A method and system for diagnosing mechanical-electrical coupling damage of a wind-solar-storage system

Abstract

The application relates to the technical field of electromechanical coupling damage diagnosis, and discloses a wind-solar-storage system electromechanical coupling damage diagnosis method and system, which comprises the following steps: a finite element mechanics model is constructed according to the geometric data, material properties and load data of a welding point area, and stress distribution data are calculated; a corrosion kinetics model is constructed according to environmental data and electrochemical data, and corrosion product parameters are obtained; an elastic modulus degradation model is established according to the corrosion product parameters, and inherent frequency degradation values and mode shape displacements are obtained; vibration response analysis is carried out on the junction box according to the inherent frequency degradation values and the mode shape displacements, and a stress concentration coefficient is obtained; and the electrical parameter change amount and the stress concentration coefficient are input into a damage failure evaluation model, and damage failure evaluation results of the electrical connection point are obtained. Through the multi-dimensional coupling model and the dynamic parameter closed-loop feedback mechanism, the application effectively improves the accuracy of electromechanical coupling damage evaluation, thereby improving the safety and operation and maintenance efficiency of the wind-solar-storage system.

Description

Technical Field

[0001] The present invention relates to the technical field of electromechanical coupling damage diagnosis, and in particular to a method and system for diagnosing electromechanical coupling damage in a wind-solar-storage system. Background Art

[0002] In wind, solar and energy storage systems, photovoltaic brackets serve as the core supporting structure, and their welding points are subjected to complex electromechanical coupling for a long time. Especially in harsh environmental conditions such as humidity and salt spray, the risk of damage is significantly increased. Welding process defects or material aging can easily lead to geometric mutations in the weld area, forming local stress concentrations. Under the action of dynamic external forces such as wind loads, component deadweight and mechanical vibration, these stress concentration areas will further induce the initiation of microcracks, and the synergistic effect of environmental humidity and corrosive media will accelerate the electrochemical corrosion process. The additional stress generated by the volume expansion of corrosion products is superimposed on the mechanical stress, causing the stress intensity factor at the crack tip to continue to increase, ultimately leading to stress corrosion cracking. This process not only weakens the structural integrity of the welding points, but also causes the local stiffness of the bracket to degrade, thereby changing its overall vibration characteristics. As the electrical hub of the photovoltaic system, the reliability of the junction box is directly affected by the vibration characteristics of the bracket.

[0003] Conventional monitoring methods often analyze the electrical parameters of the junction box independently, ignoring the mechanical stress redistribution caused by bracket vibration transmission. When the bracket's natural frequency shifts due to stiffness degradation, the vibration acceleration amplitude at the junction box's fixing points can surge, causing the internal stress concentration factor to exceed the material fatigue threshold, accelerating loosening or corrosion of the electrical connections. However, existing technologies lack cross-scale diagnostic models that integrate mechanical vibration and electrical parameters, making it difficult to achieve early and accurate early warning. Furthermore, health monitoring methods for photovoltaic bracket welds are often limited to single-physics field analysis: evaluating static stress distribution through finite element simulation, monitoring corrosion rates using electrochemical sensors, or relying on vibration signals to identify structural modal changes. These methods have significant drawbacks: First, they lack multi-field coupling effects, ignoring the interaction between stress, corrosion, and vibration, resulting in large prediction errors; second, they lack dynamic correction capabilities, making static models unable to respond to dynamic loads such as wind-induced vibration and time-varying corrosion; Furthermore, there are blind spots in system-level damage transmission, and a lack of models linking weld stiffness degradation with junction box electrical connection failure. This leads to a high rate of false positives, resulting in delayed maintenance and secondary damage.

[0004] Therefore, there is an urgent need for a multi-field coupled damage diagnosis method that integrates mechanical, electrochemical, vibration modes and electrical parameters. Through dynamic correction mechanism and closed-loop feedback strategy, it can break through the limitations of traditional single-field analysis and improve the long-term operation reliability of wind, solar and storage systems in complex environments. Summary of the Invention

[0005] In order to solve the above technical problems, the present invention provides a method and system for diagnosing electromechanical coupling damage in a wind-solar-storage system, which can solve the problem that the existing technology lacks cross-scale diagnosis that integrates mechanical vibration and electrical parameters, resulting in low accuracy of diagnostic results, and effectively improves the accuracy of electromechanical coupling damage assessment, thereby improving the safety, stability and reliability of the operation of the wind-solar-storage system.

[0006] In a first aspect, the present invention provides a method for diagnosing electromechanical coupling damage in a wind-solar-storage system, the method comprising:

[0007] Based on the geometric data, material properties and load data of the photovoltaic bracket welding point area in the wind-solar-storage system, a finite element mechanical model is constructed to calculate the stress distribution data of the welding point area;

[0008] Based on the environmental data and electrochemical data of the welding point area, a corrosion kinetics model is constructed to obtain the corrosion product parameters of the welding point area;

[0009] Based on the corrosion product data, the corrosion product expansion stress is obtained, the corrosion product expansion stress is superimposed on the finite element mechanics model, and the stress intensity factor is calculated based on linear elastic fracture mechanics;

[0010] Based on the stress intensity factor, determine whether there is a weld stiffness degradation area. If so, establish an elastic modulus degradation model for the weld stiffness degradation area based on the corrosion product parameters to obtain the natural frequency degradation value and mode displacement of the weld area.

[0011] Based on the natural frequency degradation value and mode displacement, the vibration response of the junction box on the photovoltaic bracket is analyzed to obtain the stress concentration factor;

[0012] The electrical parameter changes of the electrical connection points in the junction box are obtained, and the electrical parameter changes and stress concentration factors are input into a pre-built damage failure assessment model to obtain the damage failure assessment results of the electrical connection points.

[0013] Furthermore, the step of constructing a finite element mechanical model based on the geometric data, material properties and load data of the welding point area of ​​the photovoltaic bracket in the wind-solar-storage system and calculating the stress distribution data of the welding point area includes:

[0014] The geometric data of the photovoltaic bracket welding point area in the wind-solar-storage system is converted into a finite element mesh, and the finite element mechanical mesh is constructed based on the elastic modulus and Poisson's ratio parameters of the welding material;

[0015] Loading wind load data and self-weight load data into the finite element mechanics grid to obtain a finite element mechanics model;

[0016] The finite element mechanical model is solved to obtain the stress distribution data of the welding point area.

