SPR grating type sensor design method based on FPCL-DCNN

Abstract

A design method of an SPR grating type sensor based on FPCL-DCNN is a method for carrying out molecular-level adaptive characteristic design on a Kretschmann type SPR grating sensor, belongs to the field of sensors and artificial intelligence, and is characterized by comprising the following steps: (1) carrying out chemical reaction modification on active groups of molecules to be detected on the surface layer of a bio-based membrane; (2) introducing a Langmuir physical adsorption model; (3) determining components of the bio-based membrane which reacts with the molecules to be detected; (4) defining initial model parameters; (5) constructing a DCNN multi-mode convolutional neural network optimization model; and (6) designing a loss function and an output layer. The problem that in the prior art, interaction of a to-be-detected substance on the surface of the sensor and the to-be-detected substance cannot be accurately controlled is solved, physical and chemical modification is carried out on the to-be-detected substance, to-be-designed parameters of the sensor are input into the DCNN model, optimal SPR sensor parameters are output through a linear activation function of the output layer, and the accuracy of the SPR sensor is improved. And a new method is provided for SPR grating type sensor parameter design.

Description

Technical Field

[0001] The invention relates to the field of sensors and artificial intelligence, and mainly relates to a method for designing molecular-level adaptive characteristics of a Kretschmann-type SPR grating sensor. Background Art

[0002] Kretschmann-type SPR (Surface Plasmon Resonance, SPR) grating sensors are widely used in the field of optical sensing. With its high sensitivity, they are used for refractive index detection and molecular interaction research. This structure stimulates surface plasmon resonance through metal films and responds sensitively to small changes in the ambient refractive index. Current research focuses on material selection, structural optimization, and improvements in optical coupling technology, such as selecting gold or silver films as materials, or enhancing signal sensitivity by adjusting film thickness and incident angle. However, these designs still face multiple limitations. First, it is difficult to balance the material selection of metal films between sensitivity and stability. Silver films have high sensitivity but are easily oxidized, while gold films have good stability but low sensitivity. Second, the Kretschmann structure is highly dependent on film thickness and incident angle, which limits its response range and limits its flexibility in dynamic detection. In addition, the SPR signal is easily disturbed by ambient light and temperature changes, affecting the detection accuracy. While the multilayer film structure enhances the detection effect, it may also cause a decrease in signal repeatability due to unstable interfaces between film layers. Therefore, although Kretschmann-type SPR sensors have important application value, there is still room for improvement in material innovation, structural design and environmental interference suppression.

[0003] Kretschmann-type SPR sensors have a wide range of applications in optical sensing technology, especially in environmental monitoring, biomedical testing, chemical analysis and other fields. By exciting surface plasmon resonance, the sensor can detect tiny changes in substances with high sensitivity, so it can be widely used in important scenarios such as gas detection, toxicity analysis, pathogen identification, etc. And with the continuous improvement of modern industrial and public safety needs, Kretschmann-type SPR sensors have put forward higher requirements in terms of sensitivity, real-time response and adaptability, especially in terms of high-precision detection, dynamic change monitoring and long-term stability in complex environments. In the face of these demands, the development of SPR sensors must not only improve the recognition ability of a single signal, but also realize the simultaneous detection and analysis of multiple signals to meet the needs of multifunctional applications.

[0004] Driven by artificial intelligence and large model technology, the detection capability and application potential of Kretschmann-type SPR grating sensors have been significantly improved. Artificial intelligence algorithms can not only quickly process SPR sensor signal data and extract key features, thereby improving the signal-to-noise ratio and response speed, but also enable the sensor to more accurately distinguish target signals in complex backgrounds. The introduction of large models has also greatly expanded the application scope of detection methods, making them no longer limited to a single analysis mode, but building a multi-dimensional detection model through multi-level, cross-modal data learning, thereby achieving more accurate and robust signal recognition.

[0005] In addition, deep learning technology gives SPR sensors the ability to adaptively analyze, enabling them to dynamically adjust sensor parameters based on different detection environments to ensure that they are always in the best working state. During the design process of this sensor, the optical and physical and chemical properties of the target substance are simulated and analyzed through computer models to accurately determine the most suitable sensor structural parameters. This adaptive mechanism not only improves the long-term stability of the sensor in complex environments, but also enhances its sensitivity and real-time response capabilities, further expanding the application potential of SPR sensors in environmental monitoring, biomedicine, chemical analysis and other fields. Summary of the invention

[0006] In view of the problems existing in the above-mentioned prior art, the technical problem to be solved by the present invention is to provide a design method of SPR grating type sensor based on FPCL-DCNN (Functionalized Physical Chemical Layer-Deep Convolutional Neural Network), the specific process of which is as follows: Figure 1 shown.

[0007] The technical solution implementation steps are as follows:

[0008] (1) Modification of the active group B of the target molecule X on the surface of the biofilm by chemical reaction:

[0009] Since the biochemical and optical properties of the molecule X to be tested are unknown, and the plasma resonance reaction of the SPR sensor is related to the refractive index of the medium, and in order to accelerate the change of the refractive index of the medium and amplify the SPR signal, we modify the molecule to be tested by FPCL (Functionalized Physical Chemical Layer). First, the active group B of the molecule to be tested on the surface of the biofilm is modified in terms of chemical reaction:

[0010] The binding rate α of the molecule to be tested X and the active group B on the basement membrane surface is:

[0011]

[0012] The concentration of the molecule X that binds to the surface active group B of the basement membrane after modification is X bound for:

[0013]

[0014] The residual concentration B of the active group B on the surface of the basement membrane after modification remain for:

[0015]

[0016] Wherein, X0 is the initial concentration of the molecule X to be measured, B0 is the initial concentration of the active group B on the surface of the biofilm, k is the chemical reaction equilibrium constant, and t represents time.

[0017] (2) Introducing the Langmuir physical adsorption model:

[0018] In order to enhance the adaptability to different types of molecules, improve the stability and density of molecular fixation, adjust the detection signal response time and intensity, and use the synergistic effect of physical adsorption and chemical modification to improve the detection selectivity based on the difference between target molecules and interfering molecules, the Langmuir physical adsorption model is then introduced:

[0019] Assume that the total number of physical adsorption sites of molecule X on the surface of the base film is N, the number of sites occupied by molecule X is n, the adsorption equilibrium constant is K, and the partial pressure of molecule X is p.

