A method and system for risk assessment of the overturning instability of a conductor galloping sensor

Abstract

The present invention discloses a method and system for risk assessment of the overturning and instability of a conductor galloping sensor. The risk assessment method includes the steps of: determining the influencing factors and their mutual relationships that cause the risk of overturning and instability during the outdoor operation of the conductor galloping sensor; determining the external force on the conductor galloping sensor and the functional relationship to ensure no overturning, and establishing an external instability score T1; determining the internal force on the conductor galloping sensor and the functional relationship that the internal weak links are not damaged, and establishing an internal instability score T2; comprehensively evaluating the external instability score T1 and the internal instability score T2, and calculating the comprehensive score T of the overturning and instability risk of the conductor galloping sensor. The calculation expression of the comprehensive score T of the overturning and instability risk is T = αT1 + βT2. The present invention constructs a risk assessment model for the overturning and instability of the conductor galloping sensor, determines the overturning and instability risk function and the risk score, and effectively improves the convenience and accuracy of the risk assessment of the conductor galloping sensor.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent sensors for the power Internet of Things. Specifically, it relates to a method and system for risk assessment of the overturning and instability of a conductor galloping sensor. Background Art

[0002] The galloping phenomenon of conductors is one of the important factors affecting the safety of power transmission. In order to accurately and conveniently obtain conductor galloping data, the prior art has proposed conductor galloping detection sensors to detect conductor galloping. By analyzing, evaluating, warning, and alarming the real-time state of the conductor, it provides a scientific basis for strengthening the anti-galloping work of transmission lines in a timely manner.

[0003] The risks of overturning and instability of the conductor galloping sensor mainly come from two aspects. On the one hand, it is the overturning caused by external factors. When the conductor is covered with ice and subjected to wind excitation, galloping will occur. Since the conductor galloping sensor moves with the conductor galloping, there is a risk of overturning. On the other hand, it is the instability caused by internal factors. The conductor galloping sensor is an integral body composed of various sensor modules and a packaging shell. The internal modules are mainly fixed to the pillars inside the shell by screws. The root of the pillar is a mechanically weak link. When moving with the conductor galloping, a bending moment will be generated. When the bending moment is too large, the pillar will be damaged, so there is a risk of instability. Summary of the Invention

[0004] In view of this, the present invention provides a method and system for risk assessment of the overturning and instability of a conductor galloping sensor to determine the risk function and risk assessment method of the overturning and instability of the conductor galloping sensor, and effectively improve the convenience and accuracy of the risk assessment of the conductor galloping sensor.

[0005] To solve the above problems, the first object of the present invention is to provide a method for risk assessment of the overturning and instability of a conductor galloping sensor. The risk assessment method includes the following steps:

[0006] S 100 : Determine the influencing factors causing the risk of overturning and instability and the cross-correlation relationship between the influencing factors during the outdoor operation of the conductor galloping sensor;

[0007] S 200 : Determine the external force on the conductor galloping sensor and the functional relationship of the overall overturning risk, and establish an external instability score T1;

[0008] S 300 : Determine the internal force on the conductor galloping sensor and the installation reliability conditions of the internal weak links, and establish an internal instability score T2;

[0009] S 400: Comprehensively evaluate the external instability score T1 and the internal instability score T2, and calculate the comprehensive overturning instability risk score T of the conductor galloping sensor. The calculation expression of the comprehensive overturning instability risk score T is:

[0010] T = αT1 + βT2

[0011] Where α and β are weighting factors, and α + β = 1.

[0012] Furthermore, in step S 100 The influencing factors causing the overturning instability risk and the cross - relationships between the influencing factors include: the overall gravity G of the conductor galloping sensor, the external force F, the weight m of the circuit board, the height h of the support column, the outer diameter D of the support column, and the outer diameter d of the circuit board mounting screw. And the anti - overturning moment is greater than the overturning moment, and the stress on the weak link of the housing must be less than the allowable stress of the material.