[0017] Furthermore, the step of constructing a corrosion kinetics model based on the environmental data and electrochemical data of the welding point area to obtain the corrosion product parameters of the welding point area includes:

[0018] Based on the environmental data and electrochemical data of the welding point area, the corrosion current density of the welding point area is calculated using the polarization curve method;

[0019] The corrosion rate is calculated based on Faraday's law and corrosion current density, and the corrosion depth is obtained based on the corrosion rate.

[0020] Furthermore, the steps of obtaining corrosion product expansion stress based on corrosion product data, superimposing the corrosion product expansion stress on a finite element mechanics model, and calculating a stress intensity factor based on linear elastic fracture mechanics include:

[0021] Calculate the expansion stress of corrosion products based on the elastic modulus and corrosion depth of the welding material;

[0022] Based on linear elastic fracture mechanics, the expansion stress of corrosion products is superimposed on the maximum stress in the stress distribution data to obtain the stress intensity factor.

[0023] Furthermore, the step of determining whether there is a weld stiffness degradation region based on the stress intensity factor includes:

[0024] According to the material fracture toughness data of the welding material, the strength threshold is set;

[0025] The stress intensity factor is compared with the strength threshold. If the stress intensity factor is greater than the strength threshold, it is determined that there is a weld stiffness degradation area.

[0026] Furthermore, the step of establishing an elastic modulus degradation model of the weld stiffness degradation region based on the corrosion product parameters and obtaining the natural frequency degradation value and mode displacement of the weld region includes:

[0027] According to the corrosion depth, the elastic modulus degradation model of the weld stiffness degradation area is established to obtain the elastic modulus degradation value;

[0028] According to the elastic modulus degradation value, the natural frequency degradation value of the welding point area is calculated;

[0029] The elastic modulus degradation value is input into the finite element mechanics model, and the characteristic equation is solved through finite element modal analysis to obtain the vibration mode displacement.

[0030] Furthermore, the step of performing vibration response analysis on the junction box on the photovoltaic support according to the natural frequency degradation value and the mode displacement to obtain the stress concentration factor includes:

[0031] Calculate the vibration acceleration of the junction box on the photovoltaic bracket based on the natural frequency degradation value and mode displacement;

[0032] Based on the vibration acceleration, the peak stress of the junction box is determined, and the stress concentration factor is obtained according to the ratio of the peak stress to the nominal stress.

[0033] Furthermore, the step of obtaining the electrical parameter changes of the electrical connection points in the junction box and inputting the electrical parameter changes and the stress concentration factor into a pre-built damage and failure assessment model to obtain damage and failure assessment results of the electrical connection points includes:

[0034] Obtain the contact resistance and current of the electrical connection points in the junction box, and calculate the temperature rise of the connection points based on the Joule heating model;

[0035] Calculate the contact resistance change rate based on the contact resistance and the reference resistance;

[0036] The temperature rise of the connection point, the contact resistance change rate and the stress concentration factor are input into a pre-built damage failure assessment model to obtain the damage failure probability of the electrical connection point. The damage failure assessment model is constructed based on a support vector machine model.

[0037] Furthermore, after the step of obtaining the damage failure assessment result of the electrical connection point, the method further includes:

[0038] Based on the damage and failure assessment results of the electrical connection points, it is determined whether the state is high-risk. If so, the elastic modulus degradation model is modified based on the damage and failure assessment results.

[0039] In a second aspect, the present invention provides a wind-solar-storage system electromechanical coupling damage diagnosis system, the system comprising:

[0040] The stress corrosion analysis module is used to construct a finite element mechanics model based on the geometric data, material properties, and load data of the photovoltaic bracket welding point area in the wind-solar-storage system, and calculate the stress distribution data of the welding point area;

[0041] Based on the environmental data and electrochemical data of the welding point area, a corrosion kinetics model is constructed to obtain the corrosion product parameters of the welding point area;

[0042] Based on the corrosion product data, the corrosion product expansion stress is obtained, the corrosion product expansion stress is superimposed on the finite element mechanics model, and the stress intensity factor is calculated based on linear elastic fracture mechanics;

[0043] The stiffness vibration analysis module is used to determine whether there is a weld stiffness degradation area based on the stress intensity factor. If so, an elastic modulus degradation model of the weld stiffness degradation area is established based on the corrosion product parameters to obtain the natural frequency degradation value and vibration mode displacement of the weld area.

[0044] Based on the natural frequency degradation value and mode displacement, the vibration response of the junction box on the photovoltaic bracket is analyzed to obtain the stress concentration factor;

[0045] The damage failure assessment module is used to obtain the electrical parameter changes of the electrical connection points in the junction box, and input the electrical parameter changes and stress concentration factors into a pre-built damage failure assessment model to obtain the damage failure assessment results of the electrical connection points.

[0046] The present invention provides a method and system for diagnosing electromechanical coupling damage in a wind, solar and storage system. The present invention constructs a full-chain evaluation model for electromechanical coupling damage by integrating multi-dimensional data of mechanical stress field, electrochemical corrosion field, vibration modal field and electrical parameter field, effectively solving the problem of high misjudgment rate caused by traditional single physical field analysis and improving the accuracy of failure assessment. Through the parameterized model simplification strategy, while ensuring accuracy, the computational complexity is effectively reduced and the computational efficiency is improved. Through closed-loop feedback and self-learning capabilities, the problem of model accuracy decreasing with service time is solved, the early warning forecast rate is further reduced, and the accuracy of failure assessment is improved. The present invention effectively improves the accuracy of electromechanical coupling damage assessment through a multi-dimensional coupling model and a dynamic parameter closed-loop feedback mechanism, thereby improving the safety, stability and reliability of the operation of the wind, solar and storage system, and further improving the operation and maintenance efficiency of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 1 is a flow chart of a method for diagnosing electromechanical coupling damage in a wind-solar-storage system according to an embodiment of the present invention;

[0048] Figure 2 It is a structural diagram of the electromechanical coupling damage diagnosis system of the wind-solar-storage system in an embodiment of the present invention. DETAILED DESCRIPTION

