Multi-dimensional early warning self-adaptive control system and method for LED explosion-proof lamp
Patent Information
- Application Number
- CN202610666312.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-05-14
- Publication Date
- 2026-08-18
AI Technical Summary
[0007]基于此,有必要针对现有防爆灯具预警系统“单一阈值报警、被动响应、适配性差、能耗偏高的问题,提供一种LED防爆灯多维预警自适应控制系统及方法
[0018]本发明的有益效果为:本发明所述方法整体形成“数据采集-预处理-模型预警-风险定级-自适应调控-安全联动”的完整技术闭环,有效解决现有防爆LED照明系统智能化低、故障识别不准、预警不灵活、防护不全面的问题。通过特征筛选、模型优化实现故障精准识别与快速推理,适配嵌入式部署;通过动态阈值与分级风险管控,实现安全预警的精准高效、主动防护;通过无雷达传感器的光照自适配控制,兼顾节能、照明效果与场景适配性;整套方案结构简洁、成本低、实用性强,可广泛适配各类高危防爆场景,显著提升系统的安全性、可靠性与智能化水平。
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Figure CN122598379A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of LED explosion-proof light technology, and in particular to a multi-dimensional early warning adaptive control system and method for LED explosion-proof lights. Background Technology
[0002] Flammable and explosive hazardous work environments (such as petrochemical plants, underground mines, and dusty workshops) have extremely high requirements for the explosion-proof safety, operational reliability, and intelligent control capabilities of lighting equipment. Most existing explosion-proof LED lighting fixtures use fixed brightness or graded operating modes, requiring manual switching. They cannot automatically adjust the lighting output according to the ambient light intensity, easily leading to energy waste or insufficient lighting intensity, making it difficult to balance energy conservation needs with operational safety.
[0003] In terms of control methods, while some smart lighting products employ simple open-loop control or conventional PID control algorithms, they generally suffer from fixed parameters and poor scene adaptability. Under complex operating conditions such as dust, humidity, and corrosive gases, the controlled parameters are prone to drift, leading to unstable dimming, large overshoot, and lag, making it impossible to achieve precise and stable control of lighting brightness and drive current. Furthermore, traditional control algorithms involve high computational demands and consume significant hardware resources, making them unsuitable for low-power, low-computing-power embedded explosion-proof control equipment.
[0004] In terms of safety protection, existing explosion-proof lighting fixtures only possess simple hardware protection functions such as overcurrent, overvoltage, and overtemperature protection, lacking multi-dimensional comprehensive monitoring of the fixture's operating status. Current technology cannot identify faults and assess risk levels using multiple parameters such as current, temperature, vibration, battery voltage, humidity, dust concentration, combustible gas concentration, circuit resistance, and ambient light intensity. This makes it difficult to predict potential safety hazards such as circuit aging, poor contact, abnormal drive, and battery thermal runaway. When a fault occurs, protection actions are often only passively triggered, failing to achieve a closed-loop linkage between warning and control, posing a significant safety risk.
[0005] Furthermore, existing intelligent lighting systems generally lack a collaborative mechanism between fault warning results and lighting control strategies, and cannot adaptively adjust control parameters according to fault type and risk level. This results in the lamps still operating in normal mode under abnormal conditions, which can easily exacerbate equipment damage or even cause safety accidents.
[0006] In summary, existing explosion-proof lighting technologies have significant shortcomings in terms of scene adaptability, control precision, timely fault warning, and system coordination. They cannot meet the needs of flammable and explosive environments for intelligent, highly safe, and highly reliable lighting equipment, and therefore have considerable room for improvement. Summary of the Invention
[0007] Therefore, it is necessary to provide a multi-dimensional early warning adaptive control system and method for LED explosion-proof lights to address the problems of existing explosion-proof lighting early warning systems, such as "single threshold alarm, passive response, poor adaptability, and high energy consumption".
[0008] A multi-dimensional early warning adaptive control system for LED explosion-proof lights includes: The data acquisition module is used to collect real-time operating data of the lighting fixtures and scene environment data. The data acquisition module includes a current sensor, a temperature sensor, a vibration sensor, a combustible gas sensor, a humidity sensor, a dust sensor, a voltage sensor, and a light sensor. The early warning module is used to perform early warning analysis based on real-time collected lighting operation data and scene environment data, as well as the random forest early warning model stored therein, and generate prediction results. The self-adaptive control module is used to automatically adjust the operating parameters of the lighting fixtures based on a PID control algorithm, combined with lighting fixture operating data, scene environment data, and prediction results; and The data interaction module is used to realize real-time data interaction with the back-end management platform and mobile APP, ensuring remote control, PID parameter fine-tuning and data synchronization. The data interaction module supports LoRa and 5G dual communication modes.
[0009] In one embodiment, the random forest early warning model is trained using a random forest machine learning algorithm based on a historical fault dataset.
[0010] A multi-dimensional early warning adaptive control method for LED explosion-proof lights, based on the aforementioned multi-dimensional early warning adaptive control system for LED explosion-proof lights, includes the following steps: S1. The acquisition module collects real-time operating data of the lighting fixtures and scene environment data; wherein, the operating data of the lighting fixtures includes current, vibration, battery voltage and circuit resistance, and the scene environment data includes temperature, combustible gas concentration, humidity, dust concentration and ambient light intensity. S2. Based on the real-time collected lighting operation data and scene environment data, as well as the random forest early warning model stored therein, perform early warning analysis and generate prediction results; S3. Based on the PID control algorithm, the system automatically adjusts the operating parameters of the lighting fixtures by combining the lighting fixture operating data, scene environment data, and prediction results.
