A robot additive manufacturing molten pool state early warning method based on posterior predictive distribution

Abstract

The application discloses a kind of robot additive manufacturing molten pool state early warning method based on posterior predictive distribution, it is related to metal additive manufacturing technical field, its technical solution main point is: obtaining historical evolution vector and historical molten pool state vector;Extract the time-frequency disturbance feature of historical molten pool state vector;The historical evolution vector and time-frequency disturbance feature are input into probability prediction model, and the posterior predictive distribution of future molten pool state is obtained;K times sampling is carried out to the posterior probability distribution to obtain K prediction values, and the prediction mean and prediction variance are determined according to K prediction values;The deviation degree of prediction mean relative to normal mean is calculated, and the prediction uncertainty of prediction variance relative to normal standard deviation is calculated;According to the normal state interval of K prediction values and molten pool state variable, the out-of-bound label of K prediction values is determined, and the out-of-bound probability is determined according to the out-of-bound label;According to deviation degree, prediction uncertainty and out-of-bound probability, the abnormal risk result of future molten pool state is calculated.

Description

Technical Field

[0001] This invention relates to the field of metal additive manufacturing technology, and more specifically, to a method for early warning of the state of a molten pool in robotic additive manufacturing based on a posteriori prediction distribution. Background Technology

[0002] In metal additive manufacturing, materials undergo rapid melting, flow, solidification, and layer-by-layer deposition under the influence of a heat source. The molten pool is a localized high-temperature region formed by the interaction between the heat source and the material. Its width, length, area, brightness, temperature, boundary fluctuations, and continuity reflect heat input, material supply, scanning path, local heat accumulation, and forming stability. If the molten pool state continuously deviates from the stable range, it may lead to problems such as porosity, lack of fusion, spheroidization, poor interlayer bonding, or decreased surface forming quality.

[0003] Existing methods for monitoring the state of the molten pool typically acquire images, temperature signals, light intensity signals, or acoustic signals of the molten pool using high-speed cameras, infrared thermal imagers, photoelectric sensors, or other online sensing devices. Then, based on the acquired data, geometric features, brightness features, temperature features, or fluctuation features of the molten pool are extracted, and the state of the molten pool is identified using threshold judgment, statistical analysis, machine learning models, or deep learning models. Some methods can also trigger alarms or adjust parameters in the current printing process based on the identification results. Existing solutions for molten pool image machine learning classification, real-time molten pool monitoring, molten pool size prediction, and molten pool uncertainty modeling indicate that online molten pool monitoring and intelligent identification have become important technological directions for additive manufacturing process control.

[0004] However, the existing methods mentioned above typically focus on identifying the current state of the molten pool or making deterministic predictions of its future state. For single-pass multi-layer printing, long-path scanning, or forming processes with significant heat accumulation, molten pool anomalies are often not instantaneous but rather evolve gradually from historical heat input, material supply fluctuations, scanning position changes, and localized heat accumulation. Existing methods mostly rely on identifying the current state or determining the predicted value based on a single state, failing to quantify the overall range of future molten pool state changes. This limits the application of molten pool monitoring results in real-time adjustments to process parameters such as printing speed, laser power, and powder feed rate. Summary of the Invention

[0005] The purpose of this invention is to provide a method for early warning of molten pool status in robotic additive manufacturing based on posterior predictive distribution. This method utilizes historical molten pool status, process parameters, and scanning position information to probabilistically predict the molten pool status at future moments, obtaining the corresponding posterior predictive distribution. Based on the deviation between the posterior predictive distribution and the normal state range, the prediction uncertainty, and the probability of the prediction result exceeding the limit, the abnormal risk level of the molten pool is comprehensively determined, and corresponding early warning information is output, thereby providing a reliable basis for adjusting process parameters and controlling quality in the additive manufacturing process.

