A method for evaluating the quality of laser cladding layers on hydraulic turbines

Abstract

The present application relates to the field of laser cladding quality assessment and discloses a method for assessing the quality of a turbine laser cladding layer, comprising the following steps: obtaining ultrasonic waveform data of the turbine laser cladding layer; and establishing a joint posterior probability distribution that simultaneously includes a residual stress field and a microscopic damage field within the cladding layer, wherein the joint posterior probability distribution associates the residual stress field and the microscopic damage field with the ultrasonic waveform data via a forward physical operator coupled with a nonlinear acoustoelastic model and a micromechanical model. By deeply coupling the residual stress field and the microscopic damage field at the physical model level to achieve simultaneous solution of the two, compared to the prior art solutions that separate stress and damage and evaluate them separately or ignore one of them, the present invention solves the problem of unclear and unreliable assessment results due to confusion of physical effects.

Description

Technical Field

[0001] The present invention relates to the field of laser cladding layer quality assessment, and in particular to a method for assessing the quality of a turbine laser cladding layer. Background Art

[0002] Water turbines are the core equipment for hydropower generation. Their flow-through components, such as runner blades, are subjected to long-term erosion and cavitation by high-speed, sand-laden water flows, and their surfaces are prone to damage. In order to extend their service life and repair damaged components, laser cladding technology has been widely used as an advanced surface remanufacturing method. This technology clads a layer of metal ceramic or alloy coating with high hardness and high wear resistance on the surface of the component to resist damage. Therefore, accurate and reliable non-destructive evaluation of the internal quality of the laser cladding layer is a key link in ensuring the safe, stable and long-term operation of the turbine. At present, the evaluation of the quality of the cladding layer mainly relies on various non-destructive testing technologies, among which ultrasonic testing has become the main means due to its strong penetrating ability and sensitivity to internal defects, and is often supplemented by X-ray diffraction methods for residual stress analysis, or metallographic analysis for microstructural characterization.

[0003] However, existing technologies still face inherent technical limitations when applied to complex quality assessments of turbine laser cladding. In the cladding layer, residual stresses generated by the rapid solidification process and the inevitable microscopic metallurgical defects (pores and microcracks) are two critical physical states that coexist and intertwine. Both of these conditions perturb the propagation of ultrasonic waves, causing changes in the acoustic signal characteristics, resulting in a physical coupling and confusion. Therefore, any method that attempts to measure one of these physical quantities independently will inevitably suffer interference from the other, obscuring the source of the assessment results. Summary of the Invention

[0004] In response to the shortcomings of the existing technology, the present invention provides a method for evaluating the quality of the laser cladding layer of a turbine, which solves the problem in the existing technology that the physical effects of residual stress and microdamage are coupled with each other and are difficult to be synchronously decoupled and independently evaluated, and the evaluation result is usually a single definite value and cannot quantify its own uncertainty.

[0005] To achieve the above objectives, the present invention is implemented through the following technical solutions: A method for evaluating the quality of a hydraulic turbine laser cladding layer, comprising the following steps:

[0006] Acquiring ultrasonic waveform data for the turbine's laser cladding layer is the physical information input for the entire evaluation system. The mechanism is that any physical inhomogeneities within the cladding layer, whether due to nonlinear material response caused by residual stress or acoustic impedance mismatch caused by microscopic damage, will disrupt the propagation path, velocity, and morphology of the ultrasonic waves traveling through it. By acquiring the complete time-domain waveform signal, rather than a single characteristic parameter, the rich details imprinted on the acoustic wave by these internal conditions are preserved to the greatest extent possible, providing the most pristine and complete physical evidence for subsequent analysis.

[0007] establishing a joint posterior probability distribution that includes both a residual stress field and a microscopic damage field within the cladding layer, wherein the joint posterior probability distribution associates the residual stress field and the microscopic damage field with the ultrasonic waveform data via a forward physics operator that couples a nonlinear acoustoelastic model and a micromechanical model;

[0008] First, the micromechanical model serves as a low-level module that transforms discrete, microscopic damage information (porosity) into its impact on the macroscopic equivalent elastic properties of the material. Its role is to define a virtual medium that becomes inhomogeneous due to damage.

[0009] Subsequently, the nonlinear acoustoelastic model, acting as an upper layer, superimposes the nonlinear effects of the residual stress field on the acoustic wave propagation velocity on this virtual medium. The coupling between these two models accurately simulates the physical reality of stress and damage coexisting and acting together on acoustic waves. Therefore, this forward physics operator forms a virtual simulation channel from "hypothesized internal state" to "predicted acoustic response," providing a physical criterion for measuring the degree of match between any set of hypothetical fields and real-world observational data.

[0010] A Markov chain Monte Carlo algorithm using gradient information is used to numerically sample the joint posterior probability distribution to obtain an ensemble of solutions for the residual stress field and the microscopic damage field;

[0011] Because the posterior probability distribution is extremely complex and resides in a high-dimensional space, it cannot be solved directly, so an intelligent exploration tool is needed. An algorithm that utilizes gradient information works differently from a blind random search. It can sense the "terrain slope" of the probability distribution in the parameter space, that is, the gradient. This enables the algorithm to efficiently move to areas with higher probabilities, greatly improving the efficiency and robustness of finding all high-probability solutions in high-dimensional space. The product of this process is not a single solution, but a solution ensemble consisting of thousands of valid solution samples. Each sample in this solution ensemble is a reasonable "snapshot" of the true state of the cladding layer. The entire set constitutes a discretized approximation of the posterior probability distribution, which serves as a bridge between abstract mathematical models and specific physical analysis.

[0012] Statistical analysis is performed on the solution ensemble to generate a probabilistic quality assessment result of the cladding layer including uncertainty quantification information.