[0011] In one embodiment, the random forest early warning model in S2 is trained using a random forest machine learning algorithm based on a historical fault dataset; the training method of the random forest early warning model includes the following steps: S211. Normalize the historical fault dataset to obtain the original dataset; wherein, the historical fault dataset contains 9 original features, namely current, temperature, vibration, combustible gas concentration, humidity, dust concentration, battery voltage, circuit resistance and ambient light intensity. Normalization calculation formula: in: These are the original feature values from the historical fault dataset. This represents the minimum value of the corresponding feature in the historical fault dataset. This represents the maximum value of the corresponding feature in the historical fault dataset; S212. Redundant features in the original dataset are removed by ranking them by Gini coefficient importance to obtain the basic dataset; S213. Divide the basic dataset into a training dataset and a test dataset in a 7:3 ratio; S214. Construct a random forest early warning model using the training dataset; A forest of 100 decision trees is set up. 60% of the training dataset samples and 5-dimensional features are randomly selected from each tree to participate in the splitting. The node splitting is completed by minimizing the Gini coefficient until the tree depth is ≤10 layers or the number of node samples is ≤5. Formula for calculating the Gini coefficient before node splitting: Where D is the sample set of the current node; For category numbering, =9, corresponding to 9 output categories, namely: 1. Normal state; 2. Circuit short circuit fault; 3. Circuit aging and poor contact fault; 4. LED light source decay or damage fault; 5. Driver power supply abnormal fault; 6. Battery thermal runaway and performance decay fault; 7. Sensor failure or abnormal fault; 8. External high-risk environment linkage risk; 9. Lighting abnormality and lamp obstruction fault. This represents the proportion of the k-th class of samples in the current node. , |Dk| represents the number of samples of the kth class in the node, and |D| represents the total number of samples in the node; Formula for calculating the weighted Gini coefficient after node splitting: Where A is the splitting feature number (one of the 9 core features). , These are the two child node sample sets obtained after splitting according to the threshold of feature A. child node , The number of samples, , child node , The Gini coefficient; S215. The random forest model is compressed through pruning optimization and threshold quantization; Pruning optimization: Traverse all split nodes of 100 decision trees, calculate the decrease in Gini coefficient before and after splitting each node, remove branches and their subtrees with a decrease in Gini coefficient less than 0.001, change the current split node to a leaf node, and retain the category output corresponding to the node. Formula for calculating the decrease in the Gini coefficient: in, The Gini coefficient of the parent node before the split. The weighted Gini coefficient for the child nodes after splitting; Threshold quantization: Converts floating-point thresholds in decision tree split nodes into 16-bit fixed-point numbers; Specific calculation formula: in, For floating-point thresholds, For quantized 16-bit fixed-point numbers, This is the rounding function; S216. The random forest early warning model was validated using a test dataset; When the accuracy reaches 98% or higher, the recall reaches 97% or higher, and the recognition precision of the 9 categories reaches 96% or higher, the random forest early warning model is judged to meet the standards. The formula for calculating accuracy is: in, The number of samples whose true class matches the predicted class; The number of samples that are neither true nor predicted to belong to a certain category; This represents the number of samples that are not actually of a certain category but are predicted to belong to that category. The number of samples that are actually of a certain category but are predicted to be of a different category; The formula for calculating recall rate: For type k fault The overall recall rate is calculated as an average or weighted average of all categories: Single-class recognition accuracy For type k faults in, Let be the number of samples where the true class is class k and the model predicts the class as class k. The number of samples where the true class is not class k and the model predicts that the class is also not class k. The number of samples whose true class is not class k, but whose model predicts to be class k. This represents the number of samples where the true class is class k, but the model predicts that the sample is not class k.
[0012] In one embodiment, the method in S2 for performing early warning analysis and generating prediction results based on real-time collected lighting operation data, scene environment data, and the stored random forest early warning model includes the following steps: S221. After normalizing and quantizing the real-time collected lighting operation data and scene environment data, the input feature vector is obtained. S222. Input the input feature vector into the random forest early warning model to obtain the fault category; S223. Calculate trend features based on time series characteristics, and calculate dynamic thresholds in combination with scene environment data; Trend feature calculation formula: in, Let be the original eigenvalue at time t. Let be the original eigenvalue at time tT. The set time interval; Dynamic threshold calculation formula: in, As the baseline warning threshold, This is the threshold adjustment coefficient. For real-time environmental parameters, These are the critical values for environmental parameter safety. Adjust the length of the environmental parameter adjustment range; S224. Determine the risk level by combining the fault category obtained in step S222 with the trend characteristics and dynamic threshold comparison results obtained in step S223.
[0013] In one embodiment, the method for obtaining the fault category through the random forest early warning model in S222 includes the following steps: A. For each decision tree, starting from the root node, read the split feature number, 16-bit quantization threshold, and left and right child node indices stored in the node. B. Compare the quantized feature value of the corresponding dimension with the node threshold. If the threshold condition is met, proceed to the left child node; otherwise, proceed to the right child node. C. Repeat the process of reading nodes, comparing features, and jumping to child nodes until leaf nodes are reached; D. Use the category number stored in the leaf node as the prediction result of a single decision tree; E. Analyze the prediction results of 100 decision trees and use a simple majority voting method to obtain the fault category.
[0014] In one embodiment, the fault categories mentioned in S222 include normal state, short circuit fault, circuit aging and poor contact fault, LED light source decay or damage fault, abnormal drive power supply fault, battery thermal runaway and performance decay fault, sensor failure or abnormal fault, external high-risk environment linkage risk, and abnormal lighting and lamp obstruction fault.
[0015] In one embodiment, the risk level in S224 includes low risk, medium risk, and high risk; the criteria for determining the risk level are as follows: If the fault category is normal, the lighting operation data and scene environment data are all within the dynamic threshold range, and the trend characteristics are not greater than the first trend threshold, then it is judged as low risk. If the fault category is a non-high-risk fault, or if some data in the lighting operation data and scene environment data are close to the dynamic threshold or the first trend threshold. Trend characteristics If the second trend threshold is reached, it is determined to be of medium risk; If the fault category is a high-risk fault, or if any data in the lighting operation data and scene environment data exceeds the dynamic threshold, or the trend characteristic is greater than the second trend threshold, then it is judged as high-risk. Among them, the non-high-risk faults are LED light source attenuation or damage faults, sensor failure or abnormal faults, and abnormal lighting and lamp obstruction faults; the high-risk faults are circuit short circuit faults, circuit aging and poor contact faults, abnormal drive power supply faults, battery thermal runaway and performance degradation faults, and external high-risk environmental linkage risks.