[0020] According to the Langmuir adsorption isotherm, the surface coverage θ (indicating the degree of adsorption of molecule X on the surface of the base film) is:

[0021]

[0022] The amount of adsorbed molecule X (expressed as the amount of substance or number of molecules) n is:

[0023]

[0024] The adsorption equilibrium constant K can be expressed as:

[0025]

[0026] Where Q is the concentration of the product generated by the reaction between the molecule to be tested X and the active group B on the surface of the biofilm, B0 is the initial concentration of the active group B on the surface of the biofilm, and X bound is the concentration of the modified molecule X.

[0027] After chemical and physical modification, the residual concentration of the molecule X in the medium channel is X remain The dynamic expression that changes with time is:

[0028]

[0029] Wherein, X0 is the initial concentration of the molecule X to be tested, B0 is the initial concentration of the active group B on the surface of the biofilm, k is the chemical reaction equilibrium constant, N is the total number of physical adsorption sites on the surface of the biofilm, Q is the concentration of the product generated by the reaction between the molecule X to be tested and the active group B on the surface of the biofilm, p is the partial pressure of the molecule X, and t represents time.

[0030] (3) Determine the component Y of the biofilm that reacts with the molecule to be tested X:

[0031] First, calculate the functional group reaction matching degree F:

[0032] Determine the concentration of surface functional groups FG on the biofilm surface 基膜 :

[0033] The density of specific functional groups on the surface of the biofilm was determined by the chemical analysis method X-ray Photoelectron Spectroscopy (XPS). FG specific functional groups, the surface area of ​​the base membrane is A, then

[0034]

[0035] Estimate the concentration of reactive functional groups in the substance to be tested FG X :

[0036] For small molecules, the molecular structure can be determined by nuclear magnetic resonance (NMR) technology to clarify the types and quantities of reactive functional groups. For macromolecules, the average concentration of reactive functional groups can be estimated by combining amino acid sequence analysis or sugar composition analysis.

[0037] Assume that the molar mass of the substance to be tested is M, and each molecule contains m FG The concentration of reactive functional groups in the solution is C X (mol / L), then

[0038] FG X =C X ×m FG

[0039] Calculate the functional group reaction matching degree F:

[0040]

[0041] In the formula, K FGis the functional group reaction equilibrium constant, and C1 is the normalization constant that makes the value of F between 0 and 1.

[0042] Next, calculate the physical and chemical reaction matching degree P:

[0043] At different temperatures, the relationship between the adsorption amount of the substance to be tested on the surface of the biofilm and the partial pressure or concentration is measured, and the Langmuir adsorption isotherm is determined. At different temperatures, the adsorption heat can be calculated by the deformation of the Clausius-Clapeyron equation, and the adsorption free energy ΔG can be determined by combining the thermodynamic formula to calculate the adsorption free energy. ads ;

[0044] Calculate the physical and chemical reaction matching degree P according to the formula:

[0045]

[0046] In the formula, k P is the slope of the curve, which can be obtained from the data. ΔG0 is the median adsorption free energy. When the adsorption of the biofilm and the test substance is observed to be at a moderate level, ΔG ads =ΔG0.

[0047] Then calculate the similarity and compatibility matching degree L:

[0048]

[0049] In the formula, δ 基膜 Indicates the polarity of the basement membrane, δ X represents the polarity of the substance X to be tested, |δ 基膜 -δ X | indicates the polarity difference between the two, δ max is the predefined maximum polarity difference.

[0050] Finally, the comprehensive applicability parameter S of the bio-based membrane is calculated and determined:

[0051] S=ω1F+ω2P+ω3L

[0052] In the formula, ω1, ω2, and ω3 correspond to the weight parameters of the functional group reaction matching degree F, the physicochemical reaction matching degree P, and the similarity and solubility matching degree L, respectively, which can be determined later by the deep neural network model.

[0053] (4) Define initial model parameters:

[0054] First, the biofilm thickness d is initialized. b :

[0055] Biofilm thickness d bDirectly affects the interaction between the molecule to be detected X and the sensor surface. When the surface coverage is θ and the amount of the molecule to be detected X adsorbed per unit area is n, the thickness of the biofilm d b It can be defined by the following relationship:

[0056]

[0057] Among them, ρ b is the density of the biofilm, V X It is the effective volume after the attachment of the molecule X to be measured.

[0058] Next, initialize the material and thickness d of the metal film m :

[0059] SPR sensors usually use gold or silver as the metal layer material. The refractive index and dielectric constant of different materials will affect the sensitivity of the sensor. The following table shows some common metal refractive index and absorption coefficient data:

[0060]

[0061]

[0062] The thickness of the metal film affects the sensitivity and peak position of the SPR signal. The optimal metal film thickness can be analyzed using the reflectivity formula:

[0063] Under the structure of the substance to be tested - bio-based film - metal film, the reflectivity R is calculated using the Abélès matrix method. This method represents the optical properties of each layer with a matrix, and then multiplies them layer by layer to obtain the reflectivity of the entire structure:

[0064] The feature matrix of each layer j can be written as:

[0065]

[0066] In the formula, is the phase delay of light at layer j, n j is the refractive index of the jth layer, d j is the thickness, θ j is the angle, q j =n j cos(θ j ) for S-polarized light, or For P-polarized light, i represents an imaginary unit.

[0067] The total transmission matrix M can be expressed as:

[0068]

[0069] On this basis, the reflectivity R can be expressed as:

[0070]

[0071] Then, initialize and define the grating parameters (number of teeth N g and concave-convex spacing Λ)

[0072] The structural parameters of the grating affect the light coupling efficiency and can be described by the grating diffraction equation:

[0073] mλ=Λsin(θ)+sin(θ m )

[0074] Where m is the diffraction order, λ is the wavelength of the light source, θ and θ m The incident and diffraction angles are adjusted to adjust the number of grating teeth N. g and the concave-convex spacing Λ to achieve the best coupling angle and sensitivity.

[0075] Number of teeth N g is the number of grooves in a certain length of the grating, which is inversely proportional to the concave-convex spacing Λ and can be expressed as:

[0076]

[0077] Achieve a specific emission angle θ at a specific wavelength λ m , the grating equation can be satisfied by adjusting the concave-convex spacing Λ:

[0078]

[0079] Adjust the number of grating teeth N g and the concave-convex spacing Λ, the optimal coupling angle and sensitivity can be achieved.

[0080] Finally, initialize and define the wavelength λ and the incident angle θ of the incident light source

[0081] The wavelength λ of the incident light source and the incident angle θ have a great influence on the position of the SPR resonance peak. When light enters a low refractive index medium from a high refractive index medium, the critical angle θ at which total reflection occurs is c Defined as:

[0082]

[0083] Wherein, n1 and n2 are the refractive indices of the incident medium and the metal layer, respectively.

