A thermal infrared detection power supply intelligent management and control system

Through real-time monitoring and compensation of infrared radiation signals by multi-mode sensor modules, dynamic power supply mode and adaptive algorithm adjustment, combined with data compression and encrypted storage, the problems of measurement error, low battery life, false alarms, missed alarms and data loss in the intelligent management and control system of thermal infrared detection power supply are solved, and the system stability, energy consumption optimization and data security are achieved.

CN120165567BActive Publication Date: 2025-09-05HENAN SHENLAN JINGXING OPTOELECTRONICS TECH CO LTD
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Patent Information

Application Number
CN202510640988.6
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-05-19
Publication Date
2025-09-05
Estimated Expiration
2045-05-19

AI Technical Summary

Technical Problem

In the existing thermal infrared detection power supply intelligent management and control system, measurement errors caused by environmental changes and material aging often occur. The single power supply mode leads to a short battery life. The aging of the equipment is not taken seriously, resulting in the possibility of false alarms and missed alarms. There is a risk of data loss due to lax data management.

Method used

A multi-mode sensor module is used to monitor infrared radiation signals in real time and perform linear temperature compensation, dynamically switch power supply modes, adjust alarm thresholds and sampling frequencies based on adaptive algorithms, and combine data compression and encryption technologies for storage management.

Benefits of technology

It improves the long-term stability and data accuracy of the system, optimizes energy consumption, ensures the efficient operation of the system in different environments, protects data security, extends battery life, avoids false alarms and missed alarms, and improves the intelligence level of the system.

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Abstract

The present invention relates to the field of thermal management technology, and specifically, to a thermal infrared detection power supply intelligent management and control system. It includes a thermal infrared detection unit that monitors the infrared radiation signal and temperature change of the target area in real time based on a multi-mode sensor module, and corrects the output signal in consideration of the material aging problem; a multi-mode power supply unit dynamically switches the power supply mode to optimize energy consumption; an intelligent management and control unit adjusts the alarm threshold, sampling frequency and communication strategy based on an adaptive algorithm design; and a processing and storage unit compresses, encrypts and stores the thermal infrared detection data based on a data processing module. The infrared radiation signal and temperature change of the target area are monitored in real time by the multi-mode sensor module, and the output signal is corrected by a linear temperature compensation algorithm and aging correction, thereby improving the long-term stability of the system and the accuracy of the data. By dynamically switching the power supply mode, the optimal power supply is automatically selected according to the load demand, and the power supply voltage is adjusted to achieve the optimization of energy consumption.
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Description

Technical Field

[0001] The present invention relates to the field of thermal management technology, and in particular to a thermal infrared detection power supply intelligent management and control system. Background Art

[0002] A thermal infrared detection power supply intelligent management and control system is a comprehensive solution that integrates thermal infrared detection technology and intelligent power management. It aims to detect temperature by accurately monitoring infrared radiation from target objects while employing advanced power electronics and automatic control algorithms to efficiently and stably supply and manage power to each module within the system. This system utilizes an embedded control system and necessary communication technologies to not only ensure optimal operation of thermal infrared detection equipment but also enable remote monitoring and data transmission.

[0003] In the existing thermal infrared detection power supply intelligent management and control system, measurement errors caused by environmental changes and material aging often occur; the single power supply mode leads to a short battery life; the aging of equipment is not taken seriously, resulting in the possibility of false alarms and missed alarms; data management is not strict, resulting in the possibility of data loss. Therefore, a thermal infrared detection power supply intelligent management and control system is designed. Summary of the Invention

[0004] The purpose of the present invention is to provide a thermal infrared detection power supply intelligent management and control system to solve the problems in the existing thermal infrared detection power supply intelligent management and control system proposed in the above background technology, such as measurement errors often occur due to environmental changes and material aging; the single power supply mode leads to a short battery life; the aging of the equipment is not taken seriously, resulting in the possibility of false alarms and missed alarms; and the data management is not strict, resulting in the possibility of data loss.

[0005] To achieve the above objectives, the present invention provides a thermal infrared detection power supply intelligent management and control system, including a thermal infrared detection unit. The thermal infrared detection unit monitors the infrared radiation signal and temperature changes of the target area in real time based on a multi-mode sensor module, and corrects the output signal in consideration of material aging issues.