[0016] In one embodiment, the method in S3 that automatically adjusts the operating parameters of the lighting fixtures based on a PID control algorithm, combined with lighting fixture operating data, scene environment data, and prediction results, includes the following steps: S31. Determine the target setpoint SP of the controlled parameter based on the ambient light intensity, fault type, and risk level; wherein the controlled parameter is the LED drive current, lamp operating power, sampling frequency, and brightness threshold. S32. Calculate the actual values of the controlled parameters based on the scene environment data and the lighting operation data, and calculate the current cycle deviation; Let the first Each sampling period in, The target setpoint for the controlled parameter. The actual value of the controlled parameter; S33. Calculate the increment of the incremental PID control quantity; Control increment formula: in, ; ; ; This is the current sampling period; For the first The deviation value for each sampling period; The deviation value for each sampling period; For the first The deviation value for each sampling period; This is the proportionality coefficient; The integral time constant is... , The integral coefficient; Differential time constant , These are the differential coefficients; S34. Update the current control quantity and apply a safety limit; Current control quantity formula: S35. Automatically fine-tune the proportional coefficient based on the fault type and risk level. Integral coefficient and differential coefficients The final control quantity is calculated.
[0017] In one embodiment, the scaling factor The integral coefficient is between 1.0 and 5.0. The differential coefficient is between 0.05 and 0.3. It ranges from 0.02 to 0.2.
[0018] The beneficial effects of this invention are as follows: The method described in this invention forms a complete technical closed loop of "data acquisition - preprocessing - model early warning - risk classification - adaptive control - safety linkage", effectively solving the problems of low intelligence, inaccurate fault identification, inflexible early warning, and incomplete protection in existing explosion-proof LED lighting systems. Through feature screening and model optimization, it achieves accurate fault identification and rapid reasoning, adapting to embedded deployment; through dynamic thresholds and hierarchical risk management, it achieves accurate and efficient safety early warning and proactive protection; through radar sensor-free adaptive illumination control, it balances energy saving, lighting effect, and scene adaptability; the entire solution has a simple structure, low cost, and strong practicality, and can be widely adapted to various high-risk explosion-proof scenarios, significantly improving the safety, reliability, and intelligence level of the system. Attached Figure Description
[0019] Figure 1 This is a schematic diagram of the structure of the multi-dimensional early warning and adaptive control system for LED explosion-proof lights of the present invention; Figure 2 This is a flowchart of the multi-dimensional early warning adaptive control method for LED explosion-proof lights of the present invention; Figure 3 This is a flowchart illustrating the training method of the random forest early warning model of the present invention. Figure 4 This is a flowchart illustrating the method of the present invention for performing early warning analysis and generating prediction results based on real-time collected lighting operation data, scene environment data, and the random forest early warning model stored therein. Figure 5 This is a flowchart illustrating the method for obtaining fault categories using a random forest early warning model according to the present invention. Figure 6 This invention relates to a method for automatically adjusting the operating parameters of lighting fixtures by using a PID control algorithm as the core, combined with lighting fixture operating data, scene environment data, and prediction results.
[0020] The meanings of the numbers in the attached diagram are as follows: 100-LED Explosion-proof Light Multi-dimensional Early Warning Adaptive Control System; 10 - Data Acquisition Module; 20 - Early Warning Module; 30 - Self-adaptive control module; 40 - Data Interaction Module. Detailed Implementation
[0021] 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. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.
[0022] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," and "circumferential" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this invention and 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 this invention.
[0023] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.
[0024] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.
[0025] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can mean that the first feature is in direct contact with the second feature, or that the first feature is in indirect contact with the second feature through an intermediate medium. Furthermore, "above," "over," and "on top" of the second feature can mean that the first feature is directly above or diagonally above the second feature, or simply that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature can mean that the first feature is directly below or diagonally below the second feature, or simply that the first feature is at a lower horizontal level than the second feature.
[0026] It should be noted that when an element is referred to as being "fixed to" or "set on" another element, it can be directly on the other element or there may be an intervening element. When an element is considered to be "connected to" another element, it can be directly connected to the other element or there may be an intervening element. The terms "vertical," "horizontal," "upper," "lower," "left," "right," and similar expressions used herein are for illustrative purposes only and do not represent the only possible implementation.
[0027] Please see Figure 1 A multi-dimensional early warning adaptive control system 100 for LED explosion-proof lights according to one embodiment of the present invention includes: The acquisition module 10 is used to acquire real-time lighting operation data and scene environment data. The acquisition module 10 includes a current sensor, a temperature sensor, a vibration sensor, a combustible gas sensor, a humidity sensor, a dust sensor, a voltage sensor, and a light sensor. The early warning module 20 is used to perform early warning analysis based on real-time collected lighting operation data and scene environment data and the random forest early warning model stored therein, and generate prediction results; wherein, the random forest early warning model is trained based on historical fault datasets and trained by the random forest machine learning algorithm; The self-adaptive control module 30 is used to automatically adjust the operating parameters of the lighting fixtures based on a PID control algorithm, combined with lighting fixture operating data, scene environment data, and prediction results; and The data interaction module 40 is used to realize real-time data interaction with the back-end management platform and mobile APP, so as to ensure remote control, PID parameter fine-tuning and data synchronization. The data interaction module 40 supports LoRa and 5G dual communication modes.