[0013] By statistically refining this vast data set, the solution ensemble, the implicit information is transformed into understandable engineering conclusions. By calculating the average value of all samples, optimal estimates of the stress and damage fields can be obtained. More importantly, by analyzing the degree of dispersion or range of variation between samples, the uncertainty of the assessment results at each spatial location can be directly quantified. This uncertainty information is inherent to the method, rather than externally attached, and it directly reflects the reliability of the model inference given the current observed data. The resulting probabilistic assessment results integrate this optimal estimate with the uncertainty information, completing the complete information chain from the original acoustic signal to the final quantitative risk assessment.

[0014] Preferably, the step of obtaining ultrasonic waveform data of the turbine laser cladding layer includes:

[0015] An ultrasonic phased array probe is used to perform a full matrix capture scan on the area to be evaluated of the cladding layer to obtain a full matrix waveform data set.

[0016] The ultrasonic phased array probe is a key hardware component. Rather than a single vibrating element, it consists of multiple independently controllable piezoelectric elements within a single probe housing. Its operating mechanism is the ability to flexibly shape the acoustic field by precisely controlling the excitation and reception timing of each element. However, in this method, its more core role is as a high-throughput, multi-channel data acquisition front end.

[0017] Based on this, the Full Matrix Capture (FMC) scan performed is a specific data acquisition strategy. Its principle is to achieve complete information capture. The specific operation process is as follows: First, the system instructs the first array element in the probe to transmit an ultrasonic beam. Simultaneously, all array elements in the probe, including the transmitting array element, switch to receiving mode and synchronously record the complete waveform signal received and returned over time. Once this process is complete, the system automatically switches to the second array element as the transmitting source, and all array elements receive again. This process repeats until each array element has completed a transmission operation.

[0018] The underlying mechanism of this strategy lies in its systematic recording of all acoustic wave propagation paths between any two array elements in the probe. The resulting full-matrix waveform dataset is a massive collection of information, comprising N times N independent waveform signals (N being the total number of array elements). This dataset not only captures the signals of acoustic waves propagating along straight paths but, more importantly, fully captures the complex phenomena of scattering, diffraction, and mode conversion that occur when acoustic waves encounter residual stress regions or microscopic damage within the cladding layer. Through this exhaustive acquisition approach, acoustic waves along different paths "examine" the same internal features from different perspectives, resulting in extremely high information redundancy and complementarity at the data level. This rich information provides the essential data foundation for subsequent algorithms attempting to separate weak perturbations from two distinct physical sources: stress and damage. This dataset constitutes the single, complete experimental input for all subsequent physical modeling and statistical inference.

[0019] Preferably, before establishing the joint posterior probability distribution, the method further includes:

[0020] The residual stress field and the microscopic damage field are parameterized into finite-dimensional random variable vectors respectively by using the Karunan-Loey expansion method.

[0021] This step is necessary because a continuous physical field, with a numerical stress field at every point in the three-dimensional space of the cladding layer, is mathematically an infinite-dimensional object. Solving it directly on a computer would require processing an infinite number of unknowns, which is computationally infeasible.

[0022] The Karhunen-Loève (KL) expansion operates as an efficient dimensionality reduction. It decomposes a complex, continuously distributed field function into a linear combination of a set of predetermined, fixed spatial basis functions and a set of uncorrelated random variable coefficients to be solved. These spatial basis functions act like the building blocks of a physical field. They contain prior information about the spatial distribution characteristics of the field and can be constructed to efficiently represent fields that are smooth or have specific spatial correlations.

[0023] Specifically, this method transforms the stress and damage calculations that would normally require solving for tens to hundreds of random variables into a problem requiring only a few (tens to hundreds) of random variable coefficients. These random variable coefficients form a finite-dimensional vector, and the subsequent solution is performed entirely in this low-dimensional parameter space, rather than directly dealing with the high-dimensional physical field space.

[0024] This step is a crucial bridge between physical modeling and numerical computation. It significantly reduces the dimensionality of the problem while maintaining a sufficiently high-fidelity description of the original physical field. This parameterization process successfully transforms an infinite-dimensional functional inversion problem into a well-defined and computationally feasible finite-dimensional parameter estimation problem.

[0025] Preferably, the joint posterior probability distribution Determined by Bayes' theorem:

[0026] ;

[0027] in, is the random variable vector characterizing the residual stress field and the microscopic damage field, is the acquired ultrasonic waveform data, is the likelihood function derived from the forward physics operator, is the prior probability distribution of the random variable vector.

[0028] The ultimate goal within this framework is to obtain a "posterior probability distribution." This represents our final, most comprehensive understanding of the unknown internal state of the cladding layer (represented by a parameterized vector of random variables) after obtaining all experimental observations. It is not a single numerical solution, but rather a complete probabilistic blueprint that describes all possibilities and their corresponding confidence levels.

[0029] To construct this posterior probability distribution, two key input modules are required.

[0030] The first input module is the "likelihood function." Its mechanism is to serve as a bridge between the physical world and the abstract model. This function is derived from the complex forward physics operator established earlier. If a parameter combination can predict a waveform that closely matches the actual observation, then the corresponding likelihood function value is high, and vice versa. Therefore, the likelihood function is essentially a quantitative indicator of the "model-data" match based on the physical model.

[0031] The second input module is the "prior probability distribution." It acts as a knowledge container, mathematically incorporating all background information or physical constraints about unknown parameters known before experimental observations. Engineering experience tells us that residual stress fields typically vary smoothly, or that microdamage values cannot be negative. The prior probability distribution encodes this "common sense" or expert-level knowledge, acting as a "navigator" or "stabilizer" throughout the solution process, guiding the solution toward a more physically plausible direction and avoiding solutions that are meaningless or counterintuitive.