[0049] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0050] See also Figure 1 The first embodiment of the present invention provides a method for diagnosing electromechanical coupling damage in a wind-solar-storage system, which includes steps S10 to S60:

[0051] Step S10, constructing a finite element mechanical model based on the geometric data, material properties and load data of the welding point area of ​​the photovoltaic bracket in the wind-solar-storage system, and calculating the stress distribution data of the welding point area;

[0052] Step S20, constructing a corrosion kinetics model based on the environmental data and electrochemical data of the welding point area to obtain corrosion product parameters of the welding point area;

[0053] Step S30, obtaining corrosion product expansion stress based on the corrosion product data, superimposing the corrosion product expansion stress onto a finite element mechanics model, and calculating a stress intensity factor based on linear elastic fracture mechanics;

[0054] Step S40: Determine whether there is a weld stiffness degradation region based on the stress intensity factor. If so, establish an elastic modulus degradation model for the weld stiffness degradation region based on the corrosion product parameters to obtain the natural frequency degradation value and mode displacement of the weld region.

[0055] Step S50, performing a vibration response analysis on the junction box on the photovoltaic support according to the natural frequency degradation value and the mode displacement to obtain a stress concentration factor;

[0056] Step S60 , obtaining electrical parameter changes of electrical connection points in the junction box, and inputting the electrical parameter changes and stress concentration factors into a pre-built damage failure assessment model to obtain damage failure assessment results of the electrical connection points.

[0057] The present invention provides a diagnostic method for studying electromechanical coupling damage of photovoltaic brackets in wind-solar-storage systems. The present invention conducts a comprehensive analysis of the photovoltaic bracket and the electrical junction box. Since stress concentration at the welding points of the photovoltaic bracket will accelerate local electrochemical corrosion, the volume expansion of the corrosion product will further increase the local stress, induce crack initiation and reduce the stiffness of the material, resulting in changes in the structural vibration characteristics. After the vibration characteristics change, the dynamic load will be transmitted to the junction box through the bracket, causing changes in its internal stress. At the same time, the combined effect of the vibration inertia force and the Joule heat of the electrical connection point will cause changes in the internal electrical parameters of the junction box. Due to the changes in electrical parameters and stress, the electrical connection points in the junction box are easily damaged or fail.

[0058] Based on the above analysis process, the present invention analyzes the changes in the vibration characteristics of the bracket due to crack propagation, and the impact of such changes on the stress distribution of the photovoltaic module junction box, through the synergistic effect of stress concentration and electrochemical corrosion at the bracket welding points, and the promotion of stress corrosion cracking at the welding points by environmental humidity, so as to determine the damage state of the electrical connection points of the photovoltaic module. In the present invention, stress analysis is first performed on the welding point area of ​​the photovoltaic bracket. The specific analysis steps include:

[0059] The geometric data of the photovoltaic bracket welding point area in the wind-solar-storage system is converted into a finite element mesh, and the finite element mechanical mesh is constructed based on the elastic modulus and Poisson's ratio parameters of the welding material;

[0060] Loading wind load data and self-weight load data into the finite element mechanics grid to obtain a finite element mechanics model;

[0061] The finite element mechanical model is solved to obtain the stress distribution data of the welding point area.

[0062] In this embodiment, a 3D scanner is used to scan the weld area of ​​a photovoltaic bracket to obtain point cloud data, or geometric data, for the weld area. This point cloud data is then de-noised to obtain surface mesh data for the weld. A finite element mechanics mesh is then constructed based on the elastic modulus and Poisson's ratio parameters of the welding material. Load data is then loaded onto the finite element mechanics mesh to create a finite element mechanics model. The load data includes wind load and deadweight load. The wind load is the pressure generated by wind speed under extreme operating conditions, while the deadweight load includes the deadweight of the bracket and the weight of the photovoltaic module.

[0063] Based on the finite element mechanics model, the stress transfer path extends from the weld point to the bracket. Based on this stress transfer path, the nodal stress is solved using finite element analysis to obtain the maximum stress and shear stress at each node, thereby obtaining stress distribution data in the weld area. Based on the maximum stress in the stress distribution data, the area with the most concentrated stress is screened out, and the regional coordinates of the stress concentration area are determined.

[0064] After analyzing the stress distribution of the photovoltaic bracket, the next step is to analyze the corrosion of the welding point area. The specific steps include:

[0065] Based on the environmental data and electrochemical data of the welding point area, the corrosion current density of the welding point area is calculated using the polarization curve method;

[0066] The corrosion rate is calculated based on Faraday's law and corrosion current density, and the corrosion depth is obtained based on the corrosion rate.

[0067] In this embodiment, environmental and electrochemical data from the weld area are first acquired through an installed sensor array. Environmental data includes ambient humidity, and electrochemical data includes polarization resistance, potential, and the like. Preferably, when deploying sensors, high-stress areas (such as the heat-affected zone of a weld) can accelerate electrochemical corrosion. This is because stress concentration increases dislocation density, leading to lattice distortion, exposure of metal active sites, and accelerated anodic dissolution. Furthermore, microcracks are easily formed in stress concentration areas, providing diffusion pathways for corrosive media. Furthermore, stress concentration areas are often accompanied by geometric abrupt changes (such as weld dents and sharp corners), which can easily lead to the retention of water films and the formation of localized corrosive microenvironments. Therefore, in this embodiment, stress concentration areas are marked as key monitoring areas for corrosion modeling, and the density of humidity sensors and electrochemical microelectrodes is correspondingly increased in these stress concentration areas, for example, from a 4×4 array to a 6×6 array.

[0068] Based on the collected data, the metal corrosion rate is calculated using the polarization curve method. The polarization curve method, also known as the Stern-Geary formula, is a formula for calculating the metal corrosion rate. The corrosion rate can be calculated by measuring the potential difference and current density of the metal in a corrosive environment. Based on this formula, the polarization resistance is inversely proportional to the corrosion current density. Therefore, the corrosion current density can be derived from the polarization resistance:

[0069]

[0070] Where i corr represents the corrosion current density, β a represents the anode Tafel slope, β c represents the cathode Tafel slope, R p represents the polarization resistance, where the Tafel slope can be obtained by electrochemical experiments on the welding material, i.e., the bracket material, and the polarization resistance can be obtained by electrochemical impedance spectroscopy (EIS) measurement. 2.3 represents the engineering simplified value of ln(10).