[0028] Please see Figure 2 A multi-dimensional early warning adaptive control method for LED explosion-proof lights, implemented based on the aforementioned multi-dimensional early warning adaptive control system 100 for LED explosion-proof lights, includes the following steps: S1. The acquisition module 10 acquires real-time lighting operation data and scene environment data; wherein, the lighting operation data includes current, vibration, battery voltage and circuit resistance, and the scene environment data includes temperature, combustible gas concentration, humidity, dust concentration and ambient light intensity. S2. Based on the real-time collected lighting operation data and scene environment data, as well as the random forest early warning model stored therein, perform early warning analysis and generate prediction results; The random forest early warning model is trained using a random forest machine learning algorithm based on a historical fault dataset; please refer to [link / reference]. Figure 3 The training method for the random forest early warning model includes the following steps: S211. Normalize the historical fault dataset to obtain the original dataset; wherein, the historical fault dataset contains 9 original features, namely current, temperature, vibration, combustible gas concentration, humidity, dust concentration, battery voltage, circuit resistance and ambient light intensity. Normalization calculation formula: in: These are the original feature values from the historical fault dataset. This represents the minimum value of the corresponding feature in the historical fault dataset. This represents the maximum value of the corresponding feature in the historical fault dataset; S212. Redundant features in the original dataset are removed by ranking them by Gini coefficient importance to obtain the basic dataset; S213. Divide the basic dataset into a training dataset and a test dataset in a 7:3 ratio; S214. Construct a random forest early warning model using the training dataset; A forest of 100 decision trees is set up. 60% of the training dataset samples and 5-dimensional features are randomly selected from each tree to participate in the splitting. The node splitting is completed by minimizing the Gini coefficient until the tree depth is ≤10 layers or the number of node samples is ≤5. Formula for calculating the Gini coefficient before node splitting: Where D is the sample set of the current node; For category numbering, =9, corresponding to 9 output categories, namely: 1. Normal state; 2. Circuit short circuit fault; 3. Circuit aging and poor contact fault; 4. LED light source decay or damage fault; 5. Driver power supply abnormal fault; 6. Battery thermal runaway and performance decay fault; 7. Sensor failure or abnormal fault; 8. External high-risk environment linkage risk; 9. Lighting abnormality and lamp obstruction fault. This represents the proportion of the k-th class of samples in the current node. , |Dk| represents the number of samples of the kth class in the node, and |D| represents the total number of samples in the node; Formula for calculating the weighted Gini coefficient after node splitting: Where A is the splitting feature number (one of the 9 core features). , These are the two child node sample sets obtained after splitting according to the threshold of feature A. child node , The number of samples, , child node , The Gini coefficient; S215. The random forest model is compressed through pruning optimization and threshold quantization; Pruning optimization: Traverse all split nodes of 100 decision trees, calculate the decrease in Gini coefficient before and after splitting each node, remove branches and their subtrees with a decrease in Gini coefficient less than 0.001, change the current split node to a leaf node, and retain the category output corresponding to the node. Formula for calculating the decrease in the Gini coefficient: in, The Gini coefficient of the parent node before the split. The weighted Gini coefficient for the child nodes after splitting; Threshold quantization: Converts floating-point thresholds in decision tree split nodes into 16-bit fixed-point numbers; Specific calculation formula: in, For floating-point thresholds, For quantized 16-bit fixed-point numbers, This is the rounding function; S216. The random forest early warning model was validated using a test dataset; When the accuracy reaches 98% or higher, the recall reaches 97% or higher, and the recognition precision of the 9 categories reaches 96% or higher, the random forest early warning model is judged to meet the standards. The formula for calculating accuracy is: in, The number of samples whose true class matches the predicted class; The number of samples that are neither true nor predicted to belong to a certain category; This represents the number of samples that are not actually of a certain category but are predicted to belong to that category. The number of samples that are actually of a certain category but are predicted to be of a different category; The formula for calculating recall rate: For type k fault The overall recall rate is calculated as an average or weighted average of all categories: Single-class recognition accuracy For type k faults in, Let be the number of samples where the true class is class k and the model predicts the class as class k. The number of samples where the true class is not class k and the model predicts that the class is also not class k. The number of samples whose true class is not class k, but whose model predicts to be class k. This represents the number of samples where the true class is class k, but the model predicts that the sample is not class k.
[0029] The random forest early warning model trained and optimized through the above steps exhibits high fault identification accuracy and strong engineering applicability. Based on normalization and Gini coefficient feature selection, the model effectively reduces data redundancy and computational complexity, enabling rapid inference on embedded platforms. Employing a multi-decision tree ensemble structure with the Gini coefficient as the splitting criterion, the model achieves clear classification boundaries and strong generalization ability, stably distinguishing between normal states and nine typical fault types, and demonstrating good resistance to operating noise and data fluctuations. After pruning optimization and 16-bit fixed-point quantization, the model is smaller and more efficient, meeting the needs of real-time monitoring and rapid early warning of lighting equipment in hazardous locations. Testing has verified that the model achieves an accuracy of no less than 98%, a recall of no less than 97%, and a recognition accuracy of no less than 96% for each category. It accurately captures early fault characteristics, enabling early prediction of potential hazards, and outputs clear fault categories and risk levels, providing a reliable basis for subsequent PID adaptive adjustment and safety protection actions, significantly improving the safety, reliability, and intelligence of explosion-proof lighting systems.
[0030] Please see Figure 4 The method in S2 for performing early warning analysis and generating prediction results based on real-time collected lighting operation data, scene environment data, and the stored random forest early warning model includes the following steps: S221. After normalizing and quantizing the real-time collected lighting operation data and scene environment data, the input feature vector is obtained. S222. Input the input feature vector into the random forest early warning model to obtain the fault category; Please see Figure 5 Specifically, it includes the following steps: A. For each decision tree, starting from the root node, read the split feature number, 16-bit quantization threshold, and left and right child node indices stored in the node. B. Compare the quantized feature value of the corresponding dimension with the node threshold. If the threshold condition is met, proceed to the left child node; otherwise, proceed to the right child node. C. Repeat the process of reading nodes, comparing features, and jumping to child nodes until leaf nodes are reached; D. Use the category number stored in the leaf node as the prediction result of a single decision tree; E. Analyze the prediction results of 100 decision trees and use a simple majority voting method to obtain the fault category.
[0031] The above method only requires basic counting statistics to output a clear fault category number, without secondary parsing. It can directly provide accurate and direct decision-making basis for subsequent PID adaptive adjustment of controlled parameters such as LED drive current and operating power, as well as graded safety protection actions, realizing rapid linkage between fault early warning and system control. At the same time, the majority voting integrated decision mechanism can effectively offset the risk of misjudgment caused by sensor noise, data fluctuations, and local classification bias in a single decision tree, significantly reducing the probability of missed or misjudged faults, ensuring the recognition accuracy of 9 types of operating states and fault types, and ensuring that the model can still output reliable fault category results stably under complex and harsh working conditions such as dust, humidity, and strong vibration, further improving the safety protection capability and intelligent control level of LED explosion-proof lights.