[0006] The above-mentioned technical objective of the present invention is achieved through the following technical solution:

[0007] This invention provides a method for early warning of molten pool state in robotic additive manufacturing based on posterior predictive distribution. The method includes:

[0008] Obtain the historical evolution vector and historical molten pool state vector during the metal additive manufacturing process;

[0009] Extract the time-frequency perturbation features of the historical molten pool state vector;

[0010] The historical evolution vector and time-frequency perturbation features are input into the probabilistic prediction model. Multiple sets of model sample parameters are sampled from the posterior distribution of the model parameters of the probabilistic prediction model. Based on each set of model parameter samples, the posterior prediction distribution of the future molten pool state is obtained.

[0011] For any molten pool state variable, K samples are taken from the posterior prediction distribution of the future molten pool state to obtain K predicted values, and the predicted mean and predicted variance of any molten pool state variable are determined based on the K predicted values.

[0012] Calculate the deviation of the predicted mean of any molten pool state variable from the normal mean, and calculate the prediction uncertainty of the predicted variance of any molten pool state variable relative to the normal standard deviation.

[0013] Based on the normal state range of the K predicted values ​​and the molten pool state variables, determine the out-of-bounds labels of the K predicted values, and determine the out-of-bounds probability of the molten pool state variables based on the out-of-bounds labels.

[0014] Based on the deviation, prediction uncertainty, and out-of-bounds probability, calculate the abnormal risk results of the future molten pool state, and output early warning information of the molten pool state based on the abnormal risk results.

[0015] In one implementation scheme, the historical evolution vector of the metal additive manufacturing process is obtained, specifically: based on the current time t and the molten pool state parameters, process parameter parameters and scanning position parameters of the previous m-1 historical time points, a historical evolution vector for predicting the future state of the molten pool is constructed; wherein, the molten pool state parameters include molten pool width, molten pool area, molten pool brightness characteristics, molten pool temperature characteristics and molten pool boundary fluctuation characteristics;

[0016] To obtain the historical molten pool state vector in the metal additive manufacturing process, specifically: construct the historical molten pool state vector based on the current time t and the molten pool state parameters of the previous m-1 historical time points.

[0017] In one implementation, wavelet transform is used to extract the time-frequency perturbation features of the historical melt pool state vector.

[0018] In one implementation, the probability prediction model employs a Bayesian neural network model.

[0019] In one implementation scheme, the process of determining the normal mean and normal standard deviation of any molten pool state variable is as follows:

[0020] Obtain the normal state vector of any molten pool state variable during the stable printing process;

[0021] Calculate the normal mean of any molten pool state variable based on the normal state vector;

[0022] Calculate the normal standard deviation of any molten pool state variable based on the normal state vector and normal mean.

[0023] In one implementation, the step of calculating the deviation of the predicted mean of any melt pool state variable from the normal mean specifically involves: calculating the absolute value of the difference between the normal mean and the predicted mean, wherein the ratio of the absolute value of the difference to the normal mean is the deviation.

[0024] The calculation of the prediction uncertainty of the prediction variance relative to the normal standard deviation for any molten pool state variable is specifically as follows: the ratio of the prediction variance to the normal standard deviation is the prediction uncertainty.

[0025] In one implementation, the process of determining the normal state interval of the molten pool state variable is as follows: a preset interval coefficient is used, the difference between the normal mean and the product of the interval coefficient and the normal standard deviation is used as the minimum value of the normal state interval, and the sum of the products between the normal mean and the interval coefficient and the normal standard deviation is used as the maximum value of the normal state interval.

[0026] In one implementation scheme, the out-of-bounds labels of the K predicted values ​​are determined based on the normal state range of the K predicted values ​​and the state variables of the melt pool. Specifically, if the predicted value is within the normal state range, the out-of-bounds label of the predicted value is 0, otherwise the out-of-bounds label is 1.

[0027] In one implementation, the out-of-bounds probability of the melt pool state variable is determined based on the out-of-bounds label. Specifically, the out-of-bounds label of each predicted value is summed, and the ratio of the summation result to the number of predicted values ​​is used as the out-of-bounds probability.

[0028] In one implementation, the expression for calculating the abnormal risk result of the future molten pool state is:

[0029] ;in, This represents the abnormal risk outcome of the future molten pool state; N is the number of molten pool state variables. The importance weight of the j-th state variable; Weights for deviation; To predict the weights of uncertainty, Let be the deviation of the j-th molten pool state variable. Let the prediction uncertainty be the j-th molten pool state variable. Let be the out-of-bounds probability of the j-th molten pool state variable.