[0013] Furthermore, in step S 200 The determination process of the function relationship between the external force on the conductor galloping sensor and the overall overturning risk is as follows:

[0014] Step S 210 : Analyze the external force on the conductor galloping sensor;

[0015] When the conductor galloping sensor is in a non - vertically suspended state as a whole, the torque of the external force F on the rotation center can be expressed as:

[0016] M F = Fcosθ * X

[0017] The anti - overturning moment of gravity on the rotation center is expressed as

[0018] M G = Gsinθ * L

[0019] Where: F represents the equivalent external force; G represents the overall gravity of the conductor galloping sensor; X is the distance from the external force application point to the rotation center; L is the distance from the overall center of gravity of the conductor galloping sensor to the rotation center; θ represents the deflection angle of the conductor galloping sensor as a whole;

[0020] Step S 220 : Construct the overturning risk function P and perform normalization processing;

[0021] Among them, the relationship of the overturning risk function P is:

[0022]

[0023] Where: is the anti - overturning safety factor, M Fis the torque of the external force F on the rotation center, M G is the anti-overturning moment of the gravity on the rotation center;

[0024] Step S 230 : Establish the external instability score T1.

[0025] Furthermore, in step S 230 the calculation expression of the external instability score T1 is:

[0026]

[0027] Furthermore, in step S 300 the determination process of the internal force and the installation reliability condition of the internal weak link of the conductor galloping sensor is as follows:

[0028] Step S 310 : Calculate the bending moment N at the root of a single strut n ;

[0029] The bending moment of the circuit board on the root of a single strut is

[0030]

[0031] where m is the weight of the circuit board and h is the height of the strut;

[0032] Step S 320 : Calculate the section modulus W of the bending resistance at the root of a single strut;

[0033] The section modulus of the bending resistance is:

[0034]

[0035]

[0036] where: D represents the outer diameter of the strut, d represents the outer diameter of the circuit board mounting screw, α represents the ratio of the inner and outer diameters of the strut cross-section, and W represents the section modulus of the bending resistance;

[0037] Step S 330 : Calculate the stress value σ at the root of a single strut i ;

[0038] Referring to relevant materials on mechanics of materials, it can be obtained that:

[0039]

[0040] The stress σ at the root of a single strut is calculated i :

[0041]

[0042] Step S 340 : Obtain the reliability conditions for circuit board installation;

[0043] The satisfaction of the circuit board installation reliability conditions is as follows:

[0044]

[0045] Among them, [σ] represents the allowable stress value of the material, and k represents the safety factor, with a value range of 2 to 3;

[0046] Step S 350 : Establish the internal instability score T2.

[0047] Furthermore, in step S 350 The calculation expression of the internal instability score T2 is as follows:

[0048]

[0049] Among them, σ i represents the stress at the root of a single strut, [σ] represents the allowable stress value of the material, and k represents the safety factor, with a value range of 2 to 3.

[0050] Furthermore, according to the external instability score T1 and the internal instability score T2, the calculation expression for calculating the comprehensive overturning instability risk score T is

[0051]

[0052] The second object of the present invention is to provide an overturning instability risk assessment system for a conductor galloping sensor, and the risk assessment system includes:

[0053] A memory; and

[0054] A processor coupled to the memory, and the processor is configured to execute the overturning instability risk assessment method for the conductor galloping sensor as described above based on instructions stored in the memory.

[0055] The third object of the present invention is to provide a computer-readable storage medium, in which at least one instruction is stored, and when the instruction is loaded and executed by a processor, the overturning instability risk assessment method for the conductor galloping sensor as described above is implemented.

[0056] Compared with the prior art, the present invention has the following beneficial effects:

[0057] The method for evaluating the risk of overturning and instability of the conductor galloping sensor described in this application first determines the influencing factors causing the risk of overturning and instability and the cross-correlation relationship between the influencing factors during the outdoor operation of the conductor galloping sensor; after determining the influencing factors, the static force analysis of the conductor galloping sensor as a whole is carried out using the theoretical knowledge of material mechanics to find out the functional relationship of the overall overturning risk and establish the external instability score T1; an evaluation model for the risk of overturning and instability of the conductor galloping sensor is constructed through mechanical analysis to determine the internal force and the installation reliability conditions of the internal weak links of the conductor galloping sensor and establish the internal instability score T2; the external instability score T1 and the internal instability score T2 are comprehensively evaluated, and the comprehensive score T of the risk of overturning and instability of the conductor galloping sensor is calculated. This risk assessment method effectively improves the convenience and accuracy of the risk assessment of the conductor galloping sensor and can better play the role of the conductor galloping sensor. Description of the Drawings