[0032] Ultimately, Bayes' theorem operates by logically multiplying these two modules. It uses the "initial belief graph" (prior distribution) representing prior knowledge to gradually modify and update the "match graph" (likelihood function) representing experimental evidence, ultimately generating a "final cognitive graph" (posterior distribution) that encompasses all information. This posterior distribution is the culmination of all available information—including physical laws, prior knowledge, and experimental data—and is the core mathematical object pursued by the entire evaluation method.

[0033] Preferably, the forward physics operator transforms the random variable vector As input, its internal operations include:

[0034] According to the reconstructing the residual stress field and the microscopic damage field;

[0035] Applying the micromechanical model, an equivalent elastic tensor is calculated based on the microscopic damage field;

[0036] The nonlinear acoustoelastic model is applied to calculate an acoustoelastic tensor according to the equivalent elastic tensor and the residual stress field, and ultrasonic waveform data is predicted based on the acoustoelastic tensor.

[0037] The first stage of the computation is "decoding and reconstruction." This involves transforming the input, low-dimensional, abstract parameter vector into a physically understandable, concrete physical field distributed across the entire three-dimensional computational domain. This process generates two independent fields: a residual stress tensor and a microscopic damage scalar. This step is the starting point of the entire simulation process, transforming a purely mathematical hypothesis into a complete, hypothetical physical state within the cladding layer.

[0038] The second stage of the operation is the "macro-environmentalization of damage effects." It receives the microscopic damage field generated in the first stage as input and applies a micromechanical model to it. The mechanism of this model is that it can calculate the combined effect of these microscopic defects on the macroscopic elastic properties of the material based on the local density and morphology of microscopic damage (pores or microcracks). The output of this module is a new, non-uniform equivalent elastic tensor. This tensor no longer describes an ideal, intact matrix material, but rather a virtual medium whose stiffness varies spatially due to internal damage. This module is the unit in the entire operator specifically responsible for simulating damage effects.

[0039] The third phase of the operation is "superposition of stress effects and final simulation." This phase is the core of the physical simulation, coupling the results of the first two phases. It receives two inputs: the equivalent elastic tensor calculated in the second phase, which already includes damage effects, and the residual stress field reconstructed in the first phase. Based on these inputs, a nonlinear acoustoelastic model is applied. This model describes the physical phenomenon of how the propagation velocity of acoustic waves is affected by the stress state. The stress field is superimposed on the material, which already accounts for damage, ultimately calculating a final acoustoelastic tensor that incorporates both stress and damage effects. This final tensor provides the most complete description of the physical properties of the virtual cladding layer under a specific hypothetical state. Based on these final properties, the operator then simulates the entire process of ultrasonic emission, propagation, and reception in a virtual environment that is identical to a real experiment, thereby predicting the final ultrasonic waveform data. This predicted data is the final output of the entire forward physics operator.

[0040] Preferably, the micromechanical model is the Mori-Tanaka model.

[0041] The Mori-Tanaka model was chosen because it provides an efficient and physically explicit way to estimate the macroscopic equivalent elastic properties of materials containing randomly distributed microscopic defects. This model considers the cladding layer as a composite material, where the intact metal matrix is considered the "matrix phase" and the internal microscopic pores or microcracks are considered the "inclusion phase."

[0042] The model's inner workings are based on mean-field theory. It first analyzes the perturbations in the stress and strain fields caused by a single inclusion (a micropore) in an infinitely large matrix. The essence of the Mori-Tanaka model then lies in its ingenious approximation to account for the interactions among numerous inclusions: it assumes that each individual inclusion exists not in isolation within a pure matrix, but rather in an equivalent medium that has been "pre-perturbed" by the average influence of all other inclusions.

[0043] Using this "mean field" concept, the model estimates the average stresses and strains experienced by the matrix and all inclusions when an external load is applied. Based on these mean field quantities, the model derives a macroscopic, homogenized equivalent elastic tensor that represents the entire region of material containing damage.

[0044] Therefore, the Mori-Tanaka model serves as a dedicated "translation module" in this approach. It receives a scalar field (porosity distribution map) from an upstream module describing the spatial distribution of microscopic damage and accurately "translates" it into an equivalent elastic tensor field, understandable by the downstream nonlinear acoustoelastic model, describing the material's macroscopic mechanical response. This translation process is a crucial link between microstructure and macroscopic physical properties, quantitatively answering the core question of "how much does a given degree of damage affect the material's acoustic stiffness?"

[0045] Preferably, the Markov Chain Monte Carlo algorithm using gradient information is a Hamiltonian Monte Carlo algorithm.

[0046] This algorithm was chosen because the posterior probability distributions it encounters typically exist in a highly dimensional and complex parameter space. Traditional random walk sampling algorithms are extremely inefficient in such spaces, like a blindfolded person randomly walking across a vast mountain range—they are easily lost on low-probability "plains" or trapped in a local "valley."

[0047] The Hamiltonian Monte Carlo (HMC) algorithm operates in a completely different way, offering a far more intelligent exploration strategy. It cleverly analogizes a purely mathematical sampling problem to a dynamical system defined in classical physics. In this imaginary physical system, the unknown parameter vector to be solved is treated as the "position" of a particle, and the "potential energy" of the particle's position is directly defined by the target's posterior probability distribution—regions of higher probability correspond to "valleys" of lower potential energy.

[0048] The algorithm's core innovation lies in its introduction of an auxiliary "momentum" variable for the particle. This momentum imparts inertia to the particle. Therefore, the algorithm's sampling process is no longer a random, directionless jump. Instead, it generates new sample proposals by simulating the particle's motion in a potential energy field. The algorithm first assigns the particle a random initial momentum (a random "thrust") and then allows the particle to glide along an energy-conserving trajectory for a predetermined period of time. Momentum enables the particle to move coherently over long distances, efficiently exploring the vast space of the probability distribution, particularly along narrow "valleys."