[0032] S223. Calculate trend features based on time series characteristics, and calculate dynamic thresholds in combination with scene environment data; Trend feature calculation formula: in, Let be the original eigenvalue at time t. Let be the original eigenvalue at time tT. The set time interval; Dynamic threshold calculation formula: in, As the baseline warning threshold, This is the threshold adjustment coefficient. For real-time environmental parameters, These are the critical values for environmental parameter safety. The length of the environmental parameter adjustment range.
[0033] This example uses the core characteristic of the explosion-proof LED lighting fixture's casing temperature as the early warning target and the ambient combustible gas concentration as the scene input parameter to fully demonstrate the calculation process of the dynamic threshold: Preset basic parameters: Temperature reference warning threshold The critical temperature for the safety of combustible gas is 75℃. =25%LEL, adjustment range =25%LEL, time interval T=5.
[0034] Trend characteristic calculation: Luminaire housing temperature at time t The temperature is 62℃, at time t-5 (50 seconds ago). Let the temperature be 50℃. Substitute this into the trend characteristic formula: A trend characteristic value of 24% ≥ 20% is considered a severe deterioration trend, corresponding to a threshold adjustment coefficient. The temperature is 20℃.
[0035] Environmental parameter acquisition: real-time combustible gas concentration 35% LEL ≥ This triggers the threshold reduction logic.
[0036] Dynamic threshold calculation: Substitute into the piecewise formula: Results comparison: In the fixed threshold mode, the warning will only be triggered when the temperature rises to 75℃; in the dynamic threshold mode, the warning threshold is lowered to 67℃, and an early warning will be triggered when the temperature exceeds 67℃, which can detect the trend of thermal degradation of equipment in advance, and at the same time adapt to high-risk environments with excessive combustible gas, significantly advancing the time for safety protection.
[0037] By calculating time-series trend features, the system accurately captures the gradual degradation trend of explosion-proof lighting equipment parameters, solving the problems of single-moment sampling values being easily interfered with by environmental noise and the high rate of missed detection for slowly developing faults. Through a segmented dynamic threshold formula, the system achieves real-time adaptation of the warning threshold to the risk of the scene environment. In low-risk environments, it maintains the baseline threshold to avoid false alarms, while in high-risk environments, it lowers the threshold to improve warning sensitivity. At the same time, through the linkage of trend features and threshold adjustment coefficients, it achieves dual adaptation between the equipment's own degradation trend and external environmental risks, further improving the system's early warning capability. The overall solution has a simple calculation logic and minimal computational load. It is deeply integrated with the aforementioned random forest warning model and PID adaptive control scheme, significantly improving the operational safety and reliability of explosion-proof LED lighting systems in flammable and explosive complex working conditions.
[0038] S224. Determine the risk level by combining the fault category obtained in step S222 with the trend characteristics and dynamic threshold comparison results obtained in step S223. The risk level includes low risk, medium risk, and high risk.
[0039] The criteria for determining the risk level are as follows: If the fault category is normal, the lighting operation data and scene environment data are all within the dynamic threshold range, and the trend characteristics are not greater than the first trend threshold, then it is judged as low risk. If the fault category is a non-high-risk fault, or if some data in the lighting operation data and scene environment data are close to the dynamic threshold or the first trend threshold. Trend characteristics If the second trend threshold is reached, it is determined to be of medium risk; If the fault category is a high-risk fault, or if any data in the lighting operation data and scene environment data exceeds the dynamic threshold, or the trend characteristic is greater than the second trend threshold, then it is judged as high-risk. Among them, the non-high-risk faults are LED light source attenuation or damage faults, sensor failure or abnormal faults, and abnormal lighting and lamp obstruction faults; the high-risk faults are circuit short circuit faults, circuit aging and poor contact faults, abnormal drive power supply faults, battery thermal runaway and performance degradation faults, and external high-risk environmental linkage risks.
[0040] The criteria for determining risk levels avoid false alarms and omissions caused by ambiguous judgments. By prioritizing the highest risk level, the criteria ensure that high-risk situations are handled first, which fully complies with the safety management requirements for flammable and explosive sites.
[0041] S3. Based on the PID control algorithm, the system automatically adjusts the operating parameters of the lighting fixtures by combining the lighting fixture operating data, scene environment data, and prediction results.
[0042] Please see Figure 6 Specifically, it includes the following steps: S31. Determine the target setpoint SP of the controlled parameter based on the ambient light intensity, fault type, and risk level; wherein the controlled parameter is the LED drive current, lamp operating power, sampling frequency, and brightness threshold. S32. Calculate the actual values of the controlled parameters based on the scene environment data and the lighting operation data, and calculate the current cycle deviation; Let the first Each sampling period in, The target setpoint for the controlled parameter. The actual value of the controlled parameter; S33. Calculate the increment of the incremental PID control quantity; Control increment formula: in, ; ; ; This is the current sampling period; For the first The deviation value for each sampling period; The deviation value for each sampling period; For the first The deviation value for each sampling period; This is the proportionality coefficient; The integral time constant is... , The integral coefficient; Differential time constant , These are the differential coefficients; S34. Update the current control quantity and apply a safety limit; Current control quantity formula: S35. Automatically fine-tune the proportional coefficient based on the fault type and risk level. Integral coefficient and differential coefficients The final control quantity is calculated. The proportional coefficient... The integral coefficient is between 1.0 and 5.0. The differential coefficient is between 0.05 and 0.3. It ranges from 0.02 to 0.2.