[0058] Figure 1 It is a schematic flowchart of the method for evaluating the risk of overturning and instability of the conductor galloping sensor in an embodiment of the present invention;

[0059] Figure 2 It is a three-dimensional structure schematic diagram of the conductor galloping sensor in an embodiment of the present invention;

[0060] Figure 3 It is a schematic diagram of the structure of the circuit board bin in an embodiment of the present invention;

[0061] Figure 4 It is a partial enlarged schematic diagram of the support column in the circuit board bin in an embodiment of the present invention;

[0062] Figure 5 It is a schematic diagram of the force on the conductor galloping sensor in an embodiment of the present invention.

[0063] Description of the Reference Numerals:

[0064] 1 - Circuit board bin; 11 - First accommodation bin; 12 - First side connection plate; 13 - Support column; 2 - Connector; 3 - Solar photovoltaic battery bin. Detailed Embodiment

[0065] Next, the technical solutions of the present invention will be clearly and completely described in conjunction with the drawings. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0066] In the description of the present invention, it should be noted that unless otherwise clearly specified and defined, the terms "installation", "connection", and "coupling" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, and it can also be the communication inside two components. It can be a wireless connection or a wired connection. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0067] In addition, the technical features involved in different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0068] Please refer to Figure 1 As shown, an embodiment of the present invention provides a method for evaluating the risk of overturning and instability of a conductor galloping sensor. The risk assessment method includes the following steps:

[0069] S 100 : Determine the influencing factors causing the risk of overturning and instability during the outdoor operation of the conductor galloping sensor and the cross-correlation relationship between the influencing factors;

[0070] S 200 : Determine the functional relationship between the external forces on the conductor galloping sensor and the risk of overall overturning, and establish an external instability score T1;

[0071] S 300 : Determine the internal forces on the conductor galloping sensor and the installation reliability conditions of the internal weak links, and establish an internal instability score T2;

[0072] S 400 : Comprehensively evaluate the external instability score T1 and the internal instability score T2, and calculate the comprehensive score T of the risk of overturning and instability of the conductor galloping sensor. The calculation expression of the comprehensive score T of the risk of overturning and instability is:

[0073] T = αT1 + βT2

[0074] Where α and β are weighting factors, and α + β = 1.

[0075] It should be noted that the design object of the embodiment of the present invention is a conductor galloping sensor. Each module of the conductor galloping sensor is integrated into a whole and installed in a packaging shell. The packaging shell cooperates with the internal modules, is reasonably arranged and installed, analyzes, evaluates, warns, and alarms the real-time state of the conductor, can accurately and conveniently obtain the conductor galloping data, and provides a scientific basis for timely strengthening the anti-galloping work of the transmission line.

[0076] When the conductor galloping sensor is integrally suspended on the transmission line, without being affected by other external forces, it is only affected by the vertically downward gravity, so it will always maintain a vertically downward posture unchanged. Considering that the working environment of the conductor galloping sensor is outdoors at high altitude, it is often affected by wind force or other external forces, and the whole will deflect around the center of the transmission line.

[0077] In addition, it should be emphasized that in the embodiment of the present invention, the conductor galloping sensor will not overturn during outdoor operation. Specifically, when the conductor galloping sensor is affected by external forces, it swings within a certain angle range around the conductor, and will not enable the conductor galloping sensor to make a circumferential rotational movement around directly above the conductor.

[0078] Please refer to Figure 2 As shown, in the embodiment of the present invention, in step S 100 The influencing factors causing the risk of the conductor galloping sensor tipping over and the cross-correlation between the influencing factors include: the overall gravity M of the conductor galloping sensor, the external force F, the weight m of the circuit board, the height h of the strut, the outer diameter D of the strut, the outer diameter d of the circuit board mounting screw, and the anti-tipping moment is greater than the tipping moment. The stress on the weak link of the conductor galloping sensor housing must be less than the allowable stress of the material.

