Photo-thermal-acoustic coupling simulation optimization method and system based on photoacoustic spectrum gas detection

Abstract

The invention discloses a photo-thermal-acoustic coupling simulation optimization method and system based on photoacoustic spectrum gas detection, and relates to the technical field of trace gas detection. The method comprises the following steps: designing a geometric structure model of the photoacoustic cell, and setting simulation environment parameters; based on composite modulation incident laser excitation, multi-physical field simulation is carried out on the light, heat and sound coupling process, and a sound pressure waveform is obtained; carrying out correction processing and data analysis on the sound pressure waveform, comparing the sound pressure waveform with a preset judgment condition, and then carrying out reverse optimization on simulation model parameters; and analyzing and evaluating the parameters of the simulation model after reverse optimization to obtain a simulation optimization scheme. According to the method, the problems of simplified physical process, incomplete energy transmission chain, large deviation between the calculation result and the experiment and the like of the existing photoacoustic simulation method are solved.

Description

Technical Field

[0001] This invention relates to the field of trace gas detection technology, and in particular to a photothermal-acoustic coupling simulation optimization method and system based on photoacoustic spectroscopy gas detection. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] Trace gases refer to components of gas present in extremely low concentrations in air or other gas mixtures. Trace gas detection now has practical applications in various fields. In environmental monitoring and atmospheric science, real-time detection of greenhouse gases enables climate change assessment. In industrial safety, it is used for fault diagnosis by analyzing decomposition gases in transformer oil and for detecting SF6 decomposition gases in high-voltage power systems, enabling real-time detection of gas leaks and effectively ensuring production safety.

[0004] Currently, trace gas detection is mainly based on laser spectroscopy methods, including cavity ring-down spectroscopy (CRDS), tunable diode laser absorption spectroscopy (TDLAS), and photoacoustic spectroscopy (PAS). Among these, photoacoustic spectroscopy combines high sensitivity and high selectivity, and has advantages such as naturally zero background, no need for expensive high-reflectivity cavity mirrors or ultra-long optical path requirements, compact system structure, and ease of miniaturization, making it particularly suitable for high-precision online trace gas monitoring.

[0005] Photoacoustic spectroscopy is an indirect absorption spectroscopy technique. Its basic principle is that gas absorbs and modulates laser light, resulting in periodic heating through non-radiative relaxation. This heat excites a pressure wave (i.e., a sound wave) with the same frequency as the light modulation, which is then detected by an acoustic sensor. A photoacoustic spectroscopy (PAS) gas detection system is a complete instrument comprising a light source, a gas handling system (for controlling gas concentration ratios in laboratory settings), a photoacoustic cell, and electronic equipment for gas detection (microphone, lock-in amplifier, signal acquisition card, and computer). The most critical component is the photoacoustic cell, a closed space isolated from the outside environment where all photoacoustic effects occur.

[0006] Numerical simulation of photoacoustic cells is of great significance in photoacoustic spectroscopy research. Simulation allows for the quantitative evaluation of the acoustic performance and system response characteristics of the photoacoustic cell before experiments, enabling analysis of its operational performance, optimization of structural design, and significant reduction in experimental costs. Current simulation research mainly focuses on the following three aspects: Acoustic modal analysis: By solving for the characteristic frequencies and modal morphology of the photoacoustic cell, the main modal distribution of the cavity and the location of sound field enhancement are determined, providing a theoretical basis for subsequent acoustic sensor placement and structural optimization; Resonant frequency response analysis: Frequency sweeping is performed under specific excitation to obtain the response curve of sound pressure amplitude as a function of frequency, thereby determining the optimal operating frequency and quality factor; Structural parameter optimization: The influence of the geometric parameters (such as cavity length and radius) of the resonant cavity and buffer cavity on the sound pressure amplitude and resonant frequency is systematically studied to optimize the structure and improve photoacoustic signal intensity and system stability.

[0007] However, traditional simulation methods also have significant limitations. First, traditional models often consider only a single acoustic physical field, simulating photoacoustic effects by directly applying simplified periodic heat sources or normal velocity excitations to the acoustic module. While these methods can qualitatively obtain resonant frequencies and sound pressure distributions, they cannot reflect the actual processes of light field absorption and heat conduction, thus neglecting the influence of key optical factors such as laser power, wavelength, and beam waist position. Second, the results output by traditional acoustic simulations are often dimensionless or relative sound pressure values, which can only be used to compare the relative performance of different structures, but cannot obtain absolute sound pressure outputs with true physical meaning. Furthermore, due to the lack of a time-dimensional driving term, traditional methods cannot obtain the time-domain waveform of the sound pressure signal, and therefore cannot extract the crucial second harmonic (2f) signal from it. This makes these methods only capable of qualitative analysis, and difficult to effectively predict the experimental process and results. Summary of the Invention

[0008] To address the shortcomings of existing technologies, the purpose of this invention is to provide a photothermal-acoustic coupling simulation optimization method and system based on photoacoustic spectroscopy gas detection, which solves the problems of simplified physical processes, incomplete energy transfer chains, and large deviations between calculation results and experiments in existing photoacoustic simulation methods.

[0009] To achieve the above objectives, the present invention is implemented through the following technical solution: The first aspect of this invention provides a photothermal-acoustic coupling simulation optimization method based on photoacoustic spectroscopy gas detection, comprising the following steps: Design the geometric model of the photoacoustic cell and set the simulation environment parameters; Based on composite modulated incident laser excitation, multiphysics simulation of the optical, thermal, and acoustic coupling process is performed to obtain the sound pressure waveform. Specifically, the spatial distribution of the electric field of the incident laser in the photoacoustic cell is solved. Based on the spatial distribution of the electric field output by the electromagnetic field module, the volume heat source is calculated and the time-domain response of the temperature field is obtained. Based on the time-domain response of the temperature field, a thermal expansion sound source is constructed and the sound field response is solved. The sound pressure waveform is corrected and analyzed, and the simulation model parameters are optimized in reverse after being compared with the preset judgment conditions. The parameters of the simulation model after reverse optimization are analyzed and evaluated to obtain the simulation optimization scheme.

[0010] A second aspect of the present invention provides a photothermal-acoustic coupling simulation optimization system based on photoacoustic spectroscopy gas detection, comprising: The parameter setting module is configured to design the initial parameters of the photoacoustic cell and acquire the incident laser. The composite modulation-driven optical-thermal-acoustic fully coupled simulation module is configured to simulate the optical, thermal, and acoustic coupling processing of incident laser based on the initial parameters of the photoacoustic cell. Specifically, it solves the spatial distribution of the electric field of the incident laser in the photoacoustic cell, calculates the volume heat source based on the spatial distribution of the electric field output by the electromagnetic field module, obtains the time-domain response of the temperature field, constructs a thermal expansion sound source based on the time-domain response of the temperature field, and solves the sound field response. The data processing and analysis reverse optimization parameter module is configured to perform correction processing and data analysis on the sound pressure waveform, and then perform reverse optimization on the simulation model parameters after comparing them with preset judgment conditions. The performance and index evaluation and design optimization scheme output module is configured to analyze and evaluate the parameters of the simulation model after reverse optimization to obtain the simulation optimization scheme.