[0030] Compared with the prior art, the present invention has the following beneficial effects:

[0031] This invention utilizes historical molten pool states, process parameters, and scanning position information to probabilistically predict future molten pool states. Based on the degree of deviation of the predicted distribution from the normal state range, the prediction certainty, and the probability of exceeding the limit, it outputs abnormal risk results and provides early warning information accordingly, thereby providing a reliable reference for process adjustment and quality control in additive manufacturing. Attached Figure Description

[0032] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and form part of this application, do not constitute a limitation thereof. In the drawings:

[0033] Figure 1 A flowchart illustrating a method for early warning of molten pool status in robotic additive manufacturing based on posterior predictive distribution, provided in an embodiment of the present invention;

[0034] Figure 2 This is a schematic diagram of Abaqus additive manufacturing modeling and mesh generation provided in an embodiment of the present invention;

[0035] Figure 3a This is a schematic diagram of the Abaqus additive manufacturing process simulation-a provided for an embodiment of the present invention.

[0036] Figure 3b This is a schematic diagram of the Abaqus additive manufacturing process simulation-b provided for an embodiment of the present invention. Detailed Implementation

[0037] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0038] It should be noted that the terms "comprising" or "may include" used in the various embodiments of this application indicate the presence of the claimed function, operation, or element, and do not limit the addition of one or more functions, operations, or elements. Furthermore, as used in the various embodiments of this application, the terms "comprising," "having," and their cognates are intended only to indicate a specific feature, number, step, operation, element, component, or combination of the foregoing, and should not be construed as primarily excluding the presence of one or more other features, numbers, steps, operations, elements, components, or combinations of the foregoing, or adding one or more combinations of the foregoing.

[0039] It should be understood that terms such as "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0040] like Figure 1 As shown, this embodiment provides a method for early warning of molten pool state in robotic additive manufacturing based on posterior prediction distribution. The method includes:

[0041] S101, obtain the historical evolution vector and historical molten pool state vector in the metal additive manufacturing process.

[0042] Specifically, this embodiment uses Abaqus software (Abaqus is a commonly used finite element analysis software; its functions will not be described in detail in this embodiment) to establish the physical model of printing during the metal additive manufacturing process, and simultaneously tests the thermo-mechanical coupling model, such as... Figure 2 , Figure 3a and Figure 3b As shown, in the additive manufacturing process, each sampling time, each scanning segment, or each deposition layer is denoted as t. The molten pool state, process parameters, and spatial location information at the corresponding locations are synchronously acquired from the sensors and equipment control terminal. This embodiment performs feature extraction and state assessment on molten pool images acquired during the directional energy deposition process of 316L stainless steel, collecting data on the molten pool state, process parameter range, and scanning path of layer m at historical time points, as shown in Table 1:

[0043] Table 1

[0044]

[0045] Based on the current time t and the molten pool state parameters of the previous m-1 historical time points, these parameters are combined into a historical molten pool state vector: ;in, Indicates the width of the molten pool; Indicates the area of ​​the molten pool; Indicates the brightness characteristics of the molten pool; Indicates the temperature characteristics of the molten pool; This indicates the characteristics of molten pool boundary fluctuations.

[0046] Define the process parameter vector as follows: ,in, For heat source power, For scanning speed, This refers to the amount of powder fed or the speed of wire feeding.

[0047] The scan location information is as follows: ;in, For scan coordinates, This is the layer number or sedimentary layer index.

[0048] Combine the molten pool state, process parameters, and scanning position information into a joint state vector: Take the current time and the previous time. Construct a historical evolution vector from several historical points: Where m is the length of the history window. This represents historical evolution information used to predict future molten pool states.

[0049] S102, extract the time-frequency perturbation features of the historical molten pool state vector.

[0050] In this embodiment, to reflect the short-term fluctuations and low-frequency drift of the molten pool state, time-frequency feature extraction is performed on the molten pool state sequence within the historical window, and a time-frequency feature extraction operator is set. ,but ;in, This represents the time-frequency perturbation features extracted from the historical melt pool state sequence. Indicates from The historical melt pool state vector up to t.

