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Computer Science
Mathematics

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Building Robust Stochastic Configuration Networks with Kernel Density Estimation

This paper aims at developing robust data modelling techniques using stochastic configuration networks (SCNs), where a weighted least squares method with the well-known kernel density estimation (KDE) is used in the design of SCNs. The alternating optimization (AO) technique is applied for iteratively building a robust SCN model that can reduce some negative impacts, caused by corrupted data or outliers, in learning process. Simulation studies are carried out on a function approximation and four benchmark datasets, also a case study on industrial application is reported. Comparisons against other robust modelling techniques, including the probabilistic robust learning algorithm for neural networks with random weights (PRNNRW) and an Improved RVFL, demonstrate that our proposed robust stochastic configuration algorithm with KDE (RSC-KED) perform favourably.

Introduction
Feed-forward neural networks have been popular and widely applied in many domain applications due to its universal approximation capability. Basically, a large amount of learning algorithms are developed on the basis of the minimum of a mean squared error (MSE) criterion, which indeed is sufficient and used in uncertain data modelling problems with assumption on noise fitting a Gaussian function. However, it is generally known that, in many real applications data are not only noisy but may inevitably contain outliers [1]. In fact, the outliers can cause a great threat to the training process of neural networks as just one notorious outlier could severely distort the training, which consequently make the resulting learner model based on MSE useless.
Over the last decades, a lot of robust techniques have been established in the field of robust statistics [1][2][3], including M-estimates (maximum likelihood estimates), L-estimates (linear combination of order statistics), R-estimates (estimates based on rank transformations), and LMedS estimates (least median square). In essence, a majority of these efforts lay great emphasize on using new cost function in training the neural network model, where the conventional back-propagation (BP) algorithm is applied in tuning the model parameters, such as hidden parameters and output weights. For example in [4], M-estimator and Hampels hyperbolic tangent estimates were employed in the objective function, aiming to alleviating the impacts of outliers. Liano [5] made use of the mean log squared error (MLSE) criterion as a robust cost function with assumption that the errors follow Cauchy distribution. In [6], the author proposed a robust neural network algorithm based on a M-estimator cost function with consideration of the random sample consensus (RANSAC) framework that has become the standard method of dealing with outliers in the computer vision and image processing community [7][8][9]. However, robust neural network methods based on BP algorithm still suffer from some inherent drawbacks, including the ambiguity in selecting the initialization weights and the problem of a local minimum and slow convergence speed. On the other hand, although some methods based on SVM are also obtained and successfully verified for function approximation problems with data corrupted with outliers, [10][11][12], its effectiveness and efficiency may meet challenge when dealing with training data with high level outliers or other large scale robust modeling problems. That means more flexible learning tool together with some advanced learning algorithms are desirable.
With the increasing demands of dealing with large scale data processing, randomized methodology becomes a pathway to access a fast and effective solution in computing exercises [13,14]. The use of randomness in neural networks can be traced back to later 80's [15] and some milestones on this topic can be read in our survey paper [16]. There is few work addressing robust modeling problem based on Random Vector Functional-link (RVFL) networks [17][18][19]. In [21], the authors employed a hybrid regularization loss function with assumption of the sparsity among outliers, and proposed a probabilistic robust learning algorithm for neural networks with random weights (PRNNRW), where some parameters must be set properly and this is quite difficult to be done in practice. In [22], the authors suggested an improved version of the original RVFL networks (Imporoved RVFL), where a weighted cost function is used to improve the model's robustness by differentiating each sample's contribution for the whole objective function. Specifically, kernel density estimation (KDE) method, which acts as a non-parametric way to estimate the probability density function of a random variable by computing a smooth density estimation from data samples by placing on a each sample point a function representing its contribution to the density, is used to renew the associated penalty weights. However, these two algorithms, i.e., PRNNRW and Improved RVFL do not clarify the random selection strategy of the hidden parameters, which indeed could not fully guarantee the effectiveness of the robust algorithms.
Our recent work reported in [23] proposed a new framework of randomized learner model, termed as stochastic configuration networks (SCNs), which has been proved as universal approximators. The main contribution of the work in [23] lies in the supervisory mechanism for randomly assigning the hidden parameters throughout the training process, which can guarantee the universal approximation property of the randomized learner model. It should be pointed out that our proposed supervisory mechanism in [23] is original and unique in literature up to date. This paper is built on [23] and attempts to develop a robust version of SCNs, aiming to copy with modeling problems with data corrupted by outliers. Based on the construction process of SCN, we employ a weighted least squares objective function that consequently leads to a weighted configuration criterion (compared with the original SCN) for randomly assigning the hidden parameters. At the meantime, the penalty weights representing the degree of contribution of individual data samples to the objective function will be updated by using a well-defined kernel density estimation (KDE) method. In this paper, alternating optimization (AO) technique is employed to renew the penalty weights and the SCN model. Finally, the performance of our proposed RSC-KDE algorithm is extensively evaluated on synthetic and real data contaminated by artificial outliers, including some benchmark datasets from the UCI repository of standard machine learning datasets [24] and a dataset from engineering application [22]. Comparative studies indicate that RSC-KDE outperforms other existing randomized neural networks in terms of effectiveness and robustness.
The rest of paper is organized as follows: Section II briefly reviews stochastic configuration networks and the kernel density estimation (KDE) method. Section III details our proposed RSC-KDE algorithm. Section IV reports experimental results with comparisons and discussions. Section V concludes this paper with some remarks.

Related Work
This section briefly reviews SCN framework, of which the highlight is the configuration of hidden parameters under a supervisor mechanism. In general, SCN performs in two interrelated phases, i.e., input parameter (inner weights and biases) configuration and output parameters (output weights) determination. Details of the SCN framework can be read in [23]. Also, as a non-parametric way to estimate the probability density function of a random variable, the kernel density estimation (KDE) method is introduced here.