[0071] Since the local current density in the high stress area will increase, the difference in current density between the high stress area and the low stress area is not taken into account in the above corrosion current density calculation. Therefore, in a preferred embodiment, the present invention introduces a stress correction factor to correct the corrosion current density, thereby improving the accuracy of the corrosion current density calculation. The corrosion current density correction value can be expressed as:

[0072]

[0073] In the formula, α represents the stress corrosion sensitivity coefficient, σ represents the local stress value of the region, Indicates the material yield strength. The stress corrosion sensitivity coefficient is a preset value, the local stress value is obtained through finite element mechanics model analysis, and the material yield strength is obtained by looking up the welding material table.

[0074] After obtaining the corrosion current density, the corrosion current density is converted into the actual corrosion rate of the metal based on Faraday's law. Faraday's law describes the relationship between the amount of electricity passing through the electrode and the weight of the electrode reactants. Because the current is related to the number of electrons transferred during the metal dissolution process, and the number of electrons transferred has a stoichiometric relationship with the amount of metal dissolved, the corrosion rate of the metal can be calculated according to Faraday's law through the corrosion current density:

[0075]

[0076] Where M represents the molar mass of the metal, n represents the number of electrons in the redox reaction, F represents the Faraday constant, and ρ represents the metal density.

[0077] The corrosion depth can then be calculated based on the product of the actual corrosion rate and the corrosion time. It should be noted that the specific steps in this embodiment can refer to the conventional calculation steps of the Stern-Geary formula and Faraday's law, and will not be described in detail here.

[0078] Since corrosion products can affect the stress state of the weld, in this embodiment, the stress of the weld is further analyzed by the generation rate of corrosion products and the corrosion depth, thereby determining the impact of corrosion on the original stress. The specific analysis steps include:

[0079] Calculate the expansion stress of corrosion products based on the elastic modulus and corrosion depth of the welding material;

[0080] Based on linear elastic fracture mechanics, the expansion stress of corrosion products is superimposed on the maximum stress in the stress distribution data to obtain the stress intensity factor.

[0081] In this embodiment, based on classical elasticity and corrosion dynamics theory, corrosion expansion stress is an internal stress generated when the volume expansion of metal corrosion products is constrained by the surrounding material. This means that the volume of the corrosion products generated after metal corrosion is typically larger than the original metal volume. The corrosion products are constrained by the geometry of the surrounding uncorroded materials or structures, leading to localized stress accumulation. Therefore, the corrosion product expansion stress can be characterized by the volume expansion rate of the corrosion products, i.e., the volume increment of the corrosion products per unit volume of metal.

[0082] In conventional methods, the volume expansion rate is directly related to the corrosion rate. The corrosion depth is determined by the corrosion rate and corrosion time. Assuming that the corrosion products are evenly covered on the metal surface, the volume expansion is calculated from the corrosion depth, the corrosion area, and the corrosion product volume expansion ratio. The volume expansion is then divided by the original volume, which is obtained by multiplying the corrosion area by the original metal thickness. The volume expansion rate can be expressed as follows:

[0083]

[0084] Where △V represents the volume expansion, V represents the original volume, A represents the corrosion area, and d coor represents the corrosion depth, d0 represents the original metal thickness, Represents the volume expansion ratio of corrosion products.

[0085] The corrosion expansion stress can then be obtained by multiplying the elastic modulus of the material by the volume expansion rate:

[0086]

[0087] Where E represents the elastic modulus, Indicates corrosion expansion stress. Taking Q235B steel as an example, its elastic modulus E=210GPa.

[0088] In a preferred embodiment, based on the actual needs of engineering applications and to reduce computational complexity, the present invention simplifies the corrosion expansion stress model. It assumes that the volume expansion ratio of the corrosion product is a fixed value and incorporates it into the empirical coefficient. The relationship between the volume expansion rate and the corrosion depth is directly calibrated using experimental data, resulting in a proportional relationship between the volume expansion rate and the corrosion depth:

[0089]

[0090] Therefore, the above formula can be simplified to:

[0091]

[0092] Where V corr represents the corrosion rate, t represents the corrosion time, and A represents the corrosion area. The corrosion area can be obtained by geometric calculation based on the finite element mechanics model. In the simplified formula, it is assumed that the corrosion depth is proportional to the corrosion area. Therefore, the volume expansion ratio can be simplified to be linearly related to the corrosion depth.

[0093] In this embodiment, the complex volume expansion ratio and original thickness are omitted and replaced by experimental calibration coefficients (implied in the proportional relationship of the formula), thereby reducing the amount of real-time calculations. The following is an equivalence verification of the simplified formula and the complete formula, because:

[0094]

[0095]

[0096] Where L is the characteristic length of the corrosion area, which is assumed to be a constant. Substituting it into the simplified formula yields:

[0097]

[0098] The (γ-1) / L is calibrated as a fixed coefficient by the experimental data, thus verifying the equivalence of the simplified formula and the complete formula.

[0099] The simplified formula in this embodiment directly relates the corrosion expansion stress to the corrosion rate, time and geometric parameters through model simplification and experimental calibration, avoiding the measurement and calculation of the complex volume expansion ratio γ, and effectively reducing the calculation complexity.

[0100] After obtaining the corrosion product expansion stress, the corrosion product expansion stress and the external load stress are superimposed. The external load stress is the maximum stress in the stress distribution data. Based on linear elastic fracture mechanics, the stress is equivalent to the stress intensity factor:

[0101]

[0102] Where K I represents the stress intensity factor, Y is the geometric correction factor, a is the crack length, is the maximum stress. Among them, the crack length can be pre-set to 0.1mm, or the crack expansion rate can be calculated by the Paris formula to obtain a more accurate crack length. The specific data can be flexibly selected according to the actual calculation requirements. The geometric correction factor is determined by the shape of the welding point. For different specifications of brackets, the welding point shapes include T-type, L-type and cross-type. Among them, the stress concentration coefficient of the T-type welding point is the largest. This is because the T-type joint is subjected to eccentric force. The stress distribution of the cross-type welding point is the most uniform, and the L-type welding point is prone to stress concentration at the corners. Therefore, different geometric correction factors are pre-set according to different geometric shapes to make the stress intensity factor more accurate.