[0043] In practice, the proportionality coefficient The default value is 2.5, and the integral coefficient is... The default value is 0.1, and the differential coefficient is... The default value is 0.05, where the scaling factor is... The integral coefficient and the differential coefficients The fine-tuning principles follow four principles: 1. Scene adaptation principle: Fine-tuning needs to be combined with the actual scene. In the case of high dust and low light scene in coal mine, the scaling factor can be appropriately increased. To accelerate the response speed of light regulation; in hazardous chemical industrial parks with high humidity and high gas concentration scenarios, the integral coefficient needs to be reduced. This reduces parameter fluctuations caused by integral accumulation and allows for fine-tuning of the differential coefficients. 1. Enhance the ability to predict abnormal fluctuations; 2. Linked early warning principle: Parameter fine-tuning should be linked to the risk level. In low-risk situations, there is no need to adjust the core PID parameters, only the setpoint of the controlled parameter needs to be fine-tuned; in medium-risk situations, the proportional coefficient can be slightly adjusted. and integral coefficient (The adjustment range shall not exceed 20% of the default value); in case of severe risk, directly switch to the emergency PID parameter (proportional coefficient). =3.5, integral coefficient =0.05, differential coefficient =0.15), prioritizing the safe operation of equipment; 3. Small and gradual principle: the single fine-tuning range shall not exceed 10% of the default parameter value (except for emergency control scenarios, emergency parameters do not need to follow this range requirement, prioritizing the safety of equipment). After fine-tuning, it is necessary to observe for more than 30 minutes to confirm that the lamp operating parameters (current, power, temperature) are stable and there are no abnormal warnings before making the next fine-tuning, so as to avoid the circuit short circuit, light source damage and other faults caused by sudden parameter changes; 4. Consistency principle: for explosion-proof lamps of the same type in the same area, the PID parameter fine-tuning must be consistent to avoid uneven illumination and energy consumption in the area due to parameter differences, and at the same time facilitate the later operation and maintenance management and parameter unified optimization.
[0044] Example 1 Using the LED drive current as the controlled parameter, an incremental PID controller is used to achieve closed-loop adaptive adjustment of ambient light intensity.
[0045] Setting value confirmed: In normal operating environments and when the ambient light intensity is ≥300 lux (sufficient lighting), the drive current is set to 300mA to balance energy saving and basic lighting needs. In normal working environments, when the ambient light intensity is <300 lux (weak light), the drive current is automatically increased to 500mA to ensure sufficient lighting on the working surface, which meets the lighting standards for explosion-proof locations. When the dust concentration exceeds its dynamic threshold and the ambient light intensity is <300 lux, the driving current is kept at 500mA, and the strong light penetration mode is activated to ensure the safety of operation under poor visibility.
[0046] Deviation calculation Real-time acquisition and calculation of drive current control deviation provides accurate input for PID control. The deviation calculation formula is as follows: =Drive current setpoint - Actual drive current value PV The actual value of the driving current PV is acquired in real time by a current sensor. The acquisition frequency is synchronized with the system sampling frequency to ensure the real-time performance and accuracy of the deviation calculation and avoid dimming fluctuations caused by sampling delay.
[0047] ③PID control output An incremental PID control algorithm is adopted, based on the above deviation. Calculate control increment The increment is added to the PWM duty cycle corresponding to the current drive current to achieve closed-loop precise control of PWM dimming. The dimming accuracy reaches 1%, which can effectively avoid problems such as light flicker and brightness fluctuation, and ensure that the actual output light intensity of the lamp quickly and stably tracks the set value, which is suitable for the stringent requirements of light stability in explosion-proof places.
[0048] ④ Emergency correction of PID parameters under fault scenarios The system uses the fault categories output by the random forest early warning model to perform targeted emergency fine-tuning of the PID parameters without manual intervention. The specific correction rules are as follows: If the random forest early warning model determines that there is a "high-risk external environment linkage risk" (fault code 007), the background will automatically adjust the proportional coefficient. Fine-tuning to 3.0 with a 20% adjustment range allows for entry into emergency control scenarios, eliminating the need to follow conventional fine-tuning requirements. This significantly improves the response speed of light control, ensuring rapid activation of the strong light penetration mode and guaranteeing visibility in high-risk environments. If the random forest early warning model determines the fault as "battery thermal runaway and performance degradation" (fault code 005), the integral coefficient will be automatically adjusted. Fine-tuning to 0.05 reduces the cumulative effect of the integral, avoids continuous battery heating caused by power fine-tuning, reduces the risk of battery thermal runaway, and ensures the power supply safety and operational stability of explosion-proof lighting fixtures.
[0049] Example 2 Using the operating power of the lamps as the controlled parameter, incremental PID is used to achieve closed-loop adaptive adjustment of energy consumption.
[0050] Setting value determination: The operating power setting value of the lamp is determined based on the mains voltage (measured by a voltage sensor) and the remaining battery power (calculated by voltage / current changes). For example, when the mains voltage is >220V, the setting value is 80% of the rated power; when the battery power is ≤20%, the setting value is 50% of the rated power. Deviation calculation: ; Control output: PID algorithm outputs control quantity increment Adjusting the power output of the power management module enables dynamic regulation of operating power, preventing voltage fluctuations from damaging the equipment and reducing energy consumption. Scenario Correction: If the random forest early warning model determines that there is a "risk of battery thermal runaway", the background will automatically adjust the integral coefficient. Fine-tuning to 0.05 reduces integral accumulation and avoids continuous battery overheating caused by power fine-tuning.
[0051] Example 3 Using sampling frequency / brightness threshold as the controlled parameters, an incremental PID controller is employed to achieve adaptive mode.
[0052] Setting value determination: Based on the fault risk level of the random forest early warning model and the sensor combination data, determine the sampling frequency / brightness threshold setting value (e.g., sampling frequency of 30s in normal operation mode, sampling frequency of 5s in emergency repair mode; brightness threshold of 60% in equipment maintenance mode). Deviation calculation: ; Control output: PID algorithm outputs control quantity increment Adjust the sampling interval of the data acquisition module 10 and the brightness threshold of the LED driver circuit to achieve automatic switching of the operating mode, with a switching response of ≤0.5 seconds; Scenario Correction: If the random forest early warning model determines a scenario as "high-risk" (e.g., a short circuit), the background system will automatically adjust the differential coefficients. Fine-tuning to 0.1 enhances the predictive capability of the differential stage, quickly suppresses abnormal fluctuations in sampling frequency / brightness threshold, and ensures stable operation of emergency mode.
