observation time was not very long. However, if the rarity of the disease and previous literature are considered, this was the first study to observe the progress of BCD by multimodal imaging, and the number of cases reported was relatively large.In conclusion, in addition to atrophy of the retina and choroid capillary layers, the diameter of the choroid great vessels in type 1 BCD was also significantly reduced. In type 2 BCD patients, retinopathy was significantly aggravated, except for the macula area. Noninvasive examination of AF, IRAF, and SD-OCT have great advantages in assessing BCD progression and changes.