[0084] (5) Constructing a multimodal convolutional neural network optimization model:

[0085] First, design a multi-channel convolutional denoising feature extraction layer:

[0086] Convolutional Denoising Autoencoders (CDAE) are designed. First, convolution operations are applied to the input features (biofilm thickness, metal film material, metal film thickness, number of grating teeth, concave-convex spacing, incident angle, incident light wavelength) to map the features to multiple channels to extract features at different levels. The encoder can reduce the impact of environmental noise or data errors through denoising self-supervised learning, making the encoded features more robust during reconstruction.

[0087] Perform multi-channel convolution and treat each input parameter as an independent channel. The feature dimension is gradually increased through multiple layers of 1D convolution, and combined with the noise reduction layer, the encoding features of the convolution output are more expressive in the high-dimensional space, which facilitates the subsequent attention mechanism to capture the importance of different parameters. The specific convolution calculation formula is as follows:

[0088]

[0089] In the formula, y (l) is the convolution output of layer l, is the convolution kernel weight, x i+k-1 represents the local area of ​​the input data, b (l) is the bias term, σ is the activation function, and K is the number of convolution kernels.

[0090] Then construct a multimodal parameter space-parameter association graph convolutional network (Diverse Convolutional Neural Network, DCNN):

[0091] First, a parameter graph is constructed, and each input parameter (biofilm thickness, metal film material, metal film thickness, number of grating teeth, concave-convex spacing, incident angle, incident light wavelength) is defined as a node in the graph. The edge weights between different nodes represent the strength of the association between the parameters. The graph convolutional network calculates by assigning weights to the relationships between nodes to achieve the association modeling of sensor parameters. In this way, the model can learn the importance of each node in the overall features. The calculation formula of DCNN is as follows:

[0092]

[0093] In the formula, is the adjacency matrix with self-connection added, yes The degree matrix, H ( l ) represents the feature representation of the l-th layer node, W ( l ) is the learnable weight matrix and σ is the activation function.

[0094] An adaptive attention mechanism is used to assign weights to the edges between different parameter nodes, and the weights are adaptively adjusted to identify which parameter combinations are most sensitive to SPR detection. The weights will change dynamically, allowing the model to select the appropriate parameter combination under different test conditions. Feature conversion and convolution operations are then performed to convert the features of each node into high-level embedded features through a shared convolution kernel, and cross-node convolution operations are performed on this basis.

[0095] Then, the attention fusion mechanism - multi-layer feature fusion is completed:

[0096] The local attention mechanism is introduced. First, the multi-channel feature maps extracted by convolution are pooled to obtain global statistical information for each channel. The fully connected layer is used to compress these statistical information into weight coefficients, and then the contribution of different channels is recalibrated by attention weights. This step allows the output features of the convolution layer to be prioritized before parameter fusion, which helps the model focus on important parameters more effectively. The attention mechanism generates channel weight coefficients through global pooling and fully connected layers. The formula is as follows:

[0097]

[0098] In the formula, α c is the channel weight coefficient, W is the fully connected layer weight matrix, pool is the global pooling operation, and y (l) is the convolution output of layer l.

[0099] Construct a global attention mechanism. Usually, the feature information output by different convolutional layers has different levels. The deeper the layer, the more abstract the feature representation. When fusing multiple layers, introduce a global attention mechanism, use pooling and weighting to fuse the multi-layer DCNN and convolutional layer features to obtain a multi-dimensional feature representation, while suppressing noise or unimportant information. This ensures that before the final output, the model's contribution to each feature layer can be adaptively optimized. The formula is as follows:

[0100]

[0101] In the formula, α l is the attention weight, which is used to adjust the contribution of different feature layers, H (l) is the feature representation of the lth layer, and L is the number of pooling layers.

[0102] (6) Loss function and output layer design:

[0103] In order to obtain the numerical results of the optimal design parameters, the output layer of the model can be designed as a linear activation layer to output the optimal value of each parameter. The linear combination formula of the output is:

[0104]

[0105] Where W out and b out are the weight matrix and bias of the output layer respectively, and Z is the feature representation after multi-layer fusion.

[0106] The mean square error (MSE) loss function is used to measure the deviation between the parameter prediction value output by the model and the actual optimal value. By minimizing this loss, the model can continuously adjust the parameter prediction results during training to gradually approach the optimal sensor design. The calculation formula of the mean square error MSE is as follows:

[0107]

[0108] yi is the true value, is the predicted value and n is the number of samples.

[0109] At the same time, the mean absolute error (MAE) and R 2 The coefficient of determination further optimizes the model performance.

[0110] The calculation formula for the mean absolute error MAE is:

[0111]

[0112] yi is the true value, is the predicted value and n is the number of samples.

[0113] R 2 The formula for calculating the coefficient of determination is:

[0114]

[0115] Where yi is the true value, is the mean, and n is the sample size.

[0116] R 2 It is used to measure the proportion of variance explained by the model and indicates the degree of fit of the model. 2 The closer it is to 1, the better the model fit is.

[0117] At the same time, during the entire training process, we apply batch normalization operations after each convolutional layer or fully connected layer to ensure that the output value distribution of each layer is stable during the training process, so as to normalize the activation value and reduce the internal covariance shift, thereby improving the training speed and stability of the model. The formula for batch normalization is:

[0118]

[0119] Where E[x] and Var[x] are the batch mean and variance, respectively. ε is a decimal to prevent the denominator from being zero. After normalization, it ensures that the model learning ability is reliable. yi is the true value. is the predicted value.

[0120] In order to prevent overfitting, we use exponential decay to dynamically adjust the learning rate mechanism. When the validation set loss of the model no longer decreases significantly, we stop training to prevent overtraining.

[0121] α t =α0·e -λt

[0122] Where α0 is the initial learning rate, λ is the decay rate, and t is the number of training steps.

[0123] The model performance is evaluated using 10-fold cross validation. Through multiple feedback trainings, the model can automatically calibrate the coupling effect of metal film thickness and incident angle to ensure the highest sensitivity under the detection of each object to be tested. The process is as follows:

[0124]

[0125] In the formula, MSE i It represents the mean square error of the i-th fold, and finally the average value of 10 folds is taken to obtain the stability and generalization ability of the model.

[0126] The present invention has the following advantages over the prior art:

[0127] (1) The problem of the prior art that the interaction between the test substance and the sensor surface cannot be precisely controlled is overcome. The present invention enhances the binding force between the test molecule and the sensor surface by physically and chemically modifying the test substance, designing a specific bio-based membrane, and introducing functional groups and physical and chemical modifications. According to the reaction rate and molecular size of different test substances, the optimal biomembrane is designed for the test substance, so that the sensor can achieve rapid response and stable detection results in a shorter time. Through precise control of the membrane layer, the present invention ensures that the sensor can maintain high accuracy under changing environmental conditions.