[0053] For every 100 new sets of fault data, the random forest early warning model triggers a self-learning process, which includes the following steps: a. Retrain the random forest early warning model using the 100 newly added sets of fault data (only update the decision trees with weight changes > 0.01). b. A lightweight update package is generated and transmitted to the early warning module 20 via the data interaction module 40 to update the random forest early warning model. The iteration cycle can be set to once a week. The self-learning results are synchronously updated to the self-adaptive control module 30. This ensures that the random forest early warning model maintains its recognition accuracy and that early warnings are timely and reliable.
[0054] The beneficial effects of this invention are as follows: The method described in this invention forms a complete technical closed loop of "data acquisition - preprocessing - model early warning - risk classification - adaptive control - safety linkage", effectively solving the problems of low intelligence, inaccurate fault identification, inflexible early warning, and incomplete protection in existing explosion-proof LED lighting systems. Through feature screening and model optimization, it achieves accurate fault identification and rapid reasoning, adapting to embedded deployment; through dynamic thresholds and hierarchical risk management, it achieves accurate and efficient safety early warning and proactive protection; through radar sensor-free adaptive illumination control, it balances energy saving, lighting effect, and scene adaptability; the entire solution has a simple structure, low cost, and strong practicality, and can be widely adapted to various high-risk explosion-proof scenarios, significantly improving the safety, reliability, and intelligence level of the system.
[0055] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the 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.
[0056] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.
Claims
1. A multi-dimensional early warning adaptive control system for LED explosion-proof lights, characterized in that, include: The data acquisition module is used to collect real-time operating data of the lighting fixtures and scene environment data. The data acquisition module includes a current sensor, a temperature sensor, a vibration sensor, a combustible gas sensor, a humidity sensor, a dust sensor, a voltage sensor, and a light sensor. The early warning module is used to perform early warning analysis based on real-time collected lighting operation data and scene environment data, as well as the random forest early warning model stored therein, and generate prediction results. The self-adaptive control module is used to automatically adjust the operating parameters of the lamps based on the PID control algorithm, combined with lamp operating data, scene environment data and prediction results. as well as The data interaction module is used to realize real-time data interaction with the back-end management platform and mobile APP, ensuring remote control, PID parameter fine-tuning and data synchronization. The data interaction module supports LoRa and 5G dual communication modes.
2. The LED explosion-proof light multi-dimensional early warning adaptive control system according to claim 1, characterized in that, The random forest early warning model is trained using a random forest machine learning algorithm based on a historical fault dataset.
3. A multi-dimensional early warning adaptive control method for LED explosion-proof lights, implemented based on the multi-dimensional early warning adaptive control system for LED explosion-proof lights as described in any one of claims 1-2, characterized in that, The multi-dimensional early warning adaptive control method for LED explosion-proof lights includes the following steps: S1. The acquisition module collects real-time operating data of the lighting fixtures and scene environment data; wherein, the operating data of the lighting fixtures includes current, vibration, battery voltage and circuit resistance, and the scene environment data includes temperature, combustible gas concentration, humidity, dust concentration and ambient light intensity. S2. Based on the real-time collected lighting operation data and scene environment data, as well as the random forest early warning model stored therein, perform early warning analysis and generate prediction results; S3. Based on the PID control algorithm, the system automatically adjusts the operating parameters of the lighting fixtures by combining the lighting fixture operating data, scene environment data, and prediction results.
4. The multi-dimensional early warning adaptive control method for LED explosion-proof lights according to claim 3, characterized in that, The random forest early warning model described in S2 is trained using a random forest machine learning algorithm based on a historical fault dataset; the training method of the random forest early warning model includes the following steps: S211. Normalize the historical fault dataset to obtain the original dataset; wherein, the historical fault dataset contains 9 original features, namely current, temperature, vibration, combustible gas concentration, humidity, dust concentration, battery voltage, circuit resistance and ambient light intensity. Normalization calculation formula: in: These are the original feature values from the historical fault dataset. This represents the minimum value of the corresponding feature in the historical fault dataset. This represents the maximum value of the corresponding feature in the historical fault dataset; S212. Redundant features in the original dataset are removed by ranking them by Gini coefficient importance to obtain the basic dataset; S213. Divide the basic dataset into a training dataset and a test dataset in a 7:3 ratio; S214. Construct a random forest early warning model using the training dataset; A forest of 100 decision trees is set up. 60% of the training dataset samples and 5-dimensional features are randomly selected from each tree to participate in the splitting. The node splitting is completed by minimizing the Gini coefficient until the tree depth is ≤10 layers or the number of node samples is ≤5. Formula for calculating the Gini coefficient before node splitting: Where D is the sample set of the current node; For category numbering, =9, corresponding to 9 output categories, namely:
1. Normal state; 2. Circuit short circuit fault; 3. Circuit aging and poor contact fault; 4. LED light source decay or damage fault; 5. Driver power supply abnormal fault; 6. Battery thermal runaway and performance decay fault; 7. Sensor failure or abnormal fault; 8. External high-risk environment linkage risk; 9. Lighting abnormality and lamp obstruction fault. This represents the proportion of the k-th class of samples in the current node. , |Dk| represents the number of samples of the kth class in the node, and |D| represents the total number of samples in the node; Formula for calculating the weighted Gini coefficient after node splitting: Where A is the splitting feature number (one of the 9 core features). , These are the two child node sample sets obtained after splitting according to the threshold of feature A. child node , The number of samples, , child node , The Gini coefficient; S215. The random forest model is compressed through pruning optimization and threshold quantization; Pruning optimization: Traverse all split nodes of 100 decision trees, calculate the decrease in Gini coefficient before and after splitting each node, remove branches and their subtrees with a decrease in Gini coefficient less than 0.001, change the current split node to a leaf node, and retain the category output corresponding to the node. Formula for calculating the decrease in the Gini coefficient: in, The Gini coefficient of the parent node before the split. The weighted Gini coefficient for the child nodes after splitting; Threshold quantization: Converts floating-point thresholds in decision tree split nodes into 16-bit fixed-point numbers; Specific calculation formula: in, For floating-point thresholds, For quantized 16-bit fixed-point numbers, This is the rounding function; S216. The random forest early warning model was validated using a test dataset; When the accuracy reaches 98% or higher, the recall reaches 97% or higher, and the recognition precision of the 9 categories reaches 96% or higher, the random forest early warning model is judged to meet the standards. The formula for calculating accuracy is: in, The number of samples whose true class matches the predicted class; The number of samples that are neither true nor predicted to belong to a certain category; This represents the number of samples that are not actually of a certain category but are predicted to belong to that category. The number of samples that are actually of a certain category but are predicted to be of a different category; The formula for calculating recall rate: For type k fault The overall recall rate is calculated as an average or weighted average of all categories: Single-class recognition accuracy For type k faults in, Let be the number of samples where the true class is class k and the model predicts the class as class k. The number of samples where the true class is not class k and the model predicts that the class is also not class k. The number of samples whose true class is not class k, but whose model predicts to be class k. This represents the number of samples where the true class is class k, but the model predicts that the sample is not class k.