Revisit of Stochastic Configuration Networks
Suppose that we consider the approximation problem of unknown function f : The constructive process of SCN starts with a small size of network then adds hidden nodes and output weights incrementally (automatically) until an acceptable approximation performance is achieved. That does not require any prior knowledge about sufficient complexity of the network for the objective tasks. For instance, given a target function f : R d → R m , assume a SLFN with L − 1 hidden nodes (L = 1, 2, . . .) have already been constructed, that is, Basically, SCN can provide an effective solution for how to add β L , g L (w L and b L ) leading to f L = f L−1 + β L g L until the residual error e L = f − f L is suitable for the given task, that is, e L is smaller than an expected specific tolerance ǫ. The following Theorem 1 restates the universal approximation property of SCN, corresponding to Theorem 7 in [23].
Theorem 1. Suppose that span(Γ) is dense in L 2 space and ∀g ∈ Γ, 0 < g < b g for some b g ∈ R + . Given 0 < r < 1 and a nonnegative real number sequence {µ L } with lim L→+∞ µ L = 0 and µ L ≤ (1 − r). For L = 1, 2, . . ., denoted by If the random basis function g L is generated to satisfy the following inequality: and the output weights are constructively evaluated by

Kernel Density Estimation
Basically, the kernel density estimator computes a smooth density estimation from data samples by placing on a each sample point a function representing its contribution to the density. The distribution is obtained by summing all these contributions. Readers may refer to [25] and [26] for further details on the kernel density estimation method.
Using KDE method, the underlying probability density function of a random variable η can be estimated as where K is a "kernel function" (typically a Gaussian) centered at the data points, η k , k = 1, 2, . . . , N , and δ i are weighting coefficients (typically uniform weights are used, i.e., δ k = 1/N ).

Robust Stochastic Configuration Networks
In some industrial process, the collected samples are always contaminated by the outliers caused by the failure of the measuring or transmission devices or unusual disturbances. That means a robust neural network learner that could fit a functional model to data corrupted with outliers is of high importance in practical applications, especially on some industrial system design. This section contributes to the development of robust stochastic configuration networks (RSCNs) by using kernel density estimation (KDE). To begin with, let us shed some light on the technique of weighted least squares (WLS), which has been received considerable amount of attention in robust modeling. In general, a weighted least squares (WLS) learning strategy when training a neural network model can be formulated as follows. For a target function f : R d → R m , given a training dataset with inputs . . , N , a robust neural network model as an approximator of f can be obtained by taking consideration of the weighted least squares problem, i.e., where θ i ≥ 0 is the penalty weight representing the contribution of the corresponding sample to the objective function. g is the activation function and L is the number of hidden neurons. For j = 1, 2, . . . , L, w j , b j are the input weights and biases, respectively. β j represent the output weights.
Generally, the penalty weights θ i (i = 1, 2, . . . , N ) can be determined according to the reliability of the sample x i . It is obvious that, high reliability means the sample should be a normal data that correctly represents the process behavior, whereas low reliability indicates that the sample might be a suspected outlier or noise embodying worthless or even wrong information. Decreasing and enlarging the weight of low and high reliability samples, respectively, can eliminate and even remove the impact of the outliers. As such, the built robust model will possess extremely small sensitivity to outlying data.
It is easy to combine the new objective (6) with our SCN framework shown in Theorem 1. Before introducing WLS into the procedures based on SCN, some specified notations are needed. In practice, as the exact functional form of e L−1 is unavailable, we use its consistent estimation on According to (6), a weighted form of e L−1 (X) should be concerned, aiming to implanting the penalty weights during the constructive process of SCN. Here we can denotẽ where Given a set of penalty weights θ 1 , θ 2 , . . . , θ N , we denotẽ According to the configuration mechanism in Theorem 1 and taking into account the contribution of each sample to the global objective function, the hidden parameters (w and b) should be selected whenξ L ≥ 0.
Now it is obvious that the remaining question is how to assign penalty weights θ 1 , θ 2 , . . . , θ N along with the processes of SCN. In fact, if the probability density function of the residuals can be obtained or estimated, the reliabilities of the samples will be determined. Inspired by [25], we attempt to incorporate KDE method (as reviewed in Section 2) into our SCN framework, aiming to estimate the reliability of the sample and then assign θ i in terms of the estimated reliability of the sample. Based on (5), the probability density function of the residuals e L can be calculated as (here e L is regarded as a random variable) is the estimation window width which exhibits a strong influence on the resulting estimate,σ is the standard deviation of the residual; K is the Gaussian function defined as: With the above equations, the probability of each residual e L (x i ) (i = 1, 2, . . . , N ) can be achieved as Φ(e L (x i )). Also, it is clear that the larger the probability, the higher the reliability. Concretely, the penalty weight θ i thus can be assigned as (i = 1, 2, . . . , N ) Once the set of penalty weights θ i is assigned and fixed, the output weights β 1 , β 2 , . . . , β L can be determined by solving the followed minimization problem where It is easy to obtain the solution of (10) below So far, we can generally describe the whole learning process in building a robust SCN model, where alternating optimization (AO) technique works effectively in finding the most appropriate values of penalty weights. To begin with, we assign equal penalty weight for each sample (i.e., θ i = 1) and conduct the procedures of SCN to obtain a learner with L hidden neurons, of which the hidden parameters w and b are configured based on (9), and β is determined by (11). Then the penalty weights are updated by new residuals caused by the resultant learner. Finally, a RSCN is established by repeating this procedure until some user-defined accuracy or stopping criterion is reached. It should be clarified that, the renew process of penalty weights corresponds to the whole process similar to the original SC algorithm. That means at each step of iteration, the penalty weights remain unchanged throughout the process of building the neural network architecture using SCN framework. Once a temp learner is designed, the penalty weights will be updated and the new setting will be employed in the new round for constructing an universal approximator by SCN principles.
Based on the idea of alternating optimization (AO), the penalty weight θ i and the output weight β can be calculated iteratively by and where ν denotes the νth iteration and L (x i ) to represent the changing (with L increase) residual vector throughout the constructing process in which θ (ν) i are utilized as the present penalty weights.
Different from our previously proposed SCN framework that all samples will contribute equally to the value of the objective function, this newly designed method based on KDE treats individual samples differently and give more emphasis on the entry with higher reliability, which is equivalent to, lager value of penalty weights. This means that if the output y j is occluded or corrupted, the input entry corresponding to outliers will provide small contributions to the cost function. As a result, the noise can be handled uniformly and smoothly. Now, our proposed robust stochastic configuration algorithm, namely RSC-KDE, can be summarized as followed:
Save w L and b L in W , ξ L in Ω, respectively; 9.
Else go back to Step 4 10.
If W is not empty 13. find Break (go to Step 18); 15.