[0049] This exploration method based on physical dynamics enables the algorithm to use the gradient information of the probability distribution (i.e., the "slope of the terrain") to guide its movement direction, thereby finding and extracting samples of all high-probability areas in complex high-dimensional space with efficiency far exceeding traditional methods, providing solid computational support for ultimately obtaining reliable evaluation results.

[0050] Preferably, the gradient information of the joint posterior probability distribution required by the Hamiltonian Monte Carlo algorithm is calculated by establishing an adjoint state method solver for the forward physics operator.

[0051] The efficiency of the Hamiltonian Monte Carlo algorithm relies entirely on its ability to obtain the gradient of the target probability distribution at any point, that is, the "slope of the terrain." However, this gradient information is deeply hidden within the extremely complex forward physics operator that links the unknown parameters to the ultrasonic data. If conventional numerical methods (finite difference methods) are used to calculate the gradient, the mechanism is equivalent to measuring the slope of a mountain at a certain point. First, you need to stand at that point, then take a small step in all directions, east-west, north-south, and record each change in height. For a high-dimensional problem with hundreds or thousands of unknown parameters, this means that in order to obtain complete gradient information, you need to repeat the time-consuming forward physics simulation hundreds or even thousands of times, which is computationally infeasible.

[0052] The Adjoint-State Method provides an elegant solution that fundamentally addresses this problem with a completely different mechanism. Rather than repeatedly perturbing the input and observing the output, it directly calculates the gradient by analyzing the information flow within the system.

[0053] Its core mechanism works by solving a new "adjoint process" that is mathematically related to the original physical process (i.e., the forward process). This adjoint process can be understood as the reverse propagation of the causal chain in the original physical process. While the forward process simulates the information flow from "internal state" to "external observation," the adjoint process simulates a virtual information flow from "deviations in external observation" back to the "source of the internal state that caused the deviation."

[0054] Specifically, the method establishes a corresponding adjoint solver for the complex multiphysics forward operator. When a gradient needs to be calculated, the system first performs a forward simulation to obtain a predicted waveform and calculate the difference between it and the observed waveform. The adjoint solver then uses this difference as its "stimulus" and begins another adjoint simulation. The final output of this adjoint simulation provides the sensitivity of the final waveform difference to all initially unknown parameters simultaneously, i.e., the complete gradient vector.

[0055] The most critical advantage of this method is that the computational cost of performing an adjoint simulation is roughly equivalent to the cost of performing a forward simulation. This means that no matter how high the dimensionality of the unknown parameters is, this method can obtain complete gradient information at a computational cost of approximately two forward simulations. Therefore, this adjoint state method solver plays the role of an efficient "gradient engine" in this method. As a low-level core module serving the Hamiltonian Monte Carlo algorithm, it provides it with a continuous, cheap, and accurate gradient information, making it possible to perform robust Bayesian inference in extremely high-dimensional parameter spaces.

[0056] Preferably, the step of performing statistical analysis on the solution ensemble comprises:

[0057] reconstructing a plurality of residual stress field samples and microscopic damage field samples from the solution ensemble;

[0058] The posterior expectation field and the posterior variance field of the residual stress field and the microscopic damage field are calculated, wherein the posterior variance field is used to quantify the uncertainty.

[0059] The analysis process first involves reconstructing multiple residual stress field samples and microscopic damage field samples from the solution ensemble. The mechanism of this step lies in "decoding." The previous Monte Carlo algorithm explores and samples in a reduced, abstract parameter space. Its direct product (i.e., the solution ensemble) is a series of low-dimensional random variable vectors. These vectors themselves do not have intuitive physical meaning. Therefore, this reconstruction step acts as a decoding module, mapping each random variable vector sample back to its unique corresponding field function distributed in the full three-dimensional physical space through an inverse transformation (the Karunan-Loewe inverse expansion). After completion of this process, we obtain thousands of specific residual stress field "snapshots" and microscopic damage field "snapshots." Together, they constitute a complete probabilistic description of the true internal state of the cladding layer, providing the most direct physical input for subsequent statistical analysis.

[0060] After obtaining these field sample sets, the next step of the analysis is to calculate the posterior expectation field and the posterior variance field of the residual stress field and the microscopic damage field.

[0061] The calculation of the posterior expectation field is based on extracting the "consensus" or "central tendency" among all possible scenarios. By averaging all field samples at each spatial location, a single, smooth physical field is obtained. This posterior expectation field represents the best point estimate of the true physical field based on all available information (including prior knowledge and experimental data). It is the solution that is most likely to approximate the true situation in a probabilistic sense.

[0062] At the same time, the mechanism of calculating the posterior variance field is to self-examine and quantify the credibility of the evaluation results themselves. The size of the variance directly reflects the degree of discreteness between all field samples at a specific spatial location. If the variance value of a certain point is large, it means that different samples give very different prediction values here, which indicates that the existing observation data fails to provide strong enough constraints on the state of this point, and therefore the evaluation result here has a high uncertainty. Conversely, a very small variance value means that all samples tend to be consistent, indicating that the model has a high confidence in the evaluation results of this point. Therefore, this posterior variance field, as a core output module, is used to generate an intuitive "uncertainty map", which converts uncertainty from a vague concept into a physical quantity that can be accurately quantified and spatially visualized. This is the key to the method's realization of probabilistic evaluation.

[0063] Preferably, the statistical analysis further comprises:

[0064] A posterior probability distribution of at least one key quality indicator is calculated, and a risk probability that the key quality indicator exceeds a preset safety threshold is determined based on the distribution.

[0065] A scalar quantity with clear engineering significance is derived from the complete field evaluation results. It is not a distributed field but a single value, such as the "peak tensile stress" across the entire cladding layer or the "average porosity" in a key subregion. These indicators are often directly related to the failure mode or life prediction of structural components. The calculation module's function is to extract the values of these key indicators one by one from the thousands of previously generated stress field or damage field samples. It iterates through each stress field sample and finds the maximum tensile stress value in that sample.