[0011] A third aspect of the present invention provides a computer-readable storage medium storing a computer program adapted to be loaded by a processor and to execute the steps in the photothermal-acoustic coupling simulation optimization method based on photoacoustic spectroscopy gas detection as described in the first aspect of the present invention.

[0012] A fourth aspect of the present invention provides a computer device comprising: A processor, adapted to execute computer programs; A computer-readable storage medium storing a computer program, which, when executed by the processor, implements the photothermal-acoustic coupling simulation optimization method based on photoacoustic spectroscopy gas detection as described in the first aspect of the present invention.

[0013] A fifth aspect of the present invention provides a computer program product or computer program comprising computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium and executes the computer instructions, causing the computer device to perform the steps in the photothermal-acoustic coupling simulation optimization method based on photoacoustic spectroscopy gas detection as described in the first aspect of the present invention.

[0014] The above one or more technical solutions have the following beneficial effects: This invention discloses a photothermal-acoustic coupling simulation optimization method and system based on photoacoustic spectroscopy for gas detection. The method comprises three core components: an electromagnetic wave field module, a heat conduction module, and a thermoviscous acoustic module. First, the incident laser propagates and absorbs in the gas medium through the electromagnetic wave field module, obtaining the spatial energy density and absorption power distribution. Second, the optical absorption power output from the electromagnetic wave field module is converted into a time-modulated volumetric heat source and applied to the heat conduction module, thereby forming a periodic temperature disturbance field inside the photoacoustic resonant cavity. Finally, this temperature disturbance drives the local expansion and pressure fluctuation of the gas medium in the thermoviscous acoustic module, forming a stable standing wave sound field within the resonant cavity and generating a resonant amplification effect. By analyzing the sound pressure signal within the resonant cavity in the time or frequency domain, the gas concentration can be inverted and identified, establishing a quantitative relationship between gas concentration and key parameters such as sound pressure amplitude, modulation frequency, and laser power. Furthermore, the system's minimum detection limit and acoustic performance evaluation indicators are obtained. A full-process dynamic photoacoustic cell simulation is constructed, simultaneously incorporating the coupling effects of the optical field, thermal field, and acoustic field. It can not only more realistically reproduce the entire process from laser absorption, nonradiative relaxation, thermal expansion to sound wave generation, and achieve dynamic coupling of photothermal and acoustic fields, but also output sound pressure waveforms consistent with experiments, providing a quantifiable and repeatable theoretical basis for performance prediction and design optimization of photoacoustic systems. Furthermore, through the optimization module, it can also provide feedback to adjust various parameters, achieving reverse optimization of the detection system and outputting a complete simulation optimization scheme that meets detection requirements, including parameter settings and performance evaluation.

[0015] This invention also includes a data processing, analysis, and optimization module. This module improves and optimizes the performance of the photoacoustic system through real-time judgment and parameter adjustment. Based on the second harmonic value obtained after processing the original sound pressure level from the simulation output, it determines whether the sound pressure level reaches the microphone's detection threshold. If not, it adjusts input conditions such as light source power, modulation depth, cavity size, gas concentration, and material parameters until the output meets the detection requirements. Ultimately, this optimization module outputs a complete system design and performance evaluation scheme. This includes not only the system's minimum detection concentration, system responsivity, sound pressure-concentration-power relationship curve, resonant frequency characteristics, and sound field distribution diagram, but also sensitivity variation trends under different structural parameters, noise impact analysis, thermal and acoustic field coupling efficiency, and a comprehensive evaluation report on experimental feasibility. This auxiliary optimization process forms a complete closed-loop simulation system with two-way simulation-optimization coupling, enabling efficient evaluation and targeted optimization of the photoacoustic cell during the design phase, providing comprehensive guidance for experimental system construction and parameter selection.

[0016] This invention analyzes a resonant photoacoustic cell, which consists of multiple parts, including a photoacoustic resonant cavity for resonant amplification of photoacoustic signals; a buffer cavity for buffering airflow to reduce turbulence noise; a window for sealing the cell and made of a high-transmittance material; and an inlet / outlet for the entry and exit of sample gas.

[0017] The photoacoustic coupling dynamic simulation method proposed in this invention possesses universality and high precision, applicable to photoacoustic cell systems of different types, sizes, structures, and operating conditions. It can realistically reproduce the energy transfer and acoustic response processes in experiments, obtaining numerical results consistent with actual physical laws. This method not only enables efficient prediction of photoacoustic cell design, parameter tuning, and performance optimization during the simulation stage but also significantly reduces experimental costs and shortens the development cycle. By employing a composite modulation signal from real experiments as the driving source, this invention achieves a realistic reproduction of the entire photoacoustic detection process, accurately reflecting the overall performance and dynamic response characteristics of the photoacoustic cell under different parameter configurations. It provides an efficient, reliable, and practically valuable simulation tool for the design, evaluation, and optimization of high-sensitivity trace gas detection systems, demonstrating strong application value and broad practical application prospects.

[0018] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a flowchart of the photothermal-acoustic coupling simulation optimization method based on photoacoustic spectroscopy gas detection in Embodiment 1 of the present invention; Figure 2 This is a schematic diagram of the physical process of the photoacoustic cell in Embodiment 1 of the present invention; Figure 3 This is a front view of the photoacoustic cell simulation geometric model in Embodiment 1 of the present invention; Figure 4 This is the front view of the photoacoustic cell simulation geometric model in Embodiment 1 of the present invention; Figure 5 This is a schematic diagram of the EWFD (electric field distribution) results during the simulation process in Embodiment 1 of the present invention; Figure 6 This is a schematic diagram of the HT (temperature distribution) results during the simulation process in Embodiment 1 of the present invention; Figure 7 This is a schematic diagram of the TVAC (sound pressure distribution) results during the simulation process in Embodiment 1 of the present invention; Figure 8 This is a diagram of the photothermal-acoustic coupling simulation optimization system based on photoacoustic spectroscopy gas detection in Embodiment 2 of the present invention. Detailed Implementation

[0021] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0022] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof. The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0023] Example 1: Embodiment 1 of this invention provides a photothermal-acoustic coupling simulation optimization method for gas detection based on photoacoustic spectroscopy. Existing technologies typically only analyze a single physical field, making it difficult to achieve dynamic simulation of the entire process from laser incidence to sound wave generation. This results in numerical results lacking real physical meaning and inaccurate prediction of the response characteristics of the photoacoustic cell under actual experimental conditions. This invention establishes a dynamic simulation system covering the entire process of light absorption, heat conduction, and sound wave formation, achieving high-fidelity simulation and performance prediction of gas concentration detection experiments in a photoacoustic cell. Furthermore, through data processing, analysis, and optimization modules, it achieves reverse optimization of the detection system, forming a closed-loop simulation system with bidirectional coupling of simulation and optimization.