Performance Evaluation
In this section, the performance of our proposed RSC-KDE algorithm is demonstrated by several regression problems. First, it is evaluated on a synthetic 1-D regression problem, of which in particular the visualization of the 1-D function approximation result is provided. Then we test the proposed algorithm on some benchmark problems from the UCI repository of standard machine learning datasets. In addition, both the effectiveness and advantages of our proposed algorithm are assessed in the problem of particle size estimation of grinding processes, aiming to illustrate its practical application in the field of engineering. For each regression problem, the performance of our proposed algorithm is compared with three randomized algorithms, including RVFL, improved RVFL presented in [22], and the probabilistic learning algorithm PRNNRW proposed in [21]. It should also be mentioned that all algorithms under comparison are analyzed under several scenarios and levels of outlying data.
As commonly used in data analysis literature, the root mean squared error (RMSE) is calculated to measure the performance of function approximation on various datasets. For each regression problem, the RMSE values of the trained model are reported on the corresponding outlier-free test datasets that are different from the data used for training, in order to reflect the generalization ability of each algorithm. Both the average value and standard deviation of RMSE are reported in all our experiments, as for the consideration of the impact caused by randomness. In addition, we conduct a robustness analysis on this task about the setting of ν and L max so as to offer a basic reference for the assignment of their values for this specific problem.
It should be noted that, in our simulations, all input and output attributes were normalized into [0,1] before artificially adding certain level of outliers. All the results reported in the experimental study are based on 100 independent trials, where the average value together with standard deviation are concerned. For both regression tasks, the maximum times of random configuration T max is set as 100. For the special parameters involving in the learning process, such as the regularization factor η, the maximum number of hidden nodes L max , the expected error tolerance ǫ and the index r, we will specify their corresponding setting later in the analysis of the simulations.

1-D Function Approximation
The four algorithms are examined to approximate the 1-D function This testing function firstly appeared in [20] and later was used in [23]. Herein, the training set has 600 points randomly generated by sampling the independent variable in the range [0, 1] and using the above equation to calculate the dependent variable. The following scenario is employed to introduce different levels of outliers in this dataset. A variable percentage ξ of the data points is selected at random and substituted with background noise, of which the values are uniformly distributed on the range [-0.2, 0.8]. In particular, Fig. 1 illustrates the training dataset used in our experiments at ξ = 25% along with the demonstration of the target function. Overall, the outlier percentage ζ is changed from 0 to 30% and each of the four training algorithms under comparison is employed at each outlier percentage. Finally, the RMSE is calculated from the resultant network model. This procedure is repeated 50 times, and the average obtained RMSE scores are plotted versus ξ in Fig.  2. The resultant models (the approximated functions) at ξ = 25% are graphed in Fig. 3.  It should be noted that, apart from our proposed algorithm, we try to use different choices of the random selection range of hidden parameters, i.e., λ = 1, 10, 30, 50, 100, 150, respectively, in the experiments to demonstrate the significant impact of the setting of the range selection range on the random model's performance. Then for each λ, different neural network architectures (L = 40, 60, 100, 120, 150, 200) are used in RVFL, Improved RVFL, and PRNNRW in order to find the most favorable performance for each combination of λ and L. It is clear that from Fig. 2 that our proposed RSC-KDE algorithm contributes to the best performance among all these randomized algorithms. In particular, for λ = 1, it is found that the approximation performance of all those three algorithms (RVFL, Improved RVFL and PRNNRW) could not be accepted. That means once the random selection range of hidden parameter is assigned without any reference and consideration   of training data information, the resultant neural model may not have any universal approximation capability and generalization ability. Additionally and importantly, for this specific test function, λ = 1 could not lead to an accepted learner no matter what the number of hidden neurons is and irrespective of any level of outliers. It is also clear in Fig.3 that our proposed algorithm has indeed shown the most robustness among the four algorithms at ζ = 25%, in which λ = 1 for the other three algorithms RVFL, Improved RVFL and PRNNRW. On the other hand, the four algorithms start with very different performance even when the outlier percentage is rather low, in which it can be easily seen that our proposed algorithm could produce the best model in this regression problem even if the dataset is corrupted with low level outliers or without outliers. That could strongly support the advantage of the configuration mechanism of our proposed algorithm. Table I shows that the (cases with comparatively low outlier percentage are not listed here) test performance in scenarios as λ = 1, 30, 50, 100, respectively. Even at the extreme outlier percentage of ζ = 30%, it offers a preferable robust model with RMSE of 0.0138 ± 0.0027 that is far better than the other three algorithms. For example, Improved RVFL leads to the most optimal result among them with RMSE of 0.0255 ± 0.0036 when λ = 50.

Benchmark Datasets
We also evaluate the four algorithms on some real high-dimensional datasets that are publicly available from the UCI repository of standard machine learning datasets and the KEEL-dataset repository [24]. The specifications of the four datasets considered in this paper are summarized in Table II. The four algorithms are used to find the functional relationship of the predicted attribute (output variable) of each dataset as a function of the remaining attributes (input variable). To begin with, both the input and output attributes are normalized into [0,1] and then we randomly select 75% of the whole dataset as the training data while the left acts as the test data. Similar to the 1-D function approximation problem, we artificially introduce different levels of outliers into the training datasets. In detail, for each normalized training dataset, a variable percentage ζ of the data points is selected at random and the associated output values are substituted with background noise uniformly distributed on the range [-0.5,0.5]. Indeed, the resultant output values of each corrupted training dataset are distributed in [-0.5,1.5] while the corresponding test dataset is free from outliers or noise (here we take no account of the possible existing noise or outliers involved in the original data).
For each dataset, we evaluate the comparative algorithms (RVFL, Improved RVFL and PRNNRW) with different parameter settings of λ and L, aiming to find their most appropriate combination. In particular, for each algorithm, we tried five scenarios with λ = 0.1, 0.5, 1, 3, 5, respectively, then different choices of the neural network architect (L = [30, 50, 100, 150, 200]) are attempted for each fixed λ. The experimental procedure is repeated 50 times for each λ and L, by which we calculate the average value and standard deviation of RMSE for each problem at a different level of outliers. In Fig, 4, we only provide the comparison result for the case of λ = 1 as it is already sufficient to indicate the influence of λ in building a universal approximtor, as also addressed in the last 1-D function approximation problem. It is clear in Fig. 4 that our proposed algorithm outperforms the other three randomized algorithms at each outlier percentage.
Clearly from Table III, our proposed algorithm exhibits the best accuracy for all these four datasets at each outlier percentage. It should be noted that, the reported values of the three algorithms indeed are the best results that are chosen among all the cases of the combination of λ and L. It is obvious that, among these three algorithms: RVFL, Improved RVFL, PRNNRW, the performance of Improved RVFL is the the most closest to our proposed RSC-KDE algorithm to some extent. Although the KDE method is utilized in both Improve RVFL and RSC-KDE, our stochastic configuration scheme in the learning process greatly enhances the system's effectiveness as its generalization capability evaluated on each problem has been improved a lot.
It should be mentioned that, in Fig. 4 for λ = 1, the algorithm PRNNRW exhibits the worst accuracy on stock, laser, concrete datasets, although the changing trend along with different outlier percentage stay stable. In Table III, its results obtained by the 'best' combination of λ (with values 0.1, 0.5, 1, 3, 5) and L (30, 50, 100, 150, 200) are much better than the performance shown in Fig. 4. This phenomenon illustrates the ineffectiveness and unreasonableness when the hidden parameters are randomly assigned in [-1,1]. Apart from [-1,1], much more appropriate random selection range exists, that is the reason why we prefer more choices of λ in the experiments and try to find the influences. Indeed, this parameter setting should be related to the training data information as well as other user-defined parameters that play an important role in training a good learner, like the regularization factors considered in PRNNRW.

