A method and system for real-time detection of three-dimensional thickness of sintering material layer based on curtain scanning

Abstract

This invention relates to the technical field of iron smelting and sintering production, and collectively provides a method and system for real-time detection of the three-dimensional thickness of the sintering machine material layer based on curtain scanning. The system comprises a first lever, a second lever, and a fixed point. The first lever is fixed, with one end connected to the fixed point. A wire displacement sensor is installed at the end of the first lever furthest from the fixed point. The second lever is fixed to the fixed point, with one end in contact with the material layer, and can rotate around the fixed point. After measuring the thickness of the material layer at various locations on the sintering machine trolley using geometric principles, a 3D model of the sintering machine material layer is created using a Lagrange interpolation algorithm, resulting in a three-dimensional simulation image of the sintering machine material layer. This system offers timely and accurate detection, higher precision, and is unaffected by harsh environments such as high temperature, high humidity, and high dust levels. Installation and maintenance are simpler and more convenient, operation is more stable and reliable, and it can assist on-site workers in adjusting production schedules in real time.

Description

Technical Field

[0001] This invention relates to the technical field of iron smelting and sintering production, and in particular to a method and system for real-time detection of three-dimensional thickness of sintering material layer based on curtain scanning. Background Technology

[0002] The Industrial Internet of Things (IIoT) integrates various data acquisition and control sensors and controllers with sensing and monitoring capabilities, along with technologies such as mobile communication and intelligent analytics, into all aspects of industrial production processes. This significantly improves manufacturing efficiency, enhances product quality, reduces product costs and resource consumption, and ultimately elevates traditional industries to a new stage of intelligent manufacturing. In terms of application, IIoT applications are characterized by real-time performance, automation, embedded systems, security, and interconnectivity.

[0003] With the development of ironmaking technology, the requirements for sinter in blast furnaces are constantly increasing, making the adjustment of the bed thickness in sintering operations increasingly important. The bed thickness in a sintering machine refers to the distance from the surface of the mixture on the sintering trolley to the upper surface of the grate bars at the bottom of the trolley. It is a key operational parameter in sintering production and an important indicator for evaluating the intermediate operation of the sintering machine. The bed thickness and its stability directly affect the yield and quality of the sinter. To achieve optimal sintering, the most reasonable bed thickness must be determined. Changes in trolley speed, feed roller speed, material level in the mixing trough, and the composition, moisture, and particle size of the mixture all cause variations in bed thickness. Once the bed thickness is determined based on the sinter production requirements, it is generally not arbitrarily adjusted, but online monitoring is necessary to understand bed changes early and provide a reference for adjusting the rollers, trolley speed, bellows dampers, and ignition operations. Bed thickness affects permeability, which in turn affects the vertical sintering speed of the mixture, thus influencing the position of the BTP (Boiler Plate Tolerance). If the sintering machine speed remains constant, as the material layer thickness increases, the permeability decreases, the vertical sintering speed slows down, and BTP is delayed; as the material layer thickness decreases, the permeability improves, the vertical sintering speed speeds up, and BTP is advanced.

[0004] In the past, due to the lack of suitable detection equipment, operators usually relied on visual inspection and then adjusted the rotation speed of the roller distributor or the trolley speed based on the manually measured material layer thickness after ignition and the estimated material layer shrinkage rate. Due to observation errors and operational delays, the material layer change was often only detected after 15 to 20 mm, frequently leading to unstable material layer thickness.

[0005] In recent years, the use of material layer detection technology to test the thickness of the material layer on the sintering machine trolley has largely failed due to the equipment's inability to adapt to the harsh on-site environment. Firstly, the mixture, after previous processing, typically reaches a moisture content of 7% and a material temperature of 40-50°C, with water vapor constantly floating on the surface. Secondly, the installation location is only 1-2 meters from the igniter, with a typical ambient temperature of 50-60°C, reaching over 80-150°C during temporary shutdowns, and the work platform between the igniter and the material distributor lacks space for a protective cover. Due to the high temperature, humidity, and dust in the on-site environment, high requirements are placed on the performance indicators of the testing equipment (such as high temperature resistance, corrosion resistance, and sealing performance). Existing instruments are inadequate without proper protection.