[0103] Then, the stress intensity factor is used to determine whether the stiffness of the weld area has degraded. In this embodiment, a threshold comparison method is used to determine whether the stiffness degradation of the weld area has occurred. The strength threshold is based on the material fracture toughness data K of the welding material. IC To determine, preferably, at 0.35K IC As the intensity threshold, when K I >0.35K IC , it is determined that the stiffness of the region has degraded.

[0104] For the stiffness degradation area, an elastic modulus degradation model is established to calculate the natural frequency and mode displacement of the area. The natural frequency and mode displacement are used to characterize the stiffness degradation. The specific steps include:

[0105] According to the corrosion depth, the elastic modulus degradation model of the weld stiffness degradation area is established to obtain the elastic modulus degradation value;

[0106] According to the elastic modulus degradation value, the natural frequency degradation value of the welding point area is calculated;

[0107] The elastic modulus degradation value is input into the finite element mechanics model, and the characteristic equation is solved through finite element modal analysis to obtain the vibration mode displacement.

[0108] In this embodiment, since corrosion can cause a decrease in the elastic modulus of the material, thereby affecting the overall stiffness of the structure, an elastic modulus degradation model is established based on the corrosion depth:

[0109]

[0110] Where E0 represents the original elastic modulus of the welding material, E T represents the elastic modulus degradation value, and λ represents the corrosion stiffness attenuation coefficient.

[0111] Corrosion can lead to degradation of the elastic modulus E T Decreases, and the elastic modulus degradation value is approximately proportional to the equivalent stiffness of the photovoltaic bracket in a certain vibration mode. Therefore, when the elastic modulus degradation value decreases, the equivalent stiffness will decrease approximately year-on-year. In this embodiment, in order to simplify the calculation, it is assumed that corrosion only affects the stiffness and does not significantly change the mass distribution. Therefore, the equivalent mass of the photovoltaic bracket in the same mode remains unchanged. Therefore, the natural frequency degradation value of the welding point area can be expressed as:

[0112]

[0113] Where K d Represents the equivalent stiffness, M d Indicates equivalent mass.

[0114] Based on the elastic modulus degradation value and the original elastic modulus, the modulus reduction ratio can be obtained, and thus the stiffness reduction ratio can be obtained. The equivalent stiffness can be obtained by the original stiffness and the reduction ratio. The equivalent mass is determined by the material density and the structural mass distribution, which can be considered as a known number in this embodiment. Then, the characteristic equation is solved by finite element modal analysis:

[0115]

[0116] Where K represents the global stiffness matrix, M represents the global mass matrix, ω represents the angular frequency, ω=2πf t , φ represents the modal displacement, which is used to describe the deformation distribution of the structure in a certain mode.

[0117] The elastic modulus degradation value is input into the finite element mechanics model, K is regenerated and entered into the equation, and the eigenvector φ is solved to obtain the modal displacement. The modal displacement reflects the impact of local stiffness changes on the vibration pattern. This embodiment provides accurate and efficient data input for subsequent junction box vibration response analysis by accurately predicting frequency shifts and modal changes, thereby improving the accuracy of subsequent loss analysis.

[0118] Since the junction box of the photovoltaic module is fixed to the photovoltaic bracket, the vibration of the bracket will be transmitted to the junction box through the connection point. Therefore, changes in the vibration characteristics of the photovoltaic bracket will further affect the stress distribution of the photovoltaic module junction box, thereby causing fatigue damage to the junction box or electrical connection failure. Therefore, after obtaining the natural frequency degradation value and mode displacement, it is necessary to perform a vibration response analysis on the junction box on the photovoltaic bracket. The specific analysis steps include:

[0119] Calculate the vibration acceleration of the junction box on the photovoltaic bracket based on the natural frequency degradation value and mode displacement;

[0120] Based on the vibration acceleration, the peak stress of the junction box is determined, and the stress concentration factor is obtained according to the ratio of the peak stress to the nominal stress.

[0121] In this embodiment, assuming that the vibration is simple harmonic vibration, the displacement response can be expressed as:

[0122]

[0123] Where, is the maximum displacement of the vibration mode, t is the time, and ω is the angular frequency.

[0124] Taking the second derivative of the displacement gives the acceleration:

[0125]

[0126] The maximum acceleration amplitude is obtained as follows:

[0127]

[0128] Since ω=2πf t , and the maximum value of the mode displacement is obtained based on the mode displacement. Therefore, the vibration acceleration of the junction box can be determined as:

[0129]

[0130] The vibration acceleration a in this embodiment max This reflects the magnitude of the inertial force on the junction box under dynamic loads, allowing for the assessment of dynamic stress amplitudes. By calculating vibration acceleration, the actual motion of the junction box under the influence of bracket vibration can be quantified. Higher vibration accelerations indicate stronger vibration excitation of the junction box, potentially causing greater stress and strain in its internal structure, which in turn affects the stability of the electrical connection points.

[0131] According to stress concentration theory in elastic mechanics, geometric discontinuities can lead to significant increases in local stress. The stress concentration factor is defined as the ratio of peak stress to nominal stress. In this embodiment, the peak stress is the local peak stress under dynamic load. This value is related to the vibration acceleration, which generates dynamic inertia forces. Based on the modal superposition method, in a modal coordinate system, the dynamic response can be expressed as a linear combination of various modes. For this linear combination, modal analysis is used to obtain the stress distribution of each modal order. Then, by combining the stress distribution of each modal order with the dynamic inertia forces generated by vibration acceleration, the dynamic stress amplitude can be calculated, thereby obtaining the peak stress. The nominal stress refers to the average stress under static load and can be calculated by the ratio of the static load to the nominal cross-sectional area. The stress concentration factor is then obtained by dividing the peak stress by the nominal stress.

[0132] Based on the stress concentration factor obtained in the above steps and combined with the changes in the electrical parameters of the electrical connection points in the junction box, it is possible to perform damage and failure analysis on the electrical connection points in the junction box.