[0024] This embodiment, based on the COMSOL Multiphysics platform, realizes a simulation of dynamic coupled gas detection across the entire optical-thermal-acoustic process, driven by a real laser composite modulation signal. Figure 1As shown, it includes four core modules: light, heat, sound, and data-driven reverse optimization. In the light field module, firstly, a geometric model of the photoacoustic pool is constructed; secondly, laser source parameters are set, including power, beam waist radius, focal point, and wavenumber; the output is the spatial distribution of the electric field, which is coupled to the heat field module as an input to the fluid heat transfer physical field to participate in the construction of the heat source. In the heat field module, firstly, the electric field distribution data from the light field module is imported and substituted into the Beer-Lambert law formula to obtain the "internal heat source" of the thermal equation; secondly, the unsteady-state heat conduction equation is solved, considering the changes in physical quantities such as gas thermal conductivity and specific heat capacity with temperature, to calculate the time-varying temperature field distribution within the photoacoustic pool; finally, according to the ideal gas law, the transient change in local temperature is converted into an equivalent thermal expansion sound source. This sound source reflects the volume expansion effect of the gas due to temperature changes and forms a driving force that can excite the sound field. The temperature-time variation data output by the heat field module is used to calculate the above sound source distribution and is coupled as input to the acoustic module. In the acoustic module, firstly, the equivalent thermal expansion sound source obtained from the thermal field module is loaded as the sound field excitation term; secondly, acoustic boundary conditions are constructed, and the acoustic wave equation is solved to simulate the formation, propagation, reflection, and superposition process of sound pressure waves in the photoacoustic pool; through this solution process, the response signal of the sound pressure inside the photoacoustic pool changing with time is obtained, which is directly compared with the sound signal detected by the microphone and other sound sensors in the experiment for subsequent signal processing and performance evaluation. The processing and optimization module first performs signal processing on the final output sound pressure signal of the entire system, including removing the global DC component, filtering, FFT, normalization, and fitting. Second, based on the microphone's sensitivity, the corresponding minimum detectable sound pressure value is derived using a formula, serving as a criterion for the optimization module. If the obtained sound pressure data value is less than this minimum, it is fed back to the photoacoustic module to investigate influencing factors and modify the corresponding parameters, continuously looping the entire optimization process until the obtained sound pressure data value is greater than this minimum. When the obtained sound pressure data value is greater than this minimum, further data processing and analysis are performed, including inverse calculation of the concentration of the gas to be measured, calculation of the minimum concentration detection limit of the entire system, and the corresponding changes in concentration and various parameters. Through bidirectional closed-loop simulation of forward prediction and backward optimization, a set of optimized photoacoustic cell design schemes, including structural parameters, thermoacoustic coupling characteristics, and acoustic performance indicators (such as resonant frequency, Q value, sensitivity, and detection limit), is finally obtained. The consistency of these schemes with experimental results is verified, providing quantifiable and verifiable simulation basis for experimental design.

[0025] This embodiment designs a small-volume, high-performance photoacoustic cell, determines its size parameters, sets different materials for the cell's outer shell and internal gas, sets the concentration of the gas to be tested within the cell, its corresponding absorption coefficient, and sets the simulated ambient temperature and pressure. Using the actual laser function expression from experiments as input, it achieves composite modulation drive, adjusting parameters such as the laser beam waist radius and power to simulate the process of laser incident on the photoacoustic cell. The incident laser then propagates in the gas; due to the absorption of gas molecules, electromagnetic wave energy is absorbed and converted into heat, heating the gas in the laser-affected area, forming a local thermal expansion center, and causing temperature changes. Based on the electric field spatial distribution and average energy flux density obtained from the optical field module, it is directly coupled to the heat conduction module. Using the derived heat source formula, finite element analysis is performed at each point to obtain the temperature change caused by the absorption of laser light energy by the gas to be tested within the photoacoustic cell. The temperature change causes pressure changes through thermal expansion. This pressure disturbance is coupled into the thermoviscous acoustic module, and the temperature field distribution T′ (from the previous step) is obtained. Substituting this into the acoustic response formula, the sound pressure signal p'(t) is calculated. The sound pressure signal is the final result of the entire photoacoustic cell module. Furthermore, by analyzing the changes in sound pressure amplitude and phase with the excitation frequency, the characteristics of the photoacoustic signal are obtained.

[0026] Specifically, the following steps are included: Step 1: Design the geometric structure model of the photoacoustic cell and set the simulation environment parameters.

[0027] Step 1.1: Design the geometric structure model of the photoacoustic cell.

[0028] Creating a complete geometric model of the photoacoustic cell in simulation software includes: designing the resonant cavity structure, specifically setting the cavity length and radius; designing the buffer cavity structure, specifically setting the cavity length and radius; designing the optical window, specifically establishing the window's thickness, diameter, and position; setting material properties, assigning material characteristics to each domain in the model, including: density, thermal conductivity, specific heat capacity, etc. for solid materials (such as aluminum and quartz), and dielectric constant, thermal properties, and acoustic parameters of the gas to be detected (taking a CH4 and N2 mixture as an example) for the gas domain; defining boundary conditions, with the cavity wall defined as a rigid boundary or an adiabatic wall; and setting sound pressure detection probes inside the photoacoustic cell resonant cavity.

[0029] The purpose of this step is to establish a realistic and complete photoacoustic cell structure so that subsequent electromagnetic, thermal, and acoustic simulations can be coupled within a unified geometric framework.

[0030] In one specific implementation, the geometric structure model and simulation environment parameters of the photoacoustic cell are designed based on the physical principles of the photoacoustic cell, such as... Figure 2As shown, the physical principle of the photoacoustic cell is that a modulated laser emitted by the light source is incident, gas molecules absorb the light energy and jump, and the temperature perturbation is excited through nonradiative relaxation. The temperature perturbation causes the gas to expand thermally, and the excited sound wave is received by the microphone.

[0031] like Figure 3 and Figure 4 As shown, the simulation geometric model of the photoacoustic cell includes a resonant cavity, a buffer cavity, and a window. The initial parameters of the photoacoustic cell include the resonant cavity radius, resonant cavity length, buffer cavity radius, buffer cavity length, window size, window projection refractive index, and window material.

[0032] Step 1.2: Set simulation environment parameters Setting the environmental conditions required for simulation includes: Temperature settings: setting the ambient temperature (generally 293 K), which affects the gas's absorption coefficient, thermal properties, and sound velocity; Pressure settings: setting the internal pressure of the photoacoustic cell (generally 1 atm), which determines the gas density, refractive index, absorption linewidth, and sound velocity; Gas concentration settings: defining the concentration of the target gas (e.g., 0.5 ppm–300 ppm for CH4); setting the absorption coefficient α for different gases; Initial state settings: setting the initial gas temperature field to a uniform distribution and the initial sound pressure value to zero, serving as the starting point for the time-domain simulation.

[0033] This step ensures that the working medium of the photoacoustic cell operates under actual testing conditions, enabling the photo-thermal-acoustic coupling simulation to accurately reflect the actual response under different concentrations, temperatures, and pressures.

[0034] Step 2: Based on composite modulated incident laser excitation, perform multiphysics simulation of the optical, thermal, and acoustic coupling process.