[0006] A multi-mode power supply unit that dynamically switches power supply modes to optimize energy consumption;

[0007] An intelligent management and control unit that adjusts alarm thresholds, sampling frequencies, and communication strategies based on an adaptive algorithm design;

[0008] A processing and storage unit compresses, encrypts and stores the thermal infrared detection data based on the data processing module.

[0009] As a further improvement of the present technical solution, the multi-mode sensor module includes an infrared sensor array, a signal conditioning module and an environmental compensation module;

[0010] Wherein, the infrared sensor array is used to capture infrared radiation emitted by the target area in real time;

[0011] The signal conditioning module is used to perform amplification and filtering preprocessing operations on the received signal;

[0012] The environmental compensation module corrects the environmental temperature difference through the temperature sensor and outputs a corrected signal.

[0013] As a further improvement of the present technical solution, the specific process of correcting the ambient temperature difference by the temperature sensor and outputting the corrected signal is as follows:

[0014] The original voltage signal is compensated by a linear temperature compensation algorithm Perform dynamic correction to obtain the initial electronic signal ;

[0015] Taking into account the problem of material aging, the linear temperature compensation algorithm is modified and the corrected signal is output .

[0016] As a further improvement of this technical solution, the specific process of dynamically switching the power supply mode to optimize energy consumption is as follows:

[0017] Prioritization logic is determined by the power selector;

[0018] According to the load current Adjust the supply voltage ;

[0019] Calculate remaining capacity based on Coulomb counting method .

[0020] As a further improvement of this technical solution, the residual power is affected by the aging of the material and the static current loss of the self-discharge effect, which leads to the attenuation of the residual power. Therefore, the final residual power is calculated by the modified coulomb counting method. .

[0021] As a further improvement of this technical solution, the specific process of adjusting the alarm threshold, sampling frequency and communication strategy based on the adaptive algorithm design is as follows:

[0022] Receives signals from thermal infrared detection units ;

[0023] According to historical data and aging coefficient Dynamically adjust alarm thresholds ;

[0024] Based on the PID control algorithm according to the temperature change rate Dynamically adjust sampling frequency .

[0025] As a further improvement of this technical solution, the historical data and the aging coefficient Dynamically adjust alarm thresholds The specific steps are:

[0026] Set the baseline alarm threshold when the system starts ;

[0027] According to the aging factor Determine the temperature threshold attenuation coefficient ;

[0028] Based on baseline alarm thresholds and temperature threshold attenuation coefficient Get the alarm threshold .

[0029] As a further improvement of this technical solution, the PID control algorithm is based on the temperature change rate. Dynamically adjust sampling frequency The specific steps are:

[0030] Calculate the temperature change rate of the target area in real time , as the input error signal of the PID controller;

[0031] Mapping temperature change rate to normalized error range ;

[0032] Calculate the sampling frequency through the three steps of proportion, integration and differentiation .

[0033] As a further improvement of this technical solution, the data processing module includes a data compression module, a data encryption module and a storage management module;

[0034] Wherein, the data compression module is used to efficiently compress the processed thermal infrared detection data;

[0035] The data encryption module is used to perform AES-256 encryption on the compressed data;

[0036] The storage management module is used to manage local storage resources and adopts a circular storage strategy to achieve orderly writing and overwriting of data.

[0037] As a further improvement of this technical solution, the specific steps of the cyclic storage strategy are:

[0038] Divide local storage media into fixed-size storage blocks ;

[0039] Write data in ascending order of address, and the address pointer is updated cyclically;

[0040] When the number of available blocks Less than the total number of blocks When the number of protected blocks reaches 5%, the overwriting process is triggered and the earliest non-protected block is selected for overwriting.

[0041] When a block with CRC check failure is detected, it automatically jumps to the next available block .

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] This thermal infrared detection power supply intelligent management and control system uses a multi-mode sensor module to monitor infrared radiation signals and temperature changes in the target area in real time. It uses a linear temperature compensation algorithm and aging correction to correct the output signal, improving the system's long-term stability and data accuracy. By dynamically switching power supply modes, it automatically selects the optimal power source based on load demand and adjusts the supply voltage to optimize energy consumption.