[0006] The layer thickness detection technology for sintering machine trolleys has undergone numerous systematic and precise innovations. From the original manual observation to the widely used radar level gauges, mechanical transmission detection methods, image processing methods, and now the more suitable soft measurement methods, the development of these modern online automatic detection technologies marks the progress and arduous journey of trolley layer thickness detection technology. With the rapid development of the steel industry, large blast furnaces are placing increasingly higher demands on the quality of sintered ore, requiring strict detection and control of the material layer thickness during sintering operations. After on-site surveys of several sintering plants, it was generally reported that layer thickness detection still faces many problems and challenges. For example, mechanical rotary wheel and measuring arm layer thickness detection devices suffer from maintenance issues and frequent zero-point changes. Laser rangefinders and image processing methods have limitations when there is heavy fog or a large amount of powder. To ensure that the material layer is controlled within the pre-set target thickness, it is necessary to continue developing technologies that can adapt to harsh on-site environments and accurately detect the material layer thickness online in real time. Summary of the Invention

[0007] The purpose of this section is to outline some aspects of embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.

[0008] In view of the aforementioned existing problems, the present invention is proposed.

[0009] Therefore, the technical problem solved by this invention is that existing measurement techniques suffer from large observation errors, operational delays, and inability to adapt to harsh field environments.

[0010] To solve the above-mentioned technical problems, the present invention provides the following technical solution: a real-time detection system for three-dimensional thickness of material layer in a curtain-scanning sintering machine.

[0011] The real-time detection system consists of multiple measuring devices, each of which includes a first lever, a second lever, and a fixed point.

[0012] The first lever is fixed, with one end connected to a fixed point. A wire displacement sensor is installed at the end of the first lever away from the fixed point. The second lever is fixed to the fixed point, with one end in contact with the material layer, and can rotate around the fixed point.

[0013] As described in this invention, the real-time detection system for three-dimensional thickness of sintering material layer based on curtain scanning includes a wire displacement sensor, which features a large measurement stroke, small installation size, high precision, and compact structure. Its function is to convert mechanical motion into electrical signals that can be recorded, measured, or transmitted, including measuring the length from the sensor to the end of the second lever away from the material layer when the trolley is running.

[0014] The method for real-time detection of three-dimensional thickness of sintering material layer based on curtain scanning as described in this invention includes:

[0015] Calculate the material layer thickness in the sintering machine based on geometric principles;

[0016] Perform error analysis on the calculation results;

[0017] A real-time detection system is constructed by setting up multiple measuring devices to measure the thickness of the material layer at different locations and to build a 3D map of the material layer on the sintering machine trolley based on the Lagrange interpolation algorithm.

[0018] As described in this invention, the real-time detection method for the three-dimensional thickness of the sintering machine material layer based on curtain scanning is wherein: when the trolley is running, the cosine of the included angle between the first lever and the second lever is expressed as:

[0019]

[0020] Where θ is the angle between the first lever and the second lever, s is the length of the first lever, l is the distance from the fixed point to the end of the second lever furthest from the material layer, and d is the distance from the wire displacement sensor to the end of the second lever furthest from the material layer.

[0021] As described in this invention, the real-time detection method for the three-dimensional thickness of the sintering machine material layer based on curtain scanning is as follows: The thickness of the sintering machine material layer can be obtained from geometric relationships as follows:

[0022]

[0023] Where h is the thickness of the material layer, H is the vertical height of the fixed point from the bottom of the material layer, and L is the length of the fixed point in the second lever from the material layer.

[0024] As described in this invention, the method for real-time detection of three-dimensional thickness of sintering material layer based on curtain scanning includes: error analysis of the thickness measurement principle, including:

[0025] Define the measurement error of the wire displacement sensor as Δd, and the thickness of the material layer where the error exists. Represented as:

[0026]

[0027] The error in the material layer thickness measurement is expressed as follows:

[0028]

[0029]

[0030] The error results calculated by substituting real data show that the measurement error is small, the accuracy is high, and it fully meets the actual requirements.