[0079] Through design calculations and experience, the influencing factors affecting the conductor galloping sensor to overturn around the conductor include the magnitude and direction of the external force and the overall weight of the conductor galloping sensor. Specifically, in order to enable the conductor galloping sensor to swing within a certain angle θ range directly below the transmission line, it is necessary to strictly control the overall gravity M of the conductor galloping sensor, while the magnitude and direction of the external force are not affected by human control factors.

[0080] Specifically, through theoretical analysis and calculation, in step S 200 The determination process of the functional relationship between the external force on the conductor galloping sensor and the risk of overall tipping is as follows:

[0081] When the whole conductor galloping sensor (intelligent sensor and encapsulation housing) is suspended on the transmission line, without being affected by other external forces, it is only affected by the vertically downward gravity, so it will always maintain a vertically downward posture unchanged.

[0082] Considering that the working environment of the conductor galloping sensor is outdoors at high altitude, it is often affected by wind force or other external forces. The whole conductor galloping sensor will deflect around the center of the transmission cable. The force analysis of the conductor galloping sensor is as follows:

[0083] Please refer to Figure 5As shown in the figure, point O represents the center of the transmission wire; point M represents the overall center of gravity of the sensor; OM is the distance from the center of gravity to the rotation center, denoted as L; F represents the equivalent external force; point A represents the acting point of the equivalent external force, and OA is the distance from the acting point of the external force to the rotation center, denoted as X; θ represents the overall deflection angle of the sensor, which is also the angle between the vertical direction of the sensor and the Z direction of the three-dimensional coordinate system.

[0084] Specifically, in the embodiment of the present invention, step S 200 In it, the determination process of the functional relationship for determining the external force on the conductor galloping sensor and ensuring no overturning is as follows:

[0085] Step S 210 : Analyze the external force on the conductor galloping sensor;

[0086] As Figure 5 shown, when the overall conductor galloping sensor is in states (a) and (b), the torque of the external force F on the rotation center can be expressed as:

[0087] When the overall conductor galloping sensor is in a non-vertically suspended state, the torque of the external force F on the rotation center can be expressed as:

[0088] M F = F cosθ * X

[0089] The torque of gravity on the rotation center is expressed as

[0090] M G = G sinθ * L

[0091] Where: F represents the equivalent external force; G represents the overall gravity of the conductor galloping sensor; X is the distance from the acting point of the external force to the rotation center; L is the distance from the overall center of gravity of the conductor galloping sensor to the rotation center; θ represents the overall deflection angle of the conductor galloping sensor.

[0092] That is, the anti-overturning moment balances the overturning moment. Only when the anti-overturning moment is greater than the overturning moment will the conductor galloping sensor not have external overturning.

[0093] Step S 220 : Construct an overturning risk function P and perform normalization processing;

[0094] Among them, the relational expression of the overturning risk function P is:

[0095]

[0096] Where: is the anti-overturning safety factor, M F is the torque of the external force F on the rotation center, M G is the anti-overturning moment of gravity on the rotation center;

[0097] When the function value is less than 0, the conductor galloping sensor topples over; when the function is greater than 0, the smaller the function value, the greater the risk of its toppling over. By normalizing the risk function, an overturning risk scoring method can be established.

[0098] Step S 230 : Establish the external instability score T1.

[0099] Specifically, in step S 230 Among them, the calculation expression of the external instability score T1 is:

[0100]

[0101] It can be seen that when the external force is 0, the external instability score T1 is 0, indicating that the conductor galloping sensor will not topple over. When the external instability score T1 is larger, it indicates that the risk of the conductor galloping sensor toppling over is greater.

[0102] Specifically, in step S 300 Among them, the determination process of the internal force and the installation reliability conditions of the internal weak links of the conductor galloping sensor is as follows:

[0103] During the outdoor operation of the conductor galloping sensor, in order to ensure that the internal weak links (the cross-section of the pillar hole) of the conductor galloping sensor are not damaged, the following influencing factors are mainly considered:

[0104] The overall gravity M of the conductor galloping sensor, the external force F, the weight m of the circuit board, the height h of the pillar, the outer diameter D of the pillar, the outer diameter d of the circuit board mounting screw, and it must be ensured that the stress on the weak link of the conductor galloping sensor is less than the allowable stress of the material.