[0044] 2. This thermal infrared detection power supply intelligent management and control system uses an adaptive algorithm to dynamically adjust alarm thresholds, sampling frequencies, and communication strategies, ensuring efficient operation in diverse environments. By compressing and encrypting collected data, storage space is saved while ensuring data security. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is the overall flow chart of the present invention;

[0046] The meaning of each number in the figure is:

[0047] 1. Thermal infrared detection unit; 11. Multi-mode sensor module; 111. Infrared sensor array; 112. Signal conditioning module; 113. Environmental compensation module; 2. Multi-mode power supply unit; 3. Intelligent management and control unit; 4. Processing and storage unit; 41. Data processing module; 411. Data compression module; 412. Data encryption module; 413. Storage management module. DETAILED DESCRIPTION

[0048] The following will provide a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0049] Example: See Figure 1 As shown, a thermal infrared detection power supply intelligent management and control system is provided, including a thermal infrared detection unit 1. The thermal infrared detection unit 1 monitors the infrared radiation signal and temperature change of the target area in real time based on a multi-mode sensor module 11, and corrects the output signal in consideration of material aging problems;

[0050] In this embodiment, the multi-mode sensor module 11 includes an infrared sensor array 111 , a signal conditioning module 112 , and an environmental compensation module 113 ;

[0051] The infrared sensor array 111 is used to capture infrared radiation emitted by the target area in real time;

[0052] The signal conditioning module 112 is used to perform amplification and filtering pre-processing operations on the received signal;

[0053] The environmental compensation module 113 corrects the environmental temperature difference through the temperature sensor and outputs a corrected signal.

[0054] In this embodiment, the specific process of correcting the ambient temperature difference by the temperature sensor and outputting the corrected signal is as follows:

[0055] The original voltage signal is compensated by a linear temperature compensation algorithm Perform dynamic correction to obtain the initial electronic signal ;

[0056] Specifically, the initial electronic signal for:

[0057] ;

[0058] Where, represents the linear temperature coefficient; Indicates the change in ambient temperature;

[0059] Taking into account the problem of material aging, the linear temperature compensation algorithm is modified and the corrected signal is output .

[0060] Specifically, the corrected signal for:

[0061] ;

[0062] Where, Indicates the linear temperature coefficient that changes with time; represents the time variable;

[0063] in, ;

[0064] Where, represents the initial linear temperature coefficient; represents the aging coefficient;

[0065] Among them, the aging coefficient , whose value is related to the material type (such as silicon-based sensors ≈0.001 / year, metal oxide sensor ≈0.003 / year);

[0066] Specifically, material aging refers to the microscopic deformation or fatigue cracks of key sensor materials caused by temperature changes, which directly affects the accuracy, stability and life of the sensor.

[0067] Furthermore, the output signal is corrected by taking material aging into account to ensure data accuracy and reliability. The infrared sensor array captures infrared radiation emitted by the target area. The signal conditioning module performs pre-processing operations such as amplification and filtering on these raw signals. The environmental compensation module uses the temperature sensor data to dynamically correct the effects of ambient temperature differences through a linear temperature compensation algorithm, ultimately outputting a signal corrected for time aging. This design not only improves the system's measurement accuracy but also effectively compensates for errors caused by material aging, allowing the entire system to maintain stability and efficiency during long-term operation. It is suitable for various application scenarios requiring precise temperature monitoring, such as security, industrial testing, and environmental monitoring. In addition, through precise data acquisition and processing, the system can provide a reliable basis for subsequent power management optimization, further improving the energy efficiency and intelligence level of the overall system.

[0068] A multi-mode power supply unit 2, which dynamically switches power supply modes to optimize energy consumption;

[0069] In this embodiment, the specific process of dynamically switching the power supply mode to optimize energy consumption is as follows:

[0070] Prioritization logic is determined by the power selector;

[0071] Specifically, the priority logic is: mains power > lithium battery (capacity C ≥ 10,000 mAh) > solar energy (conversion efficiency η ≥ 22%);

[0072] According to the load current Adjust the supply voltage ;

[0073] ;

[0074] Where, Indicates system efficiency; Indicates output power; Indicates input power; represents the source current; Indicates the load voltage; represents the source voltage;

[0075] When the system is powered directly, ;

[0076] When powered by a voltage regulator, the is the regulated load voltage ;

[0077] Calculate remaining capacity based on Coulomb counting method .