[0031] As described in this invention, the method for real-time detection of three-dimensional thickness of sintering machine material layer based on curtain scanning includes: Since the material surface of the sintering machine trolley is relatively rough and actually uneven, the second lever often deviates. Error analysis of the second lever is performed, including:

[0032] Define the second lever deviation trolley running direction angle as α. From the solid geometry, the material layer thickness is still expressed as:

[0033]

[0034] Therefore, it can be seen that the method of measuring the material layer thickness of the sintering machine trolley in this invention has good robustness and can still measure the correct value on the material surface with different concavities and convexities.

[0035] As described in this invention, the method for real-time detection of three-dimensional thickness of material layer in a curtain-scanning sintering machine includes: measuring the thickness of material layer at different locations using multiple devices, including:

[0036] Multiple material layer thickness testers are installed simultaneously at different locations in a row to measure the material layer thickness in real time. The material layer thickness testers transmit the material layer thickness data to an industrial IoT computer in real time via sensors. The IoT computer uses this data and a Lagrange interpolation algorithm to construct a 3D map of the material layer on the sintering machine trolley. The 3D map helps on-site workers to monitor the material layer online, enabling them to understand changes in the material layer early and providing a reference for adjusting the rollers, trolley speed, air box dampers, ignition operations, etc.

[0037] As described in this invention, the real-time detection method for three-dimensional thickness of sintering material layer based on curtain scanning in a sintering machine includes: the Lagrange interpolation algorithm comprising:

[0038] Let the function exist There is a definition, and it is known that at point... function value on Define a number of times not exceeding The interpolation polynomial is expressed as:

[0039]

[0040] at this time, ;

[0041] Given function exist interpolation nodes The function value on is Define a number of times not exceeding interpolation function polynomial , is represented as:

[0042]

[0043] at this time,

[0044] in for A polynomial of degree 1 is called a polynomial of degree 2. Secondary interpolation basis function, and satisfying

[0045]

[0046] Easy to obtain

[0047]

[0048] As described in this invention, the real-time detection method for three-dimensional thickness of sintering material layer based on curtain scanning in a sintering machine is wherein: the Lagrange interpolation polynomial is expressed as:

[0049]

[0050] The beneficial effects of this invention are as follows: The present invention proposes a real-time detection method and system for sintering machine material layer thickness based on the Industrial Internet of Things (IIoT). This system utilizes multiple rotating rods and wire displacement sensors to convert angle information into length information using geometric principles. The length information is then transmitted to an IIoT computer for real-time processing. After measuring the thickness of the material layer at various typical locations on the sintering machine trolley, a 3D model of the sintering machine material layer is created using the Lagrange interpolation algorithm, resulting in a three-dimensional simulation image of the sintering machine material layer. This system offers timely and accurate detection, higher precision, and is unaffected by harsh environments such as high temperatures, high humidity, and high dust levels. Installation and maintenance are simpler and more convenient, operation is more stable and reliable, and it can assist on-site workers in adjusting production schedules in real time. Attached Figure Description

[0051] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0052] Figure 1 A schematic diagram of a single device monitoring the material layer thickness of a sintering machine based on a real-time detection method and system for material layer thickness in an industrial Internet of Things, provided as an embodiment of the present invention;

[0053] Figure 2 A method for real-time detection of sintering machine material layer thickness based on industrial Internet of Things and a three-dimensional image of the system when the second lever of the system undergoes displacement deviation are provided as an embodiment of the present invention;

[0054] Figure 3 A schematic diagram of a method and system for real-time detection of material layer thickness in a sintering machine based on the Industrial Internet of Things, provided as an embodiment of the present invention, for constructing a 3D model of the material layer thickness at different locations;

[0055] Figure 4 A 3D image of the sintering machine trolley material layer of a method and system for real-time detection of sintering machine material layer thickness based on industrial Internet of Things is provided as an embodiment of the present invention.