[0105] Please refer to Figure 3 、 4 As shown, in this embodiment, the encapsulation shell of the conductor galloping sensor is a three-layer separable structure. The encapsulation shell includes a circuit board bin 1, a connecting member 2, and a solar photovoltaic cell bin 3. The connecting member 2 is connected to the upper surface of the circuit board bin 1, and the solar photovoltaic cell bin 3 is connected to the upper surface of the connecting member 2, where:

[0106] The circuit board bin 1 includes a first accommodation bin 11, a first side connecting plate 12, and a pillar 13. The first side connecting plate 12 is connected to the outer periphery of the first accommodation bin 11, and the first side connecting plate 12 protrudes horizontally outward by a certain length. The pillar 13 is vertically connected to the inner surface of the first accommodation bin 11.

[0107] There are four pillars 13 at the bottom inside the first accommodation bin 11 for installing the circuit board. The circuit board is fixed on the pillars 13 of the first accommodation bin 11. When the overall package housing deflects under external force, the reliability of the circuit board installation needs to be ensured, that is, the pillars 13 will not be damaged. Through analysis, it can be concluded that the root of the pillar 13 is the weak link in mechanics. Therefore, a mechanical analysis is carried out on the root of the pillar 13.

[0108] Step S 310 : Calculate the bending moment N at the root of a single pillar m ;

[0109] From the force analysis, it can be known that the bending moment of the circuit board on the root of a single pillar 13 is:

[0110]

[0111] where m is the weight of the circuit board and h is the height of the pillar;

[0112] Step S 320 : Calculate the section modulus W of resistance to bending at the root of a single pillar;

[0113] Since the cross-section of the pillar 13 is a ring, its section modulus of resistance to bending is:

[0114]

[0115]

[0116] where: D represents the outer diameter of the pillar, d represents the outer diameter of the screw for installing the circuit board, α represents the ratio of the inner and outer diameters of the pillar cross-section, and W represents the section modulus of resistance to bending;

[0117] Step S 330 : Calculate the stress value σ at the root of a single pillar i ;

[0118] Referring to relevant materials on mechanics of materials, it can be obtained that:

[0119]

[0120] σ i represents the stress value received at the root of the pillar, and W represents the section modulus of resistance to bending;

[0121] Calculate the stress σ at the root of a single pillar i :

[0122]

[0123] Step S 340 : Obtain the reliability condition for circuit board installation;

[0124] The condition for meeting the reliability of circuit board installation is:

[0125]

[0126] Among them, [σ] represents the allowable stress value of the material, and k represents the safety factor, which generally takes a value of 2 to 3 in engineering;

[0127] Step S 350 : Establish the internal instability score T2.

[0128] Specifically, in step S 350 Among them, the calculation expression of the internal instability score T2 is:

[0129]

[0130] Among them, σ i represents the stress at the root of a single strut, [σ] represents the allowable stress value of the material, and k represents the safety factor, with a value of 2 to 3.

[0131] It can be seen that when σ is smaller, the internal instability score T2 is approximately 0, otherwise the degree of instability is larger and the score is higher.

[0132] Specifically, according to the external instability score T1 and the internal instability score T2, the calculation expression for calculating the comprehensive overturning instability risk score T is

[0133]

[0134] By analyzing the mutual relationships among the gravity, external force, deflection angle, and torque of the conductor galloping sensor, based on the theoretical knowledge of material mechanics, this invention conducts a static force analysis on it, and through the analysis of the influencing factors causing the overturning instability of the sensor, constructs an overturning instability risk assessment model for the conductor galloping sensor, determines the overturning instability risk function and risk assessment method, which can effectively improve the convenience and accuracy of the risk assessment of the conductor galloping sensor and better play the role of the conductor galloping sensor.

[0135] This invention embodiment also provides an overturning instability risk assessment system for a conductor galloping sensor. The risk assessment system includes a memory and a processor coupled to the memory, where:

[0136] The processor is configured to execute the overturning instability risk assessment method for the conductor galloping sensor as described above based on the instructions stored in the memory.