[0035] The process involves solving for the spatial distribution of the electric field within the photoacoustic cell caused by the incident laser. Based on the spatial distribution of the electric field output from the electromagnetic field module, the volumetric heat source is calculated, and the time-domain response of the temperature field is obtained. Based on the time-domain response of the temperature field, a thermal expansion sound source is constructed, and the sound field response is solved. Optical processing is implemented through the optical field module, specifically the electromagnetic wave physical field module of wave optics. Thermal processing is implemented through the thermal field module, specifically the fluid heat transfer module. Acoustic processing is implemented through the sound field module, specifically the thermoviscous acoustic module.

[0036] Step 2.1: Solve for the spatial distribution of the electric field of the incident laser in the photoacoustic cell.

[0037] In one specific implementation, laser light is essentially an electromagnetic wave. To realistically simulate the propagation characteristics of laser light within cavities and windows and obtain the spatial distribution of the electric field in the model, the simulation method proposed in this invention uses the electromagnetic wave physics module of wave optics in the COMSOL simulation software to simulate the laser incident process. This module mainly includes two functions: first, to realize the composite modulation drive of the laser to simulate the temporal characteristics of actual incident light; second, to calculate the three-dimensional spatial electric field distribution in the model after laser incident, providing basic data for subsequent analysis of light absorption heat sources and photoacoustic coupling.

[0038] Step 2.1.1: Obtain the incident laser after composite modulation.

[0039] In one specific implementation, in most photoacoustic simulation studies, the excitation signal is simplified to a single-frequency sine wave or a constant heat source, whose mathematical form is generally a constant or the following formula: (1).

[0040] in, Indicates the heat source. t represents the modulation frequency, and t represents time. This indicates the maximum amplitude of the heat source.

[0041] This modulation method can effectively excite acoustic standing waves, but its physical meaning is rather idealized and has the following problems: a) Cannot reflect the laser wavelength tuning process: This method only describes the intensity modulation, but ignores the process of the wavelength changing linearly with time (scanning) in the actual laser source, and therefore cannot reproduce the synchronous relationship between spectral scanning and signal changes in the experiment.

[0042] b) The energy input is too idealized: the sinusoidal heat source changes smoothly over time and does not contain the power drift, nonlinear response or periodic instability in real laser scanning. Therefore, the phase and amplitude of the acoustic response deviate from the actual situation.

[0043] c) Simple spectral structure: Single-frequency sinusoidal modulation only generates 1f and 2f harmonic components, which is difficult to reflect the higher-order spectral broadening and phase mismatch effect under composite modulation.

[0044] In actual photoacoustic spectroscopy measurement experiments, laser power needs to be modulated to generate periodic heat sources, thereby exciting sound waves. Therefore, in order to overcome the limitations of the modulation methods used in the traditional simulation methods and to achieve a more realistic and complete simulation, this embodiment proposes a composite modulation method that combines sawtooth wave modulation and sine wave modulation.

[0045] Specifically, sawtooth wave modulation is responsible for scanning the gas absorption spectrum to obtain the absorption spectrum curve, locate the characteristic wavelength of the gas, and identify the gas type. The specific operation involves driving the laser current to change the laser wavelength within a small range, thereby achieving a linear scan of an absorption line (such as 1650nm for CH4).

[0046] Sine wave modulation is responsible for periodic driving, generating photoacoustic signals. Specifically, a high-frequency sinusoidal current is superimposed on the laser while the wavelength is scanning, causing the wavelength to oscillate rapidly and slightly near the absorption line.

[0047] Therefore, after applying this modulation method, the time change of the heat source term in the cavity not only depends on the modulation frequency, but also dynamically adjusts with the change of the absorption coefficient, realizing the synchronous excitation of spectral scanning and acoustic resonance.

[0048] In traditional simulation methods, the laser module is set to input a constant power value. However, in the simulation method proposed in this embodiment, the functional expression of the laser in actual experiments is used as the input to the laser module. (2).

[0049] in, Represented as a power function, Set to half the resonant frequency of the photoacoustic cell. This represents the sawtooth wave modulation function. This represents the laser wavelength modulation frequency. Compared to the empirical definition of the heat source in traditional simulation methods, this embodiment uses the actual laser modulation function as the simulation input. The derived expression for the actual heat source is: (3).

[0050] in, Indicates the absorption coefficient. Indicates the concentration of the gas to be measured. Indicates laser energy flux density, Represents the vacuum permittivity. Represents the speed of light. Indicates the intensity of the laser electric field. This represents the normalization factor for laser power modulation. This represents the peak value of the laser modulation power.

[0051] This formula will be explained and derived in detail below.

[0052] In summary, using a composite modulation function driven by a real laser in the simulation helps solve the problems of traditional driving methods and offers the following advantages: a) Improved physical realism: The simulation process more closely resembles the working mode of the experimental laser source, directly reflecting the correspondence between absorption spectral line scanning and sound pressure changes within the computational domain. b) Enhanced sound pressure signal reliability: Multiple harmonic components can be generated, especially the 2f component, whose amplitude and phase characteristics are consistent with the experimental lock-in amplification output. c) More stable system response: The sawtooth scanning section provides slow energy changes, enabling the simulation to maintain convergence and stable energy transfer even at high frequencies (kHz levels). d) Wide applicability: Applicable to photoacoustic cells of various types and sizes, providing more accurate optimization basis for different types of photoacoustic cells.

[0053] Step 2.1.2: Calculate the spatial distribution of the electric field after the composite modulation driven laser is incident.

[0054] Step 2.1.2.1: Use a Gaussian beam to describe laser propagation and obtain the electric field vector.

[0055] In the photoacoustic cell experiment, the laser satisfies the paraxial condition. Therefore, a Gaussian beam is used to describe laser propagation in the simulation, which allows us to obtain the laser's intensity distribution, phase change, focusing and divergence characteristics in space, while satisfying the condition. Under the (i.e., paraxial) condition, the scalar solution for the Gaussian beam is: (4), (5), (6).

[0056] in, The radial coordinate represents the distance from the optical axis on the cross-section of the beam. These are the coordinates along the propagation direction, i.e., the focal position, describing the position of the light beam along the propagation direction. The initial amplitude of the light field. The waist radius is Let be the radius of the light beam at point z. For wave number, Let be the radius of curvature of the light wavefront. For Gouy phase, For refractive index, is the laser wavelength.

[0057] Therefore, the main setting parameters for controlling the laser in the light field module include power. Laser wavelength , wave number Waist radius Focus position .

[0058] like Figure 5 As shown, the optical field module outputs three key parameters: ewfd.k, the phase propagation rate, which determines the position of phenomena such as interference, reflection, and standing waves; ewfd.Q, which characterizes the power flow of light propagating in the medium; and ewfd.E, the electric field vector, which describes the intensity and phase of electromagnetic waves in space.

[0059] This embodiment uses the RF (EWFD) module in Wave Optics to solve the electromagnetic wave propagation equation: .

[0060] After solving, we can obtain the electric field amplitude |ewfd.E|, and the electric field vector components ewfd.Ex,ewfd.Ey,ewfd.Ez. And the phase distribution arg(ewfd.E).