Case Study: Particle Size Estimation of the Grinding Process
In order to test the effectiveness and advantages of our proposed algorithm in real applications especially in the industrial community, we address a practical industrial automation problem, that is particle size estimation of grinding process, to evaluate the four algorithms and finally demonstrate our RSC-KDE algorithm's merits on this engineering application [22]. In detail, the problem formulation as well as the specifications of our experimental setup are presented later. Some robustness analyses are conducted to see the impact of learning parameters on the robust SCN model.

Process description
Basically, the whole grinding process can be briefly reviewed as follows. To begin with, coarse fresh ore O F is fed continuously into the ball mill by the conveyor. Meanwhile, a certain amount of mill water Q F is fed by means of a pipe to maintain the proper pulp density. The knocking and tumbling action of the steel balls within the mill crushes the coarse ore to a finer size. After grinding, the mixed ore pulp including both coarser and finer particles is continuously discharged from the mill into the spiral classifier for classification. The ore pulp is diluted by dilution water Q D to improve the classification condition. Being in the control of spiral classifier, the pulp is separated into two streams namely overflow and underflow pulp. The underflow pulp with coarser particles is recycled back to the mill for regrinding, whilst the overflow pulp with finer particles, as product, is transported to the subsequent procedure (Fig. 5)

Experimental Setup
For the particle size estimation of the grinding process, the task of the data-driven compensation model is to realize the nonlinear mapping of process variables(i.e.,fresh ore feed rate O F , mill water flow rate Q F , and dilution water flow rate Q D ) to the unmodelled dynamic △r, namely, {△r} ← O F , Q F , Q D Consequently, the input vector of the improved RVFLN is denoted as x = [O F , Q F , Q D ] T , and the model output y refers to the estimation of the unmodelled dynamic △r. By combining the estimation of the unmodelled dynamic △r with the mechanism model outputr, the estimated value of the PSr is generated byr =r + △r. For each λ, we report the best results obtained by the 'most appropriate' setting of L (only for RVFL, Improved RVFL and PRNNRW), as well as the results of our proposed RSC-KDE algorithm in Table IV. For λ = 1, the test results of the four algorithms are shown in Fig. 8, where both the real and estimation values of the normalized particle size (of the whole test samples) are plotted. It can be clearly seen that RSC-KDE algorithm outperforms the other three randomized algorithms with better robustness in this case study.

Results and Discussion
Similar to the reported results in the previous subsection, apart from our proposed algorithm, we evaluate those three algorithms on different combination of λ and L. The averaged RMSE together with the standard deviation are plotted in Fig. 7, where for each λ the results of RVFL, Improved RVFL and PRNNRW are the most satisfied ones after trying different neural network architect (L = 30, 50, 100, 150, 200). It can be easily found that our proposed algorithm outperforms the other three methods in most cases. For λ = 0.1, the performance of PRNNRW is far away from the other examined algorithms, which indicates the fact that the resultant model by PRNNRW with λ = 1 does not have any generalization capability. Although the Improved RVFLN exhibits very close performance when the outlier percentage is relatively low, RSC-KDE algorithm has indeed shown the most robustness even at high outlier contamination rate. When λ = 0.5 and λ = 1, the performance of PRNNRW has been improved a lot compared with the case of λ = 0.1 but are still unaccepted for this problem. For both RVFL and Improved RVFLN, there seems no big difference between the results obtained by λ = 0.5 and λ = 1 respectively. Fig. 7 (d) demonstrates a preferable performance of PRNNRW where its test result at a rather high outlier percentage (for example ζ = 20%, 25%, 30%) is slightly better than RSC-KDE. However, our RSC-KDE algorithm still outperforms all those three algorithms at lower outlier percentage, which makes it more applicable in the practical particle size estimation problem of the grinding processes.  Figure 6: Test results of the four algorithms at ζ = 30% on particle size estimation problem

Robustness Analysis
Here we attempt to study the robustness of our proposed algorithm with different neural network architecture (L) and various setting of AO (alternating optimization) times (ν). The test performance with different combination of L and ν are reported in Table V, VI, VII, respectively corresponding to the case of ζ = 0%, ζ = 10%, and ζ = 30%. In Table V, it can be found that there is no big difference among the performance of different ν values when L is fixed. On the other hand, L = 50, , 60, 80 all can suit for this special case. However, in Table VI for ζ = 10%, the most appropriate setting of the architecture is L = 20 while the number of AO can be selected among ν = 3, 5, 8, 10, 12. Moreover, it seems not difficult to deduce that the model's performance with L = 20 is not only preferable but also can stay at a stable level when the number of AO is set equal or larger than 3. Similarly, in Table VII for ζ = 30%, the most appropriate setting of the architecture is L = 10 while the number of AO can be selected among ν = 5, 8, 10, 12, in which we can conclude that the resultant model with L = 10 can perform robustly with number of AO chosen as ν ≥ 5. Overall, the resultant model with fixed setting of the number of hidden neurons can contribute to a stable performance when the number of AO is set larger than 3. In comparison, the model's generalization capability (indicated by test performance) can be significantly influenced by the setting of L especially for cases then the training data are contaminated with high level outliers. Accordingly, some heuristic methods determining the neural network architecture deserve further study and more empirical studies on robustness analysis are needed.

Conclusions
This paper contributes a development of randomized method for robust data modelling, which is an important research topic in many domain applications. Stochastic configuration networks, which was recently proposed and reported in [23], are employed to build robust predictive models against  This work sets a basis for future researches on building robust learner models with random parameters. Extensions of the present algorithm to online version is being expected. In addition, the proposed algorithm in this paper can be easily extended to distributed learning framework for dealing with large scale robust modelling problems.