[0078] Specifically, the remaining power for:

[0079] ;

[0080] Where, Indicates the battery charge percentage at the start; Indicates time Battery charge and discharge current at each moment; Indicates the rated capacity of the battery; Represents time from 0 to time The result of integrating the ratio of the battery charge and discharge current to the battery capacity is used to calculate the change in state of charge caused by charging and discharging during this period;

[0081] In this embodiment, considering that the remaining capacity is affected by the aging of the material and the static current loss due to the self-discharge effect, which leads to the attenuation of the remaining capacity, the final remaining capacity is calculated by the modified coulomb counting method. .

[0082] Specifically, the corrected remaining power is calculated taking into account the influence of material aging on the remaining power. for:

[0083] ;

[0084] Where, Indicates time Actual battery capacity at the moment;

[0085] in, ;

[0086] Where, Indicates the initial capacity; Indicates the capacity attenuation coefficient;

[0087] And introduce the self-discharge compensation term to optimize the remaining capacity after correction , get the final remaining power ;

[0088] Specifically, the final remaining power for:

[0089] ;

[0090] Where, Represents the self-discharge compensation item;

[0091] Among them, the self-discharge compensation term for:

[0092] ;

[0093] Where, represents the temperature-dependent self-discharge rate function;

[0094] in, for:

[0095] ;

[0096] Where, Indicates the reference temperature; Indicates the reference temperature Initial self-discharge rate under ; Indicates the self-discharge temperature sensitivity coefficient;

[0097] Furthermore, the power selector first determines the optimal power source based on priority logic (mains power > lithium battery > solar energy), and adjusts the supply voltage according to the load current to match actual demand. System efficiency is evaluated by calculating the ratio of output power to input power, ensuring the high efficiency of the energy conversion process. At the same time, the unit uses coulomb counting combined with corrections for battery aging effects to accurately calculate the remaining power, taking into account and correcting the impact of battery capacity decay over time. This strategy not only improves the accuracy of battery management and extends battery life, but also enhances the adaptability and reliability of the entire system under different operating conditions. It provides a stable and efficient power support environment for thermal infrared detection, suitable for application scenarios such as security monitoring, industrial inspection, and environmental monitoring that require long-term continuous operation.

[0098] Intelligent control unit 3, intelligent control unit 3 adjusts alarm threshold, sampling frequency and communication strategy based on adaptive algorithm design;

[0099] In this embodiment, the specific process of adjusting the alarm threshold, sampling frequency and communication strategy based on the adaptive algorithm design is as follows:

[0100] Receives signals from thermal infrared detection unit 1 ;

[0101] According to historical data and aging coefficient Dynamically adjust alarm thresholds ;

[0102] In this embodiment, according to historical data and aging coefficient Dynamically adjust alarm thresholds The specific steps are:

[0103] Set the baseline alarm threshold when the system starts ;

[0104] According to the aging factor Determine the temperature threshold attenuation coefficient ;

[0105] Specifically, the temperature threshold attenuation coefficient for:

[0106] ;

[0107] Where, represents the safety factor, and ;

[0108] when , fully compensates for aging effects;

[0109] Based on baseline alarm thresholds and temperature threshold attenuation coefficient Get the alarm threshold .

[0110] Specifically, the alarm threshold for:

[0111] ;

[0112] Where, Indicates the initial temperature threshold; represents the temperature threshold attenuation coefficient;

[0113] The trigger conditions are: ;

[0114] Where, Indicates the current temperature value;

[0115] Based on the PID control algorithm according to the temperature change rate Dynamically adjust sampling frequency .