[0137] This invention embodiment also provides a computer-readable storage medium, in which at least one instruction is stored. When the instruction is loaded and executed by the processor, the overturning instability risk assessment method for the conductor galloping sensor can be realized.

[0138] Although the present invention is disclosed as above, the scope of protection of the present invention is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present disclosure, and these changes and modifications will all fall within the scope of protection of the present invention.

Claims

1. A method for risk assessment of the overturning and instability of a conductor galloping sensor, characterized in that The risk assessment method includes the steps: S 100 : Determine the influencing factors that cause the risk of overturning instability during the outdoor operation of the conductor galloping sensor and the cross-correlation relationship between the influencing factors; Among them, the influencing factors causing the risk of overturning instability and the mutual relationship between the influencing factors include: the overall gravity G of the conductor galloping sensor, the external force F, the weight m of the circuit board, the height h of the support column, the outer diameter D of the support column, and the outer diameter d of the circuit board mounting screw, and the anti-overturning moment is greater than the overturning moment, and the stress on the weak link of the housing is less than the allowable stress of the material; S 200 : Determine the functional relationship of the external force on the conductor galloping sensor and the risk of overall overturning, and establish an external instability score ; The determination process of the function relationship between the external force on the conductor galloping sensor and the risk of overall overturning is as follows: Step S 210 : Analyze the external force on the conductor galloping sensor; When the conductor galloping sensor is in a non-vertically suspended state as a whole, the torque of the external force F on the rotation center is expressed as: The anti-overturning moment of gravity on the rotation center is expressed as Wherein: F represents the equivalent external force; represents the overall gravity of the conductor galloping sensor; X is the distance from the external force application point to the rotation center; L is the distance from the overall center of gravity of the conductor galloping sensor to the rotation center; θ represents the overall deflection angle of the conductor galloping sensor; Step S 220 : Construct an overturning risk function P and perform normalization processing; Among them, the relationship of the overturning risk function P is: Wherein: is the anti-overturning safety factor; Step S 230 : Establish an external instability score ; Step S 300 : Determine the internal forces on the conductor galloping sensor and the installation reliability conditions of the internal weak links, and establish an internal instability score ; The determination process of the internal force on the conductor galloping sensor and the installation reliability condition of the internal weak link is as follows: Step S 310 : Calculate the bending moment at the root of a single support column ; The bending moment of the circuit board on the root of a single support column is Among them, is the weight of the circuit board, is the height of the support pillar; Step S 320 : Calculate the flexural section modulus at the root of a single strut ; The section modulus in bending is: Where: D represents the outer diameter of the support column, and d represents the outer diameter of the circuit board mounting screw, is expressed as the ratio of the inner and outer diameters of the cross-section of the support column; Step S 330 : Calculate the stress value at the root of a single strut ; Step S 340 : Obtain the circuit board installation reliability conditions; The condition for satisfying the installation reliability of the circuit board is: Among them, represents the allowable stress value of the material, and k represents the safety factor, with a value range of 2 to 3; Step S 350 : Establish an internal instability score ; The internal instability score has the following calculation formula: 。 2. The method for evaluating the risk of overturning and instability of a conductor galloping sensor according to claim 1, characterized in that In step S 230 among them, the calculation expression of the external instability score is as follows: 。 3. The method for evaluating the risk of overturning and instability of a conductor galloping sensor according to claim 2, wherein It also includes Step S 400 : Comprehensively evaluate the external instability score and the internal instability score , and calculate the comprehensive score of the overturning instability risk of the conductor galloping sensor ; According to the external instability score and the internal instability score , the calculation expression for calculating the comprehensive score of the overturning instability risk is: Among them, is a weight factor, and .

4. A risk assessment system for the overturning and instability of a conductor galloping sensor, characterized in that The risk assessment system includes: A memory; and A processor coupled to the memory, the processor being configured to execute the method for assessing the risk of overturning instability of the conductor galloping sensor as described in any one of claims 1-3 based on the instructions stored in the memory.

5. A computer-readable storage medium storing at least one instruction, characterized in that: When the instructions are loaded and executed by the processor, the method for assessing the risk of overturning instability of the conductor galloping sensor as described in any one of claims 1-3 above is implemented.

Images