[0133] In a preferred embodiment, the electrical parameter variation includes a temperature variation and a contact resistance variation. Specifically, the temperature variation refers to the temperature rise of the electrical connection point, that is, the temperature rise relative to the initial state (no load, no damage). Since the heating of the contact point is caused by Joule heat, which is generated by the current flowing through the connection point and the contact resistance, the temperature rise of the connection point can be expressed as:

[0134]

[0135] Where I represents the current flowing through the connection point, R contact represents the contact resistance obtained by real-time monitoring, t represents the power-on time, m represents the metal material quality of the connection point, c p It should be noted that t in the present invention represents time, and the time period it represents is determined by the formula in which it is located, and will not be distinguished by different parameters here.

[0136] In this embodiment, the heating intensity is directly reflected by the connection point temperature rise, and its value is positively correlated with the degradation of the contact resistance, that is, the degradation of material properties caused by heating is reflected by the connection point temperature rise. Since degradation such as oxidation or loosening of the contact surface will cause the contact resistance to change, in addition to the connection point temperature rise being able to reflect the degree of degradation of material properties, the rate of change of contact resistance can also reflect the degree of degradation of contact resistance. The contact resistance change rate is determined by the ratio of the contact resistance change to the reference resistance, wherein the contact resistance change is determined by the difference between the contact resistance obtained by real-time monitoring and the reference resistance, and the reference resistance is determined by the resistance value when the system is initially installed.

[0137] After obtaining the stress concentration factor, connection point temperature rise, and contact resistance change rate, these three data items are used as input data into a pre-built damage failure assessment model for loss failure assessment. In this embodiment, a support vector machine model is preferably used to construct the damage failure assessment model. An SVM classifier is used to make decisions based on the input data to obtain the damage failure probability of the electrical connection point. It should be noted that the damage failure assessment model can also be constructed using other neural network models or machine learning algorithms. The specific construction steps can be based on the conventional construction steps of the model or algorithm used, and are not limited here.

[0138] In this embodiment, the stress concentration factor, connection point temperature rise, and contact resistance change rate are used as input data for the model. Based on the above embodiments, it can be seen that the magnitude of vibration acceleration affects the degree of stress concentration. Larger vibration acceleration increases the likelihood and degree of stress concentration, thereby affecting the calculated stress concentration factor. Furthermore, higher vibration acceleration means the junction box experiences greater dynamic load per unit time, which accelerates fatigue damage to the electrical connection points. Therefore, this embodiment uses the stress concentration factor as input data for the SVM model. In addition to the coefficient itself directly reflecting the mechanical stress amplification effect caused by vibration, the stress concentration factor, due to its correlation with acceleration, indirectly reflects the impact of vibration acceleration on the electrical connection failure risk assessment and indirectly reflects the fatigue damage risk of the junction box's overall structure. The connection point temperature rise directly reflects the material degradation caused by heat, while the contact resistance change rate reflects the degree of degradation, such as oxidation or loosening, on the contact surface. These material degradations and deterioration can also lead to fatigue damage to the junction box or electrical connection failure. In this embodiment, by comprehensively determining these influencing factors, the accuracy of failure assessment can be effectively improved, and accurate data support is provided for subsequent system operation and maintenance based on effective assessment results.

[0139] In a preferred embodiment, after obtaining the loss failure assessment results, the present invention reversely corrects the stiffness degradation model parameters based on the failure warning results based on the SVM classifier, forming a "monitoring-warning-correction" closed loop, thereby maintaining the model's adaptive optimization during long-term service. Specifically, the failure probability output by the SVM is compared with a probability threshold. If it is less than or equal to the probability threshold, the model parameters remain unchanged. If it is greater than the probability threshold, it is determined to be in a high-risk state, indicating that the electrical connection point has a high risk of failure. However, this risk may be caused by two reasons: one is degradation of the electrical connection point itself, and the other is vibration transmission abnormality caused by bracket stiffness degradation. In this case, by adjusting the parameters of the stiffness degradation model, the model can more accurately reflect the actual stiffness degradation state of the bracket, thereby distinguishing the root cause of the fault. The previous embodiment has detailed that the elastic modulus degradation model is actually related to stiffness equivalence. The stiffness model here is the elastic modulus degradation model. The higher the failure probability, the more likely the current model underestimates the actual damage extent. It is necessary to reversely verify whether the stiffness model underestimates the actual degradation extent. Therefore, it is necessary to adjust the corrosion stiffness attenuation coefficient to make it closer to the actual degradation rate. If the failure probability decreases after correction, it means that the problem is mainly caused by the deviation of the bracket stiffness model, and the bracket needs to be maintained as a priority. If the failure probability is still high after correction, it is clear that the electrical connection point itself has deteriorated and requires targeted maintenance.

[0140] In this embodiment, the quantitative relationship between failure probability and parameter adjustment can be expressed as:

[0141]

[0142] Where, represents the corrected corrosion stiffness attenuation coefficient, and k represents the correction gain coefficient, which can be calibrated experimentally to ensure that the correction amplitude is proportional to the failure probability and avoid over-correction. It represents the failure probability output by the SVM model. The higher the failure probability, the more likely the current model is to underestimate the damage. It is necessary to increase the corrosion stiffness attenuation coefficient to accelerate the prediction of stiffness degradation and thus match the actual damage state.

[0143] The corrected corrosion stiffness attenuation coefficient is then used to update the elastic modulus degradation model. The updated model accuracy is verified by recalculating the natural frequency degradation value and formation displacement to determine whether the model accuracy meets the preset conditions, such as an error of less than 5%. If the model accuracy is met, the corrected corrosion stiffness attenuation coefficient is used as the latest corrosion stiffness attenuation coefficient. If it does not meet the accuracy requirements, the corrosion stiffness attenuation coefficient is adjusted by adjusting the correction gain coefficient until the model accuracy meets the accuracy requirements.

[0144] This embodiment dynamically optimizes the model parameters through real-time failure probability feedback, so that the stiffness model continuously approaches the actual damage state, effectively solving the prediction deviation problem caused by environmental time variability and material aging, and can accurately distinguish between the degradation of bracket stiffness and the degradation of the electrical connection point itself, avoiding misjudgment, thereby realizing dynamic adaptation of the model, and giving the model self-learning capabilities and a long-term reliability improvement mechanism.