Demystifying Ransomware Attacks: Reverse Engineering and Dynamic Malware Analysis of WannaCry for Network and Information Security

— Encryption has protected the Internet for some time now and it has come to raise user trust on the otherwise unsecure Internet. However, recent years have seen the use of robust encryption as stepping stone for cyber-criminal activities. Ransomware has not escaped the headlines even as it has attacked almost every sector of the society using a myriad of infection vectors. Mission critical data has been held to ransom and victims have had to part away with millions of dollars. The advent of the anonymous Bitcoin network has made matters worse where it’s been virtually infeasible to trace the perpetrators. In this paper, we endeavor to perform dynamic analysis of WannaCry ransomware samples based on malware-free infection vectors. Further, we perform reverse-engineering to dissect the ransomware code for further analysis. Results show that despite the use of resilient encryption, the ransomware like other families in the wild uses the same attack structure and cryptographic primitives. Our analysis leads us to the conclusion that this ransomware strain isn't as complex as previously reported. This detailed practical analysis tries to raise awareness to the business community on the realities and importance of IT security whilst hinting on prevention, recovery and the limitations thereof.

INTRODUCTION
The Internet today is plagued with a myriad of malware classes not limited to viruses, trojans, worms etc. Since it was not built with security in mind [1], the Internet has seen an incremental correlation between advancements in underlying technologies and malware sophistication -as technology advances, so does malware. Encryption, one of the pillars of secure technologies today, has likewise been integrated into the malware fraternity thus introducing a new form of cyberattacks -crypto ransomware attacks [2]. Cyber-attacks are no longer the works of script kiddies or hacker-wannabes but rather organized cybercriminals such as Advanced Persistent Threat actors (APT) perpetuating all forms digital crimes [3]. Organized cybercrime groups attack networks for monetary gains which is a far stronger motivation absent in amateurs. This inherently implies that attackers are well organized and have at their disposal not only the technical knowhow but capable resources to attack networks than what a security administrator might have. The philosophy behind ransomware attacks is that of extortion, making the victim's data inaccessible via encryption until a ransom demand is met. The tragedy of ransomware is that it employs the most robust and resilient forms of encryption making it computationally infeasible [4] to decrypt a victim's data without consented efforts of distributed computing. WannaCry, one of the devastating ransomware attacks which plagued over 150 countries and traversed all continents [5] in May of 2017, spared no industry niche owing to the indiscriminate nature of the attack. It attacked universities, transport sector, health sector, telecoms sector etc implying that the ICT industry cannot burry its head in the sand but rather address the emerged new challenge. Figure 1 below shows the severity and distribution of reported WannaCry attacks world over. Figure 1. Distribution of initial WannaCry attacks [6] What made WannaCry effective is not only the robust encryption schemes employed but the distribution mechanisms as well. A resilient encryption scheme is just one part needed for a successful ransomware attack but to reach all the aforementioned sectors, an effective infection mechanism is required. WannaCry used various forms of infections vectors [7] and employed network traversal by exploiting an SMB network vulnerability [8] to attack network devices on port 445 and any other physically connected devices. The media has not helped matters as it is flooded with a lot of inaccuracies and hearsay on the effect, infection vectors, prevention, mediation etc. History has however shown that the primitives used to effectuate ransomware attacks are not novel as cybercriminals tend to reuse malware code, ransomware inclusive [9]. Therefore, we in this paper, endeavor to demystify WannaCry ransomware attacks and operations. This gives insight not only into the inner workings of a particular malware but its collective strain. In light of this, we perform a full experimental dynamic and static analysis of WannaCry samples. Based on local and network behaviour of the malware samples, we suggest defense and mitigation measures for security purposes.
The rest of the paper is organized as follows: Section II discusses primitives of ransomware attack structures and components whilst the attack model is presented in Section III. The experimental test-bed and methodology are brought forth in Section IV while results and analyses are discussed in Section V and we conclude the paper in Section VI.

II. ATTACK STRUCTURE AND COMPONENTS
Ransomware attacks come mainly in two forms; locker and crypto ransomware attacks [10]. WannaCry attacks identify with the latter which employ encryption to effectuate a denial of service (DOS) attack on victim data. Crypto ransomware further subdivides into Private-key Crypto Ransomware (PrCR) and Public-key Crypto Ransomware (PuCR). PrCR inherits the challenge of symmetric key distribution and management which has subsequently led attackers to employ custom crafted classical substitution stream or block cipher. In light of the aforementioned, PrCR attacks are crackable through cryptanalysis. This has consequently led to the widespread implementation of PuCR against PrCR [11]. The diagram below in figure 2 illustrates the generic structure of crypto ransomware payload common in both PrCR and PuCR. Depending on the attack structure, the encryption key* can be generated from within the ransomware payload after a successful attack or can be downloaded from a Command and Control server (C2). Regardless of the attack structure, crypto ransomware attacks rest on three main components; encryption methodology, C2 servers and infection vectors.

A. Encryption Methodology
Encryption is the backbone component of the ransomware business model. Therefore, attackers have sought to employ the most resilient encryption algorithms not limited to RSA, AES, ECC etc. Symmetric encryption methodologies have the advantage of speed but do suffer from encryption/decryption key management whilst the resilient asymmetric encryption tends to be slower. Attackers have employed the advantages of both worlds to deploy a hybrid encryption methodology which when correctly implemented is deemed uncrackable [12]. Figure 3 below illustrates the attack structure of hybrid crypto ransomware.

Figure 3. Hybrid PuCR attack structure
In the above attack structure, the public key generated from the PuCR key pair { , } and implanted into the payload is used to encrypt the symmetric key which actually encrypts the victim's files. This is denoted by the process ( , ) = . In this approach, the key for decrypting user data, having been encrypted by , can only be decrypted by the private key residing on the C2 servers. User data encryption, which is the actual ransomware attack is denoted by the process ( , ) = . In other attack structures, the ransomware payload generates an asymmetric key pair of which the public key is used to encrypt user data whilst the ransomware seeks to exfiltrate the private key to the C2 servers for future data decryption.

B. C2 Servers
At the centre of operation of ransomware attacks lies Command and Control (C2) servers. C2 infrastructure may be owned by the attacker or could be a botnet controlled by the attacker. C2 are cardinal infrastructure and coordinating resources that the attacker harnesses to communicate with the ransomware payload once an infection is successful. Furthermore, C2 are also used to handle encryption key management and ransom payments via Bitcoin [13] and may also house the ransomware payload before it's delivered via different infection vectors. When a ransomware payload is successfully delivered to a victim, it usually beacons back to the C2 for further instructions. Earlier families of ransomware gave priority to confidentiality when communicating with C2 thus hinting on the cardinality of this component. Newer family versions however leverage the victim's system resources such as SSL to secure C2 communications. C2 may handle management of both the private and public key depending on the attack structure.