[0056] Figure 5 A photograph of the field device of a real-time detection method and system for sintering machine material layer thickness based on industrial Internet of Things provided in one embodiment of the present invention. Detailed Implementation

[0057] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0058] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0059] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0060] This invention is described in detail with reference to the schematic diagrams. When detailing the embodiments of this invention, for ease of explanation, the cross-sectional views illustrating the device structure may be partially enlarged, not adhering to the usual scale. Furthermore, the schematic diagrams are merely examples and should not be construed as limiting the scope of protection of this invention. In actual fabrication, the three-dimensional spatial dimensions of length, width, and depth should be included.

[0061] Furthermore, in the description of this invention, it should be noted that the terms "upper," "lower," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. These terms are used solely for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. In addition, the terms "first," "second," or "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0062] Unless otherwise explicitly specified and limited, the terms "installation," "connection," and "joining" in this invention should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; similarly, they can refer to mechanical connections, electrical connections, or direct connections, or indirect connections through an intermediate medium, or internal connections between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0063] Example 1

[0064] Reference Figure 1 —4, as an embodiment of the present invention, provides a method and system for real-time detection of sintering machine material layer thickness based on industrial Internet of Things, including a first lever A, a second lever B and a fixed point C; a wire displacement sensor is installed at the end of the first lever A away from the fixed point C.

[0065] S1: Calculate the material layer thickness in the sintering machine based on geometric principles;

[0066] like Figure 1 As shown, the first lever A is fixed, with one end connected to a fixed point C. A wire displacement sensor is installed at the end of the first lever A away from the fixed point C. The second lever B is fixed at the fixed point C, with one end in contact with the material layer, and can rotate around the fixed point C. When the thickness of the material layer changes, the angle between the first lever A and the second lever B also changes accordingly.

[0067] Furthermore, when the trolley is running, the cosine of the angle between the first lever A and the second lever B is expressed as:

[0068]

[0069] Where θ is the angle between the first lever A and the second lever B, s is the length of the first lever A, l is the distance from the fixed point C to the end of the second lever B away from the material layer, and d is the distance from the wire displacement sensor to the end of the second lever B away from the material layer.

[0070] It should be noted that the wire displacement sensor consists of a stretchable connecting rope wound around a hub, which is connected to a precision rotary sensor. The sensor can be an absolute encoder, incremental encoder, hybrid or conductive plastic rotary potentiometer, synchronizer, or resolver. Operationally, the wire displacement sensor is mounted in a fixed position, and the rope is attached to a moving object. The axis of motion of the moving object is aligned with the linear motion of the rope. During movement, the rope extends and contracts. An internal spring ensures that the tension of the rope remains constant. The threaded hub drives the precision rotary sensor to rotate, outputting an electrical signal proportional to the distance the rope has moved. Measuring the output signal allows determination of the displacement, direction, or speed of the moving object. Wire displacement sensors offer both analog and digital signal output options. Digital output types can utilize incremental rotary encoders, absolute encoders, etc., with output signals including square wave ABZ, sine / cosine, CANopen, RS485, MODBUS, Profibus, or Gray code / binary signals. They feature long measuring strokes (100–15000 mm), high accuracy (0.05%FS), and IP65 protection. Both the reel and housing are corrosion-resistant, and the traction rope is made of 316 stainless steel, enabling operation in harsh environments (including seawater). Optional output methods include voltage, resistance, current, incremental pulse, and absolute pulse. Analog output types can utilize precision potentiometers, Hall effect encoders, absolute encoders, etc., with output signals ranging from 4-20 mA, 0-5 V, 0-10 V, and resistance signals. Maximum stroke reaches 12500 mm, and the operating environment can achieve a maximum IP65 protection rating, suitable for a wide temperature range of -45℃ to +105℃. Figure 1 It can be seen that the wire displacement sensor is installed at a higher position and is not affected by harsh environments such as high temperature, high humidity, and high dust on the material surface of the trolley. It is simpler and more convenient to install and maintain, and its operation is more stable and reliable.