[0128] (2) The present invention innovatively applies DCNN to the design and optimization of SPR sensors, and takes the relevant physicochemical properties of the substance to be tested and the sensor structural parameters as input features, which are passed to the DCNN model for learning. DCNN is used to further learn the dependencies between the various design parameters of the sensor. Each design parameter is regarded as a node in the graph, and the edges between the nodes represent their interactions. The model can automatically identify and fuse the relationship between different parameters, so as to find the optimal parameter combination. At the same time, an adaptive attention mechanism is introduced, and the features of the convolution and graph convolution outputs are weighted through the global pooling layer to automatically adjust the influence of different features. Finally, DCNN outputs the optimal SPR sensor parameters through the linear activation function of the output layer. Through these steps, the present invention can automatically optimize the structural design of the sensor in real time according to the changes in the substance to be tested and the design requirements of the sensor, and improve the detection sensitivity and accuracy of the SPR sensor to specific substances. BRIEF DESCRIPTION OF THE DRAWINGS

[0129] Figure 1 It is a flowchart of the steps for establishing the design method of SPR grating type sensor based on FPCL-DCNN;

[0130] Figure 2 It is a schematic diagram of the structure of DCNN multimodal convolutional neural network;

[0131] Figure 3 It is the algorithm flow chart of DCNN multimodal convolutional neural network;

[0132] Figure 4 It is the result of designing the experimental data using the present invention. DETAILED DESCRIPTION

[0133] The present invention is further described in detail below through implementation cases.

[0134] The data set used in this implementation case has a total of 800 groups of samples, including 160 groups of biomedical molecules, agricultural chemical chiral molecules, environmental monitoring pollutant molecules, food safety antiseptic molecules, and pharmacological toxicity molecules. A random sampling method was used to extract 120 groups of samples from each of the five groups of data as training sets, and the remaining 40 groups were used as test sets. In the end, the total number of samples used for training was 600, and the total number of samples used for testing was 200.

[0135] The overall process of the SPR grating sensor design method based on FPCL-CNN provided by the present invention is as follows: Figure 1 As shown, the specific steps are as follows:

[0136] (1) Modify the active group B of the target molecule X on the surface of the biofilm in terms of chemical reactivity:

[0137] Modify the molecules to be tested by FPCL (Functionalized Physical Chemical Layer).

[0138] First, determine the binding rate α between the molecule to be tested X and the active group B on the surface of the basement membrane:

[0139]

[0140] Where X0 is the initial concentration of the molecule X to be tested, B0 is the initial concentration of the active group B on the surface of the biofilm, k is the chemical reaction equilibrium constant, and t is the reaction time.

[0141] These parameters can be obtained through experimental measurement or known conditions. We select any set of data from each category to show the whole process. The specific experimental values ​​are as follows:

[0142] Biomedical molecule group: X0 = 0.5 mol / L, B0 = 0.3 mol / l, k = 0.2 s -1 , when t = 5s, the binding rate α = 1-e -0.2*0.5*5 =0.393.

[0143] Agricultural chemical chiral molecule group: X0 = 0.3 mol / L, B0 = 0.2 mol / l, k = 0.15s -1 , when t = 5s, the binding rate α = 1-e -0.3*0.15*5 =0.293.

[0144] Environmental monitoring pollutant molecule group: X0 = 0.4 mol / L, B0 = 0.25 mol / l, k = 0.18 s -1 , when t = 5s, the binding rate α = 1-e -0.4*0.18*5 =0.325.

[0145] Food safety and antiseptic molecular group: X0 = 0.2 mol / L, B0 = 0.15 mol / l, k = 0.12 s -1 , when t = 5s, the binding rate α = 1-e -0.2*0.12*5 =0.113.

[0146] Pharmacological toxicity molecule group: X0 = 0.6 mol / L, B0 = 0.35 mol / l, k = 0.22 s -1 , when t = 5s, the binding rate α = 1-e -0.6*0.22*5 =0.451.

[0147] Then determine the concentration X of the molecule X that is modified and bound to the surface active group B of the basement membrane. bound

[0148] According to the formula:

[0149]

[0150] Substituting the above parameters into the equation:

[0151] Biomedical Molecules Group: X bound =0.5(1-e -0.2*0.5*5 )=0.197mol / L

[0152] Agricultural chemical chiral molecule group: X bound =0.3(1-e -0.3*0.15*5 )=0.088mol /

[0153] Environmental monitoring pollutant molecule group: X bound =0.4(1-e -0.4*0.18*5 )=0.130mol / L

[0154] Food safety preservative molecule group: X bound =0.2(1-e -0.12*0.2*5 )=0.023mol / L

[0155] Pharmacological toxicity molecule group: X bound =0.6(1-e -0.22*0.6*5 )=0.271mol / L

[0156] Finally, the residual concentration B of the modified surface active group B of the basement membrane is determined. remain

[0157] According to the formula:

[0158]

[0159] Substituting the parameters, we get:

[0160] Biomedical Molecules Group: B remain =0.3e -0.2*0.5*5 =0.110mol / L

[0161] Agricultural chemical chiral molecules group: B remain =0.2e -0.3*0.15*5 =0.112mol / L

[0162] Environmental monitoring pollutant molecule group: B remain =0.25e -0.4*0.18*5 =0.120mol / L

[0163] Food safety preservative molecule group: B remain =0.15e -0.12*0.2*5 =0.136mol / L

[0164] Pharmacological toxicity molecule group: B remain=0.35e -0.22*0.6*5 =0.104mol / L

[0165] (2) Introducing the Langmuir physical adsorption model:

[0166] According to the experimental conditions, the total number of physical adsorption sites of the molecule X to be tested on the surface of the base film is N=100, the number of sites occupied by the molecule X is n, the adsorption equilibrium constant is K=0.3, and the partial pressure of the molecule X is p=0.4atm.

[0167] According to the Langmuir adsorption isotherm, the surface coverage θ is calculated.