5. The multi-dimensional early warning adaptive control method for LED explosion-proof lights according to claim 4, characterized in that, The method in S2 for performing early warning analysis and generating prediction results based on real-time collected lighting operation data, scene environment data, and the stored random forest early warning model includes the following steps: S221. After normalizing and quantizing the real-time collected lighting operation data and scene environment data, the input feature vector is obtained. S222. Input the input feature vector into the random forest early warning model to obtain the fault category; S223. Calculate trend features based on time series characteristics, and calculate dynamic thresholds in combination with scene environment data; Trend feature calculation formula: in, Let be the original eigenvalue at time t. Let be the original eigenvalue at time tT. The set time interval; Dynamic threshold calculation formula: in, As the baseline warning threshold, This is the threshold adjustment coefficient. For real-time environmental parameters, These are the critical values for environmental parameter safety. Adjust the length of the environmental parameter adjustment range; S224. Determine the risk level by combining the fault category obtained in step S222 with the trend characteristics and dynamic threshold comparison results obtained in step S223.
6. The multi-dimensional early warning adaptive control method for LED explosion-proof lights according to claim 5, characterized in that, The method for obtaining fault categories using a random forest early warning model in S222 includes the following steps: A. For each decision tree, starting from the root node, read the split feature number, 16-bit quantization threshold, and left and right child node indices stored in the node. B. Compare the quantized feature value of the corresponding dimension with the node threshold. If the threshold condition is met, proceed to the left child node; otherwise, proceed to the right child node. C. Repeat the process of reading nodes, comparing features, and jumping to child nodes until leaf nodes are reached; D. Use the category number stored in the leaf node as the prediction result of a single decision tree; E. Analyze the prediction results of 100 decision trees and use a simple majority voting method to obtain the fault category.
7. The multi-dimensional early warning adaptive control method for LED explosion-proof lights according to claim 5, characterized in that, The fault categories described in S222 include normal state, short circuit fault, circuit aging and poor contact fault, LED light source decay or damage fault, abnormal drive power supply fault, battery thermal runaway and performance decay fault, sensor failure or abnormal fault, external high-risk environment linkage risk, and abnormal lighting and lamp obstruction fault.
8. The multi-dimensional early warning adaptive control method for LED explosion-proof lights according to claim 7, characterized in that, The risk levels described in S224 include low risk, medium risk, and high risk; the criteria for determining the risk level are as follows: If the fault category is normal, the lighting operation data and scene environment data are all within the dynamic threshold range, and the trend characteristics are not greater than the first trend threshold, then it is judged as low risk. If the fault category is a non-high-risk fault, or if some data in the lighting operation data and scene environment data are close to the dynamic threshold or the first trend threshold. Trend characteristics If the second trend threshold is reached, it is determined to be of medium risk; If the fault category is a high-risk fault, or if any data in the lighting operation data and scene environment data exceeds the dynamic threshold, or the trend characteristic is greater than the second trend threshold, then it is judged as high-risk. Among them, the non-high-risk faults are LED light source attenuation or damage faults, sensor failure or abnormal faults, and abnormal lighting and lamp obstruction faults. The high-risk faults include short circuit faults, circuit aging and poor contact faults, abnormal drive power supply faults, battery thermal runaway and performance degradation faults, and risks associated with external high-risk environments.
9. The multi-dimensional early warning adaptive control method for LED explosion-proof lights according to claim 1, characterized in that, The method in S3 that automatically adjusts the operating parameters of lighting fixtures based on PID control algorithm, combined with lighting fixture operating data, scene environment data, and prediction results, includes the following steps: S31. Determine the target setpoint SP of the controlled parameter based on the ambient light intensity, fault type, and risk level; wherein the controlled parameter is the LED drive current, lamp operating power, sampling frequency, and brightness threshold. S32. Calculate the actual values of the controlled parameters based on the scene environment data and the lighting operation data, and calculate the current cycle deviation; Let the first Each sampling period in, The target setpoint for the controlled parameter. The actual value of the controlled parameter; S33. Calculate the increment of the incremental PID control quantity; Control increment formula: in, ; ; ; This is the current sampling period; For the first The deviation value for each sampling period; The deviation value for each sampling period; For the first The deviation value for each sampling period; This is the proportionality coefficient; The integral time constant is... , The integral coefficient; Differential time constant , These are the differential coefficients; S34. Update the current control quantity and apply a safety limit; Current control quantity formula: S35. Automatically fine-tune the proportional coefficient based on the fault type and risk level. Integral coefficient and differential coefficients The final control quantity is calculated.
10. The multi-dimensional early warning adaptive control method for LED explosion-proof lights according to claim 1, characterized in that, The proportionality coefficient The integral coefficient is between 1.0 and 5.
0. The differential coefficient is between 0.05 and 0.
3. It ranges from 0.02 to 0.2.