[0061] Based on the above, the simulation method proposed in this embodiment uses a Gaussian beam as the incident light field, and its transverse electric field distribution is provided by the scalar solution of the Gaussian beam (Equation 4), which is used as the port excitation input of the COMSOL electromagnetic field module. Figure 5 As shown, COMSOL further solves the vector form of Maxwell's equations using the optical field module, obtaining the spatial electric field distribution ewfd.E under actual geometric and dielectric conditions. This numerical solution automatically includes all the characteristics of the Gaussian beam solution, such as amplitude diffusion, wavefront curvature, and Gouy phase, and can therefore be regarded as the vectorized propagation result of the Gaussian beam in the real structure.

[0062] Step 2.1.2.2: Solve for the spatial light intensity distribution based on the electric field.

[0063] In one specific implementation, this embodiment solves for the output electric field vector ewfd.E through the optical field module. This physical quantity describes the electric field distribution and phase structure of the laser in three-dimensional space. Since the light intensity is directly related to the square of the electric field amplitude, their relationship can be expressed by the following equation: (7).

[0064] in, The average optical energy flux density per unit area is the core input for constructing the volumetric heat source Q in the photothermal coupling model. Therefore, the key to this step is to accurately output the spatial electric field distribution ewfd.E from the optical field module by reasonably setting parameters such as laser wavelength, beam waist radius, incident power, and beam propagation direction, and then calculating the electric field distribution ewfd.E. This refers to the spatial light intensity distribution, reflecting the energy deposition distribution characteristics of the laser in the actual structure. This light intensity distribution is further coupled to the temperature field module, and a non-uniform volumetric heat source Q is constructed through the absorption formula, thereby introducing spatially selective thermal deposition in the gas medium and driving the subsequent thermal expansion process and acoustic response.

[0065] Step 2.2: Based on the spatial distribution of the electric field output by the electromagnetic field module, calculate the volume heat source and obtain the time-domain response of the temperature field.

[0066] In one specific implementation, during the photoacoustic spectroscopy process, after laser light is incident, the energy of the laser photons is absorbed by gas molecules. After absorbing the photons, the molecules are initially in an excited state. In the gas, the molecules undergo nonradiative relaxation through intermolecular collisions, rapidly releasing the energy as kinetic energy instead of emitting light again. This means that the light energy is directly converted into the kinetic energy of the gas molecules, macroscopically manifested as an increase in temperature.

[0067] In the simulation, the heat conduction module is used to simulate this process. Its core function is to calculate the temperature distribution and its change over time in various parts of the material based on the distribution of the heat source Q.

[0068] The specific steps are as follows: Step 2.2.1: Calculate the volumetric heat source based on the spatial distribution of the electric field using Beer-Lambert's law.

[0069] According to Beer-Lambert's law Substituting the electric field distribution and average energy flux density values ​​output by the light field module into the formula, the expression for the volumetric heat source is obtained as follows: (8).

[0070] in, Let α be the average absorbed power density and α be the gas absorption coefficient. Here, represents the gas concentration and the average energy at the corresponding laser power.

[0071] Step 2.2.2: Solve the time-domain response of the temperature field based on the heat conduction equation and the volume heat source.

[0072] Due to photothermal coupling, the volumetric heat source Q formed after the gas absorbs light energy will cause local temperature fluctuations in the gas. By inputting the volumetric heat source Q as a source term into the heat conduction physical field, the time-varying temperature field distribution inside the photoacoustic cell can be solved. The heat conduction equation is shown below: (9).

[0073] In the formula, ρ is the material density, Cp is the isobaric specific heat capacity, T is the temperature, t is the time, k is the thermal conductivity, and Q is the heat power absorbed per unit volume per unit time, i.e., the volumetric heat source. It is the rate of change of internal energy (change of temperature T) caused by the change of temperature per unit volume over time, i.e., the time-domain response of the temperature field. It is a heat diffusion term that controls the propagation of the temperature field in space, such as Figure 6 As shown. The temperature of each point inside the photoacoustic cell changes with time according to the heat conduction equation of equation (9). The temperature change will cause gas density fluctuation, which will then excite the generation of the sound field and obtain the final detectable photoacoustic signal.

[0074] Step 2.3: Construct a thermal expansion sound source based on the time-domain response of the temperature field and solve for the sound field response.

[0075] In one specific implementation, changes in the temperature field cause a local increase in gas temperature, resulting in gas volume expansion and a decrease in density. Temperature oscillations cause periodic volume expansion (thermal expansion) of the gas. This volume change drives the surrounding gas, thus forming pressure waves (sound waves), such as... Figure 7 As shown.

[0076] The formula for the sound pressure response value is derived from the ideal gas law and thermodynamic expansion relations. Sound pressure response value formula: (10).

[0077] In the formula, p'(t) is the sound pressure disturbance, and γ is the adiabatic index. It is static pressure. It is a density perturbation. The static density is T, and the temperature perturbation is T'(t). It is the static temperature. , The time-domain response of the temperature field obtained by formula 9.

[0078] Equation 10 describes the core physical mechanism of the photoacoustic effect: Small changes in local temperature can directly lead to synchronous changes in pressure, and periodic temperature modulation will directly generate periodic sound pressure oscillations. Substituting the output temperature field distribution of the heat transfer module from the previous step into the acoustic module, the temperature disturbance T'(t) is automatically calculated. This is then substituted into the acoustic response formula (10) to obtain the sound pressure value T'(t). This sound pressure signal is the signal detected by the acoustic sensor, such as... Figure 8 As shown.

[0079] In the simulation, the steps for extracting the sound pressure signal are as follows: a point probe is placed at the center of the photoacoustic cell resonant cavity to record the sound pressure value during the simulation; the simulation is run to obtain the original time-domain waveform under the set conditions of temperature, pressure, excitation, and frequency range, i.e., the change of sound pressure over time. The sound pressure signal is the final representation of the entire photoacoustic cell module. It is the final output value of the overall system operation under the settings of various parameters. By analyzing the sound pressure signal, the performance of the entire system can be intuitively reflected, and it can serve as a better basis for judgment to optimize the system.

[0080] Step 3: Correct and analyze the sound pressure waveform, and then perform reverse optimization of the simulation model parameters after comparing it with the preset judgment conditions.

[0081] In one specific implementation, the obtained sound pressure waveform is processed and analyzed, and the system feedback is achieved through an optimization module to dynamically adjust various parameters within the system. Through bidirectional closed-loop simulation of forward prediction and backward optimization, a photoacoustic cell optimization design scheme is finally obtained, which includes structural parameters, thermoacoustic coupling characteristics, and acoustic performance indicators (such as resonant frequency, Q value, sensitivity, and detection limit). This embodiment iteratively corrects key parameters such as the laser wavelength power of the optical field module, the absorption coefficient of the thermal field module, and the cavity size of the acoustic module.

[0082] The specific steps are as follows: Step 3.1: Preprocess the sound pressure waveform.

[0083] The preprocessing step is to remove the global DC component and retain only the time-varying part of the sound pressure caused by the sinusoidal modulation in the composite modulation.