[0071] Furthermore, based on geometric relationships, the formula for the sintering machine material layer thickness is:

[0072]

[0073] Where h is the thickness of the material layer, H is the vertical height of the fixed point C from the bottom of the material layer, and L is the length of the fixed point C in the second lever B from the material layer.

[0074] S2: Perform error analysis on the calculation results;

[0075] Furthermore, an error analysis is performed on the thickness measurement principle, including:

[0076] Define the measurement error of the wire displacement sensor as Δd, and the thickness of the material layer where the error exists. Represented as:

[0077]

[0078] The error in the material layer thickness measurement is expressed as:

[0079]

[0080]

[0081] It should be noted that, according to the measurement error parameter table of the wire displacement sensor, Δd = 0.05mm, and the quadratic term in the formula can be basically ignored. Assuming the length L from the fixed point C in the second lever B to the material surface is 800mm, the length l from the end of the fixed point C in the second lever B furthest from the material layer is 500mm, the length s of the first lever A is 800mm, and the length d from the wire displacement sensor to the end of the second lever B furthest from the material layer is 600mm, substituting these values ​​into the formula yields a material layer thickness measurement error Δh of -0.06mm. From the error results, the measurement error is small, the accuracy is high, and it fully meets the actual requirements.

[0082] Furthermore, an error analysis was performed on the second lever B;

[0083] Because the material surface on the sintering machine trolley is relatively rough and actually uneven, the second lever B often deviates, such as... Figure 2 As shown, assuming the second lever B deviates from the trolley's running direction by an angle α, the formula for the material layer thickness, based on solid geometry, remains the same.

[0084]

[0085] Therefore, it can be seen that the method of measuring the material layer thickness of the sintering machine trolley in this invention has good robustness and can still measure the correct value on the material surface with different concavities and convexities.

[0086] It should be noted that the present invention can ensure that the plane formed by the lever and the pull line is in a vertical horizontal state.

[0087] S3: Set up multiple devices to measure the thickness of the material layer at different locations and construct a 3D map of the material layer on the sintering machine trolley based on the Lagrange interpolation algorithm.

[0088] like Figure 3 As shown, multiple material layer thickness testers are installed simultaneously at different positions in a row to measure the material layer thickness in real time. The material layer thickness testers transmit the material layer thickness data to the industrial IoT computer in real time through sensors. The IoT computer uses this data and uses the Lagrange interpolation algorithm to construct a 3D map of the material layer on the sintering machine trolley.

[0089] Furthermore, the principle of the Lagrange interpolation algorithm is as follows: Let the function... exist There is a definition, and it is known that at point... function value on Define a number of times not exceeding The interpolation polynomial is expressed as:

[0090]

[0091] at this time, ;

[0092] Given function exist interpolation nodes The function value on is Define a number of times not exceeding interpolation function polynomial , is represented as:

[0093]

[0094] at this time,

[0095] in for A polynomial of degree 1 is called a polynomial of degree 2. Secondary interpolation basis function, and satisfying

[0096]

[0097] Easy to obtain

[0098]

[0099] Furthermore, the Lagrange interpolation polynomial can be expressed as:

[0100]

[0101] from Figure 4It can be seen that, based on the data transmitted back by the sensors, the 3D model of the material layer on the sintering machine trolley was well constructed in the computer using the Lagrange interpolation algorithm.

[0102] Example 2

[0103] Reference Figure 4 —5, is an embodiment of the present invention, which provides a method and system for real-time detection of three-dimensional thickness of material layer in a sintering machine based on curtain scanning. In order to verify the beneficial effects of the present invention, scientific demonstration is carried out through real real-time data.

[0104]

[0105] The measured data is imported into an IoT computer to build, for example... Figure 4 The image shown is a 3D image of the sintering machine's material layer. Practice has shown that this method has high accuracy and reliability, such as... Figure 5 The invention shown has been applied to the No. 3 360 sintering machine of Liuzhou Iron and Steel Group.