[0116] In this embodiment, based on the PID control algorithm according to the temperature change rate Dynamically adjust sampling frequency The specific steps are:

[0117] Calculate the temperature change rate of the target area in real time , as the input error signal of the PID controller ;

[0118] Specifically, the temperature change rate of the target area for:

[0119] ;

[0120] Where, Indicates the current sampling temperature value; Indicates the previous sampling temperature value; Indicates the time interval between two adjacent samplings;

[0121] Mapping temperature change rate to normalized error range ;

[0122] Specifically, the error range for:

[0123] ;

[0124] Where, Indicates the maximum temperature change rate allowed by the system;

[0125] Calculate the sampling frequency through the three steps of proportion, integration and differentiation .

[0126] Specifically, the sampling frequency for:

[0127] ;

[0128] Where, represents the proportional gain; represents the integral gain; represents the differential gain.

[0129] Furthermore, by performing real-time analysis of the signals collected by the thermal infrared detection unit and dynamically adjusting the alarm threshold based on the aging of the device, the system ensures more accurate and reliable alarm judgments and avoids false alarms or missed alarms due to sensor performance degradation. Simultaneously, a control algorithm automatically adjusts the sampling frequency based on the speed of temperature changes, ensuring data sensitivity while reducing system power consumption. Furthermore, it optimizes communication strategies, improving system response speed and energy efficiency, making the entire system more stable, adaptable, and intelligent in complex environments.

[0130] The processing and storage unit 4 compresses, encrypts and stores the thermal infrared detection data based on the data processing module 41.

[0131] In this embodiment, the data processing module 41 includes a data compression module 411, a data encryption module 412 and a storage management module 413;

[0132] The data compression module 411 is used to efficiently compress the processed thermal infrared detection data;

[0133] The data encryption module 412 is used to perform AES-256 encryption on the compressed data;

[0134] The storage management module 413 is used to manage local storage resources and adopt a circular storage strategy to achieve orderly writing and overwriting of data.

[0135] In this embodiment, the specific steps of the circular storage strategy are:

[0136] Divide local storage media into fixed-size storage blocks ;

[0137] Specifically, storage blocks for:

[0138] ;

[0139] Write data in ascending order of address, and the address pointer is updated cyclically;

[0140] Specifically, the address pointer is updated cyclically as follows:

[0141] ;

[0142] Where, Indicates the current new address pointer position; Indicates the address pointer position of the previous storage operation; Indicates the total number of blocks of the storage medium;

[0143] When the number of available blocks is less than 5% of the total number of blocks, the overwriting process is triggered and the earliest written non-protected block is selected for overwriting;

[0144] Specifically, when the number of available blocks Less than the total number of blocks When the overwriting process is triggered when the protected block is 5%, the earliest written non-protected block is selected for overwriting:

[0145] ;

[0146] When a block with CRC check failure is detected, it automatically jumps to the next available block .

[0147] Specifically, available blocks for:

[0148] ;

[0149] Where, Indicates the minimum valid block offset;

[0150] Furthermore, by compressing thermal infrared detection data, data volume is effectively reduced, improving transmission and storage efficiency. Encryption ensures data security during transmission and storage, preventing the leakage of sensitive information. A circular storage strategy is also adopted to rationally manage local storage resources, ensuring the system can continue to operate stably within limited storage space. This unit not only improves the intelligent level of data processing, but also enhances the system's error tolerance and long-term operational reliability, making it suitable for applications requiring long-term continuous monitoring and data recording.

[0151] The basic principles, main features, and advantages of the present invention are shown and described above. It should be understood by those skilled in the art that the present invention is not limited to the above-described embodiments. The above-described embodiments and descriptions are merely preferred examples of the present invention and are not intended to limit the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention, and such changes and modifications fall within the scope of the invention claimed.