[0066] After this process is complete, the product is no longer a collection of fields, but a new set of thousands of key quality indicator values. This set of values itself is a complete, discrete description of the posterior probability distribution of the key quality indicator. It clearly displays the range of all possible values of this key indicator and the relative likelihood of each value after integrating all the information, in the form of a histogram.

[0067] After obtaining the posterior probability distribution, the final analysis step is to determine a risk probability that the key quality indicator exceeds a preset safety threshold based on the distribution.

[0068] The mechanism behind this step is to directly compare the probabilistic analysis with engineering specifications. The "pre-set safety threshold" here is a critical value defined by engineering design standards, material performance limits, or safety regulations, such as the material's yield strength or a maximum acceptable defect size. The calculation module performs a straightforward operation: it systematically examines the set of key quality indicator values generated in the previous step and counts how many of them fall on the "dangerous" side of this safety threshold.

[0069] Ultimately, the risk probability is calculated by dividing the number of "out-of-limit" samples by the total number of samples. This final risk probability value is the ultimate output of the entire assessment method. It condenses a complex, multi-dimensional probability assessment problem into a single, extremely decision-maker-friendly percentage value. It no longer simply answers the question "What is the possible stress?" but directly and quantitatively answers the question "What is the probability that the component is in an unsafe state?" Therefore, this module is the final link connecting scientific analysis and risk management, providing the most direct and core decision-making basis for implementing risk-based maintenance strategies or implementing lean quality control.

[0070] The present invention provides a method for evaluating the quality of a turbine laser cladding layer. It has the following beneficial effects:

[0071] 1. This invention employs a unified probabilistic inversion framework, deeply coupling the residual stress field and the microscopic damage field at the physical model level to achieve simultaneous solution of both. This approach provides a more complete and physically self-consistent depiction of the internal state of the cladding layer. Compared to existing approaches that separate stress and damage, evaluating them separately or ignoring one or the other, this invention addresses the problem of ambiguous and unreliable evaluation results caused by the confusion of physical effects.

[0072] 2. This invention incorporates a comprehensive Bayesian statistical inference process. Its evaluation results are not a single deterministic value, but rather a probabilistic physical field encompassing both the posterior expectation and the posterior variance. This approach clearly reveals the reliability of the evaluation results across space. It overcomes the limitations of traditional nondestructive testing techniques, which only provide a deterministic result but fail to reflect its uncertainty. This addresses the potential for giving decision makers a false sense of security or leading to overly conservative maintenance practices.

[0073] 3. This invention integrates an efficient field parameterization method with a gradient-based Monte Carlo sampling algorithm and equips it with a dedicated adjoint state solver. This computationally efficient solution to complex high-dimensional inverse physical field problems is achieved. Compared to existing solutions that are forced to simplify the model or reduce the resolution due to the enormous computational complexity, this invention solves the dilemma of balancing physical authenticity and computational feasibility.

[0074] 4. The methodological system of this invention ultimately outputs the specific risk probability of a key quality indicator exceeding a safety threshold. It directly transforms complex field analysis into a clear, quantitative risk indicator that can be used for engineering decision-making. Compared to existing processes that disconnect measurement from risk assessment and require multi-step indirect analysis, this approach addresses the shortcomings of existing technologies, such as the accumulation of uncertainty within the information transmission chain and the inability to effectively quantify it, which ultimately leads to low transparency and credibility in risk assessments. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 Schematic diagram of the method of the present invention. DETAILED DESCRIPTION

[0076] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the present specification. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0077] Example:

[0078] Please see the attached Figure 1 The embodiment of the present invention provides a method for evaluating the quality of a hydraulic turbine laser cladding layer, comprising:

[0079] S1. In this embodiment, the first step of the evaluation method of the present invention is to obtain full matrix capture (FMC) ultrasonic waveform data of the cladding layer. This step aims to collect raw acoustic signals with high signal-to-noise ratio and high information redundancy, providing sufficient experimental input for subsequent complex inversion calculations.

[0080] Typically, a data acquisition system consists of a multi-channel ultrasonic data acquisition instrument, an ultrasonic phased array probe, and an automated precision scanning device. The ultrasonic data acquisition instrument has at least 64 parallel transmit / receive channels and a sufficiently high sampling frequency (at least ten times the probe's center frequency) to ensure undistorted waveforms.

[0081] Alternatively, the ultrasonic phased array probe is a linear array probe. The number of array elements in the probe can be selected; in some embodiments, a 64-element or 128-element probe can be used. The probe's center frequency is selected based on the thickness and material properties of the cladding layer, typically within the 5 MHz to 10 MHz range. This frequency range provides a good balance between detection resolution and acoustic penetration depth.

[0082] Specifically, the data collection process is as follows:

[0083] First, the phased array probe is mounted on the end effector of an automated precision scanning device, and good acoustic coupling is achieved between the probe and the surface of the cladding layer through water or a special coupling agent.

[0084] The scanning device is then activated, raster scanning along a pre-defined path, scanning the area of the cladding layer point by point. The scanning device's stepping accuracy is ensured by a high-resolution encoder, ensuring that the spatial coordinates of each acquisition position are accurately recorded.

[0085] In one possible implementation, the ultrasound data acquisition instrument performs a full-matrix capture (FMC) operation at each scanning location. This operation follows a specific timing logic: the system first designates the first array element as a transmitter, activating it to emit an ultrasonic pulse. Simultaneously, all H array elements (including the transmitter itself) act as receivers, synchronously recording the time-domain waveform signal for a preset duration. Once this process is complete, the system automatically designates the second array element as a transmitter, and the transmission and reception process repeats. This cycle continues until all H array elements have completed the operation as transmitters.