[0084] Specifically, the final time-domain sound pressure signal often contains the following two types of components: DC component: Non-oscillatory terms resulting from the static pressure baseline of the photoacoustic cell, sensor zero drift, or steady-state thermal accumulation.

[0085] Modulated sound pressure component (AC): This is the sound pressure waveform that varies with time periodically. It is generated by sinusoidal modulation of the laser and is used for subsequent frequency domain and harmonic analysis.

[0086] To avoid interference from DC components in subsequent data processing, baseline correction of the time-domain signal is required, which means removing the global DC components and retaining only the time-varying part of the sound pressure caused by sinusoidal modulation in the composite modulation.

[0087] Step 3.2: Use window functions to process time-domain signals to reduce spectral leakage caused by sampling truncation.

[0088] Specifically, since the sound pressure waveform is a truncated signal with a finite time length, directly performing FFT will result in discontinuities at the edges and energy leakage to other frequencies (spectral leakage). By using a window function to smoothly attenuate the signal at the end of the time domain, leakage can be effectively reduced and frequency domain resolution improved.

[0089] More specifically: Step 3.2.1: Select the window function.

[0090] For example, the Hanning window: .

[0091] in, It is a Hanning window sequence, where N is the window length (i.e., the total number of data points), and n is the number of discrete sampling points, ranging from... .

[0092] Step 3.2.2: Apply the window function to the time-domain signal.

[0093] The window function and the sound pressure time-domain signal obtained after preprocessing in step 3.1 are multiplied point by point, i.e., windowing is applied: .

[0094] in, This is the signal after windowing. It is the sound pressure time-domain signal obtained after preprocessing. Step 3.3: Perform a Fast Fourier Transform (FFT) on the windowed time-domain signal to convert it into a frequency-domain signal, and calculate the amplitude and phase of each frequency component.

[0095] Among them, the amplitude spectrum can determine the sound pressure intensity and resonance characteristics generated by gas absorption; the phase spectrum can analyze the system response delay and sound field transmission characteristics; by determining whether the sound pressure amplitude reaches its peak at the resonance frequency, it can verify whether the laser modulation frequency is aligned with the natural frequency of the photoacoustic cell. Step 3.4: Identify the second harmonic (2f) component in the amplitude spectrum. That is, extract the complex amplitude of the 2f component at the amplitude corresponding to twice the resonant frequency to obtain a pure second harmonic photoacoustic signal, thereby achieving highly sensitive quantitative analysis of gas concentration; Step 3.5: Convert the microphone noise to obtain the minimum sound pressure level limit.

[0096] According to the formula ,in, Sound pressure level (Pa) is the noise level. For reference sound pressure, air pressure is usually taken as... , The sound pressure level is in decibels, which is the microphone noise floor. This converts the microphone noise floor into a sound pressure value, which is the minimum sound pressure level that the microphone can detect.

[0097] Step 3.6: Determine the threshold of the second harmonic component based on the minimum sound pressure level limit, and correct the corresponding control parameters based on the threshold determination result.

[0098] The minimum sound pressure level is used as the judgment condition. The amplitude of the 2f component obtained after the above steps is used as the input value and compared with the judgment condition to determine whether the current detection has reached the detectable range.

[0099] Step 3.6.1: When the 2f amplitude is less than the minimum value, it means that the system cannot complete the detection of the current gas concentration. Feedback needs to be sent to the preceding module for parameter adjustment. The method used is to traverse the main control parameters of the preceding photothermal acoustic module, including the laser input power, wavelength, beam waist radius and position, gas absorption coefficient, photoacoustic cell design size, etc. The control variable method is used to adjust each parameter and perform a full-process simulation according to the simulation method described above until the 2f component amplitude is greater than the minimum value, and then proceed to the next step. Step 3.6.2: When the amplitude of 2f is greater than the minimum value, it means that the system can meet the detection of the current gas concentration. Exit the loop and proceed to the next step.

[0100] Step 3.7: Establish a concentration calibration model based on the calibration relationship between concentration and 2f amplitude, and perform quantitative inversion of gas concentration.

[0101] This step in this embodiment is a comprehensive processing step for concentration inversion and system performance analysis, generating the optimized design results. To achieve quantitative inversion of gas concentration, this embodiment obtains the corresponding 2f sound pressure amplitude through multiple sets of optical-thermal-acoustic coupled simulations under known concentration conditions, and establishes a calibration relationship between concentration and 2f amplitude.

[0102] Specifically, for different concentrations Perform a complete simulation sequentially and extract the amplitude of its 2f frequency domain component. , The linear calibration model was obtained by fitting the data using the least squares method. .

[0103] in, This represents the simulation result of the 2f component amplitude corresponding to the i-th concentration. This represents the concentration of the i-th gas. Let be the photoacoustic sensitivity of the system, and b be the background bias term. This model reflects the linear characteristics of the photoacoustic effect under low absorption conditions, that is, the higher the gas concentration, the stronger the heat source absorption, and the corresponding increase in the modulation sound pressure.

[0104] Therefore, when the 2f amplitude is obtained under arbitrary simulation conditions Then, the concentration inversion can be performed directly using the above calibration equation: .

[0105] Simultaneously, further data processing and computational analysis are performed to obtain the system's minimum detection limit and response characteristics, calculate acoustic performance indicators (such as Q value, sensitivity, and SNR), evaluate the system performance, and finally output a photoacoustic cell simulation optimization design scheme that includes complete parameter settings and performance evaluation.

[0106] The above are the specific implementation steps of the photoacoustic spectroscopy gas detection photothermal-acoustic coupling full-process dynamic simulation method proposed in this invention. This method can be applied to photoacoustic cells of various types and sizes, and is applicable to various trace gas detection simulation analyses based on photoacoustic spectroscopy technology.

[0107] Step 4: Analyze and evaluate the parameters of the simulation model after reverse optimization to obtain the simulation optimization scheme.

[0108] Step 4.1: Extract acoustic performance indicators to further analyze the system that meets the current gas concentration detection requirements.

[0109] Specifically, the main mode resonance frequency is output through the peak value of the spectrum; the 2f amplitude is obtained by identifying the second harmonic (2f) component in the amplitude spectrum; the Q value is obtained by the center frequency of the main peak in the sound pressure spectrum and the half-power bandwidth; and the signal-to-noise ratio (SNR) is calculated by the ratio of the obtained 2f component amplitude to the noise floor sound pressure value.

[0110] Step 4.2: Calculate the Limit of Detection (LOD) based on the fitted model. Specifically, the key to the lowest detection limit (LOD) lies in distinguishing between "a real signal" and "just random fluctuations of noise." In photoacoustic detection systems, noise can be considered as zero-mean Gaussian random noise. Therefore, to ensure that the detected signal is not a random fluctuation caused by noise, the internationally used 3σ noise standard is adopted as a reliable detection threshold.

[0111] The noise amplitude is obtained from steps 3.6 and 3.7. and the slope of the concentration calibration curve The lowest detection limit (LOD) can be obtained as follows: .

[0112] Step 4.3: Integrate and output the simulation optimization scheme.