C. Infection Vectors
Developing an effective crypto ransomware utilizing strong encryption techniques supported by a resilient C2 is only half the job for an effective ransomware attack. These two aforementioned components need to be supplemented by an impactful methodology that ensures that the ransomware is effectively delivered to the targeted victim. Infection vectors are the means through which attackers achieve this. Attackers use both benign and complex methodologies to deliver the ransomware payload to the victims. Malicious spam email tops the infection vector list as the most effective ransomware delivery mechanism [14]. The spam email usually carries the payload as an attachment in form of a Word macro, executable binary or even a dirty link pointing to some resource housing the ransomware. Attackers use a wide range of social engineering tactics to implore the victim to open the attachment or to follow the link which consequently results into installation of the ransomware and subsequent infection. However, spam mails are subject to filtering by email servers implying that not all sent spam mail will reach the intended victim. Attackers therefore use other infection vectors such as Exploit Kits (EK). The EternalBlue EK was the main infection vector used to propagate WannaCry [15] ransomware over the network on port 445 while the DoublePulsar EK ensued a backdoor [16]. Neutrino EK is known to ferry a wide range of ransomware including the famous Locky and Cryptowall [17]. We consider all these infection vectors and others in the construction of the infection Bayesian network of figure 4 as shown above and subsequent deduction of the attack model in the proceeding section. It's worth noting that the Bayes network above is not exhaustive and that some infection vectors harbor sub-infection vectors which can further extended the Bayesian network. These vectors tend to be interlinked in one way or the other. Figure 4 represents a directed infection vector network with various nodes sharing a relationship depicted by the ransomware propagates through different nodes until it's executed on the victim thereby generating unique attack paths. The inter-dependence of nodes in a path can be captured by a Bayesian network in which the overall likelihood of executing the ransomware on the target can be expressed as a function of conditional probabilities in the associated attack path. The infection vector Bayesian network (BiN) is thus expressed as:

III. THE ATTACK MODEL
where . is a directed acyclic graph (DAG) with nodes ∊ as discrete random variables and edges nodes ∊ denoting casual relationships.
. is a set of quantitative network parameters. Using Equation (1) and the network structure in figure 4, we deduce an attack graph for the attack model as illustrated below in figure 5. The attack model comprises: the attacking agent at source 0 which is the ransomware itself; the assets which are nodes exploited in the course of reaching the target; the goals which are the sought after security breaches. We distinguish two assets; pivot assets and critical assets. Pivot assets, representative of the node set { 0 , 1 } are not directly connected to the target whereas the critical asset e.g. 3 is connected directly to the target. Each node casts a conditional probability distribution ( | ( )) quantifying the influence imposed by the parent's sample space, where the full joint probability distribution is given as: Therefore, the probability of compromising the target given the incoming edges {2, } and {3, } can be expressed as: Following from Equation (3), we assume Markov assumption [18] that a child node depends only its parents and not the history thereof. Thus the order of the attack events prior to access of the parent node is not significant in our attack model. In light of the above, the attack scenarios of our experiments resume from the pivot nodes. Further, we use malware-free intrusions [19] as the infection vector.

IV. EXPERIMENT TESTBED AND METHODOLOGY
The experiment setup for dynamic analysis is illustrated in figure 6 below comprising the server-side component for polling behavioral features from the client-side component where the WannaCry ransomware runs. The server-side runs Cuckoo sandbox and Volatility on Linux and we follow the best practices [20] for malware containment. Our ransomware samples are collected from Malwr and VirusTotal. We test the ransomware samples on Windows virtual hosts (Windows XP, Windows 7 and Windows 8).

Figure 6. Ransomware dynamic analysis test-bed setup
To acquire the pivot and critical assets depicted in the attack model, we launch a reconnaissance attack using Nmap on the target network. The results are shown in Table I below.  [19], we implant the ransomware on the targeted victim and perform dynamic analysis. For reverse engineering the ransomware code, we perform static code dissection on the binary using an interactive disassembler IDA Pro and a debugger Ollydbg. We discuss the results of both analyses in the proceeding section.

V. RESULTS AND ANALYSES
WannaCry upon execution, unlike other ransomware strains does not employ hibernation as a sandbox evasion technique. In a couple of seconds, the ransomware encrypts all directory contents on the system except those in the SystemRoot and Program Files. It does not encrypt the *.exe or *.dll file extensions. This is only logical considering that WannaCry is not a locker ransomware. The product of the encryption process are files with the *.WNCRY extension. The ransomware note with a Bitcoin address of

A. Dynamic Analysis
The main process Wncry2 PID 1844 spawns 3 child processes; tasksche PID 1788, cmd PID 240, taskdl PID 224 and a couple more which terminate upon task completion. The spawning activity is shown in figure 8 below. The Wncry2 process masquerades internally as the Microsoft utility diskpart.exe. The process tree likewise executes VB and batch scripts used to achieve a persistence mechanism. The icacls.exe is used to grant global permissions (777 Linux equivalent) to the directory in contention. Loaded libraries at runtime include but not limited to kernel32, shell32.dll, user32 etc after which calls are made.
The sample comes with an implanted master RSA public key whose corresponding private key is retained by the attacker. Upon infection, the ransomware uses a secure PRNG function CryptGenRandom from the operating system CryptoAPI to generate a 2048-bit sub-RSA pair for use by the cryptographic service provider (CSP). The public key from this sub-pair is exported to 00000000.pky in unencrypted form. The private key thereof is exported and written to 00000000.eky after being encrypted by the implanted master RSA public key using the CryptEncrypt function. Further, a 128-bit AES key is generated in Cipher Block Chaining (CBC) mode for encryption of the victim's target files, with a unique key per file. These symmetric keys are then encrypted by the earlier public key from the sub-pair which was exported to 00000000.pky. The diagram below in figure 9 illustrates the encryption process flow. In total, the ransomware operates on four encryption keys: one RSA public key from the master key pair, two keys from the payload-generated sub-RSA pair and one AES symmetric key. The AES key is only encrypted by the payload-generated sub-RSA public key upon completion of encrypting the victim's targeted file extensions.