[0051] Regarding time-frequency feature extraction operators, in one implementation, if continuous wavelet transform is used for time-frequency analysis, it can be expressed as: ,in, For scale parameters, For translation parameters, These are wavelet basis functions. These are wavelet coefficients. The wavelet coefficients can be used to obtain characteristics of the molten pool state, such as high-frequency disturbances, low-frequency drift, and energy distribution.

[0052] S103, input the historical evolution vector and time-frequency perturbation features into the probabilistic prediction model, sample multiple sets of model sample parameters from the posterior distribution of the model parameters of the probabilistic prediction model, and obtain the posterior prediction distribution of the future molten pool state based on each set of model parameter samples.

[0053] In this embodiment, the probabilistic prediction model employs a Bayesian neural network model. This invention uses a probabilistic prediction model to predict the future state of the molten pool. The input to the probabilistic prediction model is the historical evolution vector. and time-frequency perturbation characteristics The output is the posterior predicted distribution of the future molten pool state: ,in, represents the melt pool state vector at the next moment, the next scan segment, or the next deposition layer, and D represents the historical dataset used to train the probabilistic prediction model.

[0054] Unlike conventional deterministic prediction, this invention does not output only a single predicted value for the future molten pool state, but rather a probability distribution of the future states. This distribution can be used to obtain the prediction mean, prediction variance, and prediction interval. Let the parameters of the probabilistic prediction model be... Then the posterior prediction distribution of the future molten pool state can be expressed as: ,in, This represents the posterior distribution of the model parameters given the historical dataset D. Indicates that given model parameters The predicted distribution of the future state of the molten pool obtained under the given conditions.

[0055] In this embodiment, in actual calculations, the above posterior prediction distribution can be approximated by multiple samplings. Let K sets of model parameters be obtained by sampling from the posterior distribution of the model parameters: .

[0056] The posterior prediction distribution of the future molten pool state can then be approximated as:

[0057] Where k is the number of samples, These are the model parameters obtained from the k-th sampling. Therefore, after K samplings, we can obtain K predicted future molten pool states: .

[0058] S104. For any molten pool state variable, K samples are taken from the posterior prediction distribution of the future molten pool state to obtain K predicted values, and the predicted mean and predicted variance of any molten pool state variable are determined based on the K predicted values.

[0059] Based on the description of step S104 in the above embodiment, for the j-th molten pool state variable, the predicted value obtained from the k-th sampling is denoted as... Then the predicted mean of the future state of the molten pool variable is... , where K represents the total number of predicted values.

[0060] The prediction variance is Among them, the predicted mean This represents the expected trend of future changes in the state of the molten pool, and the prediction variance. This indicates the uncertainty of the probabilistic prediction model in predicting future states. For example, if the predicted mean is still close to the normal range, but the prediction variance increases significantly, it suggests that the future state of the molten pool may be unstable. Conversely, if the predicted mean has deviated from the normal range and the prediction variance is also large, it indicates a higher risk of future anomalies.

[0061] S105, calculate the deviation of the predicted mean of any molten pool state variable from the normal mean, and calculate the prediction uncertainty of the predicted variance of any molten pool state variable from the normal standard deviation.

[0062] In this embodiment, to determine whether the future state of the molten pool is abnormal, a normal state interval needs to be established. Based on historical normal data during the stable printing process, the normal mean and standard deviation of the j-th molten pool state variable are calculated. Specifically, firstly, the normal state vector of any molten pool state variable during the stable printing process is obtained; then, the normal mean of any molten pool state variable is calculated based on the normal state vector; finally, the normal standard deviation of any molten pool state variable is calculated based on the normal state vector and the normal mean.

[0063] Specifically, the normal average is .

[0064] Normal standard deviation is Where M is the number of samples in the normal state data. Let be the value of the j-th melt pool state variable in the i-th normal sample.