[0168]

[0169] The amount of adsorbed molecule X (expressed as the amount of substance or number of molecules) n is:

[0170]

[0171] Substituting into the formula, we can get the adsorption amount of each group of molecules:

[0172] The adsorption equilibrium constant K can be expressed as:

[0173]

[0174] Through chemical reaction analysis, we can know Q, and then substitute it into the formula to get:

[0175] The Biomedical Molecules Group is:

[0176] Agricultural chemical chiral molecules group:

[0177] Environmental monitoring pollutant molecular group:

[0178] Food safety preservative molecular group:

[0179] Pharmacological toxicity molecule group:

[0180] After chemical and physical modification, the residual concentration of the molecule X in the medium channel is X remain The dynamic expression that changes with time is:

[0181]

[0182] The Biomedical Molecules Group is:

[0183]

[0184] Agricultural chemical chiral molecules group:

[0185]

[0186] Environmental monitoring pollutant molecular group:

[0187]

[0188] Food safety antiseptic molecular group:

[0189]

[0190] Pharmacological toxicity molecule group:

[0191]

[0192] (3) Determine the component Y of the biofilm that reacts with the molecule to be tested X:

[0193] First calculate the functional group reaction matching degree F:

[0194]

[0195] In the formula, K FG is the functional group reaction equilibrium constant, and C1 is the normalization constant that makes the value of F between 0 and 1.

[0196] Then determine the concentration of functional groups on the surface of the biofilm FG 基膜 :

[0197] The surface of the biofilm contains n FG =8×10 8 specific functional groups, the surface area of ​​the basement membrane is A = 10 -3 m 2 ,but

[0198] Then estimate the concentration FG of the reactive functional groups in the substance X to be tested X :

[0199] Biomedical molecule group: The molar mass of the biomedical molecule to be tested is M = 100 g / mol, and each molecule contains m FG = 6 reactive functional groups, the concentration in the solution is C X =0.6mol / L, then FG X =0.6*6=3.6mol / L=2.1672×10 24 Pieces / L.

[0200] Agricultural chemical chiral molecule group: The molar mass of the biomedical molecule to be tested is M = 150 g / mol, and each molecule contains m FG= 4 reactive functional groups, the concentration in the solution is C X =0.5mol / L, then FG X =0.5*4=2mol / L=1.204×10 24 Pieces / L.

[0201] Environmental monitoring pollutant molecule group: The molar mass of the environmental monitoring pollutant molecules to be tested is M = 120g / mol, and each molecule contains m FG = 5 reactive functional groups, the concentration in the solution is C X =0.55mol / L, then FG X =0.55*5=2.75mol / L=1.6555×10 24 Pieces / L.

[0202] Food safety and antiseptic molecule group: The molar mass of the food safety and antiseptic molecule to be tested is M = 80g / mol, and each molecule contains m FG = 3 reactive functional groups, the concentration in the solution is C X =0.45mol / L, then FG X =0.45*3=1.35mol / L=2.9488×10 24 Pieces / L.

[0203] Pharmacological toxicity molecule group: The molar mass of the pharmacological toxicity molecule to be tested is M = 180 g / mol, and each molecule contains m FG =7 reactive functional groups, the concentration in the solution is C X =0.7mol / L, then FG X =0.7*7=4.9mol / L=2.9498×10 24 Pieces / L.

[0204] Calculate the functional group reaction matching degree F:

[0205] Known functional group reaction equilibrium constant K FG =1.2×10 5 , normalization constant C1=1.5×10 25 , then according to the formula:

[0206] Agricultural chemical chiral molecules group:

[0207]

[0208] Agricultural chemical chiral molecules group:

[0209]

[0210] Environmental monitoring pollutant molecular group:

[0211]

[0212] Food safety preservative molecular group:

[0213]

[0214] Pharmacological toxicity molecule group:

[0215]

[0216] Then calculate the physical and chemical reaction matching degree P:

[0217] First determine the physical adsorption free energy ΔG ads :

[0218] At different temperatures, the relationship between the adsorption amount of the test substance on the surface of the biofilm and the partial pressure or concentration is measured, and the Langmuir adsorption isotherm is determined. At different temperatures, the adsorption heat is calculated by the deformation of the Clausius-Clapeyron equation, and the adsorption free energy is calculated by combining the thermodynamic formula to determine the physical adsorption free energy ΔG. ads as follows:

[0219] Chiral Molecules in Agricultural Chemistry: ΔG ads =-19.5 kJ / mol

[0220] Chiral Molecules in Agricultural Chemistry: ΔG ads =-19 kJ / mol

[0221] Environmental monitoring pollutant molecular group: ΔG ads =-19.2 kJ / mol

[0222] Food safety and antiseptic molecular group: ΔG ads =-19.8 kJ / mol

[0223] Pharmacological toxicity molecule group: ΔG ads =-19.6 kJ / mol

[0224] Next, calculate the physical and chemical reaction matching degree P according to the formula:

[0225] Known k P =0.5, ΔG0 = -20 kJ / mol, according to the formula, we can get

[0226] Agricultural chemical chiral molecules group:

[0227]

[0228] Agricultural chemical chiral molecules group:

[0229]

[0230] Environmental monitoring pollutant molecular group:

[0231]

[0232] Food safety antiseptic molecular group:

[0233]

[0234] Pharmacological toxicity molecule group:

[0235]

[0236] Then calculate the similarity and compatibility matching degree L:

[0237] Known δ max =10, polarity of bio-based membrane δ 基膜 =5, according to the public calculation, we can get:

[0238] Agricultural chemical chiral molecules group:

[0239] δ X =4.5, Agricultural chemical chiral molecules group:

[0240] δ X =4.8, Environmental monitoring pollutant molecular group:

[0241] δ X =4.6, Food safety antiseptic molecular group:

[0242] δ X =4.2, Pharmacological toxicity molecule group:

[0243] δ X =4.4, Finally, the comprehensive applicability parameter S of the bio-based membrane is calculated and determined:

[0244] It is known that ω1=0.4, ω2=0.3, ω3=0.3, and the following formula can be used to calculate:

[0245] Agricultural chemical chiral molecules group:

[0246] S = 0.4 × 0.92 + 0.3 × 0.91 + 0.3 × 0.95 = 0.923 Agricultural chemical chiral molecule group:

[0247] S = 0.4 × 0.85 + 0.3 × 0.88 + 0.3 × 0.98 = 0.898 Environmental monitoring pollutant molecular group:

[0248] S = 0.4 × 0.90 + 0.3 × 0.90 + 0.3 × 0.96 = 0.923 Food safety and antiseptic molecular group:

[0249] S=0.4×0.88+0.3×0.95+0.3×0.92=0.913

[0250] Pharmacological toxicity molecule group:

[0251] S=0.4×0.95+0.3×0.93+0.3×0.94=0.941

[0252] (4) Define initial model parameters:

[0253] Biofilm thickness d b =10nm;

[0254] Gold film is selected as the material of the metal film, and its thickness d m =50nm;

[0255] Grating teeth number N g =500, concave-convex spacing

[0256] The incident light source has a wavelength of λ=600nm and an incident angle of θ=45°.