B. Static Analysis
The encryption routines of WannaCry run from address 0040F08C to 0040F110 as shown in figure 10 below. Granting of global permissions to the directory in contention by icacls.exe is shown at address 0040F4FC in figure 11 below. Figure 11. Permission allocation to current directory It's worth noting that the current directory is set to hidden by the attribute "attrib +h ." at address 0040F520. One of the samples we evaluated had a kill-switch which basically is used to detect sandboxing operations. The kill-switch domain is seen at address 004313D0 as shown in figure 12 below. The ransomware variants without the kill-switch domain seem to have had been hex-edited without changing other parts of the code. This is to imply that encryption routines, their associated functions and other aspects remain unchanged. Summary characteristics of the analyzed samples is shown in Table II below.

Remediation and Prevention
: like all ransomware, WannaCry is best prevented than cured. Prevention should strongly be offline since the observed samples propagate on the network via port 445 using the exploit CVE-2017-0145 [21] against the SMB service. Since the samples overwrite the original files upon encryption, system restore efforts do not yield fruition. All observed samples do not attack system files not limited to .exe and .dll extensions. It's however impractical and illogical to rename all user files to these extensions in an effort to avoid the attack as opposed to offline backup. The DoublePulsar backdoor and EternalBlue SMB propagation are countered by patching MS17-010 which affects all Windows versions prior to Windows 10. Since the sub-RSA key pair are generated on the host, it is possible retain the primes and modulus. WanaKiwi [22] uses such an approach to derive the decryption key and subsequent decryption of the affected files where the observed exponent in all the samples was 65537 (0x10001). It should be noted however that this method only works if the memory allocated to the WannaCry process is not overwritten of flushed, i.e. no system restart or reallocation of memory.

VI. CONCLUSIONS
WannaCry ransomware is not so different from other ransomware families; it uses same encryption primitives and attack methodologies. However, unlike other ransomware, it generates a sub-RSA key pair which is used to encrypted the generated symmetric key. What made WannaCry spread fast and catch the attention of the world is the inclusion of the worm component which enabled it to self-propagate in networks with vulnerable SMB service. This infection vector is persistent and still valid for unpatched systems.
The inclusion of the kill-switch for sandbox evasion led to the demise of the initial variant of the ransomware. However, both the initial strain and the enhanced version which exclude the kill-switch are seen in the wild today on a daily basis [23]. Like other crypto ransomware, WannaCry does not encrypt system files and directories. Further, it does not check the file header before encryption but rather just the file extension. The presence of residual RSA primes in the memory address space of the WannaCry process makes it possible to derive a decryption key and subsequent decryption. Nevertheless, this recovery technique is only valid given the associated memory space is not overwritten or flushed.


s2fieldsofstudy:
Computer Science
Engineering

text:
The control system of a 2kW@20K helium refrigerator

The automatic control of a helium refrigerator includes three aspects, that is, one-button start and stop control, safety protection control, and cooling capacity control. The 2kW@20K helium refrigerator’s control system uses the SIEMENS PLC S7-300 and its related programming and configuration software Step7 and the industrial monitoring software WinCC, to realize the dynamic control of its process, the real-time monitoring of its data, the safety interlock control, and the optimal control of its cooling capacity. At first, this paper describes the control architecture of the whole system in detail, including communication configuration and equipment introduction; and then introduces the sequence control strategy of the dynamic processes, including the start and stop control mode of the machine and the safety interlock control strategy of the machine; finally tells the precise control strategy of the machine’s cooling capacity. Eventually, the whole system achieves the target of one-button starting and stopping, automatic fault protection and stable running to the target cooling capacity, and help finished the cold helium pressurization test of aerospace products.

Review
At present, in our aerospace field, the system-level test platform of pressurization and transport only has the capability of system tests in liquid nitrogen temperature area. It does not meet actual conditions of the cold helium pressurization system on the rocket, and also can't simulate some key characteristics, such as system's start impact, magnetic valves' temperature drop, and so on. So it is very necessary to extend the platform's test capability to liquid hydrogen temperature area. In the past, we usually used the way of soaking in liquid hydrogen to cool the helium to 20K, which could obtain the test condition of high pressure and low temperature, and then finished tests in liquid hydrogen temperature area. But hydrogen belongs to flammable and explosive medium, so tests are very difficult to be controlled, and have very high risk. It's almost impossible to test the vibration environment in this way.
After years of research, a 2kW@20K helium refrigerator has been developed by Technical Institute of Physics and Chemistry, Chinese Academy of Sciences. Using this helium refrigerator as a cold source to cool the high pressure helium in the pressurized tank, does not need hydrogen medium, and has much higher safety. It can also satisfy large flow experimental studies of the pressurization system, and realize the coupling of cryogenic and vibratory environment, so to better reflect the real work situation on the rocket. It enables the pressurization system to have the capability of hydrogen temperature area and high pressure system experiments, and also enhances the authenticity and coverage of the experiments.
The new aerospace products' performance test platform with 2kW@20K helium refrigerator is shown in figure 1. First, the high-pressure helium from the helium distribution station comes through the liquid nitrogen exchanger, and is cooled to 80K. Then the 80K helium is injected into the pressurized tank to be further cooled and pressurized. Cold helium from the 20K helium refrigerator exchanges heat with the injected helium inside the pressurized tank through its shell and tube heat exchanger, then returns to the helium refrigerator after heating up. In this way, the helium in the pressurized tank is constantly cooled, pressurized and cooled again. Finally, the helium reaches the temperature of 20K and the pressure of 20MPa, and the system is kept stable by the cooling capacity of the helium refrigerator [1].

General introduction of the control system of 20K helium refrigerator
For a refrigerator applied in aerospace field, to realize its equipments' unmanned monitored, temperature's precise controlled stable and fast interlock responding to accidents to ensure the system's security are the main factors to ensure its stability and reliability during its running. All of these need to be realized by the control system. The process control system of the 2kW@20K helium refrigerator uses PLC S7-300 with its matching programming and configuration software Step7, and industrial monitoring software WinCC. They are all well-known and mature international products, which can ensure the stable and reliable performance of the system, and also its low failure rate.

Structure diagram of the control system
This control system is dual-CPU redundant configured, and uses Profibus as its system bus and distributed I/O ET200M as its extension mode. The composition of the whole system is shown in figure 2.