[0145] This embodiment provides a method for diagnosing electromechanical coupling damage in a wind, solar and storage system. The present invention constructs a full-chain evaluation model for electromechanical coupling damage by integrating multi-dimensional data of mechanical stress field, electrochemical corrosion field, vibration modal field and electrical parameter field, effectively solving the problem of high misjudgment rate caused by traditional single physical field analysis and improving the accuracy of failure assessment. Through the parameterized model simplification strategy, while ensuring accuracy, the computational complexity is effectively reduced, the computational efficiency is improved, and through closed-loop feedback and self-learning capabilities, the problem of model accuracy decreasing with service time is solved, the early warning forecast rate is further reduced, and the accuracy of failure assessment is improved. The present invention solves the problem of difficult accurate early warning of electromechanical coupling damage in wind, solar and storage systems through a multi-dimensional coupling model and a dynamic parameter closed-loop feedback mechanism, effectively improving the accuracy of electromechanical coupling damage assessment, thereby improving the safety, stability and reliability of the operation of the wind, solar and storage system, and further improving the operation and maintenance efficiency of the system.

[0146] See also Figure 2 Based on the same inventive concept, a second embodiment of the present invention proposes a wind-solar-storage system electromechanical coupling damage diagnosis system, comprising:

[0147] The stress corrosion analysis module 10 is used to construct a finite element mechanical model based on the geometric data, material properties and load data of the welding point area of ​​the photovoltaic bracket in the wind-solar-storage system, and calculate the stress distribution data of the welding point area;

[0148] Based on the environmental data and electrochemical data of the welding point area, a corrosion kinetics model is constructed to obtain the corrosion product parameters of the welding point area;

[0149] Based on the corrosion product data, the corrosion product expansion stress is obtained, the corrosion product expansion stress is superimposed on the finite element mechanics model, and the stress intensity factor is calculated based on linear elastic fracture mechanics;

[0150] The stiffness vibration analysis module 20 is used to determine whether there is a weld stiffness degradation area based on the stress intensity factor. If so, an elastic modulus degradation model of the weld stiffness degradation area is established based on the corrosion product parameters to obtain the natural frequency degradation value and mode displacement of the weld area;

[0151] Based on the natural frequency degradation value and mode displacement, the vibration response of the junction box on the photovoltaic bracket is analyzed to obtain the stress concentration factor;

[0152] The damage failure assessment module 30 is used to obtain the electrical parameter changes of the electrical connection points in the junction box, and input the electrical parameter changes and stress concentration factors into a pre-built damage failure assessment model to obtain damage failure assessment results of the electrical connection points.

[0153] The technical features and technical effects of the electromechanical coupling damage diagnosis system for wind, solar and storage systems proposed in the embodiment of the present invention are the same as the method proposed in the embodiment of the present invention, and will not be described in detail here. Each module in the above-mentioned electromechanical coupling damage diagnosis system for wind, solar and storage systems can be implemented in whole or in part by software, hardware and their combination. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules.

[0154] In summary, the embodiments of the present invention provide a method and system for diagnosing electromechanical coupling damage in a wind-solar-storage system. The method constructs a finite element mechanical model based on the geometric data, material properties, and load data of the welding point area of ​​the photovoltaic bracket in the wind-solar-storage system, and calculates the stress distribution data of the welding point area. A corrosion dynamics model is constructed based on the environmental data and electrochemical data of the welding point area to obtain the corrosion product parameters of the welding point area. The corrosion product expansion stress is obtained based on the corrosion product data, and the corrosion product expansion stress is superimposed on the finite element mechanical model. The stress intensity factor is calculated based on linear elastic fracture mechanics. Based on the stress intensity factor, it is determined whether there is a weld stiffness degradation area. If so, an elastic modulus degradation model of the weld stiffness degradation area is established based on the corrosion product parameters to obtain the natural frequency degradation value and mode displacement of the weld point area. Based on the natural frequency degradation value and mode displacement, a vibration response analysis is performed on the junction box on the photovoltaic bracket to obtain the stress concentration factor. The electrical parameter change of the electrical connection point in the junction box is obtained, and the electrical parameter change and the stress concentration factor are input into a pre-constructed damage failure assessment model to obtain the damage failure assessment result of the electrical connection point. The present invention constructs a full-chain evaluation model for electromechanical coupling damage by integrating multi-dimensional data of mechanical stress field, electrochemical corrosion field, vibration modal field and electrical parameter field, effectively solving the problem of high misjudgment rate caused by traditional single physical field analysis and improving the accuracy of failure assessment. Through the parameterized model simplification strategy, while ensuring accuracy, the computational complexity is effectively reduced, the computational efficiency is improved, and through closed-loop feedback and self-learning capabilities, the problem of model accuracy decreasing with service time is solved, further reducing the early warning forecast rate and improving the accuracy of failure assessment. The present invention effectively improves the accuracy of electromechanical coupling damage assessment through multi-dimensional coupling models and dynamic parameter closed-loop feedback mechanisms, thereby improving the safety, stability and reliability of wind, solar and storage system operation, and further improving the system's operation and maintenance efficiency.

[0155] Each embodiment in this specification is described in a progressive manner, and the same or similar parts of each embodiment can be directly referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the system embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment. It should be noted that the various technical features of the above embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the various technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0156] The above-described embodiments merely represent several preferred implementations of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent. It should be noted that a person skilled in the art could make several improvements and substitutions without departing from the technical principles of the present invention, and these improvements and substitutions should also be considered within the scope of protection of the present application. Therefore, the scope of protection of the present patent application shall be based on the scope of protection of the claims.