[0086] Thus, a complete FMC data set is acquired at a single scanning position. This data set can be represented as a three-dimensional data matrix, which contains A group of time domain waveform signals, where is the total number of probe array elements. Each group of waveform signals The mathematical form is:

[0087] ;

[0088] in:

[0089] Representatives from Array element No. transmits, The number of array elements received over time Changing voltage signal;

[0090] is the index of the transmitting array element;

[0091] is the index of the receiving array element;

[0092] is the total number of elements in the phased array probe.

[0093] Alternatively, to further improve data acquisition efficiency, this step can employ a plane wave imaging (PWI) acquisition strategy. This strategy applies specific delays to the probe array elements to synthesize a plane wavefront transmitted at a specific angle (from -30 degrees to +30 degrees, in 1-degree increments). For each plane wave transmitted at a specific angle, all array elements receive the echo signal synchronously. While the signal-to-noise ratio of PWI raw data is lower than that of FMC, its acquisition speed is significantly faster, which can be compensated through subsequent signal processing.

[0094] After data acquisition is complete, the raw FMC datasets typically require preprocessing. This preprocessing step can optionally include performing baseline correction on each waveform signal to remove DC offset; applying a bandpass filter whose center frequency matches the nominal probe frequency to filter out-of-band noise; and correlating and aligning each FMC dataset with its precise spatial coordinates using the encoder data recorded by the scanner.

[0095] Finally, the output of this step is a number of pre-processed FMC data sets that strictly correspond to the spatial positions, denoted as The output data completely and losslessly preserves all the physical details of the interaction between the acoustic wave and the internal structure of the cladding layer, which is an essential guarantee for accurate physical modeling and high-confidence inversion calculations in subsequent steps.

[0096] S2. In this embodiment, the second step of the evaluation method of the present invention is to construct a parameterized computational model of the stress-damage field of the cladding layer and, based on this model, determine the joint posterior probability distribution of the field. This step, through mathematical and physical modeling, transforms a complex inverse physical problem into a parameter estimation problem that can be solved within a statistical framework.

[0097] Typically, the modeling process begins with the creation of a geometric model. Laser 3D scanning is used to obtain precise point cloud data of the cladding component to be evaluated. This data is then reverse engineered to create a high-fidelity 3D computer-aided design (CAD) model. This CAD model is then imported into finite element analysis software and subjected to high-quality meshing to form a discretized computational domain.

[0098] In this computational domain, two continuously distributed physical fields to be solved are defined: one is the residual stress tensor field , which is a second-order tensor with six independent stress components in a three-dimensional Cartesian coordinate system; the other is the microscopic damage field , which is a scalar field used to characterize the degree of damage such as porosity or microcrack density.

[0099] Specifically, since both field functions are infinite-dimensional variables, in order to enable numerical processing in computers, they need to be parameterized by dimensionality reduction. This step uses the Karhunen-Loève (KL) expansion method to express the field function as a linear combination of a set of deterministic basis functions and a set of random variables to be determined. For a general physical field , its KL expansion form is:

[0100] ;

[0101] in:

[0102] Represents a component of the physical field to be parameterized, such as the damage field or the stress field;

[0103] is the spatial position vector in the computational domain;

[0104] is the a priori mean field of the physical field, which can be set to zero based on experience or obtained from preliminary process simulation;

[0105] It is a preset eigenvalue-eigenfunction pair of the prior covariance kernel function, which contains the prior knowledge of the spatial correlation (smoothness) of the physical field;

[0106] is a set of independent random variables that obey the standard normal distribution;

[0107] is the truncation order of the expansion, and its size determines the accuracy of the model and the complexity of the calculation;

[0108] It is the index of the summation term in the expansion, which starts from 1 and numbers each mode of the expansion in sequence.

[0109] By expanding all stress component fields and damage fields as above, the original infinite-dimensional problem is transformed into solving a problem that includes all A single, finite-dimensional vector of random variables problem.

[0110] In one possible implementation, a forward physics operator is constructed based on this parameterized expression. The operator is a complex, multi-stage cascade function that takes as input a parameter vector , outputs a set of predicted FMC ultrasonic waveform data. The internal operation process of this operator includes:

[0111] First, according to the input parameter vector , using the inverse KL transform, the complete residual stress field is reconstructed on all mesh nodes in the computational domain and microscopic damage fields .

[0112] Secondly, a micromechanical model, the Mori-Tanaka method, is applied, which considers the damage field As input, the anisotropic equivalent elastic tensor due to the presence of micro defects is calculated. .

[0113] Again, the equivalent elastic tensor calculated above is and the reconstructed residual stress field Substitute them together into the constitutive relation of nonlinear acoustoelasticity theory. This theory describes how stress changes the acoustic properties of the medium, and finally calculates a final acoustoelastic tensor that includes both damage and stress effects. .

[0114] Finally, in a virtual environment that is completely consistent with the physical experiment configuration, the spectral element method (SpectralElementMethod) or the finite difference time domain method (FDTD) high-precision numerical method is used to solve the following is the elastic wave equation of the medium properties. By simulating the entire process of FMC data acquisition, the final predicted waveform data is obtained. ,in is the forward physics operator.

[0115] After the forward physics operator is constructed, Bayesian theorem is applied to determine the unknown parameters The joint posterior probability distribution of The expression of this distribution follows the Bayesian formula:

[0116] ;

[0117] in:

[0118] is the desired posterior probability distribution, which represents the observation data obtained given S1 After that, the unknown parameters The probability distribution of

[0119] For parameters Due to the characteristics of KL expansion, a standard multidimensional Gaussian distribution can be naturally set for it. ,in is the unit covariance matrix;

[0120] is the likelihood function, which quantifies the likelihood of The degree of agreement between the model prediction data and the actual observation data. The measurement noise and model error follow a zero-mean Gaussian distribution, and the likelihood function can be expressed as:

[0121] ;

[0122] in, is the covariance matrix of the noise, which describes the degree of uncertainty of the observation data.