[0257] (5) Construct DCNN multimodal convolutional neural network optimization model:

[0258] First, design a multi-channel convolutional denoising feature extraction layer:

[0259] The input feature vector X is designed to be [x1, x2, x3, x4, x5, x6, x7], where x1 represents the biofilm thickness, x2 represents the metal material, x3 represents the metal film thickness, x4 represents the number of grating teeth, x5 represents the grating concave-convex spacing, x6 represents the light source wavelength, and x7 represents the incident angle. The convolution kernel size K = 3, and the convolution kernel weight can be expressed as a matrix is a 3×3×7 tensor, the activation function is Relu, and the bias term b ( l ) is a vector of length 3. The specific convolution calculation formula is as follows:

[0260]

[0261] Then construct a multimodal parameter space-parameter association graph convolutional network (DCNN):

[0262] Construct a parameter graph, define each input parameter (biofilm thickness, metal film material, metal film thickness, number of grating teeth, concave-convex spacing, incident angle, incident light wavelength) as a node in the graph, and the edge weights between different nodes represent the strength of the association between the parameters. The graph convolutional network calculates by assigning weights to the relationship between nodes to achieve the association modeling of sensor parameters, so that the model can learn the importance of each node in the overall feature. The calculation formula of DCNN is as follows:

[0263]

[0264] In the formula, is the adjacency matrix with self-connection added, yes The degree matrix, H ( l ) represents the feature representation of the l-th layer node, W ( l ) is the learnable weight matrix, σ is the activation function, .

[0265] The weights are adjusted adaptively, and the adaptive attention mechanism is used to assign weights to the edges between different parameter nodes to identify which parameter combinations are most sensitive to SPR detection. The weights will change dynamically, allowing the model to select the appropriate parameter combination under different test conditions. Then, feature conversion and convolution operations are performed to convert the features of each node into high-level embedded features through a shared convolution kernel, and cross-node convolution operations are performed on this basis.

[0266] Finally, the attention fusion mechanism - multi-layer feature fusion is performed:

[0267] The local attention mechanism is introduced. First, the multi-channel feature maps extracted by convolution are pooled to obtain global statistical information for each channel. The fully connected layer is used to compress these statistical information into weight coefficients, and then the contribution of different channels is recalibrated by attention weights. This step allows the output features of the convolution layer to be prioritized before parameter fusion, which helps the model focus on important parameters more effectively. The attention mechanism generates channel weight coefficients through global pooling and fully connected layers. The formula is as follows:

[0268]

[0269] In the formula, α c is the channel weight coefficient, W is the fully connected layer weight matrix, pool is the global pooling operation, and y (l) is the convolution output of layer l.

[0270] Construct a global attention mechanism. Usually, the feature information output by different convolutional layers has different levels. The deeper the layer, the more abstract the feature representation. When fusing multiple layers, introduce a global attention mechanism, use pooling and weighting to fuse the multi-layer DCNN and convolutional layer features to obtain a multi-dimensional feature representation, while suppressing noise or unimportant information. This ensures that before the final output, the model's contribution to each feature layer can be adaptively optimized. The formula is as follows:

[0271] Z=α1H (1) +α2H (3) +α3H (3)

[0272] (6) Loss function and output layer design:

[0273] In order to obtain the numerical results of the optimal design parameters, the output layer of the model can be designed as a linear activation layer to output the optimal value of each parameter. The linear combination formula of the output is:

[0274]

[0275] Where W out and b out The matrices are 10×7 and 1×7 respectively; Z is the feature representation after multi-layer fusion.

[0276] At the same time, the MSE loss function is used to measure the deviation between the parameter prediction value output by the model and the actual optimal value. By minimizing this loss, the model can continuously adjust the parameter prediction results during training to gradually approach the optimal sensor design. The calculation formula of the mean square error MSE is as follows:

[0277]

[0278] MSE is used to calculate the true value yi and the predicted value The smaller the square error, the smaller the loss and the better the prediction result.

[0279] At the same time, the mean absolute error MAE and R 2 The coefficient of determination further optimizes the model performance.

[0280] The calculation formula for the mean absolute error MAE is:

[0281]

[0282] R 2 The formula for calculating the coefficient of determination is:

[0283]

[0284] At the same time, during the entire training process, we apply batch normalization operations after each convolutional layer or fully connected layer to ensure that the output value distribution of each layer is stable during the training process, so as to normalize the activation value and reduce the internal covariance shift, thereby improving the training speed and stability of the model. The formula for batch normalization is:

[0285]

[0286] Where E[x] and Var[x] are the batch mean and variance, respectively, and ε is a decimal to prevent the denominator from being zero. After normalization, it ensures that the model learning ability is reliable.

[0287] In order to prevent overfitting, we use exponential decay to dynamically adjust the learning rate mechanism. When the validation set loss of the model no longer decreases significantly, we stop training to prevent overtraining.

[0288] α t =0.01·e -0.0005t

[0289] The model performance is evaluated using 10-fold cross validation. Through multiple feedback trainings, the model can automatically calibrate the coupling effect of metal film thickness and incident angle to ensure the highest sensitivity under the detection of each object to be tested. The process is as follows:

[0290]

[0291] In the formula, MSE i It represents the mean square error of the i-th fold, and finally the average value of 10 folds is taken to obtain the stability and generalization ability of the model.

[0292] The trained DCNN neural network is tested using test set samples to implement the Kretschmann grating SPR sensor design and obtain the sensor structure design for each designed substance.

[0293] In order to verify the accuracy of the Kretschmann grating SPR sensor design of the present invention, the Kretschmann grating SPR sensor design of the present invention was carried out on 5 groups of test molecules. The experimental results are as follows Figure 4 As shown. Figure 4 It can be seen that the Kretschmann grating type SPR sensor design method established by the present invention maintains an accuracy rate of more than 98% for the unknown molecule sensor structure design, and can achieve a high accuracy rate on the basis of ensuring stability, with good performance. This shows that the Kretschmann grating type SPR sensor design method established by the present invention is effective, provides a better method for the detection of unknown molecules, and has certain practicality.