Claims

1. A method for diagnosing electromechanical coupling damage in a wind-solar-storage system, characterized in that: include: Based on the geometric data, material properties and load data of the photovoltaic bracket welding point area in the wind-solar-storage system, a finite element mechanical model is constructed to calculate the stress distribution data of the welding point area; Based on the environmental data and electrochemical data of the welding point area, a corrosion kinetics model is constructed to obtain the corrosion product parameters of the welding point area; Based on the corrosion product data, the corrosion product expansion stress is obtained, the corrosion product expansion stress is superimposed on the finite element mechanics model, and the stress intensity factor is calculated based on linear elastic fracture mechanics; Based on the stress intensity factor, determine whether there is a weld stiffness degradation area. If so, establish an elastic modulus degradation model for the weld stiffness degradation area based on the corrosion product parameters to obtain the natural frequency degradation value and mode displacement of the weld area. Based on the natural frequency degradation value and mode displacement, the vibration response of the junction box on the photovoltaic bracket is analyzed to obtain the stress concentration factor; The electrical parameter changes of the electrical connection points in the junction box are obtained, and the electrical parameter changes and stress concentration factors are input into the pre-built damage and failure assessment model to obtain the damage and failure assessment results of the electrical connection points, including: Obtain the contact resistance and current of the electrical connection points in the junction box, and calculate the temperature rise of the connection points based on the Joule heating model; Calculate the contact resistance change rate based on the contact resistance and the reference resistance; The temperature rise of the connection point, the contact resistance change rate and the stress concentration factor are input into a pre-built damage failure assessment model to obtain the damage failure probability of the electrical connection point. The damage failure assessment model is constructed based on a support vector machine model.

2. The wind-solar-storage system electromechanical coupling damage diagnosis method according to claim 1 is characterized in that: The step of constructing a finite element mechanical model based on the geometric data, material properties and load data of the welding point area of ​​the photovoltaic bracket in the wind-solar-storage system and calculating the stress distribution data of the welding point area includes: The geometric data of the photovoltaic bracket welding point area in the wind-solar-storage system is converted into a finite element mesh, and the finite element mechanical mesh is constructed based on the elastic modulus and Poisson's ratio parameters of the welding material; Loading wind load data and self-weight load data into the finite element mechanics grid to obtain a finite element mechanics model; The finite element mechanical model is solved to obtain the stress distribution data of the welding point area.

3. The wind-solar-storage system electromechanical coupling damage diagnosis method according to claim 1, characterized in that: The step of constructing a corrosion kinetics model based on the environmental data and electrochemical data of the welding point area to obtain the corrosion product parameters of the welding point area includes: Based on the environmental data and electrochemical data of the welding point area, the corrosion current density of the welding point area is calculated using the polarization curve method; The corrosion rate is calculated based on Faraday's law and corrosion current density, and the corrosion depth is obtained based on the corrosion rate.

4. The wind-solar-storage system electromechanical coupling damage diagnosis method according to claim 3 is characterized in that: The steps of obtaining the corrosion product expansion stress based on the corrosion product data, superimposing the corrosion product expansion stress on the finite element mechanics model, and calculating the stress intensity factor based on linear elastic fracture mechanics include: Calculate the expansion stress of corrosion products based on the elastic modulus and corrosion depth of the welding material; Based on linear elastic fracture mechanics, the expansion stress of corrosion products is superimposed on the maximum stress in the stress distribution data to obtain the stress intensity factor.

5. The wind-solar-storage system electromechanical coupling damage diagnosis method according to claim 1, characterized in that: The step of determining whether there is a weld stiffness degradation region according to the stress intensity factor includes: According to the material fracture toughness data of the welding material, the strength threshold is set; The stress intensity factor is compared with the strength threshold. If the stress intensity factor is greater than the strength threshold, it is determined that there is a weld stiffness degradation area.

6. The wind-solar-storage system electromechanical coupling damage diagnosis method according to claim 3, characterized in that: The step of establishing an elastic modulus degradation model of the weld stiffness degradation region based on the corrosion product parameters and obtaining the natural frequency degradation value and mode displacement of the weld region comprises: According to the corrosion depth, the elastic modulus degradation model of the weld stiffness degradation area is established to obtain the elastic modulus degradation value; According to the elastic modulus degradation value, the natural frequency degradation value of the welding point area is calculated; The elastic modulus degradation value is input into the finite element mechanics model, and the characteristic equation is solved through finite element modal analysis to obtain the vibration mode displacement.

7. The wind-solar-storage system electromechanical coupling damage diagnosis method according to claim 1, characterized in that: The step of performing vibration response analysis on the junction box on the photovoltaic support according to the natural frequency degradation value and the mode displacement to obtain the stress concentration factor includes: Calculate the vibration acceleration of the junction box on the photovoltaic bracket based on the natural frequency degradation value and mode displacement; Based on the vibration acceleration, the peak stress of the junction box is determined, and the stress concentration factor is obtained according to the ratio of the peak stress to the nominal stress.

8. The wind-solar-storage system electromechanical coupling damage diagnosis method according to claim 1, characterized in that: After the step of obtaining the damage failure assessment result of the electrical connection point, the method further includes: Based on the damage and failure assessment results of the electrical connection points, it is determined whether the state is high-risk. If so, the elastic modulus degradation model is modified based on the damage and failure assessment results.

9. A wind-solar-storage system electromechanical coupling damage diagnosis system, characterized in that: include: The stress corrosion analysis module is used to construct a finite element mechanics model based on the geometric data, material properties, and load data of the photovoltaic bracket welding point area in the wind-solar-storage system, and calculate the stress distribution data of the welding point area; Based on the environmental data and electrochemical data of the welding point area, a corrosion kinetics model is constructed to obtain the corrosion product parameters of the welding point area; Based on the corrosion product data, the corrosion product expansion stress is obtained, the corrosion product expansion stress is superimposed on the finite element mechanics model, and the stress intensity factor is calculated based on linear elastic fracture mechanics; The stiffness vibration analysis module is used to determine whether there is a weld stiffness degradation area based on the stress intensity factor. If so, an elastic modulus degradation model of the weld stiffness degradation area is established based on the corrosion product parameters to obtain the natural frequency degradation value and vibration mode displacement of the weld area. Based on the natural frequency degradation value and mode displacement, the vibration response of the junction box on the photovoltaic bracket is analyzed to obtain the stress concentration factor; The damage and failure assessment module is used to obtain the changes in electrical parameters of the electrical connection points in the junction box and input the electrical parameter changes and stress concentration factors into a pre-built damage and failure assessment model to obtain the damage and failure assessment results of the electrical connection points, including: Obtain the contact resistance and current of the electrical connection points in the junction box, and calculate the temperature rise of the connection points based on the Joule heating model; Calculate the contact resistance change rate based on the contact resistance and the reference resistance; The temperature rise of the connection point, the contact resistance change rate and the stress concentration factor are input into a pre-built damage failure assessment model to obtain the damage failure probability of the electrical connection point. The damage failure assessment model is constructed based on a support vector machine model.

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