[0123] At this point, this step completes the transformation from physical problem to mathematical model, and its final output is the complete mathematical definition of joint posterior probability distribution. This distribution function combines the physical laws (embodied in the forward operator in), from experimental observations (reflected in and likelihood functions) as well as from prior knowledge (embodied in All the information provided provides a clear goal for the next step of solving the problem through numerical methods.

[0124] S3. In this embodiment, the third step of the evaluation method of the present invention is to numerically solve the joint posterior probability distribution to obtain an ensemble of solutions representing the residual stress field and microdamage field. This step uses a Markov Chain Monte Carlo (MCMC) method. Its purpose is not to find a single maximum point in the distribution, but to approximate its overall shape by extracting a large number of random samples from it.

[0125] Specifically, the HMC algorithm draws on the concept of Hamiltonian dynamics in physics. It is a parameter vector to be sampled (In this system, analogy is given to the "position" variable) Introduce an auxiliary "momentum" variable of the same dimension Then, define a Hamiltonian , which is the total energy of the system, consisting of potential energy and kinetic energy:

[0126] ;

[0127] in:

[0128] is the potential energy of the system, which is defined as the negative logarithmic posterior probability. This is the core link between physical systems and current statistical problems: .

[0129] is the kinetic energy of the system, usually defined in quadratic form: ;

[0130] in, is a symmetric positive definite mass matrix, which in some embodiments can be simplified to the identity matrix I. Momentum variable A random draw is made from a zero-mean Gaussian distribution corresponding to the kinetic energy form, i.e. .

[0131] In one possible implementation, the HMC algorithm generates new sample proposals by simulating the evolution of the Hamiltonian system over time. In theory, in a frictionless system, the total energy The algorithm simulates the particle's movement from its current position by using a numerical integration method (Leapfrog integration method). Departure, in the potential field Move for a preset time and reach a new position Due to the errors in numerical integration, the process is not completely energy-conserving, so a Metropolis-Hastings acceptance step is required at the end to accurately correct the errors and ensure that the sampling eventually converges to the target distribution.

[0132] The key to the effective operation of the HMC algorithm is to efficiently calculate the gradient of the potential energy field , which drives the evolution of Hamiltonian dynamics. According to the definition of potential energy, its gradient is:

[0133] ;

[0134] Among them, the prior The gradient of is usually analytical and easy to compute. The challenge lies in computing the first part of the logarithmic gradient of the likelihood function, as it involves the extremely complex forward physics operator defined in S2. Find the derivative.

[0135] As an option, to address this challenge, this step is to A solver for the Adjoint-State Method was developed and implemented. The Adjoint-State Method is a technique for efficiently computing gradients for large-scale models. By solving an adjoint process related to the original physical process (the forward process), it can obtain the likelihood function with respect to all parameter vectors at once, at a cost of approximately twice that of the forward model. The gradient of . This computational efficiency is related to the parameter dimension It is basically irrelevant, so that the HMC algorithm can be applied to the high-dimensional parameter problem involved in the present invention.

[0136] During the algorithm execution phase, multiple parallel Markov chains (4 chains) are initialized and run simultaneously. By real-time monitoring of a Gelman-Rubin statistic (denoted as ) to determine whether all chains have converged to the same stationary distribution. When the values are close to 1 (less than 1.01), the chain can be considered to have converged.

[0137] The initial phase of the algorithm is called the "burn-in period" or "warm-up period." Samples from this period are discarded because the chain has not yet forgotten its initial state. After the chain converges, the algorithm continues to run and collects subsequent samples.

[0138] Ultimately, the output of this step is a set of parameter vector samples containing a large number (tens of thousands) This sample set is the target posterior probability distribution A discretized, numerical approximate representation of , which constitutes the so-called "solution ensemble." This solution ensemble is the key to connecting the abstract probabilistic model with the final concrete physical interpretation, providing a complete statistical basis for subsequent quantitative analysis and evaluation.

[0139] In this embodiment, a statistical analysis is performed on the solution ensemble to generate a probabilistic quality assessment of the cladding layer. The core task of this step is to convert the sample data output by the MCMC algorithm into a quantitative assessment of the residual stress field and micro-damage field, and to characterize the uncertainty of the assessment results in a probabilistic form.

[0140] In general, this step first performs field reconstruction. Each parameter vector sample in the solution ensemble obtained in S3 is (in From 1 to ), and back-substitute them one by one into the Karonen-Loy (KL) expansion model established in S2. Through the KL inverse transformation, for each parameter vector sample Reconstruct its unique corresponding Sample of the residual stress tensor field distributed on and microscopic damage field samples .

[0141] Specifically, after this reconstruction process, we finally obtain two sets of field samples, which are the solution ensemble of a stress field and and a damage field solution ensemble These two ensembles are the core results of the method of the present invention, which represent a set of probability-weighted possible “snapshots” of the true physical state inside the cladding layer.

[0142] In one possible implementation, a point-by-point statistical analysis is performed on the two field ensembles to extract meaningful evaluation information.

[0143] First, the posterior expectation field is calculated, which is considered to be the best point estimate of the true physical field. For the stress field, the posterior expectation is The calculation formula is:

[0144] ;

[0145] Similarly, the posterior expectation of the damage field The calculation formula is:

[0146] ;

[0147] in, is any spatial position point in the computational domain, is the total number of samples in the solution ensemble.

[0148] Secondly, in order to quantify the uncertainty of the evaluation results, the posterior variance field is calculated. For the damage field, the posterior variance at each point is The calculation formula is:

[0149] ;

[0150] The square root of the posterior variance field, also known as the posterior standard deviation field, intuitively demonstrates the spatial distribution of confidence in the evaluation results. Regions with large standard deviations indicate high uncertainty in the inversion results, while regions with small standard deviations indicate more reliable results.