[0113] The final simulation optimization scheme output includes: (1) Complete photoacoustic cell structural parameters Resonant cavity dimensions (length, radius), buffer cavity dimensions, materials used in each part of the photoacoustic cell, and microphone placement.

[0114] (2) Simulation environment settings Temperature, humidity, and air pressure; boundary condition settings; gas type, concentration, and absorption coefficient.

[0115] (3) Light source and modulation parameters Laser power; modulation frequency, sawtooth + sine wave parameters; beam waist radius w0, wavelength λ, focusing position z0.

[0116] (4) Setting physical field parameters Heat source distribution formula and parameters; heat conduction and acoustic parameters; mesh size and solver settings.

[0117] (5) Performance evaluation results Resonance frequency and error; Q value; amplitude of 2f; SNR; LOD; sound pressure distribution map, light field map, and heat source map.

[0118] The photothermal-acoustic coupling simulation optimization method based on photoacoustic spectroscopy gas detection in this embodiment has the following advantages: 1. Break through the limitations of "single-field independent simulation" and achieve deep coupling of multi-physics fields.

[0119] Traditional methods often calculate light, heat, and sound separately. For example, they might calculate light absorption first and then manually input heat into the thermal model, or omit the light field simulation step and directly use a fixed value as the heat source input. This method ignores the dynamic interaction of parameters. This method achieves coupling through real-time parameter transfer: the spatial distribution and energy deposition of the light field module are dynamically adjusted according to the power, wavelength, and spot shape of the input laser; the temperature change of the thermal field module changes with the output of the light field module; the sound pressure signal generated by the acoustic module is closely related to the output values ​​of the light and thermal field modules. This achieves deep coupling and full-process dynamic simulation of the optical, thermal, and acoustic physical fields.

[0120] 2. Construct a "forward prediction + reverse optimization closed-loop simulation" framework, which can bidirectionally couple a reverse optimization detection system. Traditional simulations only provide "forward prediction," while this method adds closed-loop logic: the final sound pressure signal is compared with the detection capability, and the result is input into the simulation model. By iteratively correcting key parameters such as the laser wavelength power of the optical field module, the absorption coefficient of the thermal field module, and the cavity size of the acoustic module, a two-way closed-loop simulation of forward prediction and backward optimization is achieved. This enables backward optimization of the detection system without the need for repeated physical experiments, significantly reducing R&D costs.

[0121] In summary, the significance of the simulation method proposed in this embodiment lies in: a) Dynamic fully coupled calculation: The optical, thermal, and acoustic processes are solved simultaneously in the time domain, avoiding errors in energy transfer assumptions and more realistically reflecting the physical processes in the experiment, thus providing better reference value. b) Composite modulation drive: The composite modulation expression of the laser in the real experiment is used as the laser input in the simulation, solving the problem that the fixed value or single modulation method used in traditional methods cannot realistically and dynamically simulate the physical process. By using the laser function expression in the experiment as the simulation input, combined with the fully coupled simulation model and method, the entire experimental process can be dynamically reconstructed. c) Harmonic response visualization: The 2f signal and phase information can be directly extracted from the system output, corresponding to the output results of the experimental lock-in amplifier. d) Adaptability: This modeling method is applicable to photoacoustic cell systems of various sizes (different resonant cavity and buffer cavity parameters) and types (including single resonant cavity, multi-resonant cavity, T-type, etc.), with a wide range of applicable scenarios. Moreover, it still converges stably for high-frequency resonant systems of 4–10kHz and can also be used for the optimization of micro photoacoustic cell structures. e) This method can realistically simulate physical processes based on different setting parameters. Therefore, it can be applied to predict the impact of different parameters on photoacoustic signals. It can find the optimal photoacoustic cell design scheme under different needs at a lower cost and higher efficiency, and has strong practical value and application prospects.

[0122] The simulation method proposed in this embodiment is the first to achieve dynamic coupling simulation of "modulation light source - light field distribution - thermal diffusion - acoustic resonance - analysis and optimization" in numerical simulation. Through this full-process photo-thermal-acoustic coupling dynamic simulation method, the dynamic photoacoustic response and 2f signal characteristics of the system can be directly predicted without actual experimental measurements, verifying the optimal combination of resonant cavity structure, modulation method, and gas parameters. This method effectively overcomes problems such as discontinuous heat source definition, fragmented energy transfer, and unstable sound field in traditional models. In summary, this method realizes a full-process simulation system from light energy injection → thermal expansion → acoustic resonance → reverse optimization. It can not only reproduce experimental-level signal morphology in the computational domain but also analyze the coupling effects of modulation frequency, phase, and cavity parameters on photoacoustic signals. Simultaneously, this full-process composite modulation photo-thermal-acoustic coupling-reverse optimization system provides a new theoretical and numerical research approach for the miniaturization and high-sensitivity design of photoacoustic spectroscopy systems, and provides a quantifiable and verifiable theoretical platform for the design and optimization of high-precision photoacoustic spectroscopy sensing systems.

[0123] Meanwhile, it should be noted that by performing multi-physics field dynamic simulation analysis on the entire process of gas photoacoustic spectroscopy measurement in the photoacoustic cell, the overall system design can be optimized more accurately, detection performance can be improved, and the structure and parameter configuration of the photoacoustic cell under different application requirements can be guided. Specifically, when designing for specific laser power requirements, the full-process multi-field coupling dynamic simulation method proposed in this invention can be used. Under the premise of fixed input power of the optical field module, the optimal performance of the system under that power condition can be achieved by adjusting parameters such as laser wavelength, beam waist position, photoacoustic cell size, absorption coefficient, ambient temperature and air pressure. When designing for specific resonance frequency requirements, the same simulation method can be used to obtain multiple optimal photoacoustic cell structure and operating parameter schemes that meet the target resonance frequency by adjusting laser parameters, gas absorption characteristics and environmental conditions. Since the geometric, optical, and acoustic parameters of the photoacoustic cell can all affect the light-heat-sound energy conversion process, the simulation method proposed in this invention realizes the coupling and optimization of the entire process from optical excitation to acoustic response. It can achieve multi-parameter balance and dynamic optimization in the system simulation stage, thereby obtaining a customized and systematic solution that meets specific application requirements while taking into account high detection sensitivity and stability.

[0124] Example 2: Embodiment 2 of the present invention provides a photothermal-acoustic coupling simulation optimization system based on photoacoustic spectroscopy gas detection, such as... Figure 8 As shown, it includes: The parameter setting module is configured to design the initial parameters of the photoacoustic cell and acquire the incident laser. The composite modulation-driven optical-thermal-acoustic fully coupled simulation module is configured to simulate the optical, thermal, and acoustic coupling processing of incident laser based on the initial parameters of the photoacoustic cell. Specifically, it solves the spatial distribution of the electric field of the incident laser in the photoacoustic cell, calculates the volume heat source based on the spatial distribution of the electric field output by the electromagnetic field module, obtains the time-domain response of the temperature field, constructs a thermal expansion sound source based on the time-domain response of the temperature field, and solves the sound field response. The data processing and analysis reverse optimization parameter module is configured to perform correction processing and data analysis on the sound pressure waveform, and then perform reverse optimization on the simulation model parameters after comparing them with preset judgment conditions. The performance and index evaluation and design optimization scheme output module is configured to analyze and evaluate the parameters of the simulation model after reverse optimization to obtain the simulation optimization scheme.