[0065] A preset interval coefficient is defined. The minimum value of the normal range is the difference between the normal mean and the product of the interval coefficient and the normal standard deviation. The maximum value of the normal range is the sum of the products of the normal mean and the interval coefficient. Therefore, the normal range is defined as follows: Where c is the interval coefficient, which can be set according to normal printing data, process experience or quality control requirements.

[0066] For ease of subsequent judgment, the normal state interval can also be written as: ,in, and They represent the first The minimum and maximum values ​​of the normal state of each molten pool state variable at future time points.

[0067] When there is significant interlayer heat accumulation or path difference during the printing process, the normal state range can be updated based on process parameters and scanning position: That is, the normal state range can dynamically change with the current process parameters, scanning position, and layer number.

[0068] Regarding deviation, the absolute value of the difference between the normal mean and the predicted mean is calculated, and the ratio of this absolute value to the normal mean is the deviation. That is, for the j-th state variable, the deviation of the predicted mean from the normal mean is defined as:

[0069] ,in, To prevent small constants with a denominator of zero.

[0070] The ratio of the predicted variance to the normal standard deviation represents the prediction uncertainty, i.e. ;in, Whether the predicted mean, reflecting the future state of the molten pool, deviates from the normal state. This reflects whether there is significant uncertainty in the forecast results.

[0071] S106. Based on the K predicted values ​​and the normal state range of the molten pool state variable, determine the out-of-bounds labels of the K predicted values, and determine the out-of-bounds probability of the molten pool state variable based on the out-of-bounds labels.

[0072] In this embodiment, to evaluate the probability that the future molten pool state falls outside the normal state range, the out-of-bounds labels of each predicted value are summed, and the ratio of the summation result to the number of predicted values ​​is taken as the out-of-bounds probability. Therefore, the first... The out-of-bounds probability of each molten pool state variable is: ;in, This is the out-of-bounds label for the k-th prediction sampling result.

[0073] The definition of the normal range is as follows: Wherein, when the predicted value of the j-th state variable obtained from the k-th prediction sampling is lower than the minimum value of the normal state or higher than the maximum value of the normal state, When it is within the normal range, By statistically analyzing the proportion of out-of-bounds samples in k prediction samplings, the probability of an out-of-bounds state in the future can be obtained.

[0074] S107: Calculate the abnormal risk results of the future molten pool state based on the deviation, prediction uncertainty and out-of-bounds probability, and output early warning information of the molten pool state based on the abnormal risk results.

[0075] In this embodiment, the expression for calculating the abnormal risk result of the future molten pool state, combining the deviation of the future molten pool state, the prediction uncertainty, and the probability of exceeding the limit, is as follows: ;in, This represents the abnormal risk outcome of the future molten pool state; N is the number of molten pool state variables. The importance weight of the j-th state variable; Weights for deviation; To predict the weights of uncertainty, Let be the deviation of the j-th molten pool state variable. Let the prediction uncertainty be the j-th molten pool state variable. Let be the out-of-bounds probability of the j-th molten pool state variable.

[0076] When the abnormal risk outcome meets: At that time, an early warning message is output. Among them, The risk threshold can be set based on normal printing data, historical alarm records, or human experience.

[0077] Warning information may include: ,in: For future abnormal risk outcomes; Risk level; The state variables of the molten pool that contribute the most to the risk.

[0078] The main contribution risk variable can be determined by the following formula: , among which, when When corresponding to the molten pool width, the risk of the future molten pool being too wide or too narrow can be output; when When corresponding to temperature or brightness, it can output the risk of future heat input being too high or too low; when When the boundary fluctuates, the risk of future instability at the molten pool boundary can be output.

[0079] In summary, the present invention integrates historical information and probability prediction distribution, so that the early warning output includes both trend prediction and credibility judgment, overcoming the shortcomings of the deterministic prediction and static threshold discrimination of the prior art.