[0151] As an option, this step also calculates the posterior probability distribution of one or more key quality indicators (KQIs). These KQIs are scalars that are of greater engineering interest and can directly reflect the service performance of the cladding layer.

[0152] In some embodiments, an important KQI is the peak tensile stress in the cladding layer. The posterior probability distribution is obtained by: for each stress field sample in the ensemble , first calculate its The first principal stress field in the field, and then find the maximum positive value (tensile stress) in the principal stress field. In this way, each field sample Corresponding to a peak tensile stress value . From this The set of values forms the posterior probability distribution of the peak tensile stress.

[0153] Another important KQI can be the volume of high damage areas The posterior probability distribution is obtained by setting a damage threshold , porosity 1%. For each damage field sample , calculate its value greater than The volume of the area . From this The set of volume values forms the posterior probability distribution of the volume of the high damage area.

[0154] In one possible implementation, the risk probability is calculated based on the posterior probability distribution obtained by the above calculation. The risk probability refers to the probability that a certain KQI exceeds its preset safety threshold. If the engineering stipulates that the peak tensile stress shall not exceed a certain critical value , then the risk probability of exceeding the limit is It can be estimated by integrating or counting the posterior distribution:

[0155] ;

[0156] in, is an indicator function whose value is 1 when the condition is met and 0 otherwise.

[0157] Finally, this step integrates all analysis results to generate a detailed, visual, and probabilistic quality assessment report. The report can optionally include:

[0158] Three-dimensional color cloud map of the posterior expected stress field and damage field;

[0159] 3D color cloud map of the posterior uncertainty (standard deviation) field;

[0160] A histogram of the posterior probability distribution of the key quality indicator (KQI), showing its mean, median, and 95% confidence interval;

[0161] A clear risk statement states, "This assessment indicates that the probability that the peak tensile stress of the cladding layer exceeds 200 MPa is 15% ± 2%," and "The probability of the presence of a high damage area with a volume greater than 1 cubic millimeter is less than 1%."

[0162] In this way, the final output of the present invention is no longer a simple, black-and-white "qualified" or "unqualified" judgment, but a rich, data-supported quantitative risk assessment report, which provides a scientific and reliable basis for subsequent maintenance, repair or usage decisions.

[0163] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A method for evaluating the quality of a hydraulic turbine laser cladding layer, characterized in that: The following steps are involved: Acquiring ultrasonic waveform data of the turbine laser cladding layer; establishing a joint posterior probability distribution that includes both a residual stress field and a microscopic damage field within the cladding layer, wherein the joint posterior probability distribution associates the residual stress field and the microscopic damage field with the ultrasonic waveform data via a forward physics operator that couples a nonlinear acoustoelastic model and a micromechanical model; A Markov chain Monte Carlo algorithm using gradient information is used to numerically sample the joint posterior probability distribution to obtain an ensemble of solutions for the residual stress field and the microscopic damage field; Statistical analysis is performed on the solution ensemble to generate a probabilistic quality assessment result of the cladding layer including uncertainty quantification information.

2. A method for evaluating the quality of a hydraulic turbine laser cladding layer according to claim 1, characterized in that: The step of obtaining ultrasonic waveform data of the turbine laser cladding layer includes: An ultrasonic phased array probe is used to perform a full matrix capture scan on the area to be evaluated of the cladding layer to obtain a full matrix waveform data set.

3. The method for evaluating the quality of a hydraulic turbine laser cladding layer according to claim 1, wherein: Before establishing the joint posterior probability distribution, the method further includes: The residual stress field and the microscopic damage field are parameterized into finite-dimensional random variable vectors respectively by using the Karunan-Loey expansion method.

4. The method for evaluating the quality of a hydraulic turbine laser cladding layer according to claim 1, wherein: The joint posterior probability distribution Determined by Bayes' theorem: ； in, is the random variable vector characterizing the residual stress field and the microscopic damage field, is the acquired ultrasonic waveform data, is the likelihood function derived from the forward physics operator, is the prior probability distribution of the random variable vector.

5. The method for evaluating the quality of a hydraulic turbine laser cladding layer according to claim 4, wherein: The forward physics operator transforms the random variable vector As input, its internal operations include: According to the reconstructing the residual stress field and the microscopic damage field; Applying the micromechanical model, an equivalent elastic tensor is calculated based on the microscopic damage field; The nonlinear acoustoelastic model is applied to calculate an acoustoelastic tensor according to the equivalent elastic tensor and the residual stress field, and ultrasonic waveform data is predicted based on the acoustoelastic tensor.

6. The method for evaluating the quality of a hydraulic turbine laser cladding layer according to claim 5, wherein: The micromechanical model is the Mori-Tanaka model.

7. The method for evaluating the quality of a hydraulic turbine laser cladding layer according to claim 1, wherein: The Markov chain Monte Carlo algorithm using gradient information is a Hamiltonian Monte Carlo algorithm.

8. The method for evaluating the quality of a hydraulic turbine laser cladding layer according to claim 7, wherein: The gradient information of the joint posterior probability distribution required by the Hamiltonian Monte Carlo algorithm is calculated by establishing an adjoint state method solver for the forward physics operator.

9. The method for evaluating the quality of a hydraulic turbine laser cladding layer according to claim 1, wherein: The step of performing statistical analysis on the solution ensemble comprises: reconstructing a plurality of residual stress field samples and microscopic damage field samples from the solution ensemble; The posterior expectation field and the posterior variance field of the residual stress field and the microscopic damage field are calculated, wherein the posterior variance field is used to quantify the uncertainty.

10. The method for evaluating the quality of a hydraulic turbine laser cladding layer according to claim 9, wherein: The statistical analysis also includes: A posterior probability distribution of at least one key quality indicator is calculated, and a risk probability that the key quality indicator exceeds a preset safety threshold is determined based on the distribution.

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