Hardware ， software and communication configurations
For the hardware, this control system uses one PLC main frame and three PLC slave stations (3 # , 4 # and 12 # stations), two ET200 distributed I/O and I/O modules, one host computer operating station, and so on. The slave computer uses S7-300 PLC control system, and uses CPU315-2PN/DP as its central process unit. According to the requirement of I/O points, the system uses the form of two distributed I/O and Profibus (field bus) communication to extend I/O modules, which can support the extension of 16 modules at most, and makes high the performance price ratio of the system. The communication between the slave computer and the operator station (host computer) is depending on Industrial Ethernet. The slave computer's main CPU integrates Industrial Ethernet interface, and supports functions such as Ethernet data communication, program download, etc. The vacuum pump, tachometer and vacuum meter in the system do not use Profibus, but use Modbus to communicate with the slave computer, through the CP communication module on the PLC main frame. This makes the system compatible with more communication modes.
For the software, the system uses Step7 V5.4 as its slave computer programming software, and WinCC V6.2 as its host computer process monitoring software. Functions of the slave computer include hardware configuration, logic programming and communication configuration. The host computer is used for configuring the system flow chart screen, parameter display screen, PID control screen, trend curve screen and alarm screen. It can also confirm alarms, record events and print reports. It makes users operate in a friendly screen for process monitoring, operation control, data processing, and so on. It enables operators to master the running situation of the refrigerator in time, and then can take effective controls to make the test of aerospace products' performance more stable and reliable. The human and machine interface of the refrigeration made by the host computer is shown in figure 3.

Sequence control strategy for the refrigerator's one-button start and stop
In order to meet the needs of different stages of the experiment, and also to operate the refrigerator in a better order, we divide the system into four modes, as shown in figure 4. The first (inside the No.1 box) is the compressor mode. In this mode, the compressor and three control valves (CV1101, CV1102, CV1103) in the gas management panel act, which makes system's high and low pressure reach to the set value and remain stable. The second (inside the No.2 box) is the middle cycle mode. In this mode, turbine's bypass valve (CV1202) and cold load's bypass valve (CV1205) act, on the base of the last mode. It feeds through the whole system (connect the cold box and room temperature part), and makes the system's high and low pressure stable. The third (inside the No.3 box) is the coldbox refrigeration mode. In this mode, turbine's control valve (CV1201) and turbine act, on the base of the last mode, meanwhile CV1202 closes, which makes system's refrigeration begin. The fourth (inside the No.4 box) is the large cycle mode. In this mode, the cold load's gas supply valve (CV1203) and gas return valve (CV1205) act, on the base of the last mode, meanwhile CV1205 closes, which supplies the interface to users. We have two alternative modes to start and stop the refrigerator, that is auto mode and manual mode, as shown in figure 3. In "manual" mode, all the parts (inside dashed boxes) can be manual started and stopped independently through their own "start" and "stop" button. In "auto" mode, the entire system can be started and stopped automatically just through one button -"system start and stop" button (except some peripheral devices, such as mechanical pump, vacuum pump, analyzer, instrument gas, cooling water unit, etc), and need not any other operations. The refrigerator's automatic start order is: compressor→middle cycle→clodbox refrigeration→large cycle ; while its automatic stop order is: clodbox refrigeration→large cycle→middle cycle→compressor.

Fault protection interlock strategy of the refrigerator
In order to ensure the safe operation of the whole refrigeration system, it is necessary to establish interlock protection for its key components and vulnerable parts. Once the refrigerator has any abnormalities, it can realize "soft landing" and ensure the safety of persons and equipments. This control system has established comprehensive and effective interlock protection measures. According to the experiences of similar equipments at home and abroad and also the needs of users, we divide system's interlocks into three categories, as shown in figure 5. When each type of interlock faults occurs, the system will respond different equipment responses in its need. This can fully ensure the safety of the system, and realize the safety guarantee of the unmanned operation. In system's "manual" mode, we can input or cutoff each mode and equipment interlock independently anytime we need. In system's "auto" mode, all the mode and equipment interlocks is automatically input or cutoff in a certain order, which realizes one-button start and stop of the system. 4. Temperature precise control strategy of the refrigerator From our system design goal, when the cold load changes, the controlled temperature should be adjusted stable in a range rapidly. The permissible range of temperature change is ±0.5K, and while the cold load reaches to 2kW, the stable temperature should not be over 20K.
To achieve the goal, temperature adjustments are divided into three levels: when temperature fluctuation is around ±0.3K, the control load is operated, with its maximum heating capacity 10% of system's refrigeration capacity; when temperature fluctuation is beyond to the temperature region, between ±0.3K and ±3K, the temperature adjustment system would start adjusting the speed of the turbine expander. When the temperature fluctuation is beyond ±3K, the control system would start adjusting the large fluctuation of low pressure. The first level adjusts temperature by the PID control loop of the control load, which would change the heating capacity of the control load to compensate temperature changes; and the second level adjusts temperature by the PID control loop of the control valve before the turbine expander, which would control the mass flow of refrigeration material, and then change the speed of the turbine expander as well as system's refrigeration capacity; and the third level adjusts temperature by large fluctuation of the low pressuree, which possibly causes two reactions: when the pressure is too low, it induces the interlock protection to stop the whole refrigerator; conversely, it induces the frequency jump protection of the compressor [2].
Keeping the high pressure and low pressure stable is the necessary condition of compressor unit's normal operation, which is archived by the PID control loops of valves in the gas management panel and the compressor. Compensation gas valve and exhaust valve are used for high pressure adjustment, while bypass valve and compressor are used for low pressure adjustment.
Step7 In equation (1), e (n) is the deviation; M is the integral initial value; K P is the proportional coefficient; T I is the integral time constant; T D is the differential time constant; and T is the sampling time.
The structure principle of PID control loops in 2kW@20K system is shown in figure 6. Inside figure 6, the small box encloses the part performed by digital PID controllers, and the big box encloses the part performed by S7-300 PLC. When the controlled object deviates from its set point, the PID controller will calculate a movement using equation (1) to cause actuator acting for adjusting the controlled object close to its set point value [3]. In 2kW@20K refrigerator， we use six PID control loops in total. Each loop's actuator and controlled object and also its PID coefficients are listed in

The test result of cold helium pressurization by 2kW/ 20K helium refrigerator
The helium refrigerator has run at the cooling capacity of 2kW@19.7±0.3K for 9 days itself [2]. And we also have used this refrigerator to help finished the cold helium pressurization experiment, which reaches the required test condition of 20MPa@20K. The refrigerator system in test site is shown in figure 7, and the result of the pressurization process is shown in figure 8.  When the temperature of the refrigerator is about 23K, the cold helium begins to be injected. Front batches are injected rapidly, and because the cold load of the helium is less than 2kW, so between injection gaps, the temperature drops. As helium pressure close to the target value, the injection speed slows. And finally, the whole system is kept stable by the cooling capacity of the helium refrigerator. The helium inside the tank is kept stable at 20MPa@20K with temperature's change inside ±0.3K, which meets the test requirement well.