Claims

1. A design method of SPR grating type sensor based on FPCL-DCNN, characterized by: (1) Modify the active groups of the target molecule on the surface of the biofilm in terms of chemical reaction; (2) Introduce the Langmuir physical adsorption model; (3) Determine the components of the biofilm that react with the target molecule; (4) Define the initial model parameters; (5) Construct a DCNN multimodal convolutional neural network optimization model; (6) Design the loss function and output layer; Specifically, it includes the following 6 steps: Step 1: chemically modifying the active group X of the molecule X on the surface of the biofilm; Since the biochemical and optical properties of the molecule X to be tested are unknown, and the plasma resonance reaction of the SPR sensor is related to the refractive index of the medium, and in order to accelerate the change of the refractive index of the medium and amplify the SPR signal, we modify the molecule to be tested by FPCL (Functionalized Physical Chemical Layer). First, the active group B of the molecule to be tested on the surface of the bio-based membrane is modified in terms of chemical reaction: The binding rate α of the molecule to be tested X and the active group B on the basement membrane surface is: The concentration of the molecule X that binds to the surface active group B of the basement membrane after modification is X bound for: The residual concentration B of the active group B on the surface of the basement membrane after modification remain for: In the formula, X0 is the initial concentration of the molecule X to be tested, B0 is the initial concentration of the active group B on the surface of the biofilm, k is the chemical reaction equilibrium constant, and t represents time; Step 2: Introduce the Langmuir physical adsorption model: In order to enhance the adaptability to different types of molecules, improve the stability and density of molecular fixation, adjust the detection signal response time and intensity, and use the synergistic effect of physical adsorption and chemical modification to improve the detection selectivity according to the difference between target molecules and interfering molecules, the Langmuir physical adsorption model was then introduced; Assume that the total number of physical adsorption sites of molecule X on the surface of the base film is N, the number of sites occupied by molecule X is n, the adsorption equilibrium constant is K, and the partial pressure of molecule X is p; According to the Langmuir adsorption isotherm, the surface coverage θ (indicating the degree of adsorption of molecule X on the surface of the base film) is: The amount of adsorbed molecule X (expressed as the amount of substance or number of molecules) n is: The adsorption equilibrium constant K can be expressed as: Where Q is the concentration of the product generated by the reaction between the molecule to be tested X and the active group B on the surface of the biofilm, B0 is the initial concentration of the active group B on the surface of the biofilm, and X bound is the concentration of the molecule X after modification; After chemical and physical modification, the residual concentration of the molecule X in the medium channel is X remain The dynamic expression that changes with time is: Wherein, X0 is the initial concentration of the molecule X to be tested, B0 is the initial concentration of the active group B on the surface of the biofilm, k is the chemical reaction equilibrium constant, N is the total number of physical adsorption sites on the surface of the biofilm, Q is the concentration of the product generated by the reaction between the molecule X to be tested and the active group B on the surface of the biofilm, p is the partial pressure of the molecule X, and t represents the time; Step 3: Determine the component Y of the bio-based membrane that reacts with the molecule X to be tested; First, calculate the functional group reaction matching degree F: Determine the concentration of surface functional groups FG on the biofilm surface 基膜 : The density of specific functional groups on the surface of the biofilm was determined by the chemical analysis method X-ray Photoelectron Spectroscopy (XPS). FG specific functional groups, the surface area of ​​the base membrane is A, then Estimate the concentration of reactive functional groups in the substance to be tested FG X : For small molecules, their molecular structure can be determined by nuclear magnetic resonance (NMR) and other techniques, thereby clarifying the types and quantities of reactive functional groups. For macromolecules (such as proteins, polysaccharides, etc.), the average concentration of reactive functional groups can be estimated by combining amino acid sequence analysis (for proteins) or glycosyl composition analysis (for polysaccharides). Assume that the molar mass of the substance to be tested is M, and each molecule contains m FG The concentration of reactive functional groups in the solution is C X (mol / L), then FG X =C X ×m FG ; Finally, the functional group reaction matching degree F is calculated: In the formula, K FG is the functional group reaction equilibrium constant, C1 is the normalization constant, making the value of F between 0 and 1; Next, calculate the physical and chemical reaction matching degree P: At different temperatures, the relationship between the adsorption amount of the substance to be tested on the surface of the biofilm and the partial pressure or concentration is measured, and the Langmuir adsorption isotherm is determined. At different temperatures, the adsorption heat can be calculated by the deformation of the Clausius-Clapeyron equation, and the adsorption free energy ΔG can be determined by combining the thermodynamic formula to calculate the adsorption free energy. ads ; Next, calculate the physical and chemical reaction matching degree P according to the formula: Where kP is the slope of the curve, which can be obtained from the data, and ΔG0 is the median adsorption free energy. When the adsorption of the biofilm and the test substance is observed to be at a moderate level, ΔG ads =ΔG0; Then calculate the similarity and compatibility matching degree L: In the formula, δ 基膜 Indicates the polarity of the basement membrane, δ X represents the polarity of the substance X to be tested, |δ 基膜 -δ X | indicates the polarity difference between the two, δ max is the predefined maximum polarity difference; Finally, the comprehensive applicability parameter S of the bio-based membrane is calculated and determined: S = ω1f + ω2P + ω3L; In the formula, ω1, ω2, and ω3 correspond to the weight parameters of the functional group reaction matching degree F, the physicochemical reaction matching degree P, and the similarity and solubility matching degree L, respectively, which can be determined later by the deep neural network model; Step 4: Define initial model parameters; First, the biofilm thickness d is initialized. b : Biofilm thickness d b Directly affects the interaction between the molecule to be detected X and the sensor surface. When the surface coverage is θ and the amount of the molecule to be detected X adsorbed per unit area is n, the thickness of the biofilm d b It can be defined by the following relationship: Among them, p b is the density of the biofilm, V X is the effective volume after the attachment of the molecule X to be measured; Next, initialize the material and thickness d of the metal film m : SPR sensors usually use gold or silver as the metal layer material. The refractive index and dielectric constant of different materials will affect the sensitivity of the sensor. The following table shows some common metal refractive index and absorption coefficient data: The thickness of the metal film affects the sensitivity and peak position of the SPR signal. The optimal metal film thickness can be analyzed using the reflectivity formula: Under the structure of the substance to be tested - bio-based film - metal film, the reflectivity R is calculated using the Abélès matrix method. This method represents the optical properties of each layer with a matrix, and then multiplies them layer by layer to obtain the reflectivity of the entire structure: The feature matrix of each layer j can be written as: In the formula, is the phase delay of light at layer j, n j is the refractive index of the jth layer, d j is the thickness, θ j is the angle, q j =n j cos(θ j ) for S-polarized light, or For P-polarized light, i represents an imaginary unit; The total transmission matrix M can be expressed as: On this basis, the reflectivity R can be expressed as: Then, initialize and define the grating parameters (number of teeth N g and concave-convex spacing Λ); The structural parameters of the grating affect the light coupling efficiency and can be described by the grating diffraction equation: mλ=Λsin(θ)+sin(θ m ); Where m