[0080] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for early warning of molten pool state in robotic additive manufacturing based on posterior predictive distribution, characterized in that the method... include: Obtain the historical evolution vector and historical molten pool state vector during the metal additive manufacturing process; Extract the time-frequency perturbation features of the historical molten pool state vector; The historical evolution vector and time-frequency perturbation features are input into the probabilistic prediction model. Multiple sets of model sample parameters are sampled from the posterior distribution of the model parameters of the probabilistic prediction model. Based on each set of model parameter samples, the posterior prediction distribution of the future molten pool state is obtained. K samples are taken from the posterior prediction distribution of the future molten pool state to obtain K predicted values, and the predicted mean and predicted variance of any molten pool state variable are determined based on the K predicted values. Calculate the deviation of the predicted mean of any molten pool state variable from the normal mean, and calculate the prediction uncertainty of the predicted variance of any molten pool state variable relative to the normal standard deviation. Based on the normal state range of the K predicted values ​​and the molten pool state variables, determine the out-of-bounds labels of the K predicted values, and determine the out-of-bounds probability of the molten pool state variables based on the out-of-bounds labels. Based on the deviation, prediction uncertainty, and out-of-bounds probability, calculate the abnormal risk results of the future molten pool state, and output early warning information of the molten pool state based on the abnormal risk results.

2. The method according to claim 1, characterized in that, To obtain the historical evolution vector in the metal additive manufacturing process, specifically: based on the current time t and the molten pool state parameters, process parameter parameters, and scanning position parameters of the previous m-1 historical time points, a historical evolution vector for predicting the future state of the molten pool is constructed; among which, the molten pool state parameters include molten pool width, molten pool area, molten pool brightness characteristics, molten pool temperature characteristics, and molten pool boundary fluctuation characteristics. To obtain the historical molten pool state vector in the metal additive manufacturing process, specifically: construct the historical molten pool state vector based on the current time t and the molten pool state parameters of the previous m-1 historical time points.

3. The method according to claim 1, characterized in that, The wavelet transform method is used to extract the time-frequency perturbation features of the historical molten pool state vector.

4. The method according to claim 1, characterized in that, The probability prediction model uses a Bayesian neural network model.

5. The method according to claim 1, characterized in that, The process for determining the normal mean and normal standard deviation of any molten pool state variable is as follows: Obtain the normal state vector of any molten pool state variable during the stable printing process; Calculate the normal mean of any molten pool state variable based on the normal state vector; Calculate the normal standard deviation of any molten pool state variable based on the normal state vector and normal mean.

6. The method according to claim 5, characterized in that, The calculation of the deviation of the predicted mean of any molten pool state variable from the normal mean specifically involves: calculating the absolute value of the difference between the normal mean and the predicted mean, and the ratio of the absolute value of the difference to the normal mean is the deviation. The calculation of the prediction uncertainty of the prediction variance relative to the normal standard deviation for any molten pool state variable is specifically as follows: the ratio of the prediction variance to the normal standard deviation is the prediction uncertainty.

7. The method according to claim 5, characterized in that, The process of determining the normal state interval of the molten pool state variable is as follows: a preset interval coefficient is used, the difference between the normal mean and the product of the interval coefficient and the normal standard deviation is the minimum value of the normal state interval, and the sum of the products between the normal mean and the interval coefficient and the normal standard deviation is the maximum value of the normal state interval.

8. The method according to claim 1, characterized in that, Based on the normal state range of the K predicted values ​​and the state variables of the molten pool, the out-of-bounds labels of the K predicted values ​​are determined. Specifically, if the predicted value is within the normal state range, the out-of-bounds label of the predicted value is 0, otherwise the out-of-bounds label is 1.

9. The method according to claim 8, characterized in that, The out-of-bounds probability of the melt pool state variable is determined based on the out-of-bounds label. Specifically, the out-of-bounds label of each predicted value is summed, and the ratio of the summation result to the number of predicted values ​​is taken as the out-of-bounds probability.

10. The method according to claim 1, characterized in that, The expression for calculating the abnormal risk result of the future molten pool state is: ;in, This represents the abnormal risk outcome of the future molten pool state; N is the number of molten pool state variables; The importance weight of the j-th state variable; Weights for deviation; To predict the weights of uncertainty, Let be the deviation of the j-th molten pool state variable. Let the prediction uncertainty be the j-th molten pool state variable. Let be the out-of-bounds probability of the j-th molten pool state variable.

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