[0125] Example 3: Embodiment 3 of the present invention provides a computer-readable storage medium storing a computer program adapted for loading by a processor and executing the steps in the photothermal-acoustic coupling simulation optimization method based on photoacoustic spectroscopy gas detection as described in Embodiment 1 of the present invention.

[0126] Example 4: Embodiment 4 of the present invention provides a computer device, the device comprising: A processor, adapted to execute computer programs; A computer-readable storage medium storing a computer program, which, when executed by the processor, implements the steps in the photothermal-acoustic coupling simulation optimization method based on photoacoustic spectroscopy gas detection as described in Embodiment 1 of the present invention.

[0127] Example 5: Embodiment 5 of the present invention provides a computer program product or computer program, which includes computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium and executes the computer instructions, causing the computer device to perform the steps in the photothermal-acoustic coupling simulation optimization method based on photoacoustic spectroscopy gas detection as described in Embodiment 1 of the present invention.

[0128] The steps and methods involved in Examples 2, 3, 4 and 5 above correspond to those in Example 1. For specific implementation methods, please refer to the relevant description section of Example 1.

[0129] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this application can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application. In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. A computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the flow or function according to the embodiments of this application is generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in or transmitted through a computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired or wireless means. The computer-readable storage medium can be any available medium that a computer can access or a data processing device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium, an optical medium, or a semiconductor medium, etc. The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A photothermal-acoustic coupling simulation optimization method based on photoacoustic spectroscopy gas detection, characterized in that, Includes the following steps: Design the geometric model of the photoacoustic cell and set the simulation environment parameters; Based on composite modulated incident laser excitation, multiphysics simulation of the optical, thermal, and acoustic coupling process is performed to obtain the sound pressure waveform. Specifically, the spatial distribution of the electric field of the incident laser in the photoacoustic cell is solved. Based on the spatial distribution of the electric field output by the electromagnetic field module, the volume heat source is calculated and the time-domain response of the temperature field is obtained. Based on the time-domain response of the temperature field, a thermal expansion sound source is constructed and the sound field response is solved. The sound pressure waveform is corrected and analyzed, and the simulation model parameters are optimized in reverse after being compared with the preset judgment conditions. The parameters of the simulation model after reverse optimization are analyzed and evaluated to obtain the simulation optimization scheme.

2. The photothermal-acoustic coupling simulation optimization method based on photoacoustic spectroscopy gas detection as described in claim 1, characterized in that, The design of the photoacoustic cell geometric model includes: designing the resonant cavity structure, specifically setting the cavity length and radius; designing the buffer cavity structure, specifically setting the cavity length and radius; designing the optical window, specifically establishing the window thickness, diameter, and position; setting material properties, assigning material characteristics to each domain in the model; defining boundary conditions; and setting sound pressure detection probes inside the photoacoustic cell resonant cavity.

3. The photothermal-acoustic coupling simulation optimization method based on photoacoustic spectroscopy gas detection as described in claim 1, characterized in that, The specific steps for solving the spatial distribution of the electric field of the incident laser in the photoacoustic cell are as follows: The incident laser after composite modulation is obtained, wherein a composite modulation method combining sawtooth wave modulation and sine wave modulation is adopted; Calculate the spatial distribution of the electric field after incident with a composite modulation-driven laser.

4. The photothermal-acoustic coupling simulation optimization method based on photoacoustic spectroscopy gas detection as described in claim 1, characterized in that, The specific steps for calculating the spatial distribution of the electric field after incident composite modulation-driven laser are as follows: Laser propagation is described using a Gaussian beam, and the electric field vector is obtained. The spatial light intensity distribution is determined based on the electric field.

5. The photothermal-acoustic coupling simulation optimization method based on photoacoustic spectroscopy gas detection as described in claim 1, characterized in that, The specific steps for calculating the time-domain response of the volumetric heat source and obtaining the temperature field based on the spatial distribution of the electric field output by the electromagnetic field module are as follows: Calculate the volumetric heat source based on the spatial distribution of the electric field using Beer-Lambert's law; The time-domain response of the temperature field is solved based on the heat conduction equation and the volumetric heat source.

6. The photothermal-acoustic coupling simulation optimization method based on photoacoustic spectroscopy gas detection as described in claim 1, characterized in that, The specific steps for correcting and analyzing the sound pressure waveform, comparing it with preset judgment conditions, and then optimizing the simulation model parameters in reverse are as follows: Preprocess the sound pressure waveform; Use window functions to process time-domain signals to reduce spectral leakage caused by sampling truncation; A fast Fourier transform is performed on the windowed time-domain signal to convert it into a frequency-domain signal, and the amplitude and phase of each frequency component are calculated. Identify second harmonic components in the amplitude spectrum; The microphone noise is converted to obtain the minimum sound pressure level limit; The second harmonic component is thresholded based on the minimum sound pressure level limit, and the corresponding control parameters are corrected based on the threshold judgment results. A concentration calibration model is established based on the calibration relationship between concentration and 2f amplitude, and the gas concentration is quantitatively inverted.

7. A photothermal-acoustic coupling simulation optimization system based on photoacoustic spectroscopy gas detection, characterized in that, include: The parameter setting module is configured to design the initial parameters of the photoacoustic cell and acquire the incident laser. The composite modulation-driven optical-thermal-acoustic fully coupled simulation module is configured to simulate the optical, thermal, and acoustic coupling processing of incident laser based on the initial parameters of the photoacoustic cell. Specifically, it solves the spatial distribution of the electric field of the incident laser in the photoacoustic cell, calculates the volume heat source based on the spatial distribution of the electric field output by the electromagnetic field module, obtains the time-domain response of the temperature field, constructs a thermal expansion sound source based on the time-domain response of the temperature field, and solves the sound field response. The data processing and analysis reverse optimization parameter module is configured to perform correction processing and data analysis on the sound pressure waveform, and then perform reverse optimization on the simulation model parameters after comparing them with preset judgment conditions. The performance and index evaluation and design optimization scheme output module is configured to analyze and evaluate the parameters of the simulation model after reverse optimization to obtain the simulation optimization scheme.

8. A computer program product, characterized in that, The computer program product includes a computer program that, when executed by a processor, implements the photothermal-acoustic coupling simulation optimization method based on photoacoustic spectroscopy gas detection as described in any one of claims 1-6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program adapted to be loaded by a processor and executed as described in any one of claims 1-6, using a photothermal-acoustic coupling simulation optimization method based on photoacoustic spectroscopy gas detection.

10. A computer device, characterized in that, include: A processor, adapted to execute computer programs; A computer-readable storage medium storing a computer program, which, when executed by the processor, implements the photothermal-acoustic coupling simulation optimization method based on photoacoustic spectroscopy gas detection as described in any one of claims 1-6.

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