[0106] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A real-time detection system for three-dimensional thickness of sintering material layer based on curtain scanning, characterized in that: The real-time detection system consists of multiple measuring devices, each of which includes: a first lever (A), a second lever (B), and a fixed point (C); The first lever (A) is fixed and one end is connected to the fixed point (C). The wire displacement sensor is installed at the end of the first lever (A) away from the fixed point (C). The second lever (B) is fixed at the fixed point (C), one end is in contact with the material layer, and it can rotate around the fixed point (C). The real-time three-dimensional thickness detection system for sintering machine material layers based on curtain scanning is executed according to the following steps: Calculate the material layer thickness in the sintering machine based on geometric principles; Perform error analysis on the calculation results; A real-time detection system is constructed by setting up multiple measuring devices to measure the thickness of the material layer at different locations and to build a 3D map of the material layer on the sintering machine trolley based on the Lagrange interpolation algorithm. The thickness of the sintering machine material layer can be obtained from geometric relationships as follows: Where h is the thickness of the material layer, H is the vertical height of the fixed point (C) from the bottom of the material layer, and L is the length of the fixed point (C) in the second lever (B) from the material layer; Error analysis was performed on the thickness measurement principle, including: Define the measurement error of the wire displacement sensor as Δd, and the thickness of the material layer where the error exists as h. ' Represented as: The error in the material layer thickness measurement is expressed as follows: Where θ is the angle between the first lever (A) and the second lever (B), s is the length of the first lever (A), l is the length of the fixed point (C) from the end of the second lever (B) away from the material layer, and d is the length from the wire displacement sensor to the end of the second lever (B) away from the material layer. Error analysis was performed on the second lever (B), including: Define the deviation angle of the second lever (B) from the trolley's running direction as α. From the solid geometry, the material layer thickness is still expressed as:

2. The real-time detection system for three-dimensional thickness of sintering material layer based on curtain scanning as described in claim 1, characterized in that, The wire displacement sensor converts mechanical motion into electrical signals that can be recorded, measured, and transmitted, including measuring the length from the sensor to the end of the second lever (B) away from the material layer when the trolley is running.

3. The real-time detection system for three-dimensional thickness of sintering material layer based on curtain scanning as described in claim 2, characterized in that, When the trolley is running, the cosine of the angle between the first lever (A) and the second lever (B) is expressed as:

4. The real-time detection system for three-dimensional thickness of sintering material layer based on curtain scanning as described in claim 3, characterized in that: The thickness of the material layer at different locations is measured by setting up multiple devices, including: Multiple material layer thickness testers are installed simultaneously at different positions in a row to measure the material layer thickness in real time. The material layer thickness testers transmit the material layer thickness data to the industrial IoT computer in real time through sensors. The IoT computer uses this data and uses the Lagrange interpolation algorithm to construct a 3D map of the material layer on the sintering machine trolley.

5. The real-time detection system for three-dimensional thickness of sintering material layer based on curtain scanning as described in claim 4, characterized in that: The Lagrange interpolation algorithm includes: Let the function f(x) be defined on [a,b], and it is known that at the point a≤x0 <x1<x2<…<x n The function values ​​y0, y1, ..., y on ≤b n Let an interpolation polynomial of degree no more than n be defined as: L n (x)=a0+a1x+…+a n x n At this time, L n (x i )=y i (i = 0, 1, 2, ..., n); Given that the function f(x) has n+1 interpolation nodes a≤x0 <x1<x2<…<x n The function values ​​on ≤b are f(x0), f(x1), ..., f(x) n Define an interpolation function polynomial L of degree no more than n. n (x), represented as: L n (x)=l0(x)y0+l1(x)y1+…+l n (x)y n At this time, L n (x i )=y i =f(x) i (i = 0, 1, 2, ..., n) Among them l i (x)(i=0,1,2,…,n) is an nth-degree polynomial, called an nth-degree interpolation basis function, and satisfies 6. The real-time detection system for three-dimensional thickness of sintering material layer based on curtain scanning as described in claim 5, characterized in that: The Lagrange interpolation polynomial is expressed as:

Images