Claims

1. A thermal infrared detection power supply intelligent management and control system, characterized by: include A thermal infrared detection unit (1), wherein the thermal infrared detection unit (1) monitors the infrared radiation signal and temperature change of the target area in real time based on a multi-mode sensor module (11), and corrects the output signal in consideration of material aging problems; A multi-mode power supply unit (2), wherein the multi-mode power supply unit (2) dynamically switches power supply modes to optimize energy consumption; The specific process of dynamically switching power supply modes to optimize energy consumption is as follows: Prioritization logic is determined by the power selector; According to the load current I load Adjust the supply voltage V supply ; Calculate the remaining capacity SOC(t) based on the Coulomb counting method; Considering that the remaining capacity is affected by material aging and the static current loss caused by the self-discharge effect, the final remaining capacity SOC(t)" is calculated by the modified Coulomb counting method; Taking into account the influence of material aging on the remaining capacity, the corrected remaining capacity SOC(t)′ is calculated as: Where C(t) = C0·e -λt ; In the formula, C0 represents the initial capacity; λ represents the capacity attenuation coefficient; SOC0 represents the percentage of battery charge at the beginning; I bat (t) represents the battery charge and discharge current at time t; And introduce the self-discharge compensation term to optimize the corrected remaining capacity SOC(t)′ to obtain the final remaining capacity SOC(t)″; Specifically, the final remaining charge SOC(t)″ is: Where, ΔSOC self Represents the self-discharge compensation item; Among them, the self-discharge compensation term ΔSOC self for: Where δ(T) represents the temperature-dependent self-discharge rate function; Where δ(T) is: Where, T0 represents the reference temperature; δ0 represents the initial self-discharge rate at the reference temperature T0; k δ Indicates the self-discharge temperature sensitivity coefficient; An intelligent management and control unit (3), wherein the intelligent management and control unit (3) is designed to adjust the alarm threshold, sampling frequency and communication strategy based on an adaptive algorithm; The specific process of adaptive algorithm design to adjust alarm threshold, sampling frequency and communication strategy is as follows: Receives signal V from thermal infrared detection unit (1) out (t); Dynamically adjust the alarm threshold T according to historical data and aging coefficient β th (t); Based on the PID control algorithm according to the temperature change rate Dynamically adjust the sampling frequency f s PID control algorithm is based on the temperature change rate Dynamically adjust the sampling frequency f s The specific steps are: Calculate the temperature change rate of the target area in real time As the input error signal of the PID controller; Map the temperature change rate to the normalized error range e(t); Calculate the sampling frequency f through the three steps of proportion, integration and differentiation s ; Processing storage unit (4). The processing storage unit (4) compresses, encrypts and stores the thermal infrared detection data based on the data processing module (41); The data processing module (41) includes a data compression module (411), a data encryption module (412) and a storage management module (413); Wherein, the data compression module (411) is used to efficiently compress the processed thermal infrared detection data; The data encryption module (412) is used to perform AES-256 encryption on the compressed data; The storage management module (413) is used to manage local storage resources and adopts a cyclic storage strategy to achieve orderly writing and overwriting of data. The specific steps of the cyclic storage strategy are: Divide the local storage medium into fixed-size storage blocks S block ; Write data in ascending order of address, and the address pointer is updated cyclically; When the number of available blocks is N free Less than the total number of blocks N blocks When the overwriting process reaches 5%, the overwriting process is triggered and the earliest written non-protected block is selected for overwriting; When a block that fails the CRC check is detected, it automatically jumps to the next available block A next .

2. The thermal infrared detection power supply intelligent management and control system according to claim 1 is characterized in that: The multi-mode sensor module (11) includes an infrared sensor array (111), a signal conditioning module (112) and an environmental compensation module (113); Wherein, the infrared sensor array (111) is used to capture infrared radiation emitted by the target area in real time; The signal conditioning module (112) is used to perform amplification and filtering preprocessing operations on the received signal; The environmental compensation module (113) corrects the environmental temperature difference through a temperature sensor and outputs a corrected signal.

3. The thermal infrared detection power supply intelligent management and control system according to claim 2 is characterized in that: The specific process of the temperature sensor correcting the ambient temperature difference and outputting the corrected signal is as follows: The original voltage signal V is compensated by the linear temperature compensation algorithm raw , perform dynamic correction and obtain the initial electronic signal V out ; Introducing the aging coefficient correction linear temperature compensation algorithm, outputting the corrected signal V out (t).

4. The thermal infrared detection power supply intelligent management and control system according to claim 1 is characterized in that: Dynamically adjust the alarm threshold T according to historical data and aging coefficient β th The specific steps of (t) are: Set the baseline alarm threshold T when the system starts th0 ; Determine the temperature threshold attenuation coefficient γ according to the aging coefficient β; Based on the benchmark alarm threshold T th0 And the temperature threshold attenuation coefficient γ to obtain the alarm threshold T th (t).

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