is the diffraction order, λ is the wavelength of the light source, θ and θ m The incident and diffraction angles are adjusted to adjust the number of grating teeth N. g and the concave-convex spacing Λ to achieve the best coupling angle and sensitivity; Number of teeth N g is the number of grooves in a certain length of the grating, which is inversely proportional to the concave-convex spacing Λ and can be expressed as: Achieve a specific emission angle θ at a specific wavelength λ m , the grating equation can be satisfied by adjusting the concave-convex spacing Λ: Adjust the number of grating teeth N g and the concave-convex spacing Λ, the best coupling angle and sensitivity can be achieved; Finally, the incident light source wavelength λ and incident angle θ are initialized and defined; The wavelength λ of the incident light source and the incident angle θ have a great influence on the position of the SPR resonance peak. When light enters a low refractive index medium from a high refractive index medium, the critical angle θ at which total reflection occurs is c Defined as: Where n1 and n2 are the refractive indices of the incident medium and the metal layer respectively; Step 5: Construct a Diverse Convolutional Neural Network (DCNN) optimization model; First, design a multi-channel convolutional denoising feature extraction layer: Convolutional Denoising Autoencoders (CDAE) are designed. First, convolution operations are applied to input features (such as biofilm thickness, metal film material, metal film thickness, number of grating teeth, concave-convex spacing, incident angle, and incident light wavelength) to map the features to multiple channels to extract features at different levels. The encoder can reduce the impact of environmental noise or data errors through denoising self-supervised learning, making the encoded features more robust during reconstruction. Then, multi-channel convolution is performed, treating each input parameter as an independent channel; the feature dimension is gradually increased through multiple layers of 1D convolution, and combined with the noise reduction layer, the encoding features of the convolution output are more expressive in the high-dimensional space, which facilitates the subsequent attention mechanism to capture the importance of different parameters. The specific convolution calculation formula is as follows: In the formula, y (l) is the convolution output of layer 1, is the convolution kernel weight, x i+k-1 represents the local area of ​​the input data, b (l) is the bias term, σ is the activation function; Next, a multimodal parameter space-parameter association graph convolutional network (Diverse Convolutional Neural Network, DCNN) is constructed; First, a parameter graph is constructed, and each input parameter (biofilm thickness, metal film material, metal film thickness, number of grating teeth, concave-convex spacing, incident angle, and incident light wavelength) is defined as a node in the graph. The edge weights between different nodes represent the strength of the association between the parameters. The graph convolutional network calculates by assigning weights to the relationships between nodes to achieve the association modeling of sensor parameters. In this way, the model can learn the importance of each node in the overall features. The calculation formula of DCNN is as follows: In the formula, is the adjacency matrix with self-connection added, yes The degree matrix, H (l) represents the feature representation of the first layer nodes, W (l) is a learnable weight matrix, σ is an activation function; An adaptive attention mechanism is used to assign weights to the edges between different parameter nodes, and the weights are adaptively adjusted to identify which parameter combinations are most sensitive to SPR detection. The weights will change dynamically, allowing the model to select the appropriate parameter combination under different test conditions. Feature conversion and convolution operations are then performed to convert the features of each node into high-level embedded features through shared convolution kernels, and cross-node convolution operations are performed on this basis. Then, the attention fusion mechanism - multi-layer feature fusion is completed; The local attention mechanism is introduced. First, the multi-channel feature maps extracted by convolution are pooled to obtain global statistical information of each channel. The fully connected layer is used to compress these statistical information into weight coefficients, and then the contribution of different channels is recalibrated by attention weights. This step allows the output features of the convolution layer to be prioritized before parameter fusion, which helps the model focus on important parameters more effectively. The attention mechanism generates channel weight coefficients through global pooling and fully connected layers. The formula is as follows: In the formula, α c is the channel weight coefficient, W is the fully connected layer weight matrix, and pool is the global pooling operation; Construct a global attention mechanism. Usually, the feature information output by different convolutional layers has different levels. The deeper the layer, the more abstract the feature representation. When multiple layers are fused, a global attention mechanism is introduced to fuse the multi-layer DCNN and convolutional layer features using pooling and weighting to obtain a multi-dimensional feature representation while suppressing noise or unimportant information. This ensures that before the final output, the contribution of the model to each feature layer can be adaptively optimized. The formula is as follows: In the formula, α l is the attention weight, which is used to adjust the contribution of different feature layers, H (l) is the feature representation of the / th layer; Step 6: Loss function and output layer design; In order to obtain the numerical results of the optimal design parameters, the output layer of the model can be designed as a linear activation layer to output the optimal value of each parameter; the linear combination formula of the output is: Where W out and b out are the weight matrix and bias of the output layer respectively; Z is the feature representation after multi-layer fusion; At the same time, the mean square error (MSE) loss function is used to measure the deviation between the parameter prediction value output by the model and the actual optimal value. By minimizing this loss, the model can continuously adjust the parameter prediction results during training to gradually approach the optimal sensor design. The calculation formula of the mean square error MSE is as follows: yi is the true value, is the predicted value, n is the number of samples; At the same time, the mean absolute error (MAE) and R 2 The coefficient of determination further optimizes the model performance; The calculation formula for the mean absolute error MAE is: yi is the true value, is the predicted value, n is the number of samples; R 2 The formula for calculating the coefficient of determination is: Where yi is the true value, is the mean value, n is the sample size; R 2 It is used to measure the proportion of variance explained by the model and indicate the degree of fit of the model. 2 The closer it is to 1, the better the model fit is. At the same time, during the entire training process, we apply batch normalization after each convolutional layer or fully connected layer to ensure that the output value distribution of each layer is stable during the training process, so as to normalize the activation value and reduce the internal covariance shift, thereby improving the training speed and stability of the model; the formula for batch normalization is: Where E[x] and Var[x] are the batch mean and variance respectively, and ε is a decimal to prevent the denominator from being zero. After normalization, it ensures that the model learning ability is reliable; In order to prevent overfitting, we use an exponential decay mechanism to dynamically adjust the learning rate. When the validation set loss of the model no longer decreases significantly, we stop training to prevent overtraining. α t ＝α0·e -λt ； In the formula, α0 is the initial learning rate, λ is the decay rate, and t is the number of training steps; The model performance is evaluated using 10-fold cross validation. Through multiple feedback trainings, the model can automatically calibrate the coupling effect of metal film thickness and incident angle to ensure the highest sensitivity under the detection of each object to be tested. The process is as follows: In the formula, MSE i It represents the mean square error of the i-th fold, and finally the average value of 10 folds is taken to obtain the stability and